From 7e4f3bc6c9e2738d1b5a2ee21ee208ef1ae70508 Mon Sep 17 00:00:00 2001 From: lcerrato Date: Wed, 8 May 2024 15:23:12 -0400 Subject: [PATCH 1/6] (grc_conversion) tlg0086 translation conversion #1399 --- data/tlg0086/tlg010/__cts__.xml | 2 +- data/tlg0086/tlg025/__cts__.xml | 6 + .../tlg025/tlg0086.tlg025.perseus-eng1.xml | 14123 ++++------------ .../tlg025/tlg0086.tlg025.perseus-eng2.xml | 3605 ++++ 4 files changed, 7215 insertions(+), 10521 deletions(-) create mode 100644 data/tlg0086/tlg025/tlg0086.tlg025.perseus-eng2.xml diff --git a/data/tlg0086/tlg010/__cts__.xml b/data/tlg0086/tlg010/__cts__.xml index 4af96fbed..b7700ae45 100644 --- a/data/tlg0086/tlg010/__cts__.xml +++ b/data/tlg0086/tlg010/__cts__.xml @@ -9,7 +9,7 @@ Nicomachean Ethics - Aristotle. The Nicomachean Ethics. Rackham, Harris, editor. London: William Heinemann; New York: G. P. Putnam's Sons, 1926 (printing). + Aristotle. The Nicomachean Ethics. Rackham, Harris, translator. London: William Heinemann; New York: G. P. Putnam's Sons, 1926 (printing). diff --git a/data/tlg0086/tlg025/__cts__.xml b/data/tlg0086/tlg025/__cts__.xml index d3d902657..4a07b13d0 100644 --- a/data/tlg0086/tlg025/__cts__.xml +++ b/data/tlg0086/tlg025/__cts__.xml @@ -6,4 +6,10 @@ τὰ Μετὰ τὰ Φυσικά Aristotle. Aristotle's Metaphysics, Vol. 1-2. Ross, William David, editor. Oxford: Clarendon Press, 1924 (printing). + + + Metaphysics + Aristotle. The Metaphysics, Vol. 1-2. Tredennick, Hugh, translator. London: William Heinemann; Cambridge, MA: Harvard University Press, 1933-35 (printing). + + \ No newline at end of file diff --git a/data/tlg0086/tlg025/tlg0086.tlg025.perseus-eng1.xml b/data/tlg0086/tlg025/tlg0086.tlg025.perseus-eng1.xml index a003a4e26..ea3dd4e53 100644 --- a/data/tlg0086/tlg025/tlg0086.tlg025.perseus-eng1.xml +++ b/data/tlg0086/tlg025/tlg0086.tlg025.perseus-eng1.xml @@ -1,10522 +1,3605 @@ - - - -%PersProse; -]> + + + + + + +Metaphysics +Aristotle +Hugh Tredennick +Perseus Project, Tufts University +Gregory Crane + +Prepared under the supervision of +Lisa Cerrato +William Merrill +Elli Mylonas +David Smith + +The Annenberg CPB/Project + - - - - - Metaphysics (English). Machine readable text - Aristotle - - Perseus Project, Tufts University - Gregory Crane - - Prepared under the supervision of - Lisa Cerrato - William Merrill - Elli Mylonas - David Smith - - The Annenberg CPB/Project - - About 830Kb - - Trustees of Tufts University - Medford, MA - Perseus Project - - - Text was scanned at St. Olaf Spring, 1992. - - - - - Aristotle - Aristotle in 23 Volumes, Vols.17, 18, translated by Hugh Tredennick. - - Cambridge, MA, Harvard University Press; London, William Heinemann - Ltd. - 1933, 1989 - - - - - - - - - - - - - - English - Greek - - - - - Spring 1993 - - WPM - (n/a) - - Tagged in conformance with Prose.e dtd. - - - 7/27, 1993 - - em - (n/a) - - Put Bekker line 1 milestone tags at the beginning of each section so that the incoming - list creator would work. Changed RREFDECL. - - - 5/27/09 - - RS - (n/a) - - $Log: aristot.met_eng.xml,v $ Revision 1.6 2011-12-16 21:31:55 lcerrato fixed - Aristotle bibls Revision 1.5 2011-11-18 20:57:56 lcerrato fixed bad bibl refs Revision 1.4 - 2011-10-28 15:27:17 lcerrato fixed bad bibl refs Revision 1.3 2010-06-16 19:18:47 rsingh04 - cleaned up bad place tags in a few texts and cleaned up the document format Revision 1.2 - 2010/06/16 15:07:22 lcerrato fixed bibls for Plut. Mor. to correct work title Revision 1.1 - 2009/10/09 19:49:17 rsingh04 more reorganizing of texts module by collection Revision 1.1 - 2009/10/08 19:12:40 rsingh04 began reorganizing texts module by collection. created - separate work directory in texts module to keep hopper files separate from in progress - files Revision 1.24 2009/07/15 18:37:40 student edited entity tags CEH Revision 1.23 - 2009/06/24 15:49:58 lcerrato fixed bad bibls Revision 1.22 2009/06/19 19:02:18 lcerrato - fixed bad bibls Revision 1.21 2009/06/08 20:52:48 student fixed bibl errors through book - 14 (end) - zr Revision 1.20 2009/06/08 19:46:37 student fixed bibl errors through book 13 - - zr Revision 1.19 2009/06/08 18:50:22 student fixed bibl errors through book 12 - zr - Revision 1.18 2009/06/08 17:51:07 student fixed bibl errors through book 11 - zr Revision - 1.17 2009/06/08 16:27:38 student fixed bibl errors through book 9 - zr Revision 1.16 - 2009/06/08 14:56:47 student fixed bibl errors through book 6 - zr Revision 1.15 2009/06/08 - 14:40:43 student fixed bibl errors through book 4 - zr Revision 1.14 2009/06/08 14:16:25 - student fixed bibl errors through book 3 - zr Revision 1.13 2009/06/05 21:18:34 student - fixed bibl errors through book 1 - zr Revision 1.12 2009/05/27 15:55:13 rsingh04 added cvs - log keyword - - - - - + +Trustees of Tufts University +Medford, MA +Perseus Digital Library Project +Perseus 2.0 +tlg0086.tlg025.perseus-eng2.xml + +Available under a Creative Commons Attribution-ShareAlike 4.0 International License + + - -

- All men naturally desire - knowledge. An indication of this is our esteem for the senses; for apart from their use we - esteem them for their own sake, and most of all the sense of sight. Not only with a view - to action, but even when no action is contemplated, we prefer sight, generally speaking, - to all the other senses. The reason of this is - that of all the senses sight best helps us to know things, and reveals many - distinctions. Now animals are by nature born with the - power of sensation, and from this some acquire the faculty of memory, whereas others do - not. Accordingly the former are more intelligent and capable of learning than those which - cannot remember. Such as cannot hear sounds (as - the bee, and any other similar type of creature) are intelligent, but cannot learn; those - only are capable of learning which possess this sense in addition to the faculty of - memory. Thus the other animals live by impressions and - memories, and have but a small share of experience; but the human race lives also by art - and reasoning. It is from memory that men - acquire experience, because the numerous memories of the same thing eventually produce the - effect of a single experience. Experience seems very similar to science and art, but actually it is through experience that men acquire - science and art; for as Polus rightly says, "experience produces art, but inexperience - chance."Plat. Gorgias - 448c, Plat. Gorg. 462b-c. Art is - produced when from many notions of experience a single universal judgement is formed with - regard to like objects. To have a judgement - that when Callias was suffering from this or that disease this or that benefited him, and - similarly with Socrates and various other individuals, is a matter of experience; but to - judge that it benefits all persons of a certain type, considered as a class, who suffer - from this or that disease (e.g. the phlegmatic or bilious when suffering from burning - fever) is a matter of art. It would seem that for practical purposes experience is in no way - inferior to art; indeed we see men of experience succeeding more than those who have - theory without experience. The reason of this - is a that experience is knowledge of particulars, but art of universals; and actions and - the effects produced are all concerned with the particular. For it is not man that the - physician cures, except incidentally, but Callias or Socrates or some other person - similarly named, who is incidentally a man as well. So if a man has theory without - experience, and knows the universal, but does not know the particular contained in it, he - will often fail in his treatment; for it is the particular that must be treated. Nevertheless we consider that knowledge and - proficiency belong to art rather than to experience, and we assume that artists are wiser - than men of mere experience (which implies that in all cases wisdom depends rather upon - knowledge); and this is because the former - know the cause, whereas the latter do not. For the experienced know the fact, but not the - wherefore; but the artists know the wherefore and the cause. For the same reason we - consider that the master craftsmen in every profession are more estimable and know more - and are wiser than the artisans, because they know the reasons of the things which are done; but - we think that the artisans, like certain inanimate objects, do things, but without knowing - what they are doing (as, for instance, fire burns); only whereas inanimate objects perform all their actions in virtue of - a certain natural quality, artisans perform theirs through habit. Thus the master - craftsmen are superior in wisdom, not because they can do things, but because they possess - a theory and know the causes. In general the sign of - knowledge or ignorance is the ability to teach, and for this reason we hold that art - rather than experience is scientific knowledge; for the artists can teach, but the others - cannot. Further, we do not consider any of - the senses to be Wisdom. They are indeed our chief sources of knowledge about particulars, - but they do not tell us the reason for anything, as for example why fire is hot, but only - that it is hot. It is therefore probable that at first the inventor of any art which - went further than the ordinary sensations was admired by his fellow-men, not merely - because some of his inventions were useful, but as being a wise and superior - person. And as more and more arts were - discovered, some relating to the necessities and some to the pastimes of life, the - inventors of the latter were always considered wiser than those of the former, because their branches of knowledge did not aim at - utility. Hence when all the discoveries of - this kind were fully developed, the sciences which relate neither to pleasure nor yet to - the necessities of life were invented, and first in those places where men had leisure. - Thus the mathematical sciences originated in the neighborhood of Egypt, because there the priestly class was allowed - leisure.Cf. Plat. - Phaedrus 274, Hdt. 2.109. The difference between art and - science and the other kindred mental activities has been stated in - theEthicsAristot. Nic. Eth. 6.1139b 14-1141b - 8.; the reason for our present discussion is that it is generally assumed - that what is called Wisdomi.e. Metaphysics. - is concerned with the primary causes and principles, so that, as has been already stated, - the man of experience is held to be wiser than the mere possessors of any power of - sensation, the artist than the man of experience, the master craftsman than the artisan; - and the speculative sciences to be more learned than the productive. Thus it is clear that Wisdom - is knowledge of certain principles and causes. Since we are investigating this kind of knowledge, we - must consider what these causes and principles are whose knowledge is Wisdom. Perhaps it - will be clearer if we take the opinions which we hold about the wise man. We consider first, then, that the wise man knows all - things, so far as it is possible, without having knowledge of every one of them - individually; next, that the wise man is he who can comprehend difficult things, such as - are not easy for human comprehension (for sense-perception, being common to all, is easy, - and has nothing to do with Wisdom); and further that in every branch of knowledge a man is - wiser in proportion as he is more accurately informed and better able to expound the - causes. Again among the sciences we consider - that that science which is desirable in itself and for the sake of knowledge is more - nearly Wisdom than that which is desirable for its results, and that the superior is more - nearly Wisdom than the subsidiary; for the wise man should give orders, not receive them; - nor should he obey others, but the less wise should obey him. Such in kind and in number are the opinions which we hold with regard to Wisdom and the - wise. Of the qualities there described the knowledge of everything must necessarily belong - to him who in the highest degree possesses knowledge of the universal, because he knows in - a sense all the particulars which it comprises. These things, viz. the most universal, are - perhaps the hardest for man to grasp, because they are furthest removed from the - senses. Again, the most exact of the sciences - are those which are most concerned with the first principles; for those which are based on - fewer principles are more exact than those which include additional principles; e.g., - arithmetic is more exact than geometry. Moreover, the science which investigates causes is more instructive than one which does - not, for it is those who tell us the causes of any particular thing who instruct us. - Moreover, knowledge and understanding which are desirable for their own sake are most - attainable in the knowledge of that which is most knowable. For the man who desires - knowledge for its own sake will most desire the most perfect knowledge, and this is the - knowledge of the most knowable, and the things which are most knowable are first - principles and causes; for it is through these and from these that other things come to be - known, and not these through the particulars which fall under them. And that science is supreme, and superior to the subsidiary, - which knows for what end each action is to be done; i.e. the Good in each particular case, - and in general the highest Good in the whole of nature. Thus as a result of all the above - considerations the term which we are investigating falls under the same science, which - must speculate about first principles and causes; for the Good, i.e. the end - , is one of the causes. That it is not a productive science - is clear from a consideration of the first philosophers. It is through wonder that men now begin and originally began to - philosophize; wondering in the first place at obvious perplexities, and then by gradual - progression raising questions about the greater matters too, e.g. about the changes of the - moon and of the sun, about the stars and about the origin of the universe. Now he who wonders and is perplexed feels that he is - ignorant (thus the myth-lover is in a sense a philosopher, since myths are composed of - wonders); therefore if it was to escape - ignorance that men studied philosophy, it is obvious that they pursued science for the - sake of knowledge, and not for any practical utility. The actual course of events bears witness to this; for speculation of - this kind began with a view to recreation and pastime, at a time when practically all the - necessities of life were already supplied. Clearly then it is for no extrinsic advantage - that we seek this knowledge; for just as we call a man independent who exists for himself - and not for another, so we call this the only independent science, since it alone exists - for itself. For - this reason its acquisition might justly be supposed to be beyond human power, since in - many respects human nature is servile; in which case, as SimonidesSimon. Fr. 3 (Hiller). says, "God - alone can have this privilege," and man should only seek the knowledge which is within his - reach. Indeed if the poets are right and the - Deity is by nature jealous, it is probable that in this case He would be particularly - jealous, and all those who excel in knowledge unfortunate. But it is impossible for the - Deity to be jealous (indeed, as the proverbCf. - Solon, Fr. 26 (Hiller); Leutsch and Schneidwin, - Paroemiographi, 1.371. says, "poets tell many a lie"), nor must - we suppose that any other form of knowledge is more precious than this; for what is most - divine is most precious. Now there are two - ways only in which it can be divine. A science is divine if it is peculiarly the - possession of God, or if it is concerned with divine matters. And this science alone - fulfils both these conditions; for (a) all believe that God is one of the causes and a - kind of principle, and (b) God is the sole or chief possessor of this sort of knowledge. - Accordingly, although all other sciences are more necessary than this, none is more - excellent. The acquisition of this knowledge, however, must in a sense result in something which is - the reverse of the outlook with which we first approached the inquiry. All begin, as we - have said, by wondering that things should be as they are, e.g. with regard to - marionettes, or the solstices, or the incommensurabilityi.e. the fact that the diagonal of a square cannot be rationally - expressed in terms of the side. of the diagonal of a square; because it seems - wonderful to everyone who has not yet perceived the cause that a thing should not be - measurable by the smallest unit. But we must - end with the contrary and (according to the proverb)i.e. deute/ron a)meino/nwn("second thoughts are - better"). Leutsch and Schneidwin 1.62. the better view, as men do even in these - cases when they understand them; for a - geometrician would wonder at nothing so much as if the diagonal were to become - measurable. Thus we have stated what is the nature of the - science which we are seeking, and what is the object which our search and our whole - investigation must attain. It is clear that we must obtain knowledge of the primary causes, - because it is when we think that we understand its primary cause that we claim to know - each particular thing. Now there are four recognized kinds of cause. Of these we hold that - one is the essence or essential nature of the thing (since the "reason why" of a thing is - ultimately reducible to its formula, and the ultimate "reason why" is a cause and - principle); another is the matter or substrate; the third is the source of motion; and the - fourth is the cause which is opposite to this, namely the purpose or "good"; for this is the end of every generative or motive - process. We have investigated these sufficiently in the PhysicsPhys. 2.3, Phys. 2.7; however, let us avail ourselves of the - evidence of those who have before us approached the investigation of reality and - philosophized about Truth. For clearly they too recognize certain principles and causes, - and so it will be of some assistance to our present inquiry if we study their teaching; - because we shall either discover some other kind of cause, or have more confidence in - those which we have just described. Most of the earliest philosophers conceived only of material - principles as underlying all things. That of which all things consist, from which they - first come and into which on their destruction they are ultimately resolved, of which the - essence persists although modified by its affections—this, they say, is an element - and principle of existing things. Hence they believe that nothing is either generated or - destroyed, since this kind of primary entity always persists. Similarly we do not say that - Socrates comes into being absolutely when he becomes handsome or cultured, - nor that he is destroyed when he loses these qualities; because the substrate, Socrates - himself, persists. In the same way nothing else - is generated or destroyed; for there is some one entity (or more than one) which always - persists and from which all other things are generated. All are not agreed, however, as to the number and character of these principles. Thales,Thales of Miletus, fl. 585 B.C. the founder of this school of philosophy,That of the Ionian monists, who sought a single - material principle of everything. says the permanent entity is water (which is - why he also propounded that the earth floats on water). Presumably he derived this - assumption from seeing that the nutriment of everything is moist, and that heat itself is - generated from moisture and depends upon it for its existence (and that from which a thing - is generated is always its first principle). He derived his assumption, then, from this; - and also from the fact that the seeds of everything have a moist nature, whereas water is - the first principle of the nature of moist things. There are someCf. Plat. Crat. 402b, Plat. Theaet. 152e, Plat. Theaet. 180c,d. who think that the - men of very ancient times, long before the present era, who first speculated about the - gods, also held this same opinion about the primary entity. For theycf. Hom. Il. 14. 201, - Hom. Il. 14.246. represented Oceanus and - Tethys to be the parents of creation, and the oath of the gods to be by water— - Styx,Cf. Hom. Il. - 2.755, Hom. Il. 14.271, Hom. Il.15.37. as they call it. Now what is most - ancient is most revered, and what is most revered is what we swear by. Whether this view of the primary entity is really ancient and - time-honored may perhaps be considered uncertain; however, it is said that this was - Thales' opinion concerning the first cause. (I say nothing of Hippo,Hippo of Samos, a medical writer and eclectic philosopher who lived in the latter - half of the fifth century B.C. Cf.Aristot. De Anima - 405b 2. because no one would presume to include him in this company, in - view of the paltriness of his intelligence.) AnaximenesThe - third Milesian monist; fl. circa 545 B.C. and - DiogenesDiogenes of Apollonia, an eclectic philosopher roughly - contemporary with Hippo. held that air is prior to water, and is of all corporeal - elements most truly the first principle. HippasusA - Pythagorean, probably slightly junior to Heraclitus. of Metapontum and HeraclitusFl. about 500 B.C. of Ephesus hold this of fire; and EmpedoclesOf Acragas; fl. 450 - B.C.—adding earth as a fourth to those already mentioned—takes all - four. These, he says, always persist, and are only generated in respect of multitude and - paucity, according as they are combined into unity or differentiated out of unity.Cf. Empedocles, Fr. 17 (Diels), - R.P. 166; Burnet, E.G.P. 108-109. Anaxagoras of Clazomenae—prior to - Empedocles in point of age, but posterior in his activities—says that the first - principles are infinite in number. For he says that as a general rule all things which - are, like fire and water,This is Aristotle's - illustration; apparently Anaxagoras did not regard the "elements" as homoeomerous (i.e. - composed of parts which are similar to one another and to the whole). Cf. Aristot. De Caelo 302a 28, Aristot. De Gen. et Corr. 314a 24. homoeomerous, - are generated and destroyed in this sense only, by combination and differentiation; - otherwise they are neither generated nor destroyed, but persist eternally.Cf. Anaxagoras Fr. 4 - (Diels); and see Burnet, E.G.P. 130. From this account it might be supposed - that the only cause is of the kind called "material." But as men proceeded in this way, - the very circumstances of the case led them on and compelled them to seek further; because - if it is really true that all generation and - destruction is out of some one entity or even more than one, why does this - happen, and what is the cause? It is surely - not the substrate itself which causes itself to change. I mean, e.g., that neither wood - nor bronze is responsible for changing itself; wood does not make a bed, nor bronze a - statue, but something else is the cause of the change. Now to investigate this is to - investigate the second type of cause: the source of motion, as we should say. Those who were the very - first to take up this inquiry, and who maintained that the substrate is one thing, had no - misgivings on the subject; but some of thosei.e. - the Eleatic school. who regard it as one thing, being baffled, as it were, by the - inquiry, say that that one thing (and indeed the whole physical world) is immovable in - respect not only of generation and destruction (this was a primitive belief and was - generally admitted) but of all other change. This belief is peculiar to them. None of those who maintained - that the universe is a unity achieved any conception of this type of cause, except perhaps - ParmenidesFounder of the above; fl. about - 475.; and him only in so far as he admits, in a sense, not one cause only but - two.i.e. in the *do/ca. Parmenides Fr. 8 (Diels); R.P. - 121. But those who recognize more - than one entity, e.g. hot and cold, or fire and earth, are better able to give a - systematic explanation, because they avail themselves of fire as being of a kinetic - nature, and of water, earth, etc., as being the opposite.Aristotle is probably thinking of Empedocles. Cf. Aristot. Met. 4.8. After these thinkers and the discovery of these causes, since they were insufficient to - account for the generation of the actual world, men were again compelled (as we have said) - by truth itself to investigate the next first principle. For presumably it is unnatural that either fire or earth or any other - such element should cause existing things to be or become well and beautifully disposed; - or indeed that those thinkers should hold such a view. Nor again was it satisfactory to - commit so important a matter to spontaneity and chance. Hence when someoneAnaxagoras. said that there is Mind in nature, just as in animals, and that this - is the cause of all order and arrangement, he seemed like a sane man in contrast with the - haphazard statements of his predecessors.Cf. Plat. Phaedo 97b-98b. We know definitely that Anaxagoras adopted this view; but - HermotimusA semi-mythical person supposed to have - been a preincarnation of Pythagoras. of - Clazomenae is credited with having stated it earlier. Those thinkers, then, who held this - view assumed a principle in things which is the cause of beauty, and the sort of cause by - which motion is communicated to things. It might be inferred that the first person to consider this - question was Hesiod, or indeed anyone else who assumed Love or Desire as a first principle - in things; e.g. Parmenides. For he says, where he is describing the creation of the - universe, - Love sheProbably Aphrodite (so - Simplicius, Plutarch). created first of all the gods . . . - Parmenides Fr. 13 (Diels)And Hesiod says,Hes. Th. 116-20. The - quotation is slightly inaccurate. - - First of all things was Chaos made, and then/Broad-bosomed Earth . . - ./And Love, the foremost of immortal beings, - thus implying that there must be in the world some cause to move things and - combine them. The question of arranging these thinkers in order of priority may be decided later. Now - since it was apparent that nature also contains the opposite of what is good, i.e. not - only order and beauty, but disorder and ugliness; and that there are more bad and common - things than there are good and beautiful: in view of this another thinker introduced Love - and StrifeEmpedocles Fr. 17, - 26 (Diels); R.P. 166. Cf. Burnet, E.G.P. 108 ff. as the respective - causes of these things— because if one - follows up and appreciates the statements of Empedocles with a view to his real meaning - and not to his obscure language, it will be found that Love is the cause of good, and - Strife of evil. Thus it would perhaps be correct to say that Empedocles in a sense spoke - of evil and good as first principles, and was the first to do so—that is, if the - cause of all good things is absolute good. These thinkers then, as I say, down to the time of - Empedocles, seem to have grasped two of the causes which we have defined in the - PhysicsAristot. Phys. 2.3, 7.: the material cause and - the source of motion; but only vaguely and indefinitely. They are like untrained soldiers - in a battle, who rush about and often strike good blows, but without science; in the same - way these thinkers do not seem to understand their own statements, since it is clear that - upon the whole they seldom or never apply them. Anaxagoras avails himself of Mind as an artificial device for producing order, and drags - it in whenever he is at a loss to explain some - necessary result; but otherwise he makes anything rather than Mind the cause of what - happens.Cf. Plat. - Phaedo 98b, Plat. Laws 967b; also Aristot. Met. 7.5. Again, Empedocles does - indeed use causes to a greater degree than Anaxagoras, but not sufficiently; nor does he - attain to consistency in their use. At any rate - Love often differentiates and Strife combines: because whenever the universe is - differentiated into its elements by Strife, fire and each of the other elements are - agglomerated into a unity; and whenever they are all combined together again by Love, the - particles of each element are necessarily again differentiated. Empedocles, then, differed from - his predecessors in that he first introduced the division of this cause, making the source - of motion not one but two contrary forces. Further, he was the first to maintain that the so-called material elements are - four—not that he uses them as four, but as two only, treating fire on the one hand - by itself, and the elements opposed to it—earth, air and water—on the other, - as a single nature.Cf. 3.14. This can be - seen from a study of his writings.e.g. Empedocles, Fr. 62 (Diels). Such, then, as I say, is his account of the nature and number of the - first principles. Leucippus,Of Miletus; fl. circa 440 - (?) B.C. See Burnet, E.G.P. 171 ff. however, and his disciple DemocritusOf Abdera; - fl. circa 420 B.C. E.G.P loc. cit. hold that the - elements are the Full and the Void—calling the one "what is" and the other "what is - not." Of these they identify the full or solid with "what is," and the void or rare with - "what is not" (hence they hold that what is not is no less real than what is,For the probable connection between the Atomists and - the Eleatics see E.G.P. 173, 175, and cf. De Gen. et Corr. - 324b 35-325a 32. because Void is as real as Body); and they say that - these are the material causes of things. And - just as those who make the underlying substance a unity generate all other things by means - of its modifications, assuming rarity and density as first principles of these - modifications, so these thinkers hold that the "differences"i.e., of the atoms. are the causes of everything else. These differences, they say, are three: shape, - arrangement, and position; because they hold that what is differs only in contour, - inter-contact, and inclination .Cf. - R.P. 194.(Of these contour means shape, inter-contact arrangement, and - inclination position.) Thus, e.g., A differs from N in shape, AN from NA in arrangement, - and Z from NThese letters will convey Aristotle's - point better to the English reader, but see critical note. in position. As for motion, whence and how it arises in - things, they casually ignored this point, very - much as the other thinkers did. Such, then, as I say, seems to be the extent of the - inquiries which the earlier thinkers made into these two kinds of cause. At the same time, however, and - even earlier the so-calledAristotle seems to have - regarded Pythagoras as a legendary person. Pythagoreans applied themselves to - mathematics, and were the first to develop this sciencePythagoras himself (fl. 532 B.C.) is said by - Aristoxenus (ap. Stobaeus 1.20.1) to have been the first - to make a theoretical study of arithmetic.; and through studying it they came to - believe that its principles are the principles of everything. And since numbers are by nature first among these - principles, and they fancied that they could detect in numbers, to a greater extent than - in fire and earth and water, many analoguesCf. - Aristot. Met. 14.6ff.. of what is and - comes into being—such and such a property of number being justice - ,Apparently (cf. infra, Aristot. Met. 1.17) they identified these not only - with properties of number but with numbers themselves. Thus justice - (properly=squareness)=4, the first square number; soul or mind=1, opportunity=7 - (Alexander). and such and such soul or mind , another - opportunity , and similarly, more or less, with all the rest—and - since they saw further that the properties and ratios of the musical scales are based on - numbers,Pythagoras himself is credited with - having discovered the ratios of the octave (2 : 1), the fifth (3 : 2) and the fourth (4 - : 3). Burnet, E.G.P. 51. and since it seemed clear that all other things have - their whole nature modelled upon numbers, and that numbers are the ultimate things in the - whole physical universe, they assumed the elements of numbers to be the elements of everything, and - the whole universe to be a proportionOr "harmony." - Cf. Aristot. De Caelo 2.9, and E.G.P. 152. or - number. Whatever analogues to the processes and parts of the heavens and to the whole - order of the universe they could exhibit in numbers and proportions, these they collected - and correlated; and if there was any deficiency - anywhere, they made haste to supply it, in order to make their system a connected whole. - For example, since the decad is considered to be a complete thing and to comprise the - whole essential nature of the numerical system, they assert that the bodies which revolve - in the heavens are ten; and there being only nineEarth, sun, moon, five planets, and the sphere of the fixed stars. that are - visible, they make the "antichthon"i.e. - "counter-earth"; a planet revolving round the "central fire" in such a way as to be - always in opposition to the earth. the tenth. We have treated this subject in greater detail elsewhereIn the lost work On the Pythagoreans; - but cf. Aristot. De Caelo 2.13.; but the - object of our present review is to discover from these thinkers too what causes they - assume and how these coincide with our list of causes. Well, it is obvious that these thinkers too consider number to be a - first principle, both as the materialSee Burnet, - E.G.P 143-146. of things and as constituting their properties and states.i.e., as a formal principle. Cf. Ross ad loc. - The elements of number, according to them, are the Even and the Odd. Of these the former - is limited and the latter unlimited; Unity consists of both (since it is both odd and even)Either because by addition it makes odd numbers even and even odd (Alexander, Theo - Smyrnaeus) or because it was regarded as the principle of both odd and even numbers - (Heath).; number is derived from Unity; and numbers, as we have said, compose the - whole sensible universe. OthersZeller attributes the authorship of this theory to - Philolaus. of this same school hold that there are ten principles, which they - enunciate in a series of corresponding pairs: (1.) Limit and the Unlimited; (2.) Odd and - Even; (3.) Unity and Plurality; (4.) Right and Left; (5.) Male and Female; (6.) Rest and - Motion; (7.) Straight and Crooked; (8.) Light and Darkness; (9.) Good and Evil; (10.) - Square and Oblong. Apparently Alcmaeon of - Croton speculated along the same lines, and - either he derived the theory from them or they from him; for [Alcmaeon was contemporary - with the old age of Pythagoras, and]This statement - is probably true, but a later addition. his doctrines were very similar to - theirs.He was generally regarded as a - Pythagorean. He says that the majority of things in the world of men are in - pairs; but the contraries which he mentions are not, as in the case of the Pythagoreans, - carefully defined, but are taken at random, e.g. white and black, sweet and bitter, good - and bad, great and small. Thus Alcmaeon only - threw out vague hints with regard to the other instances of contrariety, but the Pythagoreans - pronounced how many and what the contraries are. Thus from both these authoritiesThe section of Pythagoreans mentioned in 6, and - Alcmaeon. we can gather thus much, that the contraries are first principles of - things; and from the former, how many and what the contraries are. How these can be referred to our list of causes is not - definitely expressed by them, but they appear to reckon their elements as material; for - they say that these are the original constituents of which Being is fashioned and - composed. From this survey we can sufficiently understand the meaning of those ancients who taught - that the elements of the natural world are a plurality. Others, however, theorized about - the universe as though it were a single entity; but their doctrines are not all alike - either in point of soundness or in respect of conformity with the facts of - nature. For the purposes of our present - inquiry an account of their teaching is quite irrelevant, since they do not, while - assuming a unity, at the same time make out that Being is generated from the unity as from - matter, as do some physicists, but give a different explanation; for the physicists assume - motion also, at any rate when explaining the generation of the universe; but these - thinkers hold that it is immovable. Nevertheless thus much is pertinent to our present - inquiry. It appears that Parmenides - conceived of the Unity as one in definition,His - argument was "Everything that is is one, if 'what is' has one meaning" (pa/nta (/en, ei) to\ o)\n (\en shmai/nei, Aristot. Phys. 187a 1); but he probably believed, no - less than Melissus, in the material unity of reality. Cf. Melissus Fr. 8 (Diels). It has been suggested, however (by the Rev. C. F. - Angus), that he was simply trying to convey in figurative language a conception of - absolute existence. but MelissusOf Samos; defeated the Athenian fleet in 441 - B.C. as materially one. Hence the former says that it is finite,Melissus Fr. 8, ll. 32-3, - 42-3. and the latter that it is infinite.Melissus Fr. 3. But - Xenophanes,Of Colophon, b. 565 (?) B.C. Criticized and ridiculed most of the views of - his day, especially the anthropomorphic conception of the gods. Burnet, E.G.P. 55 ff., - esp. 61-62. Cf. Xenophanes Fr. 23 (Diels). the first - exponent of the Unity (for Parmenides is said to have been his disciple), gave no definite - teaching, nor does he seem to have grasped either of these conceptions of unity; but - regarding the whole material universe he stated that the Unity is God. This school then, as we have said, may be disregarded for the - purposes of our present inquiry; two of them, Xenophanes and Melissus, may be completely - ignored, as being somewhat too crude in their views. Parmenides, however, seems to speak - with rather more insight. For holding as he does that Not-being, as contrasted with Being, - is nothing, he necessarily supposes that Being is one and that there is nothing else (we - have discussed this point in greater detail in the Physics - Aristot. Phys. 1.3 - ); but being compelled to accord with phenomena, and assuming that Being is one in - definition but many in respect of sensation, he posits in his turn two causes, i.e. two - first principles, Hot and Cold; or in other words, Fire and Earth. Of these he ranks Hot under - Being and the other under Not-being.Cf. note on - Aristot. Met. 3.13. From the account just given, - and from a consideration of those thinkers who have already debated this question, we have - acquired the following information. From the earliest philosophers we have learned that - the first principle is corporeal (since water and fire and the like are bodies); some of - them assume one and others more than one corporeal principle, but both parties agree in - making these principles material. Others assume in addition to this cause the source - of motion, which some hold to be one and others two. Thus down to and apart from the ItalianThe Pythagoreans; so called because Pythagoras founded his society at - Croton. philosophers the other - thinkers have expressed themselves vaguely on the subject, except that, as we have said, - they actually employ two causes, and one of these—the source of motion —some - regard as one and others as two. The Pythagoreans, while they likewise spoke of two - principles, made this further addition, which is peculiar to them: they believed, not that - the Limited and the Unlimited are separate entities, like fire or water or some other such - thing, but that the Unlimited itself and the One itself are the essence of those things of - which they are predicated, and hence that number is the essence of all things. Such is the - nature of their pronouncements on this subject. They also began to discuss and define the - "what" of things; but their procedure was far too simple. They defined superficially, and - supposed that the essence of a thing is that to which the term under consideration first - applies—e.g. as if it were to be thought that "double" and "2" are the same, because - 2 is the first number which is double another. But presumably "to be double a number" is not the same as "to be the number 2." - Otherwise, one thing will be many—a consequence which actually followed in their - system.i.e., the same number might be the first - to which each of several definitions applied; then that number would be each of the - concepts so defined. This much, then, can be learned from other and earlier - schools of thought. The philosophies described above were succeeded by the system of - Plato,Compare Aristot. Met. 12.4.2-5. which in most respects accorded with them, but - contained also certain peculiar features distinct from the philosophy of the - Italians. In his youth Plato first became - acquainted with CratylusCf. Aristot. Met. 4.5.18. and the Heraclitean - doctrines—that the whole sensible world is always in a state of flux,Plat. Crat. 402a (fr. - 41 Bywater). and that there is no scientific knowledge of it—and - in after years he still held these opinions. And when Socrates, disregarding the physical - universe and confining his study to moral questions, sought in this sphere for the - universal and was the first to concentrate upon definition, Plato followed him and assumed - that the problem of definition is concerned not with any sensible thing but with entities - of another kind; for the reason that there can be no general definition of sensible things - which are always changing. These entities he - called "Ideas,"I have translated i)de/a by Idea and ei)=dos by - Form wherever Aristotle uses the words with reference to the Platonic theory. Plato - apparently uses them indifferently, and so does Aristotle in this particular connection, - but he also uses ei)=dos in the sense of form in - general. For a discussion of the two words see Taylor, Varia Socratica, - 178-267, and Gillespie, Classical Quarterly, 6.179-203. and held - that all sensible things are named afterFor this - interpretation of para\ tau=ta see Ross's note ad - loc. them sensible and in virtue of their relation to them; for the plurality of - things which bear the same name as the Forms exist by participation in them. (With regard - to the "participation," it was only the term that he changed; for whereas the Pythagoreans - say that things exist by imitation of numbers, Plato says that they exist by - participation—merely a change of term. As - to what this "participation" or "imitation" may be, they left this an open - question.) Further, he states that besides sensible things - and the Forms there exists an intermediate class, the objects of - mathematics,i.e. arithmetical numbers and - geometrical figures. which differ from sensible things in being eternal and - immutable, and from the Forms in that there are many similar objects of mathematics, - whereas each Form is itself unique. Now since the Forms are the causes of everything else, he - supposed that their elements are the elements of all things. Accordingly the material principle is the "Great and Small," and the - essence <or formal principle> is the One, since the numbers are derived from the - "Great and Small" by participation in the the One. In treating the One as a substance instead of a predicate of some - other entity, his teaching resembles that of the Pythagoreans, and also agrees with it in - stating that the numbers are the causes of Being in everything else; but it is peculiar to - him to posit a duality instead of the single Unlimited, and to make the Unlimited consist - of the "Great and Small." He is also peculiar in regarding the numbers as distinct from - sensible things, whereas they hold that things themselves are numbers, nor do they posit - an intermediate class of mathematical objects. His distinction of the One and the numbers from ordinary things (in which he differed - from the Pythagoreans) and his introduction of the Forms were due to his investigation of - logic (the earlier thinkers were strangers to Dialectic)See Aristot. Met. 4.2.19-20, and - cf. Aristot. Met. 8.4.4.; his conception - of the other principle as a duality to the belief that numbers other than primese)/cw tw=n prw/twn is - very difficult, but it can hardly be a gloss, and no convincing emendation has been - suggested. Whatever the statement means, it is probably (as the criticism which follows - is certainly) based upon a misunderstanding. From Plat. Parm. 143c, it might be inferred that the Great and Small (the - Indeterminate Dyad) played no part in the generation of numbers; but there the numbers - are not Ideal, as here they must be. In any case Aristotle is obsessed with the notion - that the Dyad is a duplicative principle (Aristot. Met. - 13.8.14), which if true would imply that it could generate no odd - number. Hence Heinze proposed reading perittw=n(odd) for - prw/twn(which may be right, although the corruption is - improbable) and Alexander tried to extract the meaning of "odd" from prw/twn by understanding it as "prime to 2." However, as Ross - points out (note ad loc.), we may keep prw/twn in the - sense of "prime" if we suppose Aristotle to be referring either (a) to the numbers - within the decad (Aristot. Met. 13.8.17) and - forgetting 9—the other odd numbers being primes; or (b) to numbers in general, and - forgetting the entire class of compound odd numbers. Neither of these alternatives is - very satisfactory, but it seems better to keep the traditional text. can be - readily generated from it, as from a matrix.For a - similar use of the word e)kmagei=on cf. Plat. Tim. 50c. - The fact, however, is just the reverse, and the theory - is illogical; for whereas the Platonists derive multiplicity from matter although their - Form generates only once,Aristotle's objection is - that it is unreasonable that a single operation of the formal upon the material - principle should result in more than one product; i.e. that the material principle - should be in itself duplicative. it is obvious that only one table can be made - from one piece of timber, and yet he who imposes the form upon it, although he is but one, - can make many tables. Such too is the relation of male to female: the female is - impregnated in one coition, but one male can impregnate many females. And these relations - are analogues of the principles referred to. This, then, is Plato's verdict upon the question which - we are investigating. From this account it is clear that he only employed two causesPlato refers several times in the dialogues to an - efficient cause (e.g. the Demiurgus,Plat. Soph. - 265b-d, Plat. Tim. 28c ff.) and a final cause - (e.g. Plat. Phil. 20d, 53e, Plat. Tim. 29d ff.); but Aristotle does not seem to - take these allusions seriously.: that of the essence, and the material cause; for - the Forms are the cause of the essence in everything else, and the One is the cause of it - in the Forms. He also tells us what the - material substrate is of which the Forms are predicated in the case of sensible things, - and the One in that of the Forms—that it is this the duality, the "Great and Small." - Further, he assigned to these two elements respectively the causation of goodCf. Plat. Phil. - 25e-26b. and of evil; a problem which, as we have said,Aristot. Met. 3.17; - 4.3. had also been considered by some of the earlier philosophers, e.g. - Empedocles and Anaxagoras. We have given only a concise and summary account of those thinkers who - have expressed views about the causes and - reality, and of their doctrines. Nevertheless we have learned thus much from them: that - not one of those who discuss principle or cause has mentioned any other type than those - which we we have distinguished in the Physics. - Aristot. Phys. 2.3 - Clearly it is after these types that they are groping, however - uncertainly. Some speak of the first - principle as material, whether they regard it as one or several, as corporeal or - incorporeal: e.g. Plato speaks of the "Great and Small"; the ItaliansSee note on Aristot. - Met. 5.15. of the Unlimited; Empedocles of Fire, Earth, Water and Air; - Anaxagoras of the infinity of homoeomeries. All - these have apprehended this type of cause; and all those too who make their first - principle air or water or "something denser than fire but rarer than air"The various references in Aristotle to material - principles intermediate between certain pairs of "elements" have been generally regarded - as applying to Anaximander's a)/peiron or Indeterminate; - but the references are so vague (cf. Aristot. Met. - 7.6, Aristot. Phys.187a 14, 189b 3, 203a 18) - that it seems better to connect them with later and minor members of the Milesian - school. Cf. Ross's note ad loc.(for some have so described the primary element). - These, then, apprehended this cause only, but others apprehended the source of - motion—e.g. all such as make Love and Strife, or Mind, or Desire a first - principle. As for the essence or - essential nature, nobody has definitely introduced it; but the inventors of the Forms - express it most nearly. For they do not conceive of the Forms as the matter - of sensible things (and the One as the matter of the Forms), nor as producing the - source of motion (for they hold that they are rather the cause of - immobility and tranquillity); but they adduce the Forms as the essential - nature of all other things, and the One as that of the Forms. The end towards which actions, changes and motions - tend they do in a way treat as a cause, but not in this sense, i.e. not in the sense in - which it is naturally a cause. Those who speak of Mind or Love assume these causes as - being something good; but nevertheless they do not profess that anything exists or is - generated for the sake of them, but only that motions originate from - them.Cf. Aristot. - Met. 3.17. Similarly also - those who hold that Unity or Being is an entity of this kind state that it is the cause of - existence, but not that things exist or are generated for the sake of it. So it follows - that in a sense they both assert and deny that the Good is a cause; for they treat it as - such not absolutely, but incidentally. It - appears, then, that all these thinkers too (being unable to arrive at any other cause) - testify that we have classified the causes rightly, as regards both number and nature. - Further, it is clear that all the principles must be sought either along these lines or in - some similar way. Let us next examine the possible difficulties arising out of the statements of each of - these thinkers, and out of his attitude to the first principles. All those who regard the - universe as a unity, and assume as its matter some one nature, and that corporeal and - extended, are clearly mistaken in many respects. They only assume elements of corporeal - things, and not of incorporeal ones, which also exist. They attempt to state the causes of - generation and destruction, and investigate the nature of everything; and at the same time - do away with the cause of motion. Then there is - their failure to regard the essence or formula as a cause of anything; and - further their readiness to call any one of the simple bodies—except earth—a - first principle, without inquiring how their reciprocal generation is effected. I refer to - fire, water, earth and air. Of these some are generated from each other by combination and - others by differentiation; and this difference - is of the greatest importance in deciding their relative priority. In one way it might - seem that the most elementary body is that from which first other bodies are produced by - combination; and this will be that body which is rarest and composed of the finest - particles. Hence all who posit Fire as first - principle will be in the closest agreement with this theory. However, even among the other - thinkers everyone agrees that the primary corporeal element is of this kind. At any rate - none of the Monists thought earth likely to be an element—obviously on account of - the size of its particles— but each of - the other three has had an advocate; for some name fire as the primary element, others - water, and others air.Cf. Aristot. Met. 3.5, 8. And yet why do they not - suggest earth too, as common opinion does? for people say "Everything is earth." And Hesiod too saysCf. Aristot. Met. 4.1. that - earth was generated first of corporeal things—so ancient and popular is the - conception found to be. Thus according to this theory anyone who suggests any of these - bodies other than fire, or who assumes something "denser than air but rarer than - water,"Cf. Aristot. Met. 7.3 n. will be wrong. On the other hand if what is posterior in generation is prior in - nature, and that which is developed and combined is posterior in generation, then the - reverse will be the case; water will be prior to air, and earth to water. So much for - those who posit one cause such as we have described. The same will apply too if - anyone posits more than one, as e.g. Empedocles says that matter consists of four - bodies; objections must occur in his case - also, some the same as before, and some peculiar to him. First, we can see things being - generated from each other in a way which shows that fire and earth do not persist as the - same corporeal entity. (This subject has been treated in my works on Natural Science.Aristot. De Caelo, - 3.7; Aristot. De Gen. et Corr. 2.6.) - Again with regard to the cause of motion in things, whether one or two should be assumed, - it must not be thought that his account is entirely correct or even reasonable.Cf. Aristot. Met. - 4.6. And in general those who - hold such views as these must of necessity do away with qualitative alteration; for on - such a theory cold will not come from hot nor hot from cold, because to effect this there - must be something which actually takes on these contrary qualities: some single element - which becomes both fire and water—which Empedocles denies. If one were to infer that - Anaxagoras recognized twoMind, and the "mixture" of - homoeomerous particles. elements, the inference would accord closely with a view - which, although he did not articulate it himself, he must have accepted as developed by - others. To say that originally everything - was a mixture is absurd for various reasons, but especially since (a) it follows that - things must have existed previously in an unmixed state; (b) it is contrary to nature for - anything to mix with anything ; (c) moreover affections and - attributes would then be separable from their substances (because what is mixed can also - be separated). At the same time, if one were to follow his doctrine carefully and - interpret its meaning, perhaps it would be seen to be more up-to-date; because when nothing was yet differentiated, obviously nothing - could be truly predicated of that substance—e.g. that it was white or black or buff - or any other color. It must necessarily have been colorless, since otherwise it would have - had one of these colors. Similarly by the same - argument it had no taste or any other such attribute; for it cannot have had any quality - or magnitude or individuality. Otherwise some particular form would have belonged to it; - but this is impossible on the assumption that everything was mixed together, for then the - form would have been already differentiated, whereas he says that everything was mixed - together except Mind, which alone was pure and unmixed.Anaxagoras. Fr. 12 - (Diels). It follows from this - that he recognizes as principles the One (which is simple and unmixed) and the Other, - which is such as we suppose the Indeterminate to be before it is determined and partakes - of some form. Thus his account is neither correct nor clear, but his meaning approximates to more recent theories and what is now more - obviously true. However, these thinkers are really concerned only with the theories of generation and - destruction and motion (for in general it is only with reference to this aspect of reality - that they look for their principles and causes). Those, however, who make their study cover the whole of reality, and - who distinguish between sensible and non-sensible objects, clearly give their attention to - both kinds; hence in their case we may consider at greater length what contributions, - valuable or otherwise, they make to the inquiry which is now before us. The so-called Pythagoreans - employ abstruser principles and elements than the physicists. The reason is that they did - not draw them from the sensible world; for mathematical objects, apart from those which - are connected with astronomy, are devoid of motion. Nevertheless all their discussions and investigations are concerned - with the physical world. They account for the generation of the sensible universe, - and - observe what happens in respect of its parts and affections and activities, and they use - up their principles and causes in this connection, as though they agreed with the - others—the physicists—that reality is just so much as is sensible and is - contained in the so-called "heavens." All the - same, as we have said,Aristot. Met. 1.8.17. the causes and principles - which they describe are capable of application to the remoter class of realities as well, - and indeed are better fitted to these than to their physical theories. But as to how there is to be motion, if all that is premissed - is Limit and the Unlimited, and Odd and Even, they do not even hint; nor how, without - motion and change, there can be generation and destruction, or the activities of the - bodies which traverse the heavens. And - further, assuming that it be granted to them or proved by them that - magnitudeAristotle uses the word - me/geqos both of magnitude in general and of spatial - magnitude or extension. Here the meaning seems to be the former. Numbers obviously have - magnitude, and might be regarded as causing it; but (except on the Number-Atomism - theory,) they are no more the cause of extension than that of gravity. is - composed of these factors, yet how is it to be explained that some bodies are light, and - others have weight? For in their premisses and statements they are speaking just as much - about sensible as about mathematical objects; and this is why they have made no mention of - fire or earth or other similar bodies, because, I presume, they have no separate - explanation of sensible things. Again, how are - we to understand that number and the modifications of number are the causes of all being and generation, both in the beginning and - now, and at the same time that there is no other number than the number of which the - universe is composed?i.e., how can number be both - reality and the cause of reality? Because when they make out that Opinion and Opportunity are in such and such a region, - and a little above or below them Injustice and Separation or Mixture, and when they state - as proof of this that each of these abstractions is a number; and that also in this region - there is already a plurality of the magnitudes composed of number, inasmuch as these - modifications of number correspond to these several regions,—is the number which we - must understand each of these abstractions to be the same number which is present in the - sensible universe, or another kind of number?The - point seems to be this. The Pythagoreans say that Opinion is a number, 3 (or 2, - according to another version), and is located in a certain region of the universe - because that region is proper to a corporeal magnitude composed of the number 3 (air was - so composed according to Syrianus). Are we to understand, says Aristotle, that the - abstract number identified with Opinion is the same as the concrete number of which air - consists? The difficulty is probably due to an attempt to combine two different - Pythagorean views of number. Plato at - least says that it is another. It is true that he too supposes that numbers are both these - magnitudes and their causes; but in his view the causative numbers are intelligible and - the others sensible. The Pythagoreans, then, may be dismissed for the present, for it is - enough to touch upon them thus briefly. As for those who posit the Forms as causes,For a discussion of the Ideal theory and Aristotle's - conception of it see Introduction; and with the whole contents of Aristot. Met. 9.1-15 cf. Aristot. Met. 13.4.6-5. in the first place in - their attempt to find the causes of things in our sensible world, they introduced an equal - number of other entities—as though a man who wishes to count things should suppose - that it would be impossible when they are few, and should attempt to count them when he - has added to them. For the Forms are as many as, or not fewer than, the things in search - of whose causes these thinkers were led to the Forms; because corresponding to each thing - there is a synonymous entity apart from the substances (and in the case of non-substantial - things there is a One over the ManyAn Idea which - represents their common denominator.), both in our everyday world and in the - realm of eternal entities.The heavenly - bodies. Again, not one of the arguments by which weAristotle is here speaking as a Platonist. Contrast the language of Aristot. Met. 13.4.7ff., and see - Introduction. try to prove that the Forms exist demonstrates our point: from some - of them no necessary conclusion follows, and from others it follows that there are Forms - of things of which we hold that there are no Forms. For according to the arguments from the sciencesScientific knowledge must have a permanent object (cf. - Aristot. Met. 1.4.2. there will be Forms - of all things of which there are sciencesIncluding - artificial products; cf. Aristot. Met. - 1.15.; and according to the "One-over-Many" argument,The fact that several particulars can have a common - quality or nature implies a single Idea of which they all partake (Plat. Rep. 596a). of negations too; and - according to the argument that "we have some conception of what has perished," of - perishable things; because we have a mental picture of these things.The theory always admitted Ideas of perishable things, - e.g. "man." The objection here is that if the memory of dead men establishes the Idea of - "man," the memory of a dead individual establishes an Idea of that (perishable) - individual. Again, of Plato's more exact arguments some establish Ideas of - relations,Plat. Phaedo - 74a-77a, Plat. Rep. 479a-480a. which we - do not hold to form a separate genus; and - others state the "Third Man."Several arguments bore - this name. Here the reference is probably to the following: If X is a man because he - resembles the Idea of Man, there must be a third "man" in whom the humanity of these two - is united. Cf.Plat. Parm. 132a-133a. And in - general the arguments for the Forms do away with things which are more important to us - exponents of the Forms than the existence of the Ideas; for they imply that it is not the Dyad that is primary, but NumberThe Indeterminate Dyad, being to Aristotle a glorified - 2, falls under the Idea of Number, which is therefore prior to it.; and that the - relative is prior to the absoluteThis seems to be a - development of the same objection. Number, which is relative, becomes prior to the - supposedly self-subsistent Dyad.; and all the other conclusions in respect of - which certain persons, by following up the views held about the Ideas, have gone against - the principles of the theory. Again, according to the assumption by which we hold that the Ideas - exist, there will be Forms not only of substances but of many other things (since the - concept is one not only in the case of substances, but also in the case of all other - things; and there are sciences not only of substances but of other things as well; and - there are a thousand other similar consequences); but according to logical necessity, and - from the views generally held about them, it follows that if the Forms are participated - in, then there can only be Ideas of substances. For they are not participated in qua accidents; each Form can only be participated in in so far as it - is not predicated of a subject. I mean, e.g., - that if anything participates in "absolute Doubleness" it participates also in "eternal," - but only accidentally; because it is an accident of Doubleness to be - eternal.Sensible double things are not eternal; - therefore they do not, in the proper sense of "participation," participate in the Idea - of Doubleness qua having the accidental attribute "eternal." - Therefore Ideas, qua participated in, are not attributes but - substances. Thus the Forms must be - substance. But the same names denote substance in the sensible as in the Ideal world; - otherwise - what meaning will there be in saying that something exists beside the particulars, i.e. - the unity comprising their multiplicity? If the - form of the Ideas and of the things which participate in them is the same, they will have - something in common (for why should Duality mean one and the same thing in the case of - perishable "twos"i.e. pairs of sensible - objects. and the "twos" which are many but eternal,i.e. mathematical 2s. and not in the case of the Idea of Duality - and a particular "two"?); but if the form is not the same, they will simply be homonyms; - just as though one were to call both Callias and a piece of wood "man," without remarking - any property common to them.The argument of 7-8 is: - Ideas are substances. The common name which an idea shares with its particulars must - mean the same of both; otherwise "participation" is merely homonymy. But as applied to - Ideas it denotes substance; therefore particulars must be substances. Above all we might - examine the question what on earth the Forms contribute to sensible things, whether - eternal or subject to generation and decay; for they are not the cause of any motion or - change in them. Again, they are no help - towards the knowledge of other thingsThis objection, like the next, is chiefly directed against the transcendence of the - Ideas. It is anticipated by Plato in Plat. Parm. - 134d.(for they are not the substance of things, otherwise they would be - in things), nor to their existence, since they are not present in the - things which partake of them. If they were, it might perhaps seem that they are causes, in - the sense in which the admixture of white causes a thing to be white; but this theory, which was first stated by AnaxagorasAnaxagoras Fr. 12ad - fin. and later by EudoxusSee note on Aristot. Met. 12.8.9. Apparently he was a Platonist - who regarded the Ideas as immanent in particulars. and others, is very readily - refutable, for it is easy to adduce plenty of impossibilities against such a view. Again, - other things are not in any accepted sense - derived from the Forms. To say - that the Forms are patterns, and that other things participate in them, is to use empty - phrases and poetical metaphors; for what is it that fashions things on the model of the - IdeasPlato says "the Demiurgus"?Plat. Tim. 28c, Plat. Tim. - 29a. Besides, anything may both be and become like something else - without being imitated from it; thus a man may become just like Socrates whether Socrates - exists or not, and even if Socrates were - eternal, clearly the case would be the same. Also there will be several "patterns," and - hence Forms, of the same thing; e.g. "animal" and "two-footed" will be patterns of "man," - and so too will the Idea of Man.Why this - consequence is objectionable is not quite clear. Perhaps it is on the ground that to - "account for appearances" in this way is not economical. Further, the Forms will be patterns not only of sensible things - but of themselves (e.g. genus in the sense of genus of species), and thus the same thing - will be both pattern and copy.The species will be - the "pattern" of individuals, and the genus of the species. - Further, it - would seem impossible that the substance and the thing of which it is the substance exist - in separation; hence how can the Ideas, if they are the substances of things, exist in - separation from them?Cf. Aristot. Met. 1.10. It is stated in the - PhaedoPlat. Phaedo 100d. that the Forms are the causes both of existence and - of generation. Yet, assuming that the Forms - exist, still the things which participate in them are not generated unless there is - something to impart motion; while many other things are generated (e.g. - house, ring) of which we hold that there are no Forms. Thus it is clearly possible that - all other things may both exist and be generated for the same causes as the things just - mentioned. Further, if the Forms are numbers, in what sense will they be causes? Is it because - things are other numbers, e.g. such and such a number Man, such and such another Socrates, - such and such another Callias? then why are those numbers the causes of these? Even if the - one class is eternal and the other not, it will make no difference. And if it is because the things of our world are ratios of - numbers (e.g. a musical concord), clearly there is some one class of things of which they - are ratios. Now if there is this something, i.e. their matter , clearly the - numbers themselves will be ratios of one thing to another. I mean, e.g., that if Callias is a numerical ratio of fire, earth, - water and air, the corresponding Idea too will be a number of certain other things which - are its substrate. The Idea of Man, too, whether it is in a sense a number or not, will - yet be an arithmetical ratio of certain things, and not a mere number; nor, on these grounds, will any Idea be a number.The point, which is not very clearly expressed, is that - the Ideas will not be pure numerical expressions or ratios, but will have a substrate - just as particulars have. Again, one number can be composed of several numbers, but how - can one Form be composed of several Forms? And if the one number is not composed of the - other numbers themselves, but of their constituents (e.g. those of the number 10,000), - what is the relation of the units? If they are specifically alike, many absurdities will - result, and also if they are not (whether (a) the units in a given number are unlike, or - (b) the units in each number are unlike those in every other number).That the words in brackets give the approximate sense - seems clear from Aristot. Met. 13.6.2-3, Aristot. Met. 13.7.15; but it is difficult to get it - out of the Greek. For in what can they differ, seeing that they have no - qualities? Such a view is neither reasonable nor compatible with our conception of - units. Further, it becomes necessary to set up another kind of number (with which calculation - deals), and all the objects which are called "intermediate" by some thinkers.Cf. vi. 4. But how or from what principles can - these be derived? or on what grounds are they to be considered intermediate between things - here and Ideal numbers? Further, each of the units in the number 2 comes - from a prior 2; but this is impossible.i.e., if 2 - is derived from a prior 2 (the Indeterminate Dyad; Aristotle always regards this as a - number 2), and at the same time consists of two units or 1s, 2 will be - prior both to itself and to 1. - Further, why should a - number <of units>, taken together, be one thing? And further, in addition to the - above objections, if the units are unlike, they should be treated as the thinkers who - assume two or four elements treat those elements; for not one of them applies the term - "element" to the common substrate, e.g. body, but to fire and earth—whether there is - a common substrate (i.e. body) or not.In the Aristot. De Gen. et Corr. 320b 23Aristotle says that - there is not. As it is, the One is - spoken of as though it were homogeneous, like fire or water. But if this is so, the - numbers will not be substances. And if there is an absolute One which is a principle, - clearly the term "one" is ambiguous; otherwise this is impossible.This last sentence shows that in what goes before A. has been regarding - the Platonic One as a unit. If this is so, he says, substance cannot be composed of it. - If on the other hand the One is something different from the unit, they ought to make - this clear. When we wish to refer substances to their principles we derive - linesThe lines, planes, and solids here discussed - are probably the Ideal lines, etc., which are immediately posterior to the Idea-Numbers. - Cf. 30, Aristot. Met. 13.6.10, Aristot. Met. 13.9.2, and see Introduction. - from "Long and Short," a kind of "Great and Small"; and the plane from "Wide and Narrow," - and the solid body from "Deep and Shallow." But in this case how can the plane contain a - line, or the solid a line and a plane? for - "Wide and Narrow" and "Deep and Shallow" are different genera. Nor is Number contained in - these objects (because "Many and Few" is yet another class); and in the same way it is - clear that none of the other higher genera will be contained in the lower. Nor, again, is - the Broad the genus of which the Deep is a species; for then body would be a kind of - plane. Further, how will it be possible for figures to contain points?Lines, planes, and solids are generated from varieties - of the Great and Small, but points cannot be, having no magnitude; how, then, can the - latter be present in the former? Plato steadily rejected this class of objects as - a geometrical fiction, but he recognized "the beginning of a line," and he frequently - assumed this latter class, i.e. the " indivisible lines."That Plato denied the existence of the point and asserted that of - indivisible lines is not directly stated elsewhere, but the same views are ascribed to - Xenocrates, and were attacked in the treatise Xenocrates De lineis insecabilibus. See - Ross ad loc. But these must have some limit; and so by the same argument which - proves the existence of the line, the point also exists.Sc. if the point is the limit of the line. In general, although Wisdom is - concerned with the cause of visible things, we have ignored this question (for we have no - account to give of the cause from which change arises),Cf. Aristot. Met. 7.5 and Aristot. Met. 1.9. and in the belief that we - are accounting for their substance we assert the existence of other substances; but as to - how the latter are the substances of the former, our explanation is - worthless—for "participation," as we have said before,Aristot. Met. 1.12. means - nothing. And as for that which we can see to - be the cause in the sciences, and through which all mind and all nature works—this - causeThe final cause. Cf. Aristot. Met. 1.6.9-10. which we hold to be one - of the first principles—the Forms have not the slightest bearing upon it either. - Philosophy has become mathematics for modern thinkers,e.g. Speusippus, for whom see Aristot. - Met. 7.2.4. although they professCf. Plat. Rep.531c-d that mathematics is only - to be studied as a means to some other end. Further, one might regard the substance which they make the material - substrate as too mathematical, and as being a predicate and differentia of substance or - matter rather than as matter itself, I mean the "Great and Small," which is like the "Rare - and Dense" of which the physicists speak,Cf. iv. - 10. holding that they are the primary differentiae of the substrate; because - these qualities are a species of excess and defect. Also with regard to motion, if the "Great and Small" is to constitute - motion, obviously the Forms will be moved; if not, whence did it come? On this view the - whole study of physics is abolished. And what is supposed to be easy, to prove that - everything is One, does not follow; because from their expositionThe word e)/kqesis has various technical - meanings. The process referred to here apparently consisted in taking, e.g., particular - men, and reducing them with reference to their common nature to a single unit or - universal, "man"; then taking "man," "horse," "dog," etc. and treating them in the same - way, until a unit is reached which embraces everything (Alexander). it does not - follow, even if you grant them all their assumptions that everything is One, but only that - there is an absolute One— and not even - this, unless you grant that the universal is a class; which is impossible in some - cases.Probably those of relative or negative - terms. Cf. Aristot. Met. 1.3. Nor is there - any explanation of the lines, planes and solids which "come after" the NumbersSee note on Aristot. - Met. 1.23.: neither as to how they exist or can exist, nor as to what - their importance is. They cannot be Forms (since they are not numbers) or Intermediates - (which are the objects of mathematics) or perishables; clearly they form yet another - fourth class. In general, to investigate the elements of existing things without distinguishing the - various senses in which things are said to exist is a hopeless task; especially when one inquires along these lines into the nature - of the elements of which things are composed. For (a) we cannot surely conceive of the - elements of activity or passivity or straightness; this is possible, if at all, only in - the case of substances. Hence to look for, or to suppose that one has found, the elements - of everything that exists, is a mistake. (b) How can one apprehend the elements of - everything ? Obviously one could not have any previous knowledge of - anything; because just as a man who is beginning to learn geometry can have previous - knowledge of other facts, but no previous knowledge of the principles of that science or - of the things about which he is to learn, so it is in the case of all other branches of - knowledge. Hence if there is a science which - embraces everythinge.g. Plato's - Dialectic.(as some say), the student of it can have no previous - knowledge at all. But all learning proceeds, wholly or in part, from what is already - known; whether it is through demonstration or through definition—since the parts of - the definition must be already known and familiar. The same is true of induction. - On the other hand, assuming that this knowledge should - turn out to be innate,Cf. the doctrine of a)na/mnhsis (recollection), Plat. Meno - 81c, Plat. Phaedo 72e. it is - astonishing that we should possess unawares the most important of the sciences. Further, - how is one to know of what elements things consist? how is it to be - established? Even this presents a - difficulty, because the facts might be disputed, as happens in the case of certain - syllables—for some say that ZA is composed of S, D and A, while others say that it - is a distinct sound and not any one of those which are familiar to us.stoixei=on means both - "an element" and "a letter of the alphabet"; hence letters are often used as analogues - of the material elements. The point here is: Is Z or rather the Greek z) a stoixei=on, or is it - further analyzable? Since this can be disputed, we must expect differences of opinion - about the elements in general. Further, how can one gain knowledge of the objects of a - particular sense-perception without possessing that sense? Yet it should be possible, that - if the elements of which all things consist, as composite sounds consist of their - peculiar Peculiar to them as sounds, not as - individual sounds. If sights and sounds had the same elements, sight, which knows those - elements as composing sights, would know them as composing sounds; i.e., we could see - sounds. elements, are the same. Thus it is obvious, from the statements of earlier thinkers - also, that all inquiry is apparently directed towards the causes described in the - Physics,Aristot. Phys. 2.3, 7. and that we cannot - suggest any other cause apart from these. They were, however, only vaguely conceived; and - although in one sense they have all been stated before, in another they have not been - stated at all. For the earliest philosophy - speaks falteringly, as it were, on all subjects; being new and in its infancy. Even - Empedocles says that bone exists by virtue of its ratio,Empedocles Fr. 96, 98 (Diels), Ritter and - Preller 175. Aristotle says that Empedocles had some idea of the essence or formal - cause, but did not apply it generally. which is the definition or essence of a - thing. But by similar reasoning both flesh - and every other thing, or else nothing at all, - must be ratio; for it must be because of this, and not because of their matter—which - he calls fire, earth, water and air—that flesh and bone and every other thing - exists. If anyone else had stated this, he - would necessarily have agreed, but his own statement was not clear. These and similar points have been explained already. We will now return to - the difficulties which might be raised about these same questions, for they may throw some - light upon subsequent difficulties.The reference is - to Book 3. See Introduction.

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The study of Truth is in - one sense difficult, in another easy. This is shown by the fact that whereas no one person - can obtain an adequate grasp of it, we cannot all fail in the attempt; - each - thinker makes some statement about the natural world, and as an individual contributes - little or nothing to the inquiry; but a combination of all conjectures results in - something considerable. Thus in so far as it - seems that Truth is like the proverbial door which no one can miss,Leutsch and Schneidewin, Paroemiographi, 2.678. in - this sense our study will be easy; but the fact that we cannot, although having some grasp - of the whole, grasp a particular part, shows its difficulty. However, since difficulty - also can be accounted for in two ways, its cause may exist not in the objects of our study - but in ourselves: just as it is with bats' eyes - in respect of daylight, so it is with our mental intelligence in respect of those things - which are by nature most obvious. It is only fair to be - grateful not only to those whose views we can share but also to those who have expressed - rather superficial opinions. They too have contributed something; by their preliminary - work they have formed our mental experience. If - there had been no Timotheus,Of Miletus, 446 (?)—357 - B.C. we should not possess much of our music; and if there had been no - Phrynis,Of Mytilene; he is referred to as still alive in Aristoph. Cl. 971. Both Phrynis and Timotheus are criticized in the fragment - of Pherecrates Chirontranslated by Rogers in the appendix to his ed. of - the Clouds. there would have been no Timotheus. It is just the - same in the case of those who have theorized about reality: we have derived certain views - from some of them, and they in turn were indebted to others. Moreover, philosophy is rightly - called a knowledge of Truth. The object of - theoretic knowledge is truth, while that of practical knowledge is action; for even when - they are investigating how a thing is so, practical men study not the eternal - principle but the relative and immediate application. But we cannot know the truth apart from the cause. Now every thing - through which a common quality is communicated to other things is itself of all those - things in the highest degree possessed of that quality (e.g. fire is hottest, because it - is the cause of heat in everything else); hence that also is most true which causes all - subsequent things to be true. Therefore in - every case the first principles of things must necessarily be true above everything - else—since they are not merely sometimes true, nor is anything the - cause of their existence, but they are the cause of the existence of other - things,—and so as each thing is in respect of existence, so it is in respect of - truth. Moreover, - it is obvious that there is some first principle, and that the causes of things are not - infinitely many either in a direct sequence or in kind. For the material generation of one - thing from another cannot go on in an infinite progression (e.g. flesh from earth, earth - from air, air from fire, and so on without a stop); nor can the source of motion (e.g. man - be moved by air, air by the sun, the sun by Strife,Aristotle is evidently thinking of Empedocles' system. with no limit to the - series). In the same way neither can the - Final Cause recede to infinity—walking having health for its object, and health - happiness, and happiness something else: one thing always being done for the sake of - another. And it is just the same with the - Formal Cause. For in the case of all intermediate terms of a series which are contained - between a first and last term, the prior term is necessarily the cause of those which - follow it; because if we had to say which of the three is the cause, we should say "the - first." At any rate it is not the last term, because what comes at the end is not the - cause of anything. Neither, again, is the intermediate term, which is only the cause of - one (and it makes no difference whether there - is one intermediate term or several, nor whether they are infinite or limited in number). - But of series which are infinite in this way, and in general of the infinite, all the - parts are equally intermediate, down to the present moment. Thus if there is no first - term, there is no cause at all. On the other hand there can be no infinite progression - downwards (where there is a beginning in the - upper direction) such that from fire comes water, and from water earth, and in this way - some other kind of thing is always being produced. There are two senses in which one thing - "comes from" another—apart from that in which one thing is said to come - after another, e.g. the Olympian "from"e)k means not only "from" but "after"; - Aristotle dismisses this latter meaning. The Isthmian fell alternatively in the same - year as the Olympian festival; when this happened the former was held in the spring and - the latter in the summer. Cf. Aristot. Met. - 5.24.5. the Isthmian games—either as a man comes from a child as - it develops, or as air comes from water. Now we - say that a man "comes from" a child in the sense that that which has become - something comes from that which is becoming: i.e. the perfect from the - imperfect. (For just as "becoming" is always intermediate between being and not-being, so - is that which is becoming between what is and what is not. The learner is becoming - informed, and that is the meaning of the statement that the informed person "comes from" - the learner.) On the other hand A comes from B - in the sense that water comes from air by the destruction of B. Hence the former class of - process is not reversible (e.g. a child cannot come from a man, for the result of the process of - becoming is not the thing which is becoming, but that which exists after the process is - complete. So day comes from early dawn, because it is after dawn; and hence dawn does not - come from day). But the other class is reversible. In both cases progression to infinity is impossible; for in the former - the intermediate terms must have an end, and in the second the process is reversible, for - the destruction of one member of a pair is the generation of the other. At the same time - the first cause, being eternal, cannot be destroyed; because, since the process of - generation is not infinite in the upper direction, that cause which first, on its - destruction, became something else, cannot possibly be eternal.The argument is elliptical and confused. The meaning is this: Since there - is an upward limit, there is a first cause which is eternal, being independent of any - other cause. Therefore this cause cannot cause other things by its destruction, in the - manner just described. Further, the Final cause of a thing is an end , and is - such that it does not happen for the sake of some thing else, but all other things happen - for its sake. So if there is to be a last term of this kind, the series will not be - infinite; and if there is no such term, there will be no Final cause. Those who introduce - infinity do not realize that they are abolishing the nature of the Good (although no one - would attempt to do anything if he were not likely to reach some limit); nor would there be any intelligence in the world, - because the man who has intelligence always acts for the sake of something, and this is a - limit, because the end is a limit. Nor again - can the Formal cause be referred back to another fuller definition; for the prior definition is always closer, and the posterior is - not; and where the original definition does not apply, neither does the subsequent - one. Further, those who hold such a view do - away with scientific knowledge, for on this view it is impossible to know anything until - one comes to terms which cannot be analyzed. Understanding, too, is impossible; for how can one conceive of things which are infinite - in this way? It is different in the case of the line, which, although in respect of - divisibility it never stops, yet cannot be conceived of unless we make a stop (which is - why, in examining an infinitei.e. infinitely - divisible. line, one cannot count the sections).It does not follow that we can apprehend that which is infinite because - we can apprehend a line which is infinitely divisible. We can only really apprehend the - line by setting a limit to its divisibility and regarding it simply as divisible into a - very great (but not infinite) number of sections. An infinite number of sections can - neither be apprehended nor counted. Even matter has to be conceived under the form of something which changes,Matter too, which is infinite in its varieties, can - only be apprehended in the form of concrete sensible objects which are liable to change. - This seems to be the meaning of the text, but Ross's reading and interpretation may be - right: see his note ad loc. and there can be nothing which is infinite.i.e. not actually, but only potentially. In any - case the concept of infinity is not infinite.Cf. - the third note above. Again, if the kinds of causes - were infinite in number it would still be impossible to acquire knowledge; - for it is only when we have become acquainted with the causes that we assume that we know - a thing; and we cannot, in a finite time, go completely through what is additively - infinite. The - effect of a lecture depends upon the habits of the listener; because we expect the - language to which we are accustomed, and anything beyond this seems not to be on the same level, but - somewhat strange and unintelligible on account of its unfamiliarity; for it is the - familiar that is intelligible. The powerful effect of familiarity is clearly shown by the - laws, in which the fanciful and puerile survivals prevail, through force of habit, against - our recognition of them. Thus some people will - not accept the statements of a speaker unless he gives a mathematical proof; others will - not unless he makes use of illustrations; others expect to have a poet adduced as witness. - Again, some require exactness in everything, while others are annoyed by it, either - because they cannot follow the reasoning or because of its pettiness; for there is - something about exactness which seems to some people to be mean, no less in an argument - than in a business transaction. Hence one must have been already trained how to take each kind of - argument, because it is absurd to seek simultaneously for knowledge and for the method of - obtaining it; and neither is easy to acquire. Mathematical accuracy is not to be demanded - in everything, but only in things which do not contain matter. Hence this method is not that of natural science, because presumably - all nature is concerned with matter. Hence we should first inquire what nature is; for in - this way it will become clear what the objects of natural science are [and whether it - belongs to one science or more than one to study the causes and principles of things].These - words have evidently been inserted to form a kind of link with the subject matter of the - Metaphysics. The book is almost certainly part of a quite independent - treatise; see Introduction.

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It is necessary, with a - view to the science which we are investigating, that we first describe the questions which - should first be discussed. These consist of all the divergent views which are held about - the first principles; and also of any other view apart from these which happens to have - been overlooked. Now for those who wish to get - rid of perplexities it is a good plan to go into them thoroughly; for the subsequent - certainty is a release from the previous perplexities, and release is impossible when we - do not know the knot. The perplexity of the mind shows that there is a "knot" in the - subject; for in its perplexity it is in much the same condition as men who are fettered: - in both cases it is impossible to make any progress. Hence we should first have studied all the difficulties, both for the - reasons given and also because those who start an inquiry without first considering the - difficulties are like people who do not know where they are going; besides, one does not - even know whether the thing required has been found or not. To such a man the - end is not clear; but it is clear to one who has already faced the - difficulties. Further, one who has heard all - the conflicting theories, like one who has heard both sides in a lawsuit, is necessarily - more competent to judge. The first difficulty is concerned with the subjectsThe principles and causes referred to in Book I. - which we discussed in our prefatory remarks. (1.) Does the study of the causes belong to - one science or to more than one?The problem is - discussed Aristot. Met. 3.2.1-10, and answered - Aristot. Met. 4.1.(2.) Has that science - only to contemplate the first principles of substance, or is it also concerned with the - principles which all use for demonstration—e.g. whether it is possible at the same - time to assert and deny one and the same thing, and other similar principles?Discussed Aristot. Met. - 3.2.10-15; answered Aristot. Met. - 4.2. And if it is concerned - with substance, (3.) is there one science which deals with all substances, or more than - one; and if more than one, are they all cognate, or should we call some of them "kinds of - Wisdom" and others something different?Discussed - Aristot. Met. 3.2.15-17; answered Aristot. Met. 4.2.9-10, Aristot. Met. 6.1. This too is a question which demands inquiry: (iv.) should we hold - that only sensible substances exist, or that there are other besides? And should we hold - that there is only one class of non-sensible substances, or more than one (as do those who - posit the Forms and the mathematical objects as intermediate between the Forms and - sensible things)?Discussed Aristot. Met. 3.2.20-30 answered Aristot. Met. 12.6-10, and also by the refutation of - the Platonic Ideas and Intermediates in Books 13 and 14. These questions, then, as I say, must be considered; and also (v.) - whether our study is concerned only with substances, or also with the essential attributes of substance; and further, with regard to Same and Other, and Like and Unlike - and Contrariety, and Prior and Posterior, and all other such terms which dialecticians try - to investigate, basing their inquiry merely upon popular opinions; we must consider whose - province it is to study all of these. Further, - we must consider all the essential attributes of these same things, and not merely what - each one of them is, but also whether each one has one oppositeDiscussed Aristot. Met. 3.2.18-19; - answered Aristot. Met. 4.2.8-25.; and - (vi.) whether the first principles and elements of things are the genera under which they - fall or the pre-existent parts into which each thing is divided; and if the genera, - whether they are those which are predicated ultimately of individuals, or the primary - genera—e.g., whether "animal" or "man" is the first principle and the more - independent of the individual.DiscussedAristot. Met. 3.3; answered Aristot. Met. 7.10, 12-13 Above all we must consider and - apply ourselves to the question (7.) whether there is any other cause per se - besides matter, and if so whether it is dissociable from matter, and whether it is - numerically one or several; and whether there is anything apart from the concrete thing - (by the concrete thing I mean matter together with whatever is predicated of it) or - nothing; or whether there is in some cases but not in others; and what these cases - are.Discussed iv. 1-8. For answers to these - questions see Aristot. Met. 7.8, 13-14; Aristot. Met. 12.6-10; Aristot. Met. 13.10. - Further, (8.) we must ask whether the first principles - are limited in number or in kindDiscussed Aristot. Met. 3.4.8-10; answered Aristot. Met. 12.4-5, Aristot. Met. 13.10.—both those in the - definitions and those in the substrate—and (ix.) whether the principles of - perishable and of imperishable things are the same or different; and whether all are - imperishable, or those of perishable things are perishable.Discussed Aristot. Met. 3.4.11-23; - for Aristotle's general views on the subject see Aristot. Met. 7.7-10, Aristot. Met. - 12.1-7. Further, there is - the hardest and most perplexing question of all: (x.) whether Unity and Being (as the - Pythagoreans and Plato maintained) are not distinct, but are the substance of things; or - whether this is not so, and the substrate is something distinctDiscussed Aristot. Met. 3.4.24-34; - answered Aristot. Met. 7.16.3-4, Aristot. Met. 10.2.(as Empedocles holds of - Love,Actually Love was no more the universal - substrate than was any other of Empedocles' elements; Aristotle appears to select it on - account of its unifying function. another thinkerHeraclitus. of fire, and another Thales. of water or airAnaximenes.); and (xi.) whether the - first principles are universal or like individual thingsDiscussed Aristot. Met. 3.6.7-9; - for the answer see Aristot. Met. 7.13-15, Aristot. Met. 13.10.; and (12.) whether they - exist potentially or actually; and further whether their potentiality or actuality depends - upon anything other than motionDiscussed Aristot. Met. 3.6.5-6; for the relation of - potentiality to actuality see Aristot. Met. - 9.1-9; for actuality and motion see Aristot. - Met. 12.6-7.; for these questions may involve considerable - difficulty. Moreover we must ask (13.) - whether numbers and lines and figures and points are substances in any sense, or not; and - if they are, whether they are separate from sensible things or inherent in them.Discussed Aristot. Met. - 3.5; answered Aristot. Met. 13.1-3, - 6-9; Aristot. Met. 14.1-3, 5, 6. - With regard to these problems not only is it difficult to attain to the truth, but it is - not even easy to state all the difficulties adequately.For another statement of the problems sketched in this chapter see Aristot. Met. 9.1, 2. (1.) Firstly, then, with - respect to the first point raised: whether it is the province of one science or of more - than one to study all the kinds of causes. How - can one science comprehend the first principles unless they are contraries? - Again, in many things they are not all present. How can a principle of motion be in immovable things? or the "nature of the Good"? for - everything which is good in itself and of its own nature is an end and thus a - cause, because for its sake other things come to be and exist; and the end - and purpose is the end of some action, and all actions involve motion; thus - it would be impossible either for this principle to exist in motionless things or for - there to be any absolute Good. Hence in mathematics too nothing is proved by means of this cause, nor is there any - demonstration of the kind "because it is better or worse"; indeed no one takes any such - consideration into account. And so for this - reason some of the sophists, e.g. Aristippus,Founder of the Cyrenaic school in the early fourth century. spurned mathematics, - on the ground that in the other arts, even the mechanical ones such as carpentry and - cobbling, all explanation is of the kind "because it is better or worse," while - mathematics takes no account of good and bad.For a - defense of mathematics see Aristot. Met. - 13.3.10-12. - On the other hand if - there are several sciences of the causes, and a different one for each different - principle, which of them shall we consider to be the one which we are seeking, or whom of - the masters of these sciences shall we consider to be most learned in the subject which we - are investigating? For it is possible for all - the kinds of cause to apply to the same object; e.g. in the case of a house the source of - motion is the art and the architect; the final cause is the function; the matter is earth - and stones, and the form is the definition. Now to judge from our discussion some time - agoCf. Aristot. - Met. 1.2.5-6. as to which of the sciences should be called Wisdom, there - is some case for applying the name to each of them. Inasmuch as Wisdom is the most sovereign and authoritative kind of - knowledge, which the other sciences, like slaves, may not contradict, the knowledge of the - end and of the Good resembles Wisdom (since everything else is - for the sake of the end ); but inasmuch as it has been defined as knowledge - of the first principles and of the most knowable, the knowledge of the essence will - resemble Wisdom. For while there are many ways - of understanding the same thing, we say that the man who recognizes a thing by its being - something knows more than he who recognizes it by its not being something; and even in the - former case one knows more than another, and most of all he who knows what it - is, and not he who knows its size or quality or natural capacity for acting or being acted - upon. Further, in all other cases too, even - in such as admit of demonstration, we consider - that we know a particular thing when we know what it is (e.g. what is the - squaring of a rectangle? answer, the finding of a mean proportional to its sides; and - similarly in other instances); but in the case of generations and actions and all kinds of - change, when we know the source of motion. This is distinct from and opposite to the end . Hence it might be supposed - that the study of each of these causes pertained to a different science.See Aristot. Met. - 4.1 (2.) Again, with respect to the - demonstrative principles as well, it may be disputed whether they too are the objects of - one sciencesc. the science which studies the four - causes. or of several.Cf. Aristot. Met. 3.1.5. By demonstrative I mean the axioms from which all demonstration - proceeds, e.g. "everything must be either affirmed or denied," and "it is impossible at - once to be and not to be," and all other such premisses. Is there one science both of - these principles and of substance, or two distinct sciences? and if there is not one, - which of the two should we consider to be the one which we are now seeking? It is not probable that - both subjects belong to one science; for why should the claim to understand these - principles be peculiar to geometry rather than to any other science? Then if it pertains - equally to any science, and yet cannot pertain to all, comprehension of these principles is no more - peculiar to the science which investigates substances than to any other science. Besides, in what sense can there in be a science of - these principles? We know already just what each of them is; at any rate other sciences - employ them as being known to us.sc. and so there - can be no science which defines them. If, however there is a demonstrative - science of them, there will have to be some underlying genus, and some of the principles - will be derived from axioms, and others will be unproved (for there cannot be demonstration of everything), since demonstration - must proceed from something, and have some subject matter, and prove something. Thus it - follows that there is some one genus of demonstrable things; for all the demonstrative - sciences employ axioms. On the other hand, if the science of - substance is distinct from the science of these principles, which is of its own nature the - more authoritative and ultimate? The axioms - are most universal, and are the first principles of everything. And whose province will it - be, if not the philosopher's, to study truth and error with respect to them?For the answer see Aristot. Met. 4.3. (3.) And in general, - is there one science of all substances, or more than one?Cf. Aristot. Met. 3.1.6. if - there is not one, with what sort of substance must we assume that this science is - concerned? On the other hand, it is not - probable that there is one science of all substances; for then there would be one - demonstrative of all attributes—assuming that every demonstrative science proceeds from accepted beliefs and studies the essential - attributes concerned with some definite subject matter. Thus to study the essential attributes connected with the same genus - is the province of the same science proceeding from the same beliefs. For the subject - matter belongs to one science, and so do the axioms, whether to the same science or to a - different one; hence so do the attributes, whether they are studied by these sciences - themselves or by one derived from them.For the - answer see Aristot. Met. 4.2.9-10, Aristot. Met. 6.1. (v.) Further, is this study - concerned only with substances, or with their attributes as well?Cf. Aristot. Met. 3.1.8-10. - I mean, e.g., if the solid is a kind of substance, and so too lines and planes, is it the - province of the same science to investigate both these and their attributes, in every - class of objects about which mathematics demonstrates anything, or of a different - science? If of the same, then the science of - substance too would be in some sense demonstrative; but it does not seem that there is any - demonstration of the "what is it?" And if of a different science, what will be the science - which studies the attributes of substance? This is a very difficult question to - answer.This problem, together with the appendix - to it stated in Aristot. Met. 3.1.9-10, is - answered in Aristot. Met. - 4.2.8-25. (iv.) Further, are we to say that only sensible substances exist, or - that others do as well? and is there really only one kind of substance, or more than one - (as they - hold who speak of the Forms and the Intermediates, which they maintain to be the objects - of the mathematical sciences)? In what sense - we Platonists hold the Forms to be both causes and independent substances has been - statedAristot. - Met. 1.6. in our original discussion on this subject. But while they - involve difficulty in many respects, not the least absurdity is the doctrine that there - are certain entities apart from those in the sensible universe, and that these are the - same as sensible things except in that the former are eternal and the latter - perishable.As it stands this is a gross - misrepresentation; but Aristotle's objection is probably directed against the conception - of Ideas existing independently of their particulars. See Introduction. For Platonists say nothing more or less than that - there is an absolute Man, and Horse, and Health; in which they closely resemble those who - state that there are Gods, but of human form; for as the latter invented nothing more or - less than eternal men, so the former simply make the Forms eternal sensibles. Again, if anyone posits Intermediates distinct from Forms and - sensible things, he will have many difficulties; because obviously not only will there be lines apart from both Ideal - and sensible lines, but it will be the same with each of the other classes.sc. of objects of mathematical sciences. Thus - since astronomy is one of the mathematical sciences, there will have to be a heaven - besides the sensible heaven, and a sun and moon, and all the other heavenly - bodies. But how are we to believe this? Nor - is it reasonable that the heaven should be immovable; but that it should move is utterly impossible.The reference is to the supposed "intermediate" heaven. A "heaven" - (including heavenly bodies) without motion is unthinkable; but a non-sensible heaven can - have no motion. It is the same with the objects of optics and the mathematical - theory of harmony; these too, for the same reasons, cannot exist apart from sensible - objects. Because if there are intermediate objects of sense and sensations, clearly there - will also be animals intermediate between the Ideal animals and the perishable - animals.If there are "intermediate," i.e. - non-sensible, sights and sounds, there must be "intermediate" faculties of sight and - hearing, and "intermediate" animals to exercise these faculties; which is - absurd. One might also raise the question with respect to what kind of objects we are to look - for these sciences. For if we are to take it that the only difference between mensuration - and geometry is that the one is concerned with things which we can perceive and the other - with things which we cannot, clearly there will be a science parallel to medicine (and to - each of the other sciences), intermediate between Ideal medicine and the medicine which we - know. Yet how is this possible? for then - there would be a class of healthy things apart from those which are sensible and from the - Ideally healthy. Nor, at the same time, is it true that mensuration is concerned with - sensible and perishable magnitudes; for then it would perish as they do. Nor, again, can - astronomy be concerned with sensible magnitudes or with this heaven of ours; for as sensible lines are not like those of which the - geometrician speaks (since there is nothing sensible which is straight or curved in that - sense; the circlei.e., the visible circle which we - draw. Like the ruler, it is geometrically imperfect; thus they touch at more than one - point. touches the ruler not at a point, but <along a line> as Protagoras - used to say in refuting the geometricians), so the paths and orbits of our heaven are not - like those which astronomy discusses, nor have the symbols of the astronomer the same - nature as the stars. Some, however, say that these so-called Intermediates between Forms - and sensibles do exist: not indeed separately from the sensibles, but in them. It would - take too long to consider in detail all the impossible consequences of this theory, but it - will be sufficient to observe the following. On this view it is not logical that only this should be so; in clearly it would be - possible for the Forms also to be in sensible things; for the same argument applies to - both. Further, it follows necessarily that two solids must occupy the same space; and that - the Forms cannot be immovable, being present in sensible things, which move. And in general, what is the object of assuming that - Intermediates exist, but only in sensible things? The same absurdities as before will - result: there will be a heaven besides the sensible one, only not apart from it, but in - the same place; which is still more impossible.The - problem is dealt with partly in Aristot. Met. - 12.6-10, where Aristotle describes the eternal moving principles, and partly in - Books 13 and 14, where he argues against the Platonic non-sensible - substances. Thus it is very difficult to - say, not only what view we should adopt in the foregoing questions in order to arrive at - the truth, but also in the case of the first principles (vi.) whether we should assume - that the genera, or the simplest constituents of each particular thing, are more truly the - elements and first principles of existing things. E.g., it is generally agreed that the - elements and first principles of speech are those things of which, in their simplest form, - all speech is composed; and not the common term "speech"; and in the case of geometrical - propositions we call those the "elements"Cf. Aristot. Met. 5.3.3. whose proofs are embodied - in the proofs of all or most of the rest. Again, in the case of bodies, both those who hold that there are several elements and - those who hold that there is one call the things of which bodies are composed and - constituted first principles. E.g., Empedocles states that fire and water and the other - things associated with them are the elements which are present in things and of which - things are composed; he does not speak of them as genera of things. Moreover in the case of other things too, if a man wishes to - examine their nature he observes, e.g., of what parts a bed consists and how they are put - together; and then he comprehends its nature. Thus to judge from these arguments the first - principles will not be the genera of things. But from the - point of view that it is through definitions that we get to know each particular thing, - and that the genera are the first principles of definitions, the genera must also be the - first principles of the things defined. And if - to gain scientific knowledge of things is to gain it of the species after which things are - named, the genera are first principles of the species. And apparently some even of - thoseThe Pythagoreans and Plato. who call - Unity or Being or the Great and Small elements of things treat them as genera. Nor again is it possible to speak of the first principles in both - senses. The formula of substance is one; but - the definition by genera will be different from that which tells us of what - parts a thing is composed. Moreover, assuming - that the genera are first principles in the truest sense, are we to consider the - primary genera to be first principles, or the final terms predicated of - individuals? This question too involves some dispute. For if universals are always more truly first principles, clearly the - answer will be "the highest genera," since these are predicated of everything. Then there - will be as many first principles of things as - there are primary genera, and so both Unity and Being will be first principles and - substances, since they are in the highest degree predicated of all things. But it is impossible for either Unity or Being to be - one genus of existing things. For there must be differentiae of each genus, - and each differentia must be onei.e., - each differentia must have Being and Unity predicated of it.; but it is - impossible either for the species of the genus to be predicated of the specific - differentiae, or for the genus to be predicated without its species.The reasons are given in Aristot. Topica, 144a 36-b11. Hence if Unity - or Being is a genus, there will be no differentia Being or Unity. But if they are not genera, neither will they be first principles, - assuming that it is the genera that are first principles. And further, the intermediate - terms, taken together with the differentiae, will be genera, down to the individuals; but - in point of fact, although some are thought to be such, others are not. Moreover the - differentiae are more truly principles than are the genera; and if they also are - principles, we get an almost infinite number of principles, especially if one makes the - ultimate genus a principle. Moreover, if Unity is really more of the nature of a principle, and - the indivisible is a unity, and every thing indivisible is such either in quantity or in - kind, and the indivisible in kind is prior to the divisible, and the genera are divisible - into species, then it is rather the lowest predicate that will be a unity (for "man" is - not the genussc. but the species. of - individual men). Further, in the case of - things which admit of priority and posteriority, that which is predicated of the things - cannot exist apart from them. E.g., if 2 is the first number, there will be no Number - apart from the species of number; and similarly there will be no Figure apart from the - species of figures. But if the genera do not exist apart from the species in these cases, - they will scarcely do so in others; because it is assumed that genera are most likely to - exist in these cases. In individuals, however, - there is no priority and posteriority. Further, where there is a question of better or - worse, the better is always prior; so there will be no genus in these cases - either. From these considerations it seems that it is the - terms predicated of individuals, rather than the genera, that are the first principles. - But again on the other hand it is not easy to say in what sense we are to understand these - to be principles; for the first principle and - cause must be apart from the things of which it is a principle, and must be able to exist - when separated from them. But why should we assume that such a thing exists alongside of the individual, except in that it is - predicated universally and of all the terms? And indeed if this is a sufficient reason, it - is the more universal concepts that should rather be considered to be principles; and so - the primary genera will be the principles.For - partial solutions to the problem see Aristot. - Met. 7.10, 12-13. In this connection there is a difficulty which is the hardest - and yet the most necessary of all to investigate, and with which our inquiry is now - concerned. (7.) If nothing exists apart from individual things, and these are infinite in - number, how is it possible to obtain knowledge of the numerically infinite? For we acquire - our knowledge of all things only in so far as they contain something universal, some one - and identical characteristic. But if this is - essential, and there must be something apart from individual things, it must be the - genera; either the lowest or the highest; but we have just concluded that this is - impossible.In Aristot. Met. 3.3. Further, assuming that - when something is predicated of matter there is in the fullest sense something apart from - the concrete whole, if there is something, must it exist apart from all - concrete wholes, or apart from some but not others, or apart from none? If nothing exists apart from individual things, nothing will be - intelligible; everything will be sensible, and there will be no knowledge of - anything—unless it be maintained that sense-perception is knowledge. Nor again will - anything be eternal or immovable, since sensible things are all perishable and in - motion. Again, if nothing is eternal, even - generation is impossible; for there must be something which becomes something, i.e. out of - which something is generated, and of this series the ultimate term must be ungenerated; - that is if there is any end to the series and generation cannot take place out of - nothing. Further, if there is generation and - motion, there must be limit too. For (a) no motion is infinite, but every one has an end; - (b) that which cannot be completely generated cannot begin to be generated, and that which - has been generated must be as soon as it has been generated. Further, if matter exists apart in virtue of being - ungenerated, it is still more probable that the substance, i.e. that which the matter is - at any given time becoming, should exist. And if neither one nor the other exists, nothing - will exist at all. But if this is impossible, there must be something, the shape or form, - apart from the concrete whole. But again, if we assume this, there is a difficulty: in what cases - shall we, and in what shall we not, assume it? Clearly it cannot be done in all cases; for - we should not assume that a particular house exists apart from particular - houses. Moreover, are we to regard the essence - of all things, e.g. of men, as one? This is absurd; for all things whose essence is one - are one. Then is it many and diverse? This too - is illogical. And besides, how does the matter become each individual one of these things, - and how is the concrete whole both matter and form?For answers to these questions see Aristot. Met. 7.8, - 13-14; Aristot. Met. 12.6-10; Aristot. Met. 13.10. (8.) Further, the following difficulty might be raised about the first - principles. If they are one in kind, none of them will be one in number, not even the Idea - of Unity or of Being. And how can there be knowledge unless there is some universal - term?If the principles are one in - kind only, particular things cannot be referred to the same principle but - only to like principles; i.e., there will be no universal terms, without which there can - be no knowledge. On the other hand if - they are numerically one, and each of the principles is one, and not, as in the case of - sensible things, different in different instances (e.g. since a given syllable is always - the same in kind, its first principles are always the same in kind, but only in kind, - since they are essentially different in number)—if the first principles are one, not - in this sense, but numerically, there will be nothing else apart from the elements; for - "numerically one" and "individual" are identical in meaning. This is what we mean by - "individual": the numerically one; but by "universal" we mean what is predicable of - individuals. Hence just as, if the elements of - languageOr "letters of the alphabet." Cf. Aristot. Met. 1.9.36n. were limited in number, - the whole of literature would be no more than those elements—that is, if there were - not two nor more than two of the same <so it would be in the case of existing things - and their principles>.For the answer to the - problem see Aristot. Met. 12.4-5, Aristot. Met. 13.10. (ix.) There is a difficulty, - as serious as any, which has been left out of account both by present thinkers and by - their predecessors: whether the first principles of perishable and imperishable things are - the same or different. For if they are the same, how is it that some things are perishable - and others imperishable, and for what cause? The school of Hesiod, and all the cosmologists, considered only what was convincing to - themselves, and gave no consideration to us. For they make the first principles Gods or - generated from Gods, and say that whatever did not taste of the nectar and ambrosia became - mortal—clearly using these terms in a sense significant to themselves; but as regards the actual applications of these causes - their statements are beyond our comprehension. For if it is for pleasure that the Gods - partake of them, the nectar and ambrosia are in no sense causes of their existence; but if - it is to support life, how can Gods who require nourishment be eternal? However, it is not worth while - to consider seriously the subtleties of mythologists; we must ascertain by cross-examining those who offer demonstration of their - statements why exactly things which are derived from the same principles are some of an - eternal nature and some perishable. And since these thinkers state no reason for this - view, and it is unreasonable that things should be so, obviously the causes and principles - of things cannot be the same. Even the thinker - who might be supposed to speak most consistently, Empedocles, is in the same case; for he - posits Strife as a kind of principle which is the cause of destruction, but none the less - Strife would seem to produce everything except the One; for everything except GodThe expressions "the One" and "God" refer to - Empedocles' Sphere: the universe as ordered and united by Love. Cf. Empedocles, Fr. 26-29 (Diels). proceeds from - it. At any rate he says From which grew all that was and is and shall be In time to come: the trees, and men and women, The beasts and birds and water-nurtured fish, And the - long-living Gods.Empedocles, - Fr. 21. 9-12. And it is obvious even apart from this; for if there had not been - Strife in things, all things would have been one, he says; for when they came together - "then Strife came to stand outermost."Empedocles, Fr. 36. 7. Hence it follows on his theory - that God, the most blessed being, is less wise than the others, since He does not know all - the elements; for He has no Strife in Him, and knowledge is of like by like: By earth (he says) we - earth perceive, by water water, By air bright air, by fire - consuming fire, Love too by love, and strife by grievous - strife.Empedocles, Fr. - 109. But—and this is the point from - which we started—thus much is clear: that it follows on his theory that Strife is no - more the cause of destruction than it is of Being. Nor, similarly, is Love the cause of - Being; for in combining things into one it destroys everything else.Cf. Aristot. Met. - 1.4.6. Moreover, of the - actual process of change he gives no explanation, except that it is so by - nature: But when Strife waxing great among the - membersi.e., of the Sphere. Sprang up to honor as the time came round Appointed them in turn by a mighty oath,Empedocles, Fr. 30. as though change were a necessity; but he exhibits no cause for the - necessity. However, thus much of his theory - is consistent: he does not represent some things to be perishable and others imperishable, - but makes everything perishable except the - elements. But the difficulty now being stated is why some things are perishable and others - not, assuming that they are derived from the same principles. The foregoing remarks may suffice to show that the principles cannot be the - same. If however they are different, one - difficulty is whether they too are to be regarded as imperishable or as perishable. For if - they are perishable, it is clearly necessary that they too must be derived from something - else, since everything passes upon dissolution into that from which it is derived. Hence - it follows that there are other principles prior to the first principles; but this is impossible, whether the series stops or - proceeds to infinity. And further, how can perishable things exist if their principles are - abolished? On the other hand if the principles are imperishable, why should some - imperishable principles produce perishable things, and others imperishable things? This is - not reasonable; either it is impossible or it requires much explanation. Further, no one has so much as attempted to maintain - different principles; they maintain the same principles for everything. But they swallow - down the difficulty which we raised firsti.e., - whether all things have the same principles. as though they took it to be - trifling.For Aristotle's views about the - principles of perishable and imperishable things see Aristot. Met. 7.7-10, Aristot. Met. - 12.1-7. But the hardest question of all to investigate and also the most - important with a view to the discovery of the truth, is whether after all Being and Unity - are substances of existing things, and each of them is nothing else than Being and Unity - respectively, or whether we should inquire what exactly Being and Unity are, there being - some other nature underlying them. Some take - the former, others the latter view of the nature of Being and Unity. Plato and the - Pythagoreans hold that neither Being nor Unity is anything else than itself, and that this - is their nature, their essence being simply Being and Unity. But the physicists, e.g. Empedocles, explain what Unity is by reducing - it to something, as it were, more intelligible—or it would seem that by Love - Empedocles means Unity; at any rate Love is the cause of Unity in all things. Others - identify fire and others air with this Unity and Being of which things consist and from - which they have been generated. Those who - posit more numerous elements also hold the same view; for they too must identify Unity and - Being with all the principles which they recognize. And it follows that unless one assumes Unity and Being to be substance in - some sense, no other universal term can be substance; for Unity and Being are the most - universal of all terms, and if there is no - absolute Unity or absolute Being, no other concept can well exist apart from the so-called - particulars. Further, if Unity is not substance, clearly number cannot be a separate - characteristic of things; for number is units, and the unit is simply a particular kind of - one. On the - other hand, if there is absolute Unity and Being, their substance must be Unity and Being; - for no other term is predicated universally of Unity and Being, but only these terms - themselves. Again, if there is to be absolute Being and absolute Unity, it is very hard to - see how there can be anything else besides these; I mean, how things can be more than - one. For that which is other than what is, - is not; and so by Parmenides' argumentBy to\ o)/n Parmenides meant "what is," i.e. the real universe, - which he proved to be one thing because anything else must be "what is not," or - non-existent. The Platonists meant by it "being" in the abstract. Aristotle ignores this - distinction. it must follow that all things are one, i.e. Being. In either case there - is a difficulty; for whether Unity is not a substance or whether there is absolute Unity, - number cannot be a substance. It has already - been stated why this is so if Unity is not a substance; and if it is, there is the same - difficulty as about Being. For whence, if not from the absolute One or Unity, can there be - another one? It must be not-one; but all things are either one, or many of which each is - one. Further, if absolute Unity is indivisible, by Zeno's axiom it will be - nothing. For that which neither when added - makes a thing greater nor when subtracted makes it smaller is not an existent thing, he - saysCf. Zeno, Fr. - 2, and see Burnet, E.G.P. sects. 157 ff.; clearly assuming that what - exists is spatial magnitude. And if it is a spatial magnitude it is corporeal, since the - corporeal exists in all dimensions, whereas the other magnitudes, the plane or line, when - added to a thing in one way will increase it, but when added in another will not; and the - point or unit will not increase a thing in any way whatever. But since Zeno's view is unsound, and it is possible for a thing to be - indivisible in such a way that it can be defended even against his argument (for such a - thinge.g., a point is indivisible and has no - magnitude, yet added to other points it increases their number. when added will - increase a thing in number though not in size)—still how can a - magnitude be composed of one or more such indivisible things? It is like - saying that the line is composed of points. Moreover, even if one supposes the case to be such that number is generated, as some say, from the One itself and from something else - which is not one, we must none the less inquire why and how it is that the thing generated - will be at one time number and at another magnitude, if the not-one was inequality and the - same principle in both cases.The reference is to - the Platonists. Cf. Aristot. Met. 14.1.5, 6; - Aristot. Met. 14.2.13, 14. For it is - not clear how magnitude can be generated either from One and this principle, or from a - number and this principle.For the answer to this - problem see Aristot. Met. 7.16.3, 4; Aristot. Met. 10.2; and cf. Aristot. Met. 13.8. (13.) Out of this arises the - question whether numbers, bodies, planes and points are substances or not. If not, the - question of what Being is, what the substances of things are, baffles us; for - modifications and motions and relations and dispositions and ratios do not seem to - indicate the substance of anything; they are all predicated of a substrate, and none of - them is a definite thing. As for those things - which might be especially supposed to indicate substance—water, earth, fire and air, - of which composite bodies are composed— their heat and cold and the like are - modifications, not substances; and it is only the body which undergoes these modifications - that persists as something real and a kind of substance. Again, the body is less truly substance than the plane, and the plane - than the line, and the line than the unit or point; for it is by these that the body is - defined, and it seems that they are possible without the body, but that the body cannot - exist without them. This is why the vulgar and - the earlier thinkers supposed that substance and Being are Body, and everything else the - modifications of Body; and hence also that the first principles of bodies are the first - principles of existing things; whereas later thinkers with a greater reputation for wisdom - supposed that substance and Being are numbers. As we have said, then, if these things are not - substance, there is no substance or Being at all; for the attributes of these things - surely have no right to be called existent things. On the other hand, if it be agreed that - lines and points are more truly substance than bodies are, yet unless we can see to what - kind of bodies they belong (for they cannot be in sensible bodies) there - will still be no substance. Further, it is - apparent that all these lines are divisions of Body, either in breadth or in depth or in length. Moreover every kind of shape is - equally present in a solid, so that if "Hermes is not in the stone,"Apparently a proverbial expression. neither is - the half-cube in the cube as a determinate shape. Hence neither is the plane; for if any kind of plane were in it, so - would that plane be which defines the half-cube. The same argument applies to the line and - to the point or unit. Hence however true it may be that body is substance, if planes, - lines and points are more truly substance than Body is, and these are not substance in any - sense, the question of what Being is and what is the substance of things baffles - us. Because, in addition to the above - arguments, absurd results follow from a consideration of generation and destruction; for - it seems that if substance, not having existed before, now exists, or having existed - before, subsequently does not exist it suffers these changes in the process of generation - and destruction. But points, lines and planes, although they exist at one time and at - another do not, cannot be in process of being either generated or destroyed; for whenever bodies are joined or divided, at one time, when - they are joined one surface is instantaneously produced, and at another, when they are - divided, two. Thus when the bodies are combined the surface does not exist but has - perished; and when they are divided, surfaces exist which did not exist before. (The - indivisible point is of course never divided into two.) And if they are - generated and destroyed, from what are they generated? It is very much the same with "the present moment" in time. This too - cannot be generated and destroyed; but nevertheless it seems always to be different, not - being a substance. And obviously it is the same with points, lines and planes, for the - argument is the same; they are all similarly either limits or divisions.For arguments against the substantiality of numbers and - mathematical objects see Aristot. Met. 13.1-3, - 6-9; Aristot. Met. 14.1-3, 5, - 6. In general one might wonder why we should seek for other entities - apart from sensible things and the Intermediates:Cf. Aristot. Met. 3.2.20ff.. e.g., for the - Forms which we Platonists assume. If it is for - the reason that the objects of mathematics, while differing from the things in our world - in another respect, resemble them in being a plurality of objects similar in form, so that - their principles cannot be numerically determined (just as the principles of all language - in this world of ours are determinate not in number but in kind—unless one takes - such and such a particular syllable or sound, - for the principles of these are determinate in number too— and similarly with the Intermediates, for in their case too there is - an infinity of objects similar in form), then if there is not another set of objects apart - from sensible and mathematical objects, such as the Forms are said to be, there will be no - substance which is one both in kind and in number, nor will the principles of things be - determinate in number, but in kind only. Thus - if this is necessarily so, it is necessary for this reason to posit the Forms also. For - even if their exponents do not articulate their theory properly, still this is what they - are trying to express, and it must be that they maintain the Forms on the ground that each - of them is a substance, and none of them exists by accident. On the other hand, if we are to assume that the Forms exist, and that - the first principles are one in number but not in kind, we have already statedAristot. Met. 3.4.9, - 10. the impossible consequences which must follow.This problem is not stated in ch. 1., but is akin to - problems 5. and 8., which see. (12.) Closely - connected with these questions is the problem whether the elements exist potentially or in - some other sense. If in some other sense, there - will be something else prior to the first principles. For the potentiality is prior to the actual - cause, and the potential need not necessarily always become actual. On the other hand, if - the elements exist potentially, it is possible for nothing to exist; for even that which - does not yet exist is capable of existing. That which does not exist may come to be, but - nothing which cannot exist comes to be.For the - relation of potentiality to actuality see Aristot. Met. - 9.1-9. The second point raised in this connection in ch. 1 is not discussed - here; for actuality and motion see Aristot. Met. 12.6, - 7. (xi.) Besides the foregoing problems about the first principles we - must also raise the question whether they are universal or such as we describe the - particulars to be. For if they are universal, there will be no substances; for no common - term denotes an individual thing, but a type; and substance is an individual - thing. But if the common predicate be - hypostatized as an individual thing, Socrates will be several beings: himself, and Man, - and Animal—that is, if each predicate denotes one particular thing. These then are the consequences if the principles are - universal. If on the other hand they are not universal but like particulars, they will not - be knowable; for the knowledge of everything is universal. Hence there will have to be - other universally predicated principles prior to the first principles, if there is to be - any knowledge of them.For the answer to this - problem see Aristot. Met. 7.13-15, Aristot. Met. 13.10.

- - -

There is a - science which studies Being qua Being, and the properties inherent - in it in virtue of its own nature. This science is not the same as any of the so-called - particular sciences, for none of the others contemplates Being generally qua Being; they divide off some portion of it and study the attribute of this - portion, as do for example the mathematical sciences. But since it is for the first principles and the most ultimate causes - that we are searching, clearly they must belong to something in virtue of its own nature. - Hence if these principles were investigated by those also who investigated the elements of - existing things, the elements must be elements of Being not incidentally, but qua Being. Therefore it is of Being qua Being - that we too must grasp the first causes. The term "being" is used in various senses, but with reference - to one central idea and one definite characteristic, and not as merely a common epithet. - Thus as the term "healthy" always relates to health (either as preserving it or as - producing it or as indicating it or as receptive of it), and as "medical" relates to the art of medicine (either as possessing - it or as naturally adapted for it or as being a function of medicine)—and we shall - find other terms used similarly to these— so "being " is used in various senses, but always with reference to one principle. For - some things are said to "be" because they are substances; others because they are - modifications of substance; others because they are a process towards substance, or - destructions or privations or qualities of substance, or productive or generative of - substance or of terms relating to substance, or negations of certain of these terms or of - substance. (Hence we even say that not-being is not-being.) And so, just as there is one science of all healthy things, so - it is true of everything else. For it is not only in the case of terms which express one - common notion that the investigation belongs to one science, but also in the case of terms - which relate to one particular characteristic; for the latter too, in a sense, express one - common notion. Clearly then the study of things which are, qua being, also - belongs to one science. Now in every case - knowledge is principally concerned with that which is primary, i.e. that upon which all - other things depend, and from which they get their names. If, then, substance is this - primary thing, it is of substances that the philosopher must grasp the first principles - and causes. Now of every single class of things, as there is - one perception, so there is one science: e.g., - grammar, which is one science, studies all articulate sounds. Hence the study of all the species of Being qua - Being belongs to a science which is generically one, and the study of the several species - of Being belongs to the specific parts of that science. Now - if Being and Unity are the same, i.e. a single nature, in the sense that they are - associated as principle and cause are, and not as being denoted by the same definition - (although it makes no difference but rather helps our argument if we understand them in - the same sense), since "one man" and "man" and - "existent man" and "man" are the same thing, i.e. the duplication in the statement "he is - a man and an existent man" gives no fresh meaning (clearly the concepts of - humanity and existence are not dissociated in respect of either coming to be or ceasing to - be), and similarly in the case of the term "one," so that obviously the additional term in - these phrases has the same significance, and Unity is nothing distinct from - Being; and further if the substance of each - thing is one in no accidental sense, and similarly is of its very nature something which - is—then there are just as many species of Being as of Unity. And to study the - essence of these species (I mean, e.g., the study of Same and Other and all the other - similar concepts— roughly speaking all - the "contraries" are reducible to this first principle; but we may consider that they - have been sufficiently studied in the "Selection of Contraries"It is uncertain to what treatise Aristotle refers; in any case it is not - extant.) is the province of a science which is generically one. And there are just as many divisions of philosophy as there are kinds of - substance; so that there must be among them a First Philosophy and one which follows upon - it. For Being and Unity at once entail - genera, and so the sciences will correspond to these genera. The term "philosopher" is - like the term "mathematician" in its uses; for mathematics too has divisions—there - is a primary and a secondary science, and others successively, in the realm of - mathematics. Now since it is the province of one science to study opposites, and the opposite of - unity is plurality, and it is the province of one science to study the negation and - privation of Unity, because in both cases we are studying Unity, to which the negation (or - privation) refers, stated either in the simple form that Unity is not present, or in the - form that it is not present in a particular class; in the latter case Unity is modified by - the differentia, apart from the content of the negation (for the negation of Unity is its - absence); but in privation there is a substrate of which the privation is - predicated.— The opposite of Unity, - then, is Plurality; and so the opposites of the above-mentioned concepts—Otherness, - Dissimilarity, Inequality and everything else which is derived from these or from - Plurality or Unity— fall under the - cognizance of the aforesaid science. And one of them is Oppositeness; for this is a form - of Difference, and Difference is a form of Otherness. Hence since the term "one" is used in various senses, so too will - these terms be used; yet it pertains to one science to take cognizance of them all. For - terms fall under different sciences, not if they are used in various senses, but if their - definitions are neither identical nor referable to a common notion. And since everything is referred to that which is primary, e.g. - all things which are called "one" are referred to the primary "One," we must admit that - this is also true of Identity and Otherness and the Contraries. Thus we must first - distinguish all the senses in which each term is used, and then attribute them to the - primary in the case of each predicate, and see how they are related to it; for some will - derive their name from possessing and others from producing it, and others for similar - reasons. Thus - clearly it pertains to one science to give an account both of these concepts and of - substance (this was one of the questions raised in the "Difficulties"See Aristot. Met. - 3.1.8-10, Aristot. Met. 3.2.18, - 19.), and it is the function of the philosopher to be able to study all - subjects. If this is not so, who is it who in will - investigate whether " Socrates" and " Socrates seated" are the same thing; or whether one - thing has one contrary, or what the contrary is, or how many meanings it has?Cf. Aristot. Met. - 10.4. and similarly with all other such questions. Thus since these are the essential modifications of Unity qua Unity and of Being qua Being, and not qua numbers or lines or fire, clearly it a pertains to that - sciencei.e., Philosophy or Metaphysics. to - discover both the essence and the attributes of these concepts. And those who investigate them err, not in being unphilosophical, but - because the substance, of which they have no real knowledge, is prior. For just as number - qua number has its peculiar modifications, e.g. oddness and - evenness, commensurability and equality, excess and defect, and these things are inherent - in numbers both considered independently and in relation to other numbers; and as - similarly other peculiar modifications are inherent in the solid and the immovable and the - moving and the weightless and that which has weight; so Being qua - Being has certain peculiar modifications, and it is about these that it is the - philosopher's function to discover the truth. And here is evidence of this fact. Dialecticians and sophists wear the same appearance as - the philosopher, for sophistry is Wisdom in appearance only, and dialecticians discuss all - subjects, and Being is a subject common to - them all; but clearly they discuss these concepts because they appertain to - philosophy. For sophistry and dialectic are - concerned with the same class of subjects as philosophy, but philosophy differs from the - former in the nature of its capability and from the latter in its outlook on life. - Dialectic treats as an exercise what philosophy tries to understand, and sophistry seems - to be philosophy; but is not. Further, the second column of contraries is privative, and everything - is reducible to Being and Not being, and Unity and Plurality; e.g. Rest falls under Unity - and Motion under Plurality. And nearly everyone agrees that substance and existing things - are composed of contraries; at any rate all speak of the first principles as - contraries— some as Odd and Even,The Pythagoreans. some as Hot and Cold,Perhaps Parmenides. some as Limit and - Unlimited,The Platonists. some as Love and - Strife.Empedocles. And it is apparent that - all other things also are reducible to Unity and Plurality (we may assume this reduction); - and the - principles adduced by other thinkers fall entirely under these as genera. It is clear, then, from these considerations also, - that it pertains to a single science to study Being qua Being; for - all things are either contraries or derived from contraries, and the first principles of - the contraries are Unity and Plurality. And these belong to one science, whether they have - reference to one common notion or not. Probably the truth is that they have not; but - nevertheless even if the term "one" is used in various senses, the others will be related - to the primary sense (and similarly with the contraries)— even if Being or Unity is not a universal and the same in all cases, - or is not separable from particulars (as it presumably is not; the unity is in some cases - one of reference and in others one of succession). For this very reason it is not the - function of the geometrician to inquire what is Contrariety or Completeness or Being or - Unity or Identity or Otherness, but to proceed from the assumption of them. Clearly, then, it - pertains to one science to study Being qua Being, and the - attributes inherent in it qua Being; and the same science - investigates, besides the concepts mentioned above, Priority and Posteriority, Genus and - Species, Whole and Part, and all other such concepts. We must pronounce whether it pertains to - the same science to study both the so-called - axioms in mathematics and substance, or to different sciences. It is obvious that the - investigation of these axioms too pertains to one science, namely the science of the - philosopher; for they apply to all existing things, and not to a particular class separate - and distinct from the rest. Moreover all thinkers employ them—because they are - axioms of Being qua Being, and every genus possesses - Being— but employ them only in so far - as their purposes require; i.e., so far as the genus extends about which they are carrying - out their proofs. Hence since these axioms apply to all things qua - Being (for this is what is common to them), it is the function of him who studies Being - qua Being to investigate them as well. For this reason no one who is pursuing a particular - inquiry—neither a geometrician nor an arithmetician—attempts to state whether - they are true or false; but some of the physicists did so, quite naturally; for they alone - professed to investigate nature as a whole, and Being. But inasmuch as there is a more ultimate type of thinker than the - natural philosopher (for nature is only a genus of Being), the investigation of these - axioms too will belong to the universal thinker who studies the primary reality. - Natural - philosophy is a kind of Wisdom, but not the primary kind. As for the attempts of some of those who discuss how the truth should - be received, they are due to lack of training in logic; for they should understand these - things before they approach their task, and not investigate while they are still - learning. Clearly then it is the function of - the philosopher, i.e. the student of the whole of reality in its essential nature, to - investigate also the principles of syllogistic reasoning. And it is proper for him who - best understands each class of subject to be able to state the most certain principles of - that subject; so that he who understands the modes of Being qua - Being should be able to state the most certain principles of all things. Now this person is the philosopher, and the most certain - principle of all is that about which one cannot be mistaken; for such a principle must be - both the most familiar (for it is about the unfamiliar that errors are always made), and - not based on hypothesis. For the principle - which the student of any form of Being must grasp is no hypothesis; and that which a man - must know if he knows anything he must bring with him to his task. Clearly, then, it is a principle of this kind that is the most certain of - all principles. Let us next state what this principle is. "It is impossible for the same attribute at once to belong and - not to belong to the same thing and in the same - relation"; and we must add any further qualifications that may be necessary to meet - logical objections. This is the most certain of all principles, since it possesses the - required definition; for it is impossible for - anyone to suppose that the same thing is and is not, as some imagine that Heraclitus - saysFor examples of Heraclitus's paradoxes cf. - Heraclitus Fr. 36, 57, 59 (Bywater); and for their - meaning see Burnet, E.G.P. 80.—for what a man says does not necessarily - represent what he believes. And if it is - impossible for contrary attributes to belong at the same time to the same subject (the - usual qualifications must be added to this premiss also), and an opinion which contradicts - another is contrary to it, then clearly it is impossible for the same man to suppose at - the same time that the same thing is and is not; for the man who made this error would - entertain two contrary opinions at the same time. Hence all men who are demonstrating anything refer back to this as an - ultimate belief; for it is by nature the starting-point of all the other axioms as - well. There - are some, however, as we have said, who both state themselves that the same thing can be - and not be, and say that it is possible to hold this view. Many even of the physicists adopt this - theory. But we have just assumed that it is impossible at once to be and not to be, and by - this means we have proved that this is the most certain of all principles. Some, indeed, demand to have the law proved, but this - is because they lack educationsc., in - logic.; for it shows lack of education not to know of what we should require proof, - and of what we should not. For it is quite impossible that everything should have a proof; - the process would go on to infinity, so that even so there would be no proof.Every proof is based upon some hypothesis, to prove - which another hypothesis must be assumed, and so on ad infinitum. If on the other - hand there are some things of which no proof need be sought, they cannot say what - principle they think to be more self-evident. Even in the case of this law, however, we - can demonstrate the impossibility by refutation, if only our opponent makes some - statement. If he makes none, it is absurd to seek for an argument against one who has no - arguments of his own about anything, in so far as he has none; for such a person, in so - far as he is such, is really no better than a vegetable. And I say that proof by refutation differs from simple proof in that - he who attempts to prove might seem to beg the fundamental question, whereas if the - discussion is provoked thus by someone else, refutation and not proof will - result. The starting-point for all such - discussions is not the claim that he should state that something is or is not so (because this might be supposed to be a begging of the - question), but that he should say something significant both to himself and to another - (this is essential if any argument is to follow; for otherwise such a person cannot reason - either with himself or with another); and if - this is granted, demonstration will be possible, for there will be something already - defined. But the person responsible is not he who demonstrates but he who acquiesces; for - though he disowns reason he acquiesces to reason. Moreover, he who makes such an admission - as this has admitted the truth of something apart from demonstration [so that not - everything will be "so and not so"]. Thus in the first place it is obvious that this at any rate is - true: that the term "to be" or "not to be" has a definite meaning; so that not everything - can be "so and not so." Again, if "man" has one meaning, let this be "two-footed - animal." By "has one meaning" I mean this: if - X means "man," then if anything is a man, its humanity will consist in being X. And it - makes no difference even if it be said that "man" has several meanings, provided that they - are limited in number; for one could assign a different name to each formula. For instance, it might be said that "man" has not one meaning - but several, one of which has the formula "two-footed animal," and there might be many - other formulae as well, if they were limited in number; for a particular name could be - assigned to each for formula. If on the other - hand it be said that "man" has an infinite number of meanings, obviously there can be no - discourse; for not to have one meaning is to have no meaning, and if words have no meaning - there is an end of discourse with others, and even, strictly speaking, with oneself; - because it is impossible to think of anything if we do not think of one thing; and even if - this were possible, one name might be assigned to that of which we think. Now let this name, as we said at the beginning, have a - meaning; and let it have one meaning. Now it is impossible that "being man" should have - the same meaning as "not being man," that is, if "man" is not merely predicable of one - subject but has one meaning (for we do not - identify "having one meaning" with "being predicable of one subject," since in this case - "cultured" and "white" and "man" would have one meaning, and so all things would be one; - for they would all have the same meaning). And it will be impossible for the same thing to - be and not to be, except by equivocation, as e.g. one whom we call "man" others might call "not-man"; but the problem is whether the same thing can at once be and not be - "man," not in name , but in fact . If "man" and "not-man" have - not different meanings, clearly "not being a man" will mean nothing different from "being - a man"; and so "being a man" will be "not being a man"; they will be one. For "to be one" means, as in the case of "garment" and - "coat," that the formula is one. And if "being man" and "being not-man" are to be one, - they will have the same meaning; but it has been proved above that they have different - meanings. If then anything can be truly said to be "man," it must be "two-footed animal"; - for this is what "man" was intended to mean. And if this is necessarily so, it is impossible that at the same time the same thing - should not be "two-footed animal." For "to be necessarily so" means this: that it is - impossible not to be so. Thus it cannot be true to say at the same time that the same - thing is and is not man. And the same argument - holds also in the case of not being man; because "being man" and "being not-man" have different - meanings if "being white" and "being man" have different meanings (for the opposition is - much stronger in the former case so as to produce different meanings). And if we are told that "white" too means one and the same - thing,i.e. the same as "man." we shall say - again just what we said before,Aristot. Met. 4.4.12. that in that case all - things, and not merely the opposites, will be one. But if this is impossible, what we have - stated follows; that is, if our opponent answers our question; but if when asked the - simple question he includes in his answer the negations, he is not answering our - question. There is nothing to prevent the - same thing from being "man" and "white" and a multitude of other things; but nevertheless - when asked whether it is true to say that X is man, or not, one should return an answer - that means one thing, and not add that X is white and large. It is indeed impossible to - enumerate all the infinity of accidents; and so let him enumerate either all or - none. Similarly therefore, even if the same - thing is ten thousand times "man" and "not-man," one should not include in one's answer to - the question whether it is "man" that it is at the same time also "not-man," unless one is - also bound to include in one's answer all the other accidental things that the subject is - or is not. And if one does this, he is not - arguing properly. In general those who talk like this do - away with substance and essence, for they are - compelled to assert that all things are accidents, and that there is no such thing as - "being essentially man" or "animal." For if there is to be such a thing as "being - essentially man," this will not be "being not-man" nor "not-being man" (and yet these are - negations of it); for it was intended to have one meaning, i.e. the substance of - something. But to denote a substance means - that the essence is that and nothing else; and if for it "being essentially man" is the - same as either "being essentially not-man" or "essentially not-being man," the essence - will be something else. Thus they are - compelled to say that nothing can have such a definition as this, but that all things are - accidental; for this is the distinction between substance and accident: "white" is an - accident of "man," because although he is white, he is not white in essence. And since the accidental always implies a predication - about some subject, if all statements are accidental, there will be nothing primary about - which they are made; so the predication must proceed to infinity. But this is impossible, for - not even more than two accidents can be combined in predication. An accident cannot be an - accident of an accident unless both are accidents of the same thing. I mean, e.g., that "white" is "cultured" and "cultured" "white" - merely because both are accidents of a man. But it is not in this sense—that both - terms are accidents of something else—that Socrates is cultured. Therefore since - some accidents are predicated in the latter and some in the former sense, such as are - predicated in the way that "white" is of Socrates cannot be an infinite series in the - upper direction; e.g. there cannot be another accident of "white Socrates," for the sum of - these predications does not make a single statement. Nor can "white " have a further accident, such as "cultured"; for the - former is no more an accident of the latter than vice versa; and besides we have - distinguished that although some predicates are accidental in this sense, others are - accidental in the sense that "cultured" is to Socrates; and whereas in the former case the - accident is an accident of an accident, it is not so in the latter; and thus not all - predications will be of accidents. Therefore - even so there will be something which denotes substance. And if this is so, we have proved - that contradictory statements cannot be predicated at the same time. Again, if all contradictory predications of the same subject at the same - time are true, clearly all things will be one. For if it is equally possible either to - affirm or deny anything of anything, the same thing will be a trireme and a wall and a - man; which is what necessarily follows for those who hold the theory of Protagoras.i.e., that all appearances and opinions are - true. For if anyone thinks that a man is not a trireme, he is clearly not a - trireme; and so he also is a trireme if the contradictory statement is true. And the result is the dictum of Anaxagoras, "all - things mixed together" - Fr. 1 (Diels). - ; so that nothing truly exists. It seems, then, that they are speaking of the - Indeterminate; and while they think that they are speaking of what exists, they are really - speaking of what does not; for the Indeterminate is that which exists potentially but not - actually. But indeed they must admit the - affirmation or negation of any predicate of any subject, for it is absurd that in the case - of each term its own negation should be true, and the negation of some other term which is - not true of it should not be true. I mean, e.g., that if it is true to say that a man is - not a man, it is obviously also true to say that he is or is not a trireme. Then if the affirmation is true, so must the negation - be true; but if the affirmation is not true the negation will be even truer than the - negation of the original term itself. Therefore if the latter negation is true, the negation of - "trireme" will also be true; and if this is true, the affirmation will be true - too. And not only does this follow for those who hold this - theory, but also that it is not necessary either to affirm or to deny a - statement. For if it is true that X is both - man and not-man, clearly he will be neither man nor not-man; for to the two statements - there correspond two negations, and if the former is taken as a single statement - compounded out of two, the latter is also a single statement and opposite to it. Again, either this - applies to all terms, and the same thing is both white and not-white, and existent and - non-existent, and similarly with all other assertions and negations; or it does not apply - to all, but only to some and not to others. And if it does not apply to all, the exceptions will be admittedi.e., it will be admitted that in certain cases where an attribute is - true of a subject, the negation is not true; and therefore some propositions are - indisputable.; but if it does apply to all, again either (a) the negation will be - true wherever the affirmation is true, and the affirmation will be true wherever the - negation is true, or (d) the negation will be true wherever the assertion is true, but the - assertion will not always be true where the negation is true. And in the latter case there will be something which definitely is - not, and this will be a certain belief; and if that it is not is certain and knowable, the - opposite assertion will be still more knowable. But if what is denied can be equally truly - asserted, it must be either true or false to state the predicates separately and say, - e.g., that a thing is white, and again that it - is not-white. And if it is not-true to state - them separately, our opponent does not say what he professes to say, and nothing exists; - and how can that which does not exist speak or walk?If our opponent holds that you can only say "A is B and not B," (1) he contradicts - every statement that he makes; (2) he must say that what exists does not exist. - Therefore nothing exists, and so he himself does not exist; but how can he speak or walk - if he does not exist? And again all things will be one, as we said before,Aristot. Met. - 4.4.27. and the same thing will be "man" and "God" and "trireme" and the - negations of these terms. For if it is equally - possible to assert or deny anything of anything, one thing will not differ from another; - for if anything does differ, it will be true and unique. And similarly even if it is - possible to make a true statement while separating the predicates, what we have stated - follows. Moreover it follows that all statements would be true and all false; and that our - opponent himself admits that what he says is false. Besides, it is obvious that discussion - with him is pointless, because he makes no real statement. For he says neither "yes" nor "no," but "yes and no"; and again he - denies both of these and says "neither yes nor no"; otherwise there would be already some - definite statement. Again, if when the assertion is true the - negation is false, and when the latter is true the affirmation is false, it will be - impossible to assert and deny with truth the same thing at the same time. But perhaps it will be said that this is the point at - issue. Again, is the man wrong who supposes that a thing - is so or not so, and he who supposes both right? If he is right, what is the meaning of - saying that "such is the nature of reality"?If - everything is both so and not so, nothing has any definite nature. And if he is - not right, but is more right than the holder of the first view, reality will at once have - a definite nature, and this will be true, and not at the same time not-true. And if all men are equally right and wrong, an - exponent of this view can neither speak nor mean anything, since at the same time he says - both "yes" and "no." And if he forms no judgement, but "thinks" and "thinks not" - indifferently, what difference will there be between him and the vegetables? Hence it is quite evident that no one, either of those who profess - this theory or of any other school, is really in this position. Otherwise, why does a man walk to Megara and not stay at home, when he thinks he ought to make the journey? - Why does he not walk early one morning into a well or ravine, if he comes to it, instead - of clearly guarding against doing so, thus showing that he does not think - that it is equally good and not good to fall in? Obviously then he judges that the one - course is better and the other worse. And if - this is so, he must judge that one thing is man and another not man, and that one thing is sweet and another not sweet. For when, - thinking that it is desirable to drink water and see a man, he goes to look for them, he - does not look for and judge all things indifferently; and yet he should, if the same thing - were equally man and not-man. But as we have - said, there is no one who does not evidently avoid some things and not others. Hence, as - it seems, all men form unqualified judgements, if not about all things, at least about - what is better or worse. And if they do this - by guesswork and without knowledge, they should be all the more eager for truth; just as a - sick man should be more eager for health than a healthy man; for indeed the man who - guesses, as contrasted with him who knows, is not in a healthy relation to the - truth. Again, - however much things may be "so and not so," yet differences of degree are inherent in the - nature of things. For we should not say that 2 and 3 are equally even; nor are he who - thinks that 4 is 5, and he who thinks it is 1000, equally wrong: hence if they are not - equally wrong, the one is clearly less wrong, and so more right. If then that which has more the nature of something is nearer to that - something, there will be some truth to which the more true is nearer. And even if there is not, - still there is now something more certain and true, and we shall be freed from the - undiluted doctrine which precludes any mental determination. From the same view proceeds the theory of - Protagoras, and both alike must be either true or false. For if all opinions and - appearances are true, everything must be at once true and false; for many people form - judgements which are opposite to those of others, and imagine that those who do not think - the same as themselves are wrong: hence the same thing must both be and not be. And if this is so, all opinions must be true; for those - who are wrong and those who are right think contrarily to each other. So if reality is of - this nature, everyone will be right. Clearly then both these - theories proceed from the same mental outlook. But the method of approach is not the same - for all cases; for some require persuasion and others compulsion. The ignorance of those who have formed this judgement through - perplexity is easily remedied, because we are dealing not with the theory but with their mental outlook; but those who hold the - theory for its own sake can only be cured by refuting the theory as expressed in their own - speech and words. This view comes to those who are perplexed from their observation of sensible things. - (1.) The belief that contradictions and contraries can be true at the same time comes to - them from seeing the contraries generated from the same thing. Then if what is not cannot be generated, the thing must have existed - before as both contraries equally—just as Anaxagoras saysCf. Aristot. Met. 4.4.28. - that everything is mixed in everything; and also Democritus, for he too saysCf. Aristot. Met. - 1.4.9. that Void and Plenum are present equally in any part, and yet the - latter is , and the former is not. To those, then, who base their judgement on these considerations, we - shall say that although in one sense their theory is correct, in another they are - mistaken. For "being" has two meanings, so that there is a sense in which something can be - generated from "not-being," and a sense in which it cannot; and a sense in which the same - thing can at once be and not be; but not in the same respect. For the same thing can "be" - contraries at the same time potentially, but not actually. And further, we shall request them to conceive another kind also of - substance of existing things, in which there is absolutely no motion or destruction or - generation. And (2.) similarly the theory that there is truth in appearances has come to some people - from an observation of sensible things. They - think that the truth should not be judged by the number or fewness of its upholders; and - they say that the same thing seems sweet to some who taste it, and bitter to others; so - that if all men were diseased or all insane, except two or three who were healthy or sane, - the latter would seem to be diseased or insane, and not the others. And further they say that many of the animals as well get from - the same things impressions which are contrary to ours, and that the individual himself - does not always think the same in matters of sense-perception. Thus it is uncertain which - of these impressions are true or false; for one kind is no more true than another, but - equally so. And hence Democritus saysCf. Ritter and - Preller, 204. that either there is no truth or we cannot discover it. And in general it is - because they suppose that thought is sense-perception, and sense-perception physical - alteration, that they say that the impression given through sense-perception is - necessarily true; for it is on these grounds that both Empedocles and Democritus and - practically all the rest have become obsessed by such opinions as these. For Empedocles says that those who change their bodily - condition change their thought: For according to that which - is present to them doth thought increase in men.Empedocles Fr. 106. And in another passage he says: And as they change into a different nature, so it ever comes to them - to think differently.Empedocles Fr. 108. And Parmenides too declares in the same way: For as each at any time hath the temperament of his many-jointed limbs, so - thought comes to men. For for each and every man the substance of his limbs is that very - thing which thinks; for thought is that which preponderates.Empedocles Fr. 16; quoted also (in a - slightly different form; see critical notes) by Theophrastus, - De Sensu 3. There is also recorded a saying of Anaxagoras to some of his - disciples, that things would be for them as they judged them to be. And they say that in Homer too clearly held this view, because - he made Hector,The only passage in our text of - Homer to which this reference could apply isHom. Il. - 23.698; but there the subject is Euryalus, not Hector. when he was - stunned by the blow, lie with thoughts deranged—thus implying that even those who - are "out of their minds" still think, although not the same thoughts. Clearly then, if - both are kinds of thought, reality also will be "both so and not so." It is along this path that the consequences are most difficult; - for if those who have the clearest vision of such truth as is possible (and these are they - who seek and love it most) hold such opinions and make these pronouncements about the - truth, surely those who are trying to be philosophers may well despair; for the pursuit of - truth will be "chasing birds in the air."Cf. - Leutsch and Schneidewin, Paroemiographi Graeci, 2.677. - But the reason why - these men hold this view is that although they studied the truth about reality, they - supposed that reality is confined to sensible things, in which the nature of the - Indeterminate, i.e. of Being in the sense which we have explained,Aristot. Met. 4.4.28. is - abundantly present. (Thus their statements, though plausible, are not true; this form of the criticism is more suitable than that - which EpicharmusFl. early 5th century; held views - partly Pythagorean, partly Heraclitean. applied to Xenophanes.) And further, - observing that all this indeterminate substance is in motion, and that no true predication - can be made of that which changes, they supposed that it is impossible to make any true - statement about that which is in all ways and entirely changeable. For it was from this supposition that there blossomed forth the - most extreme view of those which we have mentioned, that of the professed followers of - Heraclitus, and such as Cratylus held, who ended by thinking that one need not say - anything, and only moved his finger; and who criticized Heraclitus for saying that one - cannot enter the same river twice,Heraclitus Fr. 41 (Bywater). for he himself held - that it cannot be done even once. But we shall reply to this theory also that although that which is - changeable supplies them, when it changes, with some real ground for supposing that it "is - not," yet there is something debatable in this; for that which is shedding any quality - retains something of that which is being shed, and something of that which is coming to be - must already exist. And in general if a thing is ceasing to be, there will be something - there which is ; and if a thing is coming to be, that from which it comes and - by which it is generated must be ; and this cannot go on to infinity. But let - us leave this line of argument and remark that quantitative and qualitative change are not - the same. Let it be granted that there is - nothing permanent in respect of quantity; but it is by the form that we - recognize everything. And again those who hold the theory that we are attacking deserve - censure in that they have maintained about the whole material universe what they have - observed in the case of a mere minority of sensible things. For it is only the realm of sense around us which continues subject to - destruction and generation, but this is a practically negligible part of the whole; so - that it would have been fairer for them to acquit the former on the ground of the latter - than to condemn the latter on account of the former. Further, we shall obviously say to these thinkers too the same as we said some time - agoAristot. - Met. 4.5.7.; for we must prove to them and convince them that there is a - kind of nature that is not moved (and yet - those who claim that things can at once be and not be are logically compelled to admit - rather that all things are at rest than that they are in motion; for there is nothing for - them to change into, since everything exists in everything). And as concerning reality, - that not every appearance is real, we shall say, first, that indeed the perception, at - least of the proper object of a sense, is not false, but the impression we get of it is - not the same as the perception. And then we - may fairly express surprise if our opponents raise the question whether magnitudes and - colors are really such as they appear at a distance or close at hand, as they appear to - the healthy or to the diseased; and whether heavy things are as they appear to the weak or - to the strong; and whether truth is as it appears to the waking or to the - sleeping. For clearly they do not really - believe the latter alternative—at any rate no one, if in the night he thinks that he - is at Athens whereas he is really in - Africa, starts off to the Odeum.A concert-hall (used also for other purposes) built by - Pericles. It lay to the south-east of the Acropolis. And again concerning the - future (as indeed Plato saysPlat. Theaet. 171e, 178cff..) the opinion of the - doctor and that of the layman are presumably not equally reliable, e.g. as to whether a - man will get well or not. And again in the - case of the senses themselves, our perception of a foreign object and of an object proper - to a given sense, or of a kindred object and of an actual object of that sense itself, is - not equally reliableAn object of taste is foreign - to the sense of sight; a thing may look sweet without tasting sweet. Similarly although - the senses of taste and smell (and therefore their objects) are kindred (Aristot. De Sensu 440b 29), in judging tastes the - sense of taste is the more reliable.; but in the case of colors sight, and not - taste, is authoritative, and in the case of flavor taste, and not sight. But not one of - the senses ever asserts at the same time of the same object that it is "so and not - so." Nor even at another time does it make a conflicting statement about the quality, - but only about that to which the quality belongs. I mean, e.g., that the same wine may - seem, as the result of its own change or of that of one's body, at one time sweet and at - another not; but sweetness, such as it is when it exists, has never yet changed, and there - is no mistake about it, and that which is to be sweet is necessarily of such a - nature. Yet all these theories destroy the - possibility of anything's existing by necessity, inasmuch as they destroy the existence of - its essence; for "the necessary" cannot be in one way and in another; and so if anything - exists of necessity, it cannot be "both so and not so." And - in general, if only the sensible exists, without animate things there would be nothing; - for there would be no sense-faculty. That - there would be neither sensible qualities nor sensations is probably trueCf. Aristot. De Anima - 425b 25-426b 8.(for these depend upon an effect produced in the - percipient), but that the substrates which cause the sensation should not exist even apart - from the sensation is impossible. For - sensation is not of itself, but there is something else too besides the sensation, which - must be prior to the sensation; because that which moves is by nature prior to that which is - moved, and this is no less true if the terms are correlative. But there are some, both of those who - really hold these convictions and of those who merely profess these views, who raise a - difficulty; they inquire who is to judge of the healthy man, and in general who is to - judge rightly in each particular case. But such questions are like wondering whether we - are at any given moment asleep or awake; and - all problems of this kind amount to the same thing. These people demand a reason for - everything. They want a starting-point, and want to grasp it by demonstration; while it is - obvious from their actions that they have no conviction. But their case is just what we - have stated beforeAristot. Met. 4.4.2.; for they require a reason for things which have - no reason, since the starting-point of a demonstration is not a matter of - demonstration. The first class, then, may be - readily convinced of this, because it is not hard to grasp. But those who look only for - cogency in argument look for an impossibility, for they claim the right to contradict - themselves, and lose no time in doing so. Yet - if not everything is relative, but some things are self-existent, not every appearance - will be true; for an appearance is an appearance to someone. And so he who says that - all appearances are true makes everything - relative. Hence those who demand something - cogent in argument, and at the same time claim to make out a case, must guard themselves - by saying that the appearance is true; not in itself, but for him to whom it - appears, and at, the time when it appears, and in the way and manner in - which it appears. And if they make out a case without this qualification, as a - result they will soon contradict themselves; for it is possible in the case of the same man for a thing to appear honey to the sight, - but not to the taste, and for things to appear different to the sight of each of his two - eyes, if their sight is unequal. For to those who assert (for the reasons previously - stated - Aristot. Met. 4.5.7-17. - ) that appearances are true, and that all things are therefore equally false and - true, because they do not appear the same to all, nor always the same to the same person, - but often have contrary appearances at the same time (since if one crosses the fingers touch says that an object is two, - while sight says that it is only oneCf. Aristot. Problemata 958b 14, 959a 5, 965a 36.), - we shall say "but not to the same sense or to the same part of it in the same way and at - the same time"; so that with this qualification the appearance will be true. But perhaps it is - for this reason that those who argue not from a sense of difficulty but for argument's - sake are compelled to say that the appearance is not true in itself, but true to the - percipient; and, as we have said before, are - compelled also to make everything relative and dependent upon opinion and sensation, so - that nothing has happened or will happen unless someone has first formed an opinion about - it; otherwise clearly all things would not be relative to opinion. Further, if a thing is one, it is relative to one thing or to something - determinate. And if the same thing is both a half and an equal, yet the equal is not - relative to the double. If to the thinking - subject "man" and the object of thought are the same, "man" will be not the thinking - subject but the object of thought; and if each thing is to be regarded as relative to the - thinking subject, the thinking subject will be relative to an infinity of specifically - different things. That the most certain of all beliefs is that opposite statements are - not both true at the same time, and what follows for those who maintain that they are - true, and why these thinkers maintain this, may be regarded as adequately stated. And - since the contradiction of a statement cannot be true at the same time of the same thing, - it is obvious that contraries cannot apply at the same time to the same thing. For in each pair of contraries one is a privation no - less than it is a contrary—a privation of substance. And privation is the negation - of a predicate to some defined genus. Therefore - if it is impossible at the same time to affirm and deny a thing truly, it is also - impossible for contraries to apply to a thing at the same time; either both must apply in - a modified sense, or one in a modified sense and the other absolutely. Nor indeed can there be any - intermediate between contrary statements, but of one thing we must either assert or deny - one thing, whatever it may be. This will be plain if we first define truth and falsehood. - To say that what is is not, or that what is not is, is false; but to say that what is is, - and what is not is not, is true; and therefore also he who says that a thing is or is not - will say either what is true or what is false. But neither what is nor what is not is said not to be or to be. Further, an - intermediate between contraries will be intermediate either as grey is between black and - white, or as "neither man nor horse" is between man and horse. If in the latter sense, it - cannot change (for change is from not-good to good, or from good to not-good); but in fact it is clearly always changing; for change - can only be into the opposite and the intermediate. And if it is a true intermediate, in - this case too there would be a kind of change into white not from not-white; but in fact - this is not seen.It is not qua grey (i.e. intermediate between white and black) that grey changes to white, - but qua not-white (i.e. containing a certain proportion of - black). - Further, - the understanding either affirms or denies every object of understanding or thought (as is - clear from the definitionAristot. Met. 4.7.1.) whenever it is right or wrong. When, in asserting or denying, it - combines the predicates in one way, it is right; when in the other, it is wrong. Again, unless it is maintained merely for argument's sake, the - intermediate must exist beside all contrary terms; so that one will say what is neither - true nor false. And it will exist beside what is and what is not; so that there will be a - form of change beside generation and destruction. Again, there will also be an intermediate in all - classes in which the negation of a term implies the contrary assertion; e.g., among - numbers there will be a number which is neither odd nor not-odd. But this is impossible, - as is clear from the definition.What definition - Aristotle had in mind we cannot tell; but it must have stated that every number is - either even or odd. Again, there will be an - infinite progression, and existing things will be not only half as many again, but even - more. For again it will be possible to deny - the intermediate in reference both to its assertion and to its negation, and the result - will be somethingIf besides A and not-A there is an - intermediate B, besides B and not-B there will be an intermediate C which is neither B - nor not-B; and so on.; for its essence is something distinct. Again, when a man is asked whether a thing is white and says "no," he has - denied nothing except that it is <white>, and its not-being <white> is a - negation. Now - this view has occurred to certain people in just the same way as other paradoxes have also - occurred; for when they cannot find a way out from eristic arguments, they submit to the - argument and admit that the conclusion is true. Some, then, hold the theory for this kind of reason, and others because they require an - explanation for everything. In dealing with all such persons the starting-point is from - definition; and definition results from the - necessity of their meaning something; because the formula, which their term implies, will - be a definition.Cf. Aristot. Met. 4.4.5, 6. The doctrine of Heraclitus, which says that - everything is and is not,Cf. Aristot. Met. 4.3.10. seems to make all things - true; and that of AnaxagorasCf. Aristot. Met. 4.4.28. seems to imply an - intermediate in contradiction, so that all things are false; for when things are mixed, - the mixture is neither good nor not-good; and so no statement is true. It is obvious from this - analysis that the one-sided and sweeping statements which some people make cannot be - substantially true—some maintaining that nothing is true (for they say that there is - no reason why the same rule should not apply to everything as applies to the - commensurability of the diagonal of a squareA stock - example of impossibility and falsity; see Index.), and some that everything is - true. These theories are almost the same as - that of Heraclitus. For the theory which says that all things are true and all false also - makes each of these statements separately; so that if they are impossible in combination they are - also impossible individually. And again obviously there are contrary statements, which - cannot be true at the same time. Nor can they all be false, although from what we have - said, this might seem more possible. But in - opposing all such theories we must demand, as was said in our discussion above,Aristot. Met. - 4.4.5. not that something should be or not be, but some significant - statement; and so we must argue from a definition, having first grasped what "falsehood" - or "truth" means. And if to assert what is true is nothing else than to deny what is - false, everything cannot be false; for one part of the contradiction must be - true. Further, if everything must be either - asserted or denied, both parts cannot be false; for one and only one part of the - contradiction is false. Indeed, the consequence follows which is notorious in the case of - all such theories, that they destroy themselves; for he who says that everything is true makes the opposite theory true too, and - therefore his own untrue (for the opposite theory says that his is not true); and he who - says that everything is false makes himself a liar. And if they make exceptions, the one that the opposite theory alone is - not true, and the other that his own theory alone is not false, it follows none the less that they postulate an infinite number - of true and false statements. For the statement that the true statement is true is also - true; and this will go on to infinity. Nor, as is obvious, are those right who say that all things are - at rest; nor those who say that all things are in motion. For if all things are at rest, - the same things will always be true and false, whereas this state of affairs is obviously - subject to change; for the speaker himself once did not exist, and again he will not - exist. And if all things are in motion, nothing will be true, so everything will be false; - but this has been proved to be impossible. Again, it must be that which is that changes, for change is from something - into something. And further, neither is it true that all things are at rest or in motion - sometimes, but nothing continuously; for there is something The sphere of the fixed stars; cf. Aristot. Met. 12.6, 12.7.1, 12.8.18. which always moves that which is - moved, and the "prime mover" is itself unmoved.Cf. - Aristot. Met. 12.7.

- - -

"Beginning"a)rxh/ means "starting-point," "principle," "rule" or "ruler." - means: (a) That part of a thing from which one may first move; eg., a line or a journey - has one beginning here , and another at the opposite extremity. (b) The point from - which each thing may best come into being; e.g., a course of study should sometimes be - begun not from what is primary or from the starting-point of the subject, but from the - point from which it is easiest to learn. (c) That thing as a result of whose presence - something first comes into being; e.g., as the keel is the beginning of a ship, and the - foundation that of a house, and as in the case of animals some thinkers suppose the - heartThis was Aristotle's own view,Aristot. De Gen. An. 738b 16. to be the - "beginning," others the brain,So Plato held,Plat. Tim. 44 d. and others something similar, - whatever it may be. (d) That from which, although not present in it, a thing first comes - into being, and that from which motion and change naturally first begin, as the child - comes from the father and mother, and fighting from abuse. (e) That in accordance with - whose deliberate choice that which is moved is moved, and that which is changed is - changed; such as magistracies, authorities, monarchies and despotisms. (f) Arts are also called "beginnings,"As directing principles. especially the architectonic arts. (g) - Again, "beginning" means the point from which a thing is first comprehensible, this too is - called the "beginning" of the thing; e.g. the hypotheses of demonstrations. ("Cause" can - have a similar number of different senses, for all causes are "beginnings.") It is a common property, - then, of all "beginnings" to be the first thing from which something either exists or - comes into being or becomes known; and some beginnings are originally inherent in things, - while others are not. Hence "nature" is a - beginning, and so is "element" and "understanding" and "choice" and "essence" and "final - cause"—for in many cases the Good and the Beautiful are the beginning both of - knowledge and of motion. "Cause" means: (a) in one sense, that as the result of whose presence - something comes into being—e.g. the bronze of a statue and the silver of a cup, and - the classessc. of material—metal, wood, - etc. which contain these; (b) in another sense, the form or pattern; - that is, the essential formula and the classes which contain it—e.g. the ratio 2:1 - and number in general is the cause of the octave—and the parts of the - formula. (c) The source of the first - beginning of change or rest; e.g. the man who plans is a cause, and the father is the - cause of the child, and in general that which produces is the cause of that which is - produced, and that which changes of that which is changed. (d) The same as "end"; i.e. the - final cause; e.g., as the "end" of walking is health. For why does a man walk? "To be healthy," we say, and by saying this - we consider that we have supplied the cause. (e) All those means towards the end which - arise at the instigation of something else, as, e.g. fat-reducing, purging, drugs and - instruments are causes of health; for they all have the end as their object, - although they differ from each other as being some instruments, others actions. These are roughly all - the meanings of "cause," but since causes are spoken of with various meanings, it follows - that there are several causes (and that not in an accidental sense) of the same thing. - E.g., both statuary and bronze are causes of the statue; not in - different connections, but qua statue. However, they are not causes - in the same way, but the one as material and the other as the source of - motion. And things are causes of each other; as e.g. labor of vigor, and vigor of - labor—but not in the same way; the one as an end , and the other as - source of motion . And again the same thing is sometimes the cause of contrary results; because that which - by its presence is the cause of so-and-so we sometimes accuse of being, by its absence, - the cause of the contrary—as, e.g., we say that the absence of the pilot is the - cause of a capsize, whereas his presence was the cause of safety. And both, presence and privation, are moving - causes. Now there are four senses which are most obvious - under which all the causes just described may be classed. The components of syllables; the material of manufactured articles; - fire, earth and all such bodies; the parts of a whole; and the premisses of a syllogistic conclusion; are causes in the - material sense. Of these some are causes as substrate: e.g. the parts; and - others as essence : the whole, and the composition, and the form. The seed and the physician and the contriver and in - general that which produces, all these are the source of change or stationariness. The - remainder represent the end and good of the others; for the - final cause tends to be the greatest good and end of the rest. Let it be assumed that it makes no difference whether - we call it "good" or "apparent good." In kind , then, there are these four - classes of cause. The modes of cause are - numerically many, although these too are fewer when summarized. For causes are spoken of in many senses, and even of those which are - of the same kind, some are causes in a prior and some in a posterior sense; e.g., the - physician and the expert are both causes of health; and the ratio 2:1 and number are both - causes of the octave; and the universals which include a given cause are causes of its - particular effects. Again, a thing may be a - cause in the sense of an accident, and the classes which contain accidents; e.g., the - cause of a statue is in one sense Polyclitus and in another a sculptor, because it is an - accident of the sculptor to be Polyclitus. And the universal terms which include accidents are - causes; e.g., the cause of a statue is a man, or even, generally, an animal; because - Polyclitus is a man, and man is an animal. And - even of accidental causes some are remoter or more proximate than others; e.g., the cause - of the statue might be said to be "white man" or "cultured man," and not merely - "Polyclitus" or "man." And besides the distinction of causes - as proper and accidental , some are termed causes in a - potential and others in an actual sense; e.g., the cause of - building is either the builder or the builder who builds. And the same distinctions in meaning as we have already described will - apply to the effects of the causes; e.g. to this statue, or - a statue, or generally an image; and to this bronze, or - bronze, or generally material.Effects, just like - causes (10), may be particular or general. The metal-worker produces (a) the bronze for - a particular statue by the sculptor, (b) bronze for a statue, (c) metal for an - image. And it is the same with accidental effects. Again, the proper and - accidental senses will be combined; e.g., the cause is neither "Polyclitus" nor "a - sculptor" but "the sculptor Polyclitus." However, these classes of cause are in all six in number, each - used in two senses. Causes are (1.) particular, (2.) generic, (3.) accidental, (4.) - generically accidental; and these may be either stated singly or (5, 6) in - combinationThe cause of a statue may be said to - be (1) a sculptor, (2) an artist, (3) Polyclitus, (4) a man, (5) the sculptor Polyclitus - (combination of (1) and (3)), (6) an artistic man (combination of (2) and - (4)).; and further they are all either - actual or potential. And there is this - difference between them, that actual and particular causes coexist or do not coexist with - their effects (e.g. this man giving medical treatment with this - man recovering his health, and this builder with this building - in course of erection); but potential causes do not always do so; for the house and the - builder do not perish together. "Element" means (a) the primary immanent thing, formally indivisible - into another form, of which something is composed. E.g., the elements of a sound are the - parts of which that sound is composed and into which it is ultimately divisible, and which - are not further divisible into other sounds formally different from themselves. If an - element be divided, the parts are formally the same as the whole: e.g., a part of water is - water; but it is not so with the syllable. (b) - Those who speak of the elements of bodies similarly mean the parts into which - bodies are ultimately divisible, and which are not further divisible into other parts - different in form. And whether they speak of one such element or of more than one, this is - what they mean. (c) The term is applied with a - very similar meaning to the "elements" of geometrical figures, and generally to the - "elements" of demonstrations; for the primary demonstrations which are contained in a - number of other demonstrations are called "elements" of demonstrations.Cf. Aristot. Met. 3.3.1. - Such are the primary syllogisms consisting of three terms and with one middle - term. (d) The term "element" is also applied - metaphorically to any small unity which is useful for various purposes; and so that which - is small or simple or indivisible is called an "element." (e) Hence it comes that the most universal things are elements; - because each of them, being a simple unity, is present in many things—either in all - or in as many as possible. Some too think that unity and the point are first - principles. (f) Therefore since what are - called generaThis must refer to the highest genera, - which have no definition because they cannot be analyzed into genus and differentia ( - Ross). are universal and indivisible (because they have no formula), some people - call the genera elements, and these rather than the differentia, because the genus is more - universal. For where the differentia is present, the genus also follows; but the - differentia is not always present where the genus is. And it is common to all cases that - the element of each thing is that which is primarily inherent in each thing. "Nature"On the meaning of fu/sis cf. Burnet, E.G.P. pp. 10-12, 363-364. means: (a) in one - sense, the genesis of growing things—as would be suggested by pronouncing the - u of fu/sis - long—and (b) in another, that immanent thingProbably the seed (Bonitz). from which a growing thing first begins to grow. (c) - The source from which the primary motion in every natural object is induced in that object - as such. All things are said to grow which gain - increase through something else by contact and organic unity (or adhesion, as in the case - of embryos). Organic unity differs from - contact; for in the latter case there need be nothing except contact, but in both the - things which form an organic unity there is some one and the same thing which produces, - instead of mere contact, a unity which is organic, continuous and quantitative (but not - qualitative). Again, "nature" means (d) the - primary stuff, shapeless and unchangeable from its own potency, of which any natural - object consists or from which it is produced; e.g., bronze is called the "nature" of a - statue and of bronze articles, and wood that of wooden ones, and similarly in all other - cases. For each article consists of these - "natures," the primary material persisting. It is in this sense that men call the elements - of natural objects the "nature," some calling it fire, others earth or air or water, - others something else similar, others some of these, and others all of them. Again in another sense "nature" means (e) the substance - of natural objects; as in the case of those who say that the "nature" is the primary - composition of a thing, or as Empedocles says: Of nothing that exists is there nature, but - only mixture and separation of what has been mixed; nature is but a name given to these by - men.Empedocles Fr. 8 - (Diels). Hence as regards those things which exist or are produced by nature, - although that from which they naturally are produced or exist is already present, we say - that they have not their nature yet unless they have their form and shape. That which comprises both of these exists by nature; - e.g. animals and their parts. And nature is both the primary matter (and this in two - senses: either primary in relation to the thing, or primary in general; e.g., in bronze - articles the primary matter in relation to those articles is bronze, but in general it is - perhaps water—that is if all things which can be melted are water) and the form or - essence, i.e. the end of the process, of generation. Indeed from this sense of "nature," - by an extension of meaning, every essence in general is called "nature," because the - nature of anything is a kind of essence. From what has been said, then, the primary and proper sense of - "nature" is the essence of those things which contain in themselves as such a source of - motion; for the matter is called "nature" because it is capable of receiving the nature, - and the processes of generation and growth are called "nature" because they are motions - derived from it. And nature in this sense is the source of motion in natural objects, - which is somehow inherent in them, either potentially or actually. "Necessary" means: (a) That without which, as a concomitant condition, - life is impossible; e.g. respiration and food are necessary for an animal, because it - cannot exist without them. (b) The conditions without which good cannot be or come to be, - or without which one cannot get rid or keep free of evil—e.g., drinking medicine is - necessary to escape from ill-health, and sailing to Aegina is necessary to recover one's money. (c) The compulsory and compulsion; i.e. that which hinders and - prevents, in opposition to impulse and purpose. For the compulsory is called necessary, - and hence the necessary is disagreeable; as indeed EvenusOf Poros; sophist and poet, contemporary with Socrates. says: "For - every necessary thing is by nature grievous."Evenus Fr. 8 (Hiller). And compulsion is a kind of necessity, as - Sophocles says: "Compulsion makes me do this of necessity."Soph. El. 256 (the quotation is slightly - inaccurate). And necessity is held, rightly, to be - something inexorable; for it is opposed to motion which is in accordance with purpose and - calculation. (d) Again, what cannot be otherwise we say is necessarily so. It is from this sense of "necessary" that all others - are somehow derived; for the term "compulsory" is used of something which it is necessary - for one to do or suffer only when it is impossible to act according to impulse, because of the - compulsion: which shows that necessity is that because of which a thing cannot be - otherwise; and the same is true of the concomitant conditions of living and of the good. - For when in the one case good, and in the other life or existence, is impossible without - certain conditions, these conditions are necessary, and the cause is a kind of - necessity. (e) - Again, demonstration is a "necessary" thing, because a thing cannot be otherwise if the - demonstration has been absolute. And this is the result of the first premisses, when it is - impossible for the assumptions upon which the syllogism depends to be otherwise. Thus of necessary things, some have an external cause of their - necessity, and others have not, but it is through them that other things are of necessity - what they are. Hence the "necessary" in the - primary and proper sense is the simple , for it cannot be in more than one - condition. Hence it cannot be in one state and in another; for if so it would ipso facto - be in more than one condition. Therefore if there are certain things which are eternal and - immutable, there is nothing in them which is compulsory or which violates their - nature. The - term "one" is used (1.) in an accidental, (2.) in an absolute sense. (1.) In the - accidental sense it is used as in the case of "Coriscus"Coriscus of Scepsis was a Platonist with whom Aristotle was probably - acquainted; but the name is of course chosen quite arbitrarily. and "cultured" - and "cultured Coriscus" (for "Coriscus" and "cultured" and "cultured Coriscus" mean the - same); and "cultured" and "upright" and "cultured upright Coriscus." For all these terms - refer accidentally to one thing; "upright" and "cultured" because they are accidental to - one substance, and "cultured" and "Coriscus" because the one is accidental to the - other. And similarly in one sense "cultured - Coriscus" is one with "Coriscus," because one part of the expression is accidental to the - other, e.g. "cultured" to "Coriscus"; and "cultured Coriscus" is one with "upright - Coriscus," because one part of each expression - is one accident of one and the same thing. It is the same even if the accident is applied - to a genus or a general term; e.g., "man" and "cultured man" are the same, either because - "cultured" is an accident of "man," which is one substance, or because both are accidents - of some individual, e.g. Coriscus. But they do - not both belong to it in the same way; the one belongs presumably as genus in - the substance, and the other as condition or affection of the - substance. Thus all things which are said to be "one" in an accidental sense are said to - be so in this way. (2.) Of those things which are said to be in themselves one, (a) some - are said to be so in virtue of their continuity; e.g., a faggot is made continuous by its - string, and pieces of wood by glue; and a continuous line, even if it is bent, is said to be one, - just like each of the limbs; e.g. the leg or arm. And of these things themselves those - which are naturally continuous are one in a truer sense than those which are artificially - continuous. "Continuous" means that whose - motion is essentially one, and cannot be otherwise; and motion is one when it is - indivisible, i.e. indivisible in time . Things are essentially continuous - which are one not by contact only; for if you put pieces of wood touching one another you - will not say that they are one piece of wood, or body, or any other - continuous thing. And things which are - completely continuous are said to be "one" even if they contain a joint, and still more - those things which contain no joint; e.g., the shin or the thigh is more truly one than - the leg, because the motion of the leg may not be one. And the straight line is more truly one than the bent. We call the - line which is bent and contains an angle both one and not one, because it may or may not - move all at once; but the straight line always moves all at once, and no part of it which - has magnitude is at rest while another moves, as in the bent line. (b) Another sense of "one" is that the substrate is uniform in - kind. Things are uniform whose form is - indistinguishable to sensation; and the - substrate is either that which is primary, or that which is final in relation to the end. - For wine is said to be one, and water one, as being something formally indistinguishable. - And all liquids are said to be one (e.g. oil and wine), and melted things; because the - ultimate substrate of all of them is the same, for all these things are water or - vapor. (c) - Things are said to be "one" whose genus is one and differs in its opposite differentiae. - All these things too are said to be "one" because the genus, which is the substrate of the - differentiae, is one (e.g., "horse," "man" and "dog" are in a sense one, because they are - all animals); and that in a way very similar to that in which the matter is one. Sometimes these things are said to be "one" in this - sense, and sometimes their higher genus is said to be one and the same (if they are final - species of their genus)—the genus, that is, which is above the genera of which their - proximate genus is one; e.g., the isosceles and equilateral triangles are one and the same - figure (because they are both triangles), but not the same triangles. (d) Again, things are said to - be "one" when the definition stating the essence of one is indistinguishable from a - definition explaining the other; for in itself every definition is distinguishable - <into genus and differentiae>. In this way that which increases and decreases is - one, because its definition is one; just as in the case of planes the definition of the - form is one. And in general those things whose - concept, which conceives the essence, is indistinguishable and cannot be separated either - in time or in place or in definition, are in the truest sense one; and of these such as - are substances are most truly one. For universally such things as do not admit of - distinction are called "one" in so far as they do not admit of it; e.g., if "man" qua "man" does not admit of distinction, he is one man; and similarly - if qua animal, he is one animal; and if qua - magnitude, he is one magnitude. Most things, then, are said to be "one" because they produce, or - possess, or are affected by, or are related to, some other one thing; but some are called - "one" in a primary sense, and one of these is substance. It is one either in continuity or - in form or in definition; for we reckon as more than one things which are not continuous, - or whose form is not one, or whose definition is not one. Again, in one sense we call anything whatever "one" if it is - quantitative and continuous; and in another sense we say that it is not "one" unless it is - a whole of some kind, i.e. unless it is one in form (e.g., if we saw the - parts of a shoe put together anyhow, we should not say that they were one — except - in virtue of their continuity; but only if they were so put together as to be a shoe, and - to possess already some one form). Hence the - circumference of a circle is of all lines the most truly one, because it is whole and - complete. The essence of "one" is to be a kind of starting - point of number; for the first measure is a starting point, because that by which first we - gain knowledge of a thing is the first measure of each class of objects. "The one," then, is the starting-point of what is knowable in - respect of each particular thing. But the unit is not the same in all classes, for in one it is the quarter-tone, and in another the - vowel or consonant; gravity has another unit, and motion another. But in all cases the - unit is indivisible, either quantitatively or formally. Thus that which is quantitatively and qua - quantitative wholly indivisible and has no position is called a unit; and that which is - wholly indivisible and has position, a point; that which is divisible in one sense, a - line; in two senses, a plane; and that which is quantitatively divisible in all three - senses, a body. And reversely that which is - divisible in two senses is a plane, and in one sense a line; and that which is in no sense - quantitatively divisible is a point or a unit; if it has no position, a unit, and if it - has position, a point. Again, some things are one numerically, others formally, others - generically, and others analogically; numerically, those whose matter is one; formally, - those whose definition is one; generically, those which belong to the same category; and - analogically, those which have the same relation as something else to some third - object. In every case the latter types of - unity are implied in the former: e.g., all things which are one numerically are also one - formally, but not all which are one formally are one numerically; and all are one generically - which are one formally, but such as are one generically are not all one formally, although - they are one analogically; and such as are one analogically are not all one - generically. It is obvious also that "many" will have the opposite meanings to "one." Some things are - called "many" because they are not continuous; others because their matter (either primary - or ultimate) is formally divisible; others because the definitions of their essence are - more than one. "Being" means (1.) accidental being, (2.) absolute being. (1.) E.g., we say that the - upright person "is" cultured, and that the man "is" cultured, and that the cultured person - "is" a man; very much as we say that the cultured person builds, because the builder - happens to be cultured, or the cultured person a builder; for in this sense "X is Y" means - that Y is an accident of X. And so it is with - the examples cited above; for when we say that "the man is cultured" and "the cultured - person is a man" or "the white is cultured" or "the cultured is white," in the last two - cases it is because both predicates are accidental to the same subject, and in the first - case because the predicate is accidental to what is ; and we say that "the - cultured is a man" because "the cultured" is accidental to a man. (Similarly "not-white" is said to "be," because the subject of which - "not-white" is an accident, is .) These, then, are the senses in which things are said to "be" accidentally: either - because both predicates belong to the same subject, which is ; or because the - predicate belongs to the subject, which is ; or because the subject to which - belongs that of which it is itself predicated itself is . (2.) The senses of essential - being are those which are indicated by the figures of predicationThe categories. For the full list of these see Aristot. Categories 1b 25-27.; for "being" has - as many senses as there are ways of predication. Now since some predicates indicate (a) - what a thing is, and others its (b) quality, (c) quantity, (d) relation, (e) activity or - passivity, (f) place, (g) time, to each of these corresponds a sense of "being." There is no difference between "the man is recovering" - and "the man recovers"; or between "the man is walking" or "cutting" and "the man walks" - or "cuts"; and similarly in the other cases. (3.) Again, "to - be" and "is" mean that a thing is true, and "not to be" that it is false. Similarly too in affirmation and negation; e.g., in " - Socrates is cultured" "is" means that this is true; or in "Socrates is not-white" that - this is true; but in "the diagonal is not commensurable"Cf. Aristot. Met. 1.2.15."is - not" means that the statement is false. (4.) Again, "to be" <or "is"> means that some of - these statements can be made in virtue of a potentiality and others in virtue of an - actuality. For we say that both that which - sees potentially and that which sees actually is "a seeing thing." And in the - same way we call "understanding" both that which can use the understanding, - and that which does ; and we call "tranquil" both that in which tranquillity - is already present, and that which is potentially tranquil. Similarly too in the case of substances. For we say that Hermes is in - the stone,Cf. Aristot. Met. 3.5.6. and the half of the line in the whole; and we call - "corn" what is not yet ripe. But when a thing is potentially existent and when not, must - be defined elsewhere.Aristot. Met. 9.9. "Substance" means (a) simple - bodies, e.g. earth, fire, water and the like; and in general bodies, and the things, - animal or divine, including their parts, which are composed of bodies. All these are - called substances because they are not predicated of any substrate, but other things are - predicated of them. (b) In another sense, - whatever, being immanent in such things as are not predicated of a substrate, is the cause - of their being; as, e.g., the soul is the cause of being for the animal. (c) All parts immanent in things which define and indicate - their individuality, and whose destruction causes the destruction of the whole; as, e.g., - the plane is essential to the body (as someThe - Pythagoreans and Platonists. hold) and the line to the plane. And number in general is thought by someThe Pythagoreans and Platonists. to be of this nature, on the - ground that if it is abolished nothing exists, and that it determines - everything. (d) Again, the - essence , whose formula is the definition, is also called the substance of - each particular thing. Thus it follows that "substance" has - two senses: the ultimate subject, which cannot be further predicated of something else; - and whatever has an individual and separate existence. The shape and form of each - particular thing is of this nature. "The same" means (a) accidentally the same. E.g., "white" and - "cultured" are the same because they are accidents of the same subject; and "man" is the - same as "cultured," because one is an accident of the other; and "cultured" is the same as - "man" because it is an accident of "man"; and "cultured man" is the same as each of the - terms "cultured" and "man," and vice versa; for both "man" and "cultured" are used in the - same way as "cultured man," and the latter in the same way as the former. Hence none of these predications can be made - universally. For it is not true to say that every man is the same as "the cultured"; - because universal predications are essential to things, but accidental predications - are not so, but are made of individuals and with a single application. " Socrates" and - "cultured Socrates" seem to be the same; but " Socrates" is not a class-name, and hence we - do not say "every Socrates" as we say "every man." Some things are said to be "the same" in this sense, but (b) others in - an essential sense, in the same number of senses as "the one" is essentially one; for - things whose matter is formally or numerically one, and things whose substance is one, are - said to be the same. Thus "sameness" is clearly a kind of unity in the being, either of - two or more things, or of one thing treated as more than one; as, e.g., when a thing is - consistent with itself; for it is then treated as two. Things are called "other" of which either - the forms or the matter or the definition of essence is more than one; and in general - "other" is used in the opposite senses to "same." Things are - called "different" which, while being in a sense the same, are "other" not only - numerically, but formally or generically or analogically; also things whose genus is not - the same; and contraries; and all things which contain "otherness" in their - essence. Things are called "like" which have the same attributes in all respects; or more of - those attributes the same than different; or whose quality is one. Also that which has a - majority or the more important of those attributes of something else in respect of which - change is possible (i.e. the contraries) is like that thing. And "unlike" is used in the - opposite senses to "like." The term "opposite" is applied - to (a) contradiction; (b) contraries; (c) relative terms; (d) privation; (e) state; (f) - extremes; e.g. in the process of generation and destruction. And (g) all things which - cannot be present at the same time in that which admits of them both are called opposites; - either themselves or their constituents. "Grey" and "white" do not apply at the same time - to the same thing, and hence their constituents are opposite. "Contrary" means: (a) attributes, - generically different, which cannot apply at the same time to the same thing. (b) The most - different attributes in the same genus; or (c) in the same subject; or (d) falling under - the same faculty. (e) Things whose difference is greatest absolutely, or in genus, or in - species. Other things are called "contrary" - either because they possess attributes of this kind, or because they are receptive of - them, or because they are productive of or liable to them, or actually produce or incur - them, or are rejections or acquisitions or possessions or privations of such - attributes. And since "one" and "being" have - various meanings, all other terms which are used in relation to "one" and "being" must - vary in meaning with them; and so "same," "other" and "contrary" must so vary, and so must - have a separate meaning in accordance with each category. Things are called "other in species" (a) which belong to the same genus and are not - subordinate one to the other; or (b) which are in the same genus and contain a differentia; - or (c) which contain a contrariety in their essence. (d) Contraries, too (either all of them or those which are called so - in a primary sense), are "other in species" than one another; and (e) so are all things of - which the formulae are different in the final species of the genus (e.g., "man" and - "horse" are generically indivisible, but their formulae are different); and (f) attributes - of the same substance which contain a difference. "The same in species" has the opposite - meanings to these. "Prior" and "posterior" mean: (1.) (a) In one sense (assuming that - there is in each genus some primary thing or starting-point) that which is nearer to some - starting-point, determined either absolutely and naturally, or relatively, or locally, or - by some agency; e.g., things are prior in space because they are nearer either to some - place naturally determined, such as the middle or the extreme, or to some chance relation; - and that which is further is posterior. (b) In - another sense, prior or posterior in time . Some things are prior as being - further from the present, as in the case of past events (for the Trojan is prior to the - Persian war, because it is further distant from the present); and others as being nearer - the present, as in the case of future events (for the Nemean are prior to the Pythian - games because they are nearer to the present, regarded as a starting-point and as - primary). (c) In another sense, in respect of motion (for that which is nearer - to the prime mover is prior; e.g., the boy is prior to the man). This too is a kind of - starting point in an absolute sense. (d) In respect of potency; for that which is superior - in potency, or more potent, is prior. Such is that in accordance with whose will the - other, or posterior, thing must follow, so that according as the former moves or does not - move, the latter is or is not moved. And the will is a - "starting-point." (e) In respect of order; - such are all things which are systematically arranged in relation to some one determinate - object. E.g., he who is next to the leader of the chorus is prior to him who is next but - one, and the seventh string is prior to the eighthThe octachord to which Aristotle refers was composed of the following notes: E - ((upa/th) F (parupa/th) G (lixano/s) A (me/sh) B (parame/sh) C - (tri/th) D (paranh/th) - E (nh/th).; for in one case the leader is the - starting-point, and in the other the middleStrictly - speaking there was no middle string in the octachord; the name was taken over from the - earlier heptachord EFGABbCD, in which there was no parame/sh. The me/sh was apparently what we - should call the tonic. Cf. Aristot. Met. 14.6.5; - Aristot. Problemata 919b 20. - string. In - these examples "prior" has this sense; but (2.) in another sense that which is prior in - knowledge is treated as absolutely prior; and of things which are prior in this sense the - prior in formula are different from the prior in perception . - Universals are prior in formula, but particulars in perception. And in formula the - attribute is prior to the concrete whole: e.g. "cultured" to "the cultured man"; for the - formula will not be a whole without the part. Yet "cultured" cannot exist apart from some cultured person. Again, (3.) attributes of prior subjects are called prior; e.g., - straightness is prior to smoothness, because the former is an attribute of the line in itself, and - the latter of a surface. Some things, then, are called prior and posterior in this sense; but - others (iv.) in virtue of their nature and substance, namely all things which can exist - apart from other things, whereas other things cannot exist without them. This distinction - was used by Plato.Not, apparently, in his - writings.(And since "being" has various meanings, (a) the substrate, and - therefore substance, is prior; (b) potential priority is different from actual - priority. Some things are prior potentially, - and some actually; e.g., potentially the half-line is prior to the whole, or the part to - the whole, or the matter to the substance; but actually it is posterior, because it is - only upon dissolution that it will actually exist.) Indeed, in a sense all things which are called "prior" or "posterior" - are so called in this connection; for some things can exist apart from others in - generation (e.g. the whole without the parts), and others in destruction (e.g. the parts - without the whole). And similarly with the other examples. "Potency"Or "capacity" or "potentiality." means: (a) the source of motion - or change which is in something other than the thing changed, or in it qua other. E.g., the science of building is a potency which is not present in the - thing built; but the science of medicine, which is a potency, may be present in the - patient, although not qua patient. Thus "potency" means the source in general of change or motion in - another thing, or in the same thing qua other; or the source of a thing's being moved or changed by another - thing, or by itself qua other (for in virtue of that principle by - which the passive thing is affected in any way we call it capable of being affected; - sometimes if it is affected at all, and sometimes not in respect of every affection, but - only if it is changed for the better). (b) The - power of performing this well or according to intention; because sometimes we say that - those who can merely take a walk, or speak, without doing it as well as they intended, - cannot speak or walk. And similarly in the case of passivity. (c) All states in virtue of which things are unaffected generally, or - are unchangeable, or cannot readily deteriorate, are called "potencies." For things are - broken and worn out and bent and in general destroyed not through potency but through - impotence and deficiency of some sort; and things are unaffected by such processes which - are scarcely or slightly affected because they have a potency and are potent and are in a - definite state. Since "potency" has all these meanings, "potent" (or "capable") will mean (a) that which - contains a source of motion or change (for even what is static is "potent" in a sense) - which takes place in another thing, or in itself qua other. - (b) That - over which something else has a potency of this kind. (c) That which has the potency of - changing things, either for the worse or for the better (for it seems that even that which - perishes is "capable" of perishing; otherwise, if it had been incapable, it would not have - perished. As it is, it has a kind of disposition or cause or principle which induces such - an affection. Sometimes it seems to be such as - it is because it has something, and sometimes because it is - deprived of something; but if privation is in a sense a state or "habit," - everything will be "potent" through having something; and so a thing is - "potent" in virtue of having a certain "habit" or principle, and also in virtue of having - the privation of that "habit," if it can have privation; and if privation is - not in a sense "habit," the term "potent" is equivocal). (d) A thing is "potent" if neither any other thing nor itself qua other contains a potency or principle destructive of it. (e) All - these things are "potent" either because they merely might chance to happen or not to - happen, or because they might do so well . Even in inanimate things this kind - of potency is found; e.g. in instruments; for they say that one lyre "can" be played, and - another not at all, if it has not a good tone. "Impotence" is a privation of potency—a kind of - abolition of the principle which has been described—either in general or in - something which would naturally possess that principle, or even at a time when it would - naturally already possess it (for we should not use "impotence"—in respect of - begetting—in the same sense of a boy, a man and a eunuch). Again, there is an "impotence" corresponding to each kind of - potency; both to the kinetic and to the successfully kinetic. Some things are said to be "impotent" in - accordance with this meaning of "impotence," but others in a different sense, namely - "possible" and "impossible." "Impossible" means: (a) that whose contrary is necessarily - true; e.g., it is impossible that the diagonal of a square should be commensurable with - the sides, because such a thing is a lie, whose contrary is not only true but inevitable. - Hence that it is commensurable is not only a lie but necessarily a lie. And the contrary of the impossible, i.e. the - possible, is when the contrary is not necessarily a lie; e.g., it is possible that a man - should be seated, for it is not necessarily a lie that he should not be seated. - "Possible," then, means in one sense, as we have said, that which is not necessarily a - lie; in another, that which is true; and in another, that which may be true. (The "power" in - geometryA square was called a du/namis. Plat. Rep 587d; - Plat. Tim. 31c. is so called by an extension of - meaning.) These are the senses of "potent" which do not - correspond to "potency." Those which do correspond to it all refer to the first meaning, - i.e. "a - source of change which exists in something other than that in which the change takes - place, or in the same thing qua other." Other things are said to be "potent"sc. in a passive sense, which the English word "potent" - cannot bear. because something else has such a potency over them; others because it does not possess it; others because it possesses it - in a particular way. The term "impotent" is similarly used. Thus the authoritative - definition of "potency" in the primary sense will be "a principle producing change, which - is in something other than that in which the change takes place, or in the same thing qua other." "Quantity" means that which is divisible into constituent parts, - eachi.e., if there are only two. or every - one of which is by nature some one individual thing. Thus plurality, if it is numerically - calculable, is a kind of quantity; and so is magnitude, if it is measurable. "Plurality" - means that which is potentially divisible into non-continuous parts; and "magnitude" that - which is potentially divisible into continuous parts. Of kinds of magnitude, that which is - continuous in one direction is length; in two directions, breadth; in three, - depth. And of these, plurality, when - limited, is a number; length, a line; breadth, a plane; depth, a body. Again, some things - are essentially quantitative, but others only accidentally; e.g. the line is essentially, - but "cultured" accidentally quantitative. And - of the former class some are quantitative in virtue of their substance, e.g. the fine - (because the definition which describes it is quantitative in some form); and others are attributes and conditions of a substance of this - kind— e.g., "much" and "little," "long" and "short," "broad" and "narrow," "deep" - and "shallow," "heavy" and "light," etc. Moreover, "great" and "small," and "greater" and "smaller," whether used absolutely or - relatively to one another, are essential attributes of quantity; by an extension of - meaning, however, these terms are also applied to other things. Of things called quantitative in an accidental sense, one kind is so - called in the sense in which we said above that "cultured" or "white" is - quantitative—because the subject to which they belong is quantitative; and others in - the sense that motion and time are so called—for these too are said in a sense to be - quantitative and continuous, since the subjects of which they are attributes are - divisible. I mean, not the thing moved, but that through or along which the motion has - taken place; for it is because the latter is quantitative that the motion is quantitative, - and because the motion is quantitative that the time is also. "Quality" means (a) in one sense, the - differentia of essence; e.g., a man is an animal of a certain quality because he is - two-footed; and so is a horse, because it is four-footed. Also a circle is a geometrical - figure of a certain quality, because it has no angles; which shows that the essential differentia - is quality. In this one sense, then, "quality" - means differentia of essence; but (b) in another it is used as of immovable and - mathematical objects, in the sense that numbers are in a way qualitative—e.g. such - as are composite and are represented geometrically not by a line but by a plane or solid - (these are products respectively of two and of three factors)—and in general means - that which is present besides quantity in the essence. For the essence of each number is - that which goes into it once; e.g. that of 6 is not what goes twice or three times, but - what goes once; for 6 is once 6. (c) All - affections of substance in motion in respect of which bodies become different when they - (the affections) change—e.g. heat and cold, whiteness and blackness, heaviness and - lightness, etc. (d) The term is used with reference to goodness and badness, and in - general to good and bad. Thus there are, roughly speaking, two meanings which the term - "quality" can bear, and of these one is more fundamental than the other. Quality in the - primary sense is the differentia of the essence; and quality in numbers falls under this - sense, because it is a kind of differentia of essences, but of things either not in motion - or not qua in motion. Secondly, there are the affections of things - in motion qua in motion, and the differentiae of motions. Goodness and badness fall under these - affections, because they denote differentiae - of the motion or functioning in respect of which things in motion act or are acted upon - well or badly. For that which can function or be moved in such-and-such a way is good, and - that which can function in such-and-such a way and in the contrary way is bad. Quality - refers especially to "good" and "bad" in the case of living things, and of these - especially in the case of such as possess choice. Things are called "relative" (a) In the sense that - "the double" is relative to the half, and "the triple" to the third; and in general the - "many times greater" to the "many times smaller," and that which exceeds to the thing - exceeded. (b) In the sense that the thing which heats or cuts is relative to the thing - heated or cut; and in general the active to the passive. (c) In the sense that the - measurable is relative to the measure, and the knowable to knowledge, and the sensible to - sensation. (a) In the first sense they are said to be numerically relative; either simply, or in a - definite relation to numbers or to 1. E.g., "the double" in relation to 1 is a definite - number; the "many times as great" is in a numerical relation to 1, but not in a definite - relation such as this or that ; the relation of that which is 1.5 times something else to that - something is a definite numerical relation to a number; and that which is (n+1)/n times - something else is in an indefinite relation to a number, just as "the many times as great" - is in an indefinite relation to 1. The - relation of that which exceeds to that which is exceeded is numerically quite indefinite, - for number is commensurate, and is not predicated of the incommensurate; whereas that - which exceeds, in relation to that which is exceeded, is "so much" plus something more; - and this something more is indefinite, for it is indifferently equal or not equal to the - "so much." Thus not only are all these things - said to be relative in respect of number, but also the "equal" and "like" and "same," - though in another way: for all these terms are used in respect of "one". Things are "the - same" whose essence is one; "like" whose quality is one; "equal" whose quantity is one. - Now "one" is the starting-point and standard of number; and so all these relations involve - number, though not all in the same way. (b) Active and passive things are called relative in virtue of - an active or passive potentiality or actualization of the potentialities; e.g., that which - can heat is called relative to that which can be heated, because it can heat; and again - the thing heating is called relative to the thing heated, and the thing cutting to the - thing cut, because their potentialities are actualized. Numerical relations, on the other - hand, are not actualized (except as has been - described elsewhere)The reference is quite - uncertain, but cf. Aristot. Met. 9.9.4, 5. The - point is that the actualization of a numerical (or geometrical) relation does not imply - an active functioning, as in the case of the potentialities just described.; they - have no actualizations in respect of motion. Of things potentially relative, some are further relative in respect of particular - times; as, e.g., that which has made or will make is relative to that which has been or - will be made. It is in this way that a father is called father of a son; the one has - acted, and the other has been acted upon, in a particular way. Again, some things are - relative in virtue of a privation of their potentiality; such is "the impossible" and all - similar terms, e.g. "the invisible." Thus relative terms which involve number and potentiality are - all relative because their very essence contains a reference to something else; but not - because something else is related to their essence. But (c) that which is measurable or - knowable or thinkable is called relative because something else is related to its - essence. For "thinkable" signifies that - there is a thought which thinks it; but thought is not relative to that of which it is the - thought (for then the same thing would have been said twice). And similarly sight is the - sight of something; not of that of which it is the sight, although this is of course - true—it is relative to some color or other similar thing. To describe it in the other way—"the sight of the object of - sight"—would be to say the same thing twice. Things, then, which are called relative of - their own nature are so called, some in these senses, and others because the classes which - contain them are of this kind. E.g., medicine is reckoned as relative because its genus, - science, is thought to be a relative thing. Further, there are the properties in virtue of which the things which possess them are - called relative; e.g., "equality" is relative because "the equal" is relative, and - "similarity" because "the similar" is relative. Other things are accidentally relative; - e.g., a man is relative because he happens to be "double" something else, and "double" is - a relative term; or "white" is relative if the same thing happens to be white as well as - double. "Perfect" <or "complete"> means: (a) That outside which it is impossible to find - even a single one of its parts; e.g., the complete time of each thing is that outside - which it is impossible to find any time which is a part of it. (b) That which, in respect - of goodness or excellence, cannot be surpassed in its kind; e.g., a doctor and a musician - are "perfect" when they have no deficiency in respect of the form of their peculiar - excellence. And thus by an extension of the - meaning we use the term in a bad connection, and speak of a "perfect" humbug and a - "perfect" thief; since indeed we call them "good"— e.g. a "good" thief and a "good" humbug. (c) And goodness is a kind of perfection. For each thing, and every - substance, is perfect when, and only when, in respect of the form of its peculiar - excellence, it lacks no particle of its natural magnitude. (d) Things which have attained - their end, if their end is good, are called "perfect"; for they are perfect in virtue of - having attained the end. Hence, since the end - is an ultimate thing, we extend the meaning of the term to bad senses, and speak of - perishing "perfectly" or being "perfectly" destroyed, when the destruction or calamity - falls short in no respect but reaches its extremity. Hence, by an extension of the - meaning, death is called an "end," because they are both ultimate things. And the ultimate - object of action is also an end. Things, then, which are called "perfect" in themselves are so called - in all these senses; either because in respect of excellence they have no deficiency and - cannot be surpassed, and because no part of them can be found outside them; or because, in - general, they are unsurpassed in each particular class, and have no part outside. - All other - things are so called in virtue of these, because they either produce or possess something - of this kind, or conform to it, or are referred in some way or other to things which are - perfect in the primary sense. "Limit" means: (a) The furthest part of each thing, and the first - point outside which no part of a thing can be found, and the first point within which all - parts are contained. (b) Any form of magnitude or of something possessing - magnitude. (c) The end of each thing. (This - end is that to which motion and action proceed, and not the end - from which. But sometimes it is both the end from which and the end to - which, i.e. the final cause.) (d) The reality or essence of each thing; for this is the - limit of our knowledge of it, and if it is a limit of the knowledge, it is also a limit of - the thing. Thus it is obvious that "limit" has not only as many senses as "beginning" but - even more; because the beginning is a kind of limit, but not every limit is a - beginning. "That in virtue of which" has various meanings. (a) The form or essence of each - individual thing; e.g., that in virtue of which a man is good is "goodness itself." (b) - The immediate substrate in which a thing is naturally produced; as, e.g., color is - produced in the surface of things. Thus "that in virtue of which" in the primary sense is - the form , and in the secondary sense, as it were, the matter of - each thing, and the immediate substrate. And - in general "that in virtue of which" will exist in the same number of senses as - "cause." For we say indifferently "in virtue - of what has he come?" or "for what reason has he come?" and "in virtue of what has he - inferred or inferred falsely?" or "what is the cause of his inference or false inference?" - (And further, there is the positional sense of kaq' o(/, - "in which he stands," or "in which he walks"; all these examples denote place or - position.) Hence "in virtue of itself" must also have various meanings. It denotes (a) The essence - of each particular; e.g., Callias is in virtue of himself Callias and the essence of - Callias. (b) Everything contained in the definition; e.g., Callias is in virtue of himself - an animal, because "animal" is present in the definition, since Callias is a kind of - animal. (c) Any attribute which a thing has - received directly in itself or in any of its parts; e.g., the surface is white in virtue - of itself; and man lives in virtue of himself, because the soul is a part of the man, and - life is directly contained in it. (d) That which has no other cause. Man has many causes: - "animal," "twofooted," etc.; but nevertheless man is in virtue of himself man. (e) All - things which belong to a thing alone and qua alone; and hence that - which is separate is "in virtue of itself."This - seems to be a slightly irrelevant reference to kaq' - a(uto/ in the sense of "independent"; but corruption in the text has made - the true reading uncertain. - "Disposition" means - arrangement of that which has parts, either in space or in potentiality or in form. It - must be a kind of position, as indeed is clear from the word, "disposition." "Having"(/ecis means not only - "having" but "habit" or "state." Cf. Latin, habitus. means (a) In one sense an - activity, as it were, of the haver and the thing had, or as in the case of an action or - motion; for when one thing makes and another is made, there is between them an act of - making. In this way between the man who has a garment and the garment which is had, there - is a "having." Clearly, then, it is impossible to have a "having" in this - sense; for there will be an infinite series if we can have the having of what we - have. But (b) there is another sense of - "having" which means a disposition, in virtue of which the thing which is disposed is - disposed well or badly, and either independently or in relation to something else. E.g., - health is a state, since it is a disposition of the kind described. Further, any part of - such a disposition is called a state; and hence the excellence of the parts is a kind of - state. "Affection" means (a) In one sense, a quality in virtue of which alteration is possible; - e.g., whiteness and blackness, sweetness and bitterness, heaviness and lightness, etc. (b) - The actualizations of these qualities; i.e. the alterations already realized. (c) More - particularly, hurtful alterations and motions, and especially hurts which cause suffering. (d) Extreme cases of misfortune and - suffering are called "affections."The English - equivalent for pa/qos in this sense would be "calamity" - or "disaster." We speak of "privation": (a) In one sense, if a thing does not possess - an attribute which is a natural possession, even if the thing itself would not naturally - possess itThis is not a proper sense of privation, - as Aristotle implies by choosing an example from everyday speech.; e.g., we say - that a vegetable is "deprived" of eyes. (b) If a thing does not possess an attribute which - it or its genus would naturally possess. E.g., a blind man is not "deprived" of sight in - the same sense that a mole is; the latter is "deprived" in virtue of its genus, but the - former in virtue of himself.i.e., a mole is blind - as being a member of a blind genus, whereas a man is blind only as an individual. Of - course moles are not really blind, but we still speak as though they - were. (c) If a thing has not an - attribute which it would naturally possess, and when it would naturally possess it (for - blindness is a form of privation; but a man is not blind at any age, but only - if he lacks sight at the age when he would naturally possess itThe qualification refers, I suppose, to the fact that an embryo does not - naturally possess sight.), and similarly if itThe subject seems to be indefinite, but no doubt Aristotle is thinking - primarily of the particular example which he has just given. A man "is not called blind - if he does not see in the dark, or if he does not see with his ears, or if he does not - see sound, or if he does not see what is behind him or too far away" ( Ross). - lacks an attribute in the medium and organ and relation and manner in which it would - naturally possess it. (d) The forcible removal - of anything is called privation. (e) Privation has as many senses as there are senses of - negation derived from the negative affix (a)-). For we - call a thing "unequal" because it does not possess equality (though it would naturally do - so); and "invisible" either because it has no color at all or because it has only a faint - one; and "footless" either because it has no feet at all or because it has rudimentary - feet. Again, a negative affix may mean - "having something in a small degree"—e.g. "stoneless"— that is, having it in some - rudimentary manner. Again, it may mean having it "not easily" or "not well"; e.g., - "uncutable" means not only that which cannot be cut, but that which cannot be cut easily - or well. And again, it may mean not having a thing at all; for it is not the one-eyed man, - but the man who lacks sight in both eyes, who is called blind. Hence not every man is good - or bad, moral or immoral; there is also the intermediate state. "To have" <or "possess"> - is used in various senses. (a) To direct in accordance with one's own nature or impulse; - whence we say that fever "possesses" a man, and despots "possess" cities, and people who - wear clothes "possess" them. (b) We speak of anything as "having" in which, as receptive - material, something is present. E.g., the bronze "has" the shape of the statue, and the - body "has" the disease. (c) In the sense that - the container holds the contained; for when A is contained in B, we say that A is held by - B. E.g., we say that the vessel holds the liquid, and the city holds men, and the ship - holds sailors, and so too that the whole "holds" the parts. (d) The same term is applied to that which prevents anything from - moving or acting in accordance with its own impulse; as pillars hold <up> the - weights which are imposed upon them, and as the - poets make AtlasCf. Hes. Th. - 517. hold up the heaven, because otherwise it would fall upon the earth - (as some of the physicistse.g., Empedocles held - that the heavens were kept in place by the velocity of their rotation;Aristot. De Caelo 284a 24, 295a 16 (Ritter and - Preller, 170 b). maintain also). It is in this sense that we say that "that which - holds together" holds what it holds together; because otherwise the latter would disperse, - each part in accordance with its own impulse. "To be in a - thing" is used similarly in senses corresponding to those of "to have." "To come from something" - means: (a) In one sense, to come from something as matter, and this in two ways: in - respect either of the primary genus or of the ultimate species. E.g., in the one sense - everything liquefiable comes from water, and in the other the statue comes from - bronze. (b) To come from something as the - first moving principle; e.g., "from what comes fighting?" From abuse; because this is the - beginning of a fight. (c) To come from the combination of matter and form (as the parts - come from the whole, and the verse from the Iliad , and the stones from - the house); for the shape is an end, and that is a complete thing which has attained its - end. (d) In the sense that the form is made - out of the part of its definition; as, e.g., "man" is made out of "two-footed " and the - syllable out of its elementIn the sense that - stoixei=on("letter") forms part of the definition of - "syllable."(this is a different way from that in which the statue is made out of - the bronze; for the composite entity is made out of perceptible material, but the form is also made - out of the material of the form). These, then, - are some of the meanings of "from" <or "out of">, but (e) sometimes one of these - senses only partially applies; e.g., the child comes from the father and mother, and - plants from the earth, because they come from some part of those things. (f) It means - "after" in time; e.g., we say that night comes from day, and storm from fine weather, - because one comes after the other. And we - speak thus of some of these things in view of their alternation with each other, as in the - examples just mentioned, and of others in view merely of their succession in time; e.g., - "the voyage was made from the equinox," meaning that it was made after it; and "the - Thargelia are from the Dionysia," meaning after the Dionysia.The (city) Dionysia were celebrated in March; the Thargelia (a festival - in honor of Apollo and Artemis) at the end of May. "Part" means: (a) That into which a - quantity can be in any way divided; for that which is taken from a quantity qua quantity is always called a part of that quantity—e.g., we - call 2 part (in a sense) of 3. (b) In another sense the term is only applied to those - "parts" in sense (a) which measure the whole; hence in one sense we call 2 part of 3, and - in another not. Again, (c) those divisions - into which the form, apart from quantity, can be divided, are also called parts of the - form. Hence species are called parts of their genus. (d) That into which the - whole (either the form or that which contains - the form) is divided, or of which it is composed. E.g., of a bronze sphere or cube not - only is the bronze (i.e. the material which - contains the form) a part, but also the angle. (e) The elements in the definition of each - thing are also called parts of the whole. Hence the genus is even called a part of the - species, whereas in another sense the species is part of the genus. "Whole" means: (a) That from - which no part is lacking of those things as composed of which it is called a natural - whole. (b) That which so contains its contents that they form a unity; and this in two - ways, either in the sense that each of them is a unity, or in the sense that the unity is - composed of them. For (i) the universal, or - term generally applied as being some whole thing, is universal in the sense that it - contains many particulars; because it is predicated of each of them, and each and all of - them (e.g. man, horse, god) are one; because they are all living things. And (2) that - which is continuous and limited is a whole when it is a unity composed of several parts - (especially if the parts are only potentially present in it; but otherwise even if they - are present actually). And of these things - themselves, those which are so naturally are more truly wholes than those which are so - artificially; just as we said of "the one," because "wholeness" is a kind of "oneness." - Again, - since a quantity has a beginning, middle and end, those to which position makes no - difference we describe as "all," and those to which position makes a difference we - describe as "whole," and those to which both descriptions can be applied, as both "all" - and "whole." These are all things whose nature - remains the same in transposition, but whose shape does not; e.g. wax or a coat. They are - described as both "whole" and "all"; for they have both characteristics. Water, however, - and all liquids, and number, are described as "all"; we do not speak of a "whole number" - or "whole water" except by an extension of meaning. Things are described as "all" in the - plural qua differentiated which are described as "all" in the - singular qua one; all this number, all these units. We do not describe any - chance quantity as "mutilated"; it must have parts, and must be a whole. The number 2 is - not mutilated if one of its 1's is taken away—because the part lost by mutilation is - never equal to the remainder—nor in general is any number mutilated; because the - essence must persist. If a cup is mutilated, it must still be a cup; but the number is no - longer the same. Moreover, not even all things - which have dissimilar parts are mutilated; for a number has in a sense dissimilar as well - as similar parts—e.g. 2, 3. But in general of things whose position makes no - difference, e.g. water or fire, none is mutilated;— to be mutilated, things must be such as have their position according to - their essence. Further, they must be - continuous; for a musical scale is composed of dissimilar parts, and has position; but it - does not become mutilated. Moreover, even things which are wholes are not mutilated by the - removal of any of their parts; the parts removed must be neither proper to - their essence nor in any chance location. E.g., a cup is not mutilated if a hole is made - in it, but only if the handle or some projection is broken; and a man is not mutilated if he loses flesh or his spleen, but if he - loses some extremity; and not every extremity, but only such as cannot grow again when - completely removed. Hence bald people are not mutilated. The term "genus" <or "race"> is - used: (a) When there is a continuous generation of things of the same type; e.g., "as long - as the human race exists" means "as long as the generation of human beings is - continuous." (b) Of anything from which things derive their being as the prime mover of - them into being. Thus some are called Hellenes by race, and others Ionians, because some - have Hellen and others Ion as their first ancestor. (Races are called after the male ancestor rather than after the - material.Aristotle regards the mother as - providing the material, and the father the formal element of the child. Cf. Aristot. Met. 1.6.8, Aristot. Met. 8.4.5. Some derive their race from the female as well; - e.g. "the descendants of PyrrhaWife of Deucalion, - the Greek Noah..") (c) In the sense that the plane is the "genus" of plane - figures, and the solid of solids (for each one of the figures is either a particular plane - or a particular solid); i.e., that which underlies the differentiae. (d) In the sense that in formulae the first component, which is - stated as part of the essence, is the genus, and the qualities are said to be its - differentiae. The term "genus," then, is used in all these senses—(a) in respect of - continuous generation of the same type; (b) in respect of the first mover of the same type - as the things which it moves; (c) in the sense of material. For that to which the - differentia or quality belongs is the substrate, which we call material. Things are called "generically - different" whose immediate substrates are different and cannot be resolved one into the - other or both into the same thing. E.g., form and matter are generically different, and - all things which belong to different categories of being; for some of the things of which - being is predicated denote the essence, others a quality, and others the various other - things which have already been distinguished. For these also cannot be resolved either - into each other or into any one thing. "False" means: (i) false as a thing ; (a) because - it is not or cannot be substantiated; such are the statements that the diagonal of a - square is commensurable, or that you are - sitting. Of these one is false always, and the other sometimes; it is in these senses that - these things are not facts. (b) Such things as - really exist, but whose nature it is to seem either such as they are not, or like things - which are unreal; e.g. chiaroscuro and dreams. For these are really something, but not - that of which they create the impression. Things, then, are called false in these senses: - either because they themselves are unreal, or because the impression derived from them is - that of something unreal. (2.) A false statement is the statement of what is not, - in so far as the statement is false. Hence every definition is untrue of anything other - than that of which it is true; e.g., the definition of a circle is untrue of a triangle. - Now in one sense there is only one definition of each thing, namely that of its essence; - but in another sense there are many definitions,Here Aristotle is using the word lo/gos not in the - strict sense of "definition" but in the looser sense of "a statement about - something." since the thing itself, and the thing itself qualified (e.g. - "Socrates" and "cultured Socrates") are in a sense the same. But the false definition is not strictly a definition of anything. - Hence it was foolish of AntisthenesThe Cynic; - contemporary and renegade "disciple" of Socrates. He taught that definition, and even - predication, are strictly speaking impossible. A simple entity can only be named; a - complex entity can only be "defined" by naming its simple constituents. Cf. Aristot. Met. 8.3.7, 8; Plat. Theaet. 201d-202c, Plat. Soph. 251b, - c. to insist that nothing can be described except by its proper - definition: one predicate for one subject; from which it followed that contradiction is - impossible, and falsehoodCf. Plat. Euthyd. 283e-284c, 286c, d. nearly so. But - it is possible to describe everything not only by its own definition but by that of - something else; quite falsely, and yet also in a sense truly—e.g., 8 may be - described as "double" by the definition of 2. Such are the meanings of "false" in these cases. (3.) - A false man is one who readily and deliberately makes such statements, for the sake of - doing so and for no other reason; and one who induces such statements in others—just - as we call things false which induce a false impression. Hence the proof in the - HippiasPlat. Hipp. Min 365-375. that the same - man is false and true is misleading; for it - assumes (a) that the false man is he who is able to deceive, i.e. the man who - knows and is intelligent; (b) that the man who is willingly bad is better. This false - assumption is due to the induction; for when he says that the man who limps willingly is - better than he who does so unwillingly, he means by limping pretending to - limp. For if he is willingly lame, he is presumably worse in this case just as he is in - the case of moral character. "Accident" <or "attribute"> means that which applies to - something and is truly stated, but neither necessarily nor usually; as if, for example, - while digging a hole for a plant one found a treasure. Then the finding of treasure is an - accident to the man who is digging the hole; for the one thing is not a necessary - consequence or sequel of the other, nor does one usually find treasure while - planting. And a cultured man might be white; but since this does not happen - necessarily or usually, we call it an accident. Thus since there are attributes and - subjects, and some attributes apply to their subjects only at a certain place and time, - any attribute which applies to a subject, but not because it was a particular subject or - time or place, will be an accident. Nor is - there any definite cause for an accident, but only a chance, i.e. indefinite, cause. It - was by accident that X went to Aegina if - he arrived there, not because he intended to go there but because he was carried out of - his course by a storm, or captured by pirates. The accident has happened or exists, but in virtue not of itself but of something else; - for it was the storm which was the cause of his coming to a place for which he was not - sailing—i.e. Aegina. "Accident" has also another sense,i.e. "property." namely, whatever belongs to each thing in virtue - of itself, but is not in its essence; e.g. as having the sum of its angles equal to two - right angles belongs to the triangle. Accidents of this kind may be eternal, but none of - the former kind can be. There is an account of this elsewhere.The reference is probably to the Aristot. - Analytica Posteriora 75a 18, 39-41.

- - -

It is the principles and - causes of the things which are that we are seeking; and clearly of the things - which are qua being. There is a cause of health and physical - fitness; and mathematics has principles and elements and causes; and in general every - intellectual science or science which involves intellect deals with causes and principles, - more or less exactly or simply considered. But - all these sciences single out some existent thing or class, and concern themselves with - that; not with Being unqualified, nor qua Being, nor do they give - any account of the essence; but starting from it, some making it clear to perception, and - others assuming it as a hypothesis, they demonstrate, more or less cogently, the essential - attributes of the class with which they are dealing. Hence obviously there is no demonstration of substance or essence from - this method of approach, but some other means of exhibiting it. And similarly they say - nothing as to whether the class of objects with which they are concerned exists or not; - because the demonstration of its essence and that of its existence belong to the same - intellectual process. And since physical - science also happens to deal with a genus of Being (for it deals with the sort of substance which contains in itself the - principle of motion and rest), obviously it is neither a practical nor a productive - science. For in the case of things produced - the principle of motion (either mind or art or some kind of potency) is in the producer; - and in the case of things done the will is the agent—for the thing done and the - thing willed are the same. Thus if every intellectual activity is either practical or - productive or speculative, physics will be a speculative science; but speculative about - that kind of Being which can be moved, and about formulated substance for the most part - only qua inseparable from matter. But we must not fail to observe how the essence and the - formula exist, since without this our inquiry is ineffectual. Now of things defined, i.e. of essences, some apply in the sense that "snub" does, and - some in the sense that "concave" does. The difference is that "snub" is a combination of - form with matter; because the "snub" is a concave nose , whereas concavity is - independent of sensible matter. Now if all physical - terms are used in the same sense as "snub"—e.g. nose, eye, face, flesh, bone, and in - general animal; leaf, root, bark, and in general vegetable (for not one of these has a - definition without motion; the definition invariably includes matter)—it is clear - how we should look for and define the essence in physical things, and why it is the - province of the physicist to study even some aspects of the soul, so far as it is not - independent of matter. It is obvious, then, from these considerations, that physics is a form - of speculative science. And mathematics is also speculative; but it is not clear at - present whether its objects are immutable and separable from matter; it is clear, however, - that some branches of mathematics study their objects qua immutable - and qua separable from matter. Obviously it is the province of a - speculative science to discover whether a thing is eternal and immutable and separable - from matter; not, however, of physics (since - physics deals with mutable objects) nor of mathematics, but of a science prior to both. - For physics deals with things which exist separately but are not immutable; and some - branches of mathematics deal with things which are immutable, but presumably not - separable, but present in matter; but the primary science treats of things which are both - separable and immutable. Now all causes must - be eternal, but these especially; since they are the causes of what is visible of things - divine. Hence there will be three speculative philosophies: mathematics, physics, and - theology— since it is obvious that if - the divine is present anywhere, it is present in this kind of entity; and also the most - honorable science must deal with the most honorable class of subject. The speculative sciences, - then, are to be preferred to the other sciences, and "theology" to the other speculative - sciences. One might indeed raise the question whether the primary philosophy is universal - or deals with some one genus or entity; because even the mathematical sciences differ in - this respect—geometry and astronomy deal with a particular kind of entity, whereas - universal mathematics applies to all kinds alike. Then if there is not some other substance besides those which are - naturally composed, physics will be the primary science; but if there is a substance which - is immutable, the science which studies this will be prior to physics, and will be primary - philosophy, and universal in this sense, that it is primary. And it will be the province - of this science to study Being qua Being; what it is, and what the - attributes are which belong to it qua Being. But since the simple term - "being" is used in various senses, of which we saw that one was accidental , - and another true (not-being being used in the sense of "false"); and since - besides these there are the categories, e.g. the "what," quality, quantity, place, time, - and any other similar meanings; and further besides all these the potential and - actual : since the term "being" has various senses, it must first be said - of what "is" accidentally, that there can be no speculation about it. This is shown by the fact that no science, whether practical, - productive or speculative, concerns itself with it. The man who produces a house does not - produce all the attributes which are accidental to the house in its construction; for they - are infinite in number. There is no reason why the house so produced should not be - agreeable to some, injurious to others, and beneficial to others, and different perhaps - from every other existing thing; but the act of building is productive of none of these - results. In the same way the geometrician - does not study the accidental attributes of his figures, nor whether a triangle is - different from a triangle the sum of whose angles is equal to two right angles. And this - accords with what we should reasonably expect, because "accident" is only, as it were, a - sort of name. Hence in a way PlatoCf. Plat. Soph. 254a. was not far wrong in making - sophistry deal with what is nonexistent; because the sophists discuss the accident more, perhaps, than any other - people—whether "cultured" and "grammatical,"i.e. able to read and write. The sophistic argument is given by Alexander as follows: A - is grammatical; therefore grammatical A=A. A is cultured; therefore cultured A=A. - Therefore grammatical=cultured, and he who is grammatical must be cultured. But B, - though grammatical, is not cultured. Therefore the grammatical is not the same as the - cultured. and "cultured Coriscus" and "Coriscus,"If Coriscus is the same as cultured Coriscus, he is the same as cultured - cultured Coriscus, and soad infinitum. Cf. Soph. Elench. - 173a 34. are the same or different; and whether everything that is, but - has not always been, has come into being, so that if a man who is cultured has become - grammatical, he has also, being grammatical, - become culturedIf A, being cultured, has become - grammatical, then being cultured he is grammatical. Then being grammatical he is - cultured. But he has not always, being grammatical, been cultured. So if that which is - but has not always been must have come to be, then being grammatical he has become - cultured; i.e., he must have been both grammatical before he was cultured and cultured - before he was grammatical; which is absurd ( Ross).; and all other such - discussions. Indeed it seems that the accidental is something closely akin to the - nonexistent. This is clear too from such - considerations as the following: of things which are in other senses there is - generation and destruction, but of things which are accidentally there is - not.i.e., the process of becoming or change takes - place in the subject—the man , who is accidentally cultured, becomes - grammatical, and when the process is complete "the cultured" is - accidentally grammatical; but it does not become so. Nevertheless we - must state further, so far as it is possible, with regard to the accidental, what its - nature is and through what cause it exists. At the same time it will doubtless also appear - why there is no science of it. Since, then, there are among existing things some which are invariable - and of necessity (not necessity in the sense of compulsion,Cf. Aristot. Met. 5.5.2. - but that by which we mean that it cannot be otherwise - Aristot. Met. 5.5.3 - ), and some which are not necessarily so, nor always, but usually: this is the - principle and this the cause of the accidental. For whatever is neither always nor usually - so, we call an accident. E.g., if in the - dog-daysThe period from July 3 to August 11, - during which the dog-star Sirius rises and sets with the sun. we have storm and - cold, we call it an accident; but not if we have stifling and intense heat, because the - latter always or usually comes at this time, but not the former. It is accidental for a - man to be white (since this is neither always nor usually so), but it is not accidental - for him to be an animal. It is by accident that a - builder restores to health, because it is not a builder but a doctor who naturally does - this; but the builder happened accidentally to be a doctor. A confectioner, aiming at - producing enjoyment, may produce something health-giving; but not in virtue of his - confectioner's art. Hence, we say, it was accidental; and he produces it in a sense, but - not in an unqualified sense. For there are - potencies which produce other things, but there is no art or determinate potency of - accidents, since the cause of things which exist or come to be by accident is also - accidental. Hence, since not everything is - or comes to be of necessity and always, but most things happen usually, the accidental - must exist. E.g., the white man is neither always nor usually cultured; but since this - sometimes happens, it must be regarded as accidental. Otherwise, everything must be - regarded as of necessity. Therefore the cause - of the accidental is the matter, which admits of variation from the usual. We must take this as our starting-point: Is everything either - "always" or "usually"? This is surely impossible. Then besides these alternatives there is - something else: the fortuitous and accidental. But again, are things usually - so, but nothing always , or are there things which are eternal? These - questions must be inquired into laterCf. Aristot. Met. 12.6-8.; but it is clear that there is no science of the - accidental—because all scientific knowledge is of that which is always - or usually so. How else indeed can one learn it or teach it to another? For a - fact must be defined by being so always or usually; e.g., honey-water is usually - beneficial in case of fever. But science will - not be able to state the exception to the rule: when it is not beneficial—e.g. at - the new moon; because that which happens at the new moon also happens either always or - usually; but the accidental is contrary to this. We have now explained the nature and - cause of the accidental, and that there is no science of it. It is obvious that there are principles - and causes which are generable and destructible apart from the actual processes of - generation and destructionOn the analogy of - accidental events; see 2. 5.; for if this is not true, everything will be of - necessity: that is, if there must necessarily be some cause, other than accidental, of - that which is generated and destroyed. Will A be, or not? Yes, if B happens; otherwise - not. And B will happen if C does. It is clear - that in this way, as time is continually subtracted from a limited period, we shall come - to the present. Accordingly So-and-so will die by disease or violence if he goes out; and - this if he gets thirsty; and this if something else happens; and thus we shall come to - what is the case now, or to something which has already happened. E.g. "if he is thirsty"; - this will happen if he is eating pungent food, and this is either the case or - not. Thus of necessity he will either die or - not die. And similarly if one jumps over to the past, the principle is the same; for - this—I mean that which has just happened—is already present in something. - Everything, then, which is to be, will be of necessity; e.g., he who is alive must - die—for some stage of the process has been reached already; e.g., the contraries are - present in the same body—but whether by disease or violence is not yet determined; - it depends upon whether so-and-so happens. Clearly, then, the series goes back to some starting-point, which does not go back to - something else. This, therefore, will be the starting-point of the fortuitous, and nothing - else is the cause of its generation. But to what sort of starting-point and cause this - process of tracing back leads, whether to a material or final or moving cause, is a - question for careful consideration. So much, then, for the accidental sense of "being"; we have - defined it sufficiently. As for "being" qua truth, and "not-being" - qua falsity, since they depend upon combination and - separation, and taken together are concerned - with the arrangement of the parts of a contradiction (since the true has affirmation when - the subject and predicate are combined, and negation where they are divided; but the false - has the contrary arrangement. How it happens - that we combine or separate in thought is another question. By "combining or separating in - thought" I mean thinking them not as a succession but as a unitysc., "or not as a unity but as a succession" (this is - separating in thought).); for "falsity" and "truth" are not in - things —the good, for example, being true, and the bad - false—but in thought ; and with regard to simple concepts and essences - there is no truth or falsity even in thought; —what points we must study in connection with being and not-being in this sense, - we must consider later. But since the combination and separation exists in thought and not - in things, and this sense of "being" is different from the proper senses (since thought - attaches or detaches essence or quality or quantity or some other category), we may - dismiss the accidental and real sensesi.e., the - senses in which the verb "to be" is used to express an accidental or a true - relation. of "being." For the cause of - the one is indeterminate and of the other an affection of thought; and both are connected with - the remaining genus of "being," and do not indicate any objective reality. Let us - therefore dismiss them, and consider the causes and principles of Being itself qua Being. [We have made it clear in our distinction of the number of - senses in which each term is used that "being" has several senses.]This sentence is almost certainly a later and clumsy addition to show the - connection with the following book.

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The term - "being" has several senses, which we have classified in our discussionAristot. Met. - 5.7. of the number of senses in which terms are used. It denotes first - the " what " of a thing, i.e. the individuality; and then the quality or - quantity or any other such category. Now of all these senses which "being" has, the - primary sense is clearly the "what," which denotes the substance - (because when we describe the quality of a - particular thing we say that it is "good or bad," and not "five feet high" or "a man"; but - when we describe what it is, we say not that it is "white" or "hot" or "five - feet high," but that it is "a man" or "a god"), and all other things are said to "be" - because they are either quantities or qualities or affections or some other such - thing. Hence one might raise the question whether - the terms "to walk" and "to be well" and "to sit" signify each of these things as "being," - or not; and similarly in the case of any other such terms; for not one of them by nature - has an independent existence or can be separated from its substance. Rather, if anything - it is the thing which walks or sits or is well that is existent. The reason why these things are more truly existent is - because their subject is something definite; i.e. the substance and the individual, which - is clearly implied in a designation of this kind, since apart from it we cannot speak of - "the good" or "sitting." Clearly then it is by reason of the substance that each of the - things referred to exists. Hence that which - is primarily, not in a qualified sense but absolutely, will be - substance. Now "primary" has several meanings; but - nevertheless substance is primary in all senses, both in definition and in knowledge and - in time. For none of the other categories can exist separately, but substance - alone; and it is primary also in definition, - because in the formula of each thing the formula of substance must be inherent; and we - assume that we know each particular thing most truly when we know what "man" - or "fire" is— rather than its quality or quantity or position; because we know each of - these points too when we know what the quantity or quality is. Indeed, the question which was raised long ago, is - still and always will be, and which always baffles us—"What is Being?"—is in - other words "What is substance?" Some say that it is oneThe Milesians and Eleatics.; others, more than one; some, - finiteThe Pythagoreans and Empedocles.; - others, infinite.Anaxagoras and the - Atomists. And so for us too our chief and primary and practically our only - concern is to investigate the nature of "being" in the sense of substance. Substance is thought to - be present most obviously in bodies. Hence we call animals and plants and their parts - substances, and also natural bodies, such as fire, water, earth, etc., and all things - which are parts of these or composed of these, either of parts or them or of their - totality; e.g. the visible universe and its parts, the stars and moon and sun. We must consider whether (a) these are the only - substances, or (b) these and some others, or (c) some of these, or (d) some of these and - some others, or (e) none of these, but certain others. SomeThe Pythagoreans. hold that the bounds of body—i.e. the - surface, line, point and unit—are substances, and in a truer sense than body or the - solid. Again, someThe pre-Socratics. believe that there is nothing of this kind - besides sensible things, while others believe in eternal entities more numerous and more - real than sensible things. Thus Plato posited - the Forms and the objects of mathematics as two kinds of substance, and as a third the - substance of sensible bodies; and - SpeusippusPlato's nephew and successor as the - head of the Academy. assumed still more kinds of substances, starting with "the - One," and positing principles for each kind: one for numbers, another for magnitudes, and - then another for the soul. In this way he multiplies the kinds of substance. SomeThe followers of Xenocrates, successor to - Speusippus. again hold that the Forms and numbers have the same nature, and that - other things—lines and planes—are dependent upon them; and soon back to the - substance of the visible universe and sensible things. We must consider, then, with regard to these matters, which of the - views expressed is right and which wrong; and what things are substances; and whether - there are any substances besides the sensible substances, or not; and how sensible - substances exist; and whether there is any separable substance (and if so, why and how) or - no substance besides the sensible ones. We must first give a rough sketch of what - substance is. The term "substance" is used, if not in more, at least in four principal cases; for both - the essence and the universal and the genus are held to be the substance of the - particular, and fourthly the substrate. The substrate is that of which the rest are - predicated, while it is not itself predicated of anything else. Hence we must first - determine its nature, for the primary substrate is considered to be in the truest sense - substance. Now - in one sense we call the matter the substrate; in another, the - shape ; and in a third, the combination of the two. By matter I mean, for - instance, bronze; by shape, the arrangement of the form; and by the combination of the - two, the concrete thing: the statue. Thus if the form is prior to the matter and more - truly existent, by the same argument it will also be prior to the combination. We have now stated in - outline the nature of substance—that it is not that which is predicated of a - subject, but that of which the other things are predicated. But we must not merely define - it so, for it is not enough. Not only is the statement itself obscure, but also it makes - matter substance; for if matter is not substance, it is beyond our power to say what else - is. For when everything else is removed, - clearly nothing but matter remains; because all the other things are affections, products - and potencies of bodies, and length, breadth and depth are kinds of quantity, and not - substances. For quantity is not a substance; rather the substance is that to which these - affections primarily belong. But when we take - away length and breadth and depth we can see no thing remaining, unless it be the - something bounded by them; so that on this view matter must appear to be the only - substance. By matter I mean that which in - itself is neither a particular thing nor a quantity nor designated by any of the - categories which define Being. For there is - something of which each of these is predicated, whose being is different from that of each - one of the categories; because all other things are predicated of substance, but this is - predicated of matter. Thus the ultimate substrate is in itself neither a particular thing - nor a quantity nor anything else. Nor indeed is it the negations of these; for the - negations too will only apply to it accidentally. If we hold this view, it follows that matter is - substance. But this is impossible; for it is accepted that separability and individuality - belong especially to substance. Hence it would seem that the form and the combination of - form and matter are more truly substance than matter is. The substance, then, which consists of both—I mean of matter and - form—may be dismissed, since it is posterior and obvious. Matter too is in a sense - evident. We must consider the third type, for this is the most perplexing. Now it is agreed that some sensible things are substances, and so we - should begin our inquiry in connection with these. It is convenient to advance to the more intelligiblesc. by nature. All learning proceeds by induction from that which is - intelligible to us (i.e., the complex facts and objects of our experience, - which are bound up with sensation and therefore less intelligible in themselves), to - that which is intelligible in itself (i.e., the simple universal principles of - scientific knowledge).; for learning is always acquired in this way, by advancing - through what is less intelligible by nature to what is more so. And just as in actions it - is our task to start from the good of the individual and make absolute good good for the - individual,Cf. Aristot. Ethics 1129b 5. so it is our task to start from what is more - intelligible to oneself and make what is by nature intelligible intelligible to - oneself. Now that which is intelligible and - primary to individuals is often but slightly intelligible, and contains but little - reality; but nevertheless, starting from that which is imperfectly intelligible but - intelligible to oneself, we must try to understand the absolutely intelligible; advancing, - as we have said, by means of these very things which are intelligible to us. Since we distinguished at the beginningAristot. Met. 7.3.1. the - number of ways in which substance is defined, and since one of these appeared to be - essence, we must investigate this. First, let - us make certain linguistic statements about it. The essence - of each thing is that which it is said to be per se. "To be you" is not "to be cultured," - because you are not of your own nature cultured. Your essence, then, is that which you are - said to be of your own nature. But not even all of this is - the essence; for the essence is not that which is said to be per se in the sense that - whiteness is said to belong to a surface,Cf. Aristot. Met. 5.18.3, 4. because "being a - surface" is not "being white." Nor is the - essence the combination of both, "being a white surface." Why? Because the word itself is - repeated. Hence the formula of the essence of - each thing is that which defines the term but does not contain it. Thus if "being a white - surface" is the same as "being a smooth surface," "white" and "smooth" are one and the - same.The statement that "to be a white surface" - is the same as "to be a smooth surface" tells us nothing fresh about surface; it simply - identifies "white" with "smooth." Aristotle has in mind Democritus's theory of color - (that it is an impression conveyed to our eyes from the superficial texture of the - object; Theophrastus, De Sensu 73-75); cf.Aristot. De Sensu 442b 11, Aristot. De Gen. et Corr. 316a 1. But since in the other - categories too there are compounds with substance (because there is a substrate for each - category, e.g. quality, quantity, time, place and motion), we must inquire whether there - is a formula of the essence of each one of them; whether these compounds, e.g. "white - man," also have an essence. Let the compound be denoted by X.Literally "cloak," but the word is chosen quite arbitrarily. Cf. Aristot. Met. 8.6.4. What is the essence of - X? "But this is not even a per se expression." We reply - that there are two ways in which a definition can be not per se true of its subject: (a) - by an addition, and (b) by an omission. In one - case the definition is not per se true because the term which is being defined is combined - with something else; as if, e.g., in defining whiteness one were to state the definition - of a white man. In the other, because something else (which is not in the definition) is - combined with the subject; as if, e.g., X were to denote "white man," and X were defined - as "white." "White man" is white, but its essence is not "to be white." But is "to be X" an - essence at all? Surely not. The essence is an - individual type; but when a subject has something distinct from it predicated of it, it is - not an individual type. E.g., "white man" is not an individual type; that is, assuming - that individuality belongs only to substances. Hence essence belongs to all things the - account of which is a definition. We have a - definition, not if the name and the account signify the same (for then all accounts would - be definitions; because any account can have a name, so that even "the Iliad - " will be a definition), but if the account is of something primary. Such are all - statements which do not involve the predication of one thing of another. Hence essence will belong to nothing except species of - a genus, but to these only; for in these the predicate is not considered to be related to - the subject by participation or affection, nor as an accident. But of everything else as - well, if it has a name, there will be a formula of what it means—that X - belongs to Y; or instead of a simple formula one more exact—but no definition, nor - essence. Or - perhaps "definition," like the "what," has more than one sense. For the "what" in one - sense means the substance and the individual, and in another each one of the categories: quantity, quality, etc. Just as "is" applies to everything, although not in the same - way, but primarily to one thing and secondarily to others; so "what it is" applies in an - unqualified sense to substance, and to other things in a qualified sense. For we might ask - also what quality "is," so that quality also is a "what it is"; not however without - qualification, but just as in the case of not-being some say by a verbal quibble that - not-being "is"—not in an unqualified sense, but "is" not-being—so too with - quality. Now - although we must also consider how we should express ourselves in each particular case, it - is still more important to consider what the facts are. Hence now, since the language - which we are using is clear, similarly essence also will belong primarily and simply to - substance, and secondarily to other things as well; just as the "what it is" is not - essence simply, but the essence of a quality or quantity. For it must be either by equivocation that we say that these things - are , or by adding and subtracting qualifications, as we say that the - unknowable is knownsc. to be unknowable.; - since the truth is that we use the terms neither equivocally nor in the same sense, but - just as we use the term "medical" in relation to one and the same thing; - but not - of one and the same thing, nor yet equivocally. The term "medical" is - applied to a body and a function and an instrument, neither equivocally nor in one sense, - but in relation to one thing.Cf. Aristot. Met. 4.2.2. However, in whichever way one - chooses to speak of these things, it matters nothing; but this point is clear: that the - primary and unqualified definition, and the essence, belong to substances. It is true that - they belong equally to other things too, but not primarily . For if we assume - this, it does not necessarily follow that there is a definition of anything which means - the same as any formula; it must mean the same as a particular kind of formula, i.e. the - formula of one thing— one not by - continuity like the Iliad, or things which are arbitrarily combined, but in - one of the proper senses of "one." And "one" has the same variety of senses as "being." - "Being" means sometimes the individual thing, sometimes the quantity, sometimes the - quality. Hence even "white man" will have a formula and definition; but in a different - sense from the definition of "whiteness" and "substance." The question arises: If one denies that a - formula involving an added determinant is a definition, how can there be a definition of - terms which are not simple but coupled? Because they can only be explained by adding a - determinant. I mean, e.g., there is "nose" - and "concavity" and "snubness," the term compounded of the two, because the one is present - in the other. Neither "concavity" nor "snubness" is an accidental, but a per se affection - of the nose.Snubness is a per se affection of the - nose, because it applies only to the nose and cannot be explained apart from it, but the - same can hardly be said of concavity. Aristotle himself uses the word (koilo/ths) elsewhere in other connections. Nor are they attributes in the sense that "white" is of - Callias or a man, because Callias is white and is by accident a man; but in the sense that - "male" is an attribute of animal, and equality of quantity, and all other attributes which - we say belong per se. That is, all things which - involve the formula or name of the subject of the affection, and cannot be explained apart - from it. Thus "white" can be explained apart from "man," but not "female" apart from - "animal." Thus either these terms have no essence or definition, or else they have it in a - different sense, as we have said. But there is also another difficulty about them. If "snub nose" is the - same as "concave nose," "snub" will be the same as "concave." But if not, since it is - impossible to speak of "snub" apart from the thing of which it is a per se affection - (because "snub" means a concavity in the nose), either it is impossible to call the nose - snub, or it will be a tautology, "concave-nose nose" because "snub nose" will equal - "concave-nose nose." Hence it is absurd that - such terms as these should have an essence. Otherwise there will be an infinite - regression; for in "snub-nose nose" there will be yet another nose. Clearly, then, there is - definition of substance alone. If there were definition of the other categories also, it - would have to involve an added determinant, as in the case of the qualitative; and of the - odd, for this cannot be defined apart from number; nor can "female" apart from - "animal." By "involving an added determinant" - I mean descriptions which involve a tautology, as in the above examples. Now if this is - true, there will be no definition of compound expressions either; e.g., "odd number." We - fail to realize this because our terms are not used accurately. If on the other hand there - are definitions of these too, either they are defined in a different way, or, as we have - said, "definition" and "essence" must be used in more than one sense; thus in one sense there will be no definition of anything, and - nothing will have an essence, except substances; and in another those other things will - have a definition and essence. It is obvious, then, that the definition is the formula of - the essence, and that the essence belongs either only to substances, or - especially and primarily and simply. We must inquire whether the essence is the same as the - particular thing, or different. This is useful for our inquiry about substance; because a - particular thing is considered to be nothing other than its own substance, and the essence - is called the substance of the thing. In - accidental predications, indeed, the thing itself would seem to be different from its - essence; e.g., "white man" is different from - "essence of white man." If it were the same, "essence of man" and "essence of white man" - would be the same. For "man" and "white man" are the same, they say, and therefore - "essence of white man" is the same as "essence of man." But perhaps it is not necessarily true that the essence of accidental - combinations is the same as that of the simple terms; because the extremes of the - syllogism are not identical with the middle term in the same way.The argument consists of two syllogisms: White=essence of white man. - Man=white man. Therefore man=essence of white man. But essence of man=man. Therefore - essence of man=essence of white man. The conclusion is faulty because whereas the first - identity is assumed to be absolute, the second is accidental. Perhaps it might be - thought to follow that the accidental extremes are identical; e.g. "essence of white" and - "essence of cultured"; but this is not admitted.Aristotle seems to mean that both "essence of white man and "essence of cultured man" - might be proved by the former syllogism to be identical in the same way with the middle - term "man," in which case it would seem that "essence of white" and "essence of - cultured" are the same. There is, however, the same fallacy as before. But in per se - expressions, is the thing necessarily the same as its essence, e.g., if there are - substances which have no other substances or entities prior to them, such as some hold the - Ideas to be? For if the Ideal Good is to be - different from the essence of good, and the Ideal Animal and Being from the essence of - animal and being, there will be other substances and entities and Ideas besides the ones - which they describe; and prior to them, if essence is substance. And if they are separate - from each other, there will be no knowledge of the Ideas, and the essences will not - exist (by "being separate" I mean if neither - the essence of good is present in the Ideal Good, nor "being good" in the essence of - good); for it is when we know the essence of it that we have knowledge of a thing. And it - is the same with other essences as with the essence of good; so that if the essence of - good is not good, neither will the essence of being "be," nor the essence of one be - one. Either all essences exist alike, or none - of them; and so if not even the essence of being "is," neither will any other essence - exist. Again that to which "essentially good" does not apply cannot be good. Hence "the - good" must be one with the essence of good, "the beautiful" with the essence of beauty, - and so with all terms which are not dependent upon something else, but self-subsistent and - primary.The example of the Ideas as per se terms - is used by Aristotle to show incidentally the fallacy of the Ideal theory: there can be - no self-subsistent entity apart from the essence. For it is enough if this is so, even if they are not Forms; or perhaps - rather even if they are. (At the same time it is clear also that if the Ideas are such as - some hold, the substrate will not be substance; for the Ideas must be substances, but not - involving a substrate, because if they did involve one they would exist in virtue of its - participation in them.)This criticism is irrelevant - to the point under discussion. It simply points out that the Ideal theory conflicts with - received opinion (cf. Aristot. Met. - 7.3.1). That each individual thing is one and the same with its essence, and - not merely accidentally so, is apparent, not - only from the foregoing considerations, but because to have knowledge of the individual is - to have knowledge of its essence; so that by setting out examples it is evident that both - must be identical. But as for the accidental - term, e.g. "cultured" or "white," since it has two meanings, it is not true to say that - the term itself is the same as its essence; for both the accidental term and that of which - it is an accident are "white," so that in one sense the essence and the term itself are - the same, and in another they are not, because the essence is not the same as "the man" or - "the white man," but it is the same as the affection. The absurdity <of separating a thing - from its essence> will be apparent also if one supplies a name for each essence; for - then there will be another essence besides the original one, e.g. the essence of "horse" - will have a further essence. Yet why should not some things be identified with their - essence from the outset,i.e. to avoid the infinite - series implied in the last sentence. if essence is substance? Indeed not only are - the thing and its essence one, but their formula is the same, as is clear from what we have - just stated; for it is not by accident that the essence of "one," and "the one," are - one. Moreover, if they are different, there - will be an infinite series; for the essence of "one" and "the one" will both exist; so - that in that case too the same principle will apply.i.e. since there is a distinct term "essence of one" besides "one," there will be a - third distinct term "essence of essence of one"; and so on as in the case of "horse" - above. Clearly, then, in the case of primary and self-subsistent terms, the - individual thing and its essence are one and the same. It is obvious that the sophistical - objections to this thesis are met in the same way as the question whether Socrates is the - same as the essence of Socrates; for there is no difference either in the grounds for - asking the question or in the means of meeting it successfully. We have now explained in - what sense the essence is, and in what sense it is not, the same as the individual - thing. Of - things which are generated, some are generated naturally, others artificially, and others - spontaneously; but everything which is generated is generated by something and from - something and becomes something. When I say "becomes something" I mean in any of the - categories; it may come to be either a particular thing or of some quantity or quality or - in some place. Natural generation is the generation of - things whose generation is by nature. That from - which they are generated is what we call matter; that by which, is something which exists - naturally; and that which they become is a man or a plant or something else of this kind, - which we call substance in the highest degree. All things which are generated naturally or artificially have matter; for it is possible - for each one of them both to be and not to be, and this possibility is the matter in each - individual thing. And in general both that from - which and that in accordance with which they are generated, is nature; for the thing - generated, e.g. plant or animal, has a nature. And that by which they are generated is the - so-called "formal" nature, which has the same form as the thing generated (although it is - in something else); for man begets man. Such is the - generation of things which are naturally generated; the other kinds of generation are - called productions. All productions proceed from either art or potency or - thought. Some of them are also generated - spontaneously and by chance in much the same way as things which are naturally generated; - for sometimes even in the sphere of nature the same things are generated both from seed - and without it.e.g. fish (Aristot. Hist. An. 569a 11) and insects (Aristot. Hist. An. 539a 24). We shall consider - cases of this kind later.In Aristot. Met. 7.9. - Things are - generated artificially whose form is contained in the soul (by "form" I mean the essence - of each thing, and its primary substance); for - even contraries have in a sense the same form.The - logical connection is: It is sufficient to say that the form of objects which are - artificially produced is contained in the soul; for although artificial production can - produce contrary effects, the form of the positive effect is the absence of the form of - the negative effect, so that in a sense they have the same form. For the - substance of the privation is the opposite substance; e.g., health is the substance of - disease; for disease is the absence of health, and health is the formula and knowledge in - the soul. Now the healthy subject is produced as the result of this reasoning: since - health is so-and-so, if the subject is to be healthy, it must have such-and-such a - quality, e.g. homogeneity; and if so, it must have heat. And the physician continues reasoning until he arrives at what he - himself finally can do; then the process from this point onwards, i.e. the process towards - health, is called "production." Therefore it follows in a sense that health comes from - health and a house from a house; that which has matter from that which has not (for the - art of medicine or of building is the form of health or the house). By - substance without matter I mean the essence. In generations and motions part of the process is - called cogitation, and part production—that which proceeds from the starting-point - and the form is cogitation, and that which proceeds from the conclusion of the cogitation - is production. Each of the other intermediate measures is carried out in the same way. I - mean, e.g., that if A is to be healthy, his physical condition will have to be made - uniform. What, then, does being made uniform entail? So-and-so; and this will be achieved if he is made hot. What does this - entail? So-and-so; now this is potentially present, and the thing is now in his - power. The - thing which produces, and from which the process of recovering health begins, is the form - in the soul, if the process is artificial; if spontaneous, it is whatever is the - starting-point of the production for the artificial producer; as in medical treatment the - starting-point is, perhaps, the heating of the patient; and this the doctor produces by - friction. Heat in the body, then, is either a part of health, or is followed (directly or - through several intermediaries) by something similar which is a part of health. This is - the ultimate thing, namely that produces, and in this sense is a part of, health—or - of the house (in the form of stones)There is no real analogy between the casual - relationship of heat to health and of stones to a house. The former is both material and - efficient; the latter only material. Cf. Aristot. Met. - 7.9.1. or of other things. Therefore, as we say, generation would be - impossible if nothing were already existent. It is clear, then, that some part must - necessarily pre-exist; because the matter is a part, since it is matter which pre-exists - in the product and becomes something. But then is matter part of the formula? Well, we define - bronze circles in both ways; we describe the matter as bronze, and the form as - such-and-such a shape; and this shape is the proximate genus in which the circle is - placed. The bronze circle, then, has its - matter in its formula. Now as for that from which, as matter, things are generated, some - things when they are generated are called not "so-and-so," but "made of so-and-so"; e.g., - a statue is not called stone, but made of stone. But the man who becomes healthy is not - called after that from which he becomes healthy. This is because the generation proceeds - from the privation and the substrate, which we call matter (e.g., both "the man" and "the - invalid" become healthy), but it is more - properly said to proceed from the privation; e.g., a man becomes healthy from being an - invalid rather than from being a man. Hence a healthy person is not called an invalid, but - a man, and a healthy man. But where the privation is obscure and has no name—e.g. in - bronze the privation of any given shape, or in bricks and wood the privation of the shape - of a house—the generation is considered to proceed from these materials, as in the - former case from the invalid. Hence just as in - the former case the subject is not called that from which it is generated, so in this case - the statue is not called wood, but is called by a verbal change not wood, but wooden; not - bronze, but made of bronze; not stone, but made of stone; and the house is called not - bricks, but made of bricks. For if we consider - the matter carefully, we should not even say without qualification that a statue is - generated from wood, or a house from bricks; because that from which a thing is generated - should not persist, but be changed. This, then, is why we speak in this way. Now since that which is - generated is generated by something (by which I mean the starting-point of - the process of generation), and from something (by which let us understand - not the privation but the matter; for we have already distinguished the meanings of - these), and becomes something (i.e. a sphere or circle or whatever else it - may be); just as the craftsman does not produce the substrate, i.e. the bronze, so neither - does he produce the sphere; except accidentally, inasmuch as the bronze sphere is a - sphere, and he makes the former. For to make an - individual thing is to make it out of the substrate in the fullest sense. I mean that to - make the bronze round is not to make the round or the sphere, but something else; i.e. to - produce this form in another medium. For if we make the form, we must make it out of - something else; for this has been assumed. E.g., we make a bronze sphere; we do this in the sense - that from A, i.e. bronze, we make B, i.e. a sphere. If, then, we make the spherical form itself, clearly we shall have to - make it in the same way; and the processes of generation will continue to - infinity. It is therefore obvious that the form (or - whatever we should call the shape in the sensible thing) is not generated—generation - does not apply to it— nor is the essence generated; for this is that which is - induced in something else either by art or by nature or by potency. But we do cause a bronze sphere to be, for we produce it from - bronze and a sphere; we induce the form into this particular matter, and the result is a - bronze sphere. But if the essence of sphere in general is generated, something must be - generated from something; for that which is generated will always have to be divisible, - and be partly one thing and partly another; I mean partly matter and partly - form. If then a sphere is the figure whose - circumference is everywhere equidistant from the center, part of this will be the medium - in which that which we produce will be contained, and part will be in that medium; and the - whole will be the thing generated, as in the case of the bronze sphere. It is obvious, - then, from what we have said, that the thing in the sense of form or essence is not - generated, whereas the concrete whole which is called after it is generated; and that in - everything that is generated matter is present, and one part is matter and the other - form. Is there then some sphere besides the - particular spheres, or some house besides the bricks? Surely no individual thing would - ever have been generated if form had existed thus independently.If forms are self-subsistent substances, individual substances cannot be - generated from them; for the individual contains the form, but one substance cannot - contain another actually existing substance (Aristot. - Met. 7.8.8). Form, however, is not a substance but a characteristic. - Form means "of such a kind"; it is not a definite individual, but we produce or generate - from the individual something "of such a kind"; and when it is generated it is an - individual "of such a kind." The whole - individual, Callias or Socrates, corresponds to "this bronze sphere," but "man" and - "animal" correspond to bronze sphere in general. Obviously - therefore the cause which consists of the Forms (in the sense in which some speak of them, - assuming that there are certain entities besides particulars), in respect at least of - generation and destruction, is useless; nor, for this reason at any rate, should they be - regarded as self-subsistent substances. Indeed - in some cases it is even obvious that that which generates is of the same kind as that - which is generated—not however identical with it, nor numerically one with it, but - formally one—e.g. in natural productions (for man begets man), unless something - happens contrary to nature, as when a horse sires a mule. And even these cases are - similar; for that which would be common to both horse and ass, the genus immediately above - them, has no name; but it would probably be both, just as the mule is both.Normally the sire communicates his form to the - offspring. In the case of a mule, the material element contributed by the dam, which is - an ass, limits the effect of the formal element contributed bu the sire, which is a - horse; but even so the form of the sire is generically the same as that of the - offspring. - Thus obviously there is - no need to set up a form as a pattern (for we should have looked for Forms in these cases - especially, since living things are in a special sense substances); the thing which - generates is sufficient to produce, and to be the cause of the form in the matter. The - completed whole, such-and-such a form induced in this flesh and these bones, is Callias or - Socrates. And it is different from that which generated it, because the matter is - different but identical in form, because the form is indivisible. The question might be raised - why some things are generated both artificially and spontaneously—e.g. - health—and others not; e.g. a house. The reason is that in some cases the - matter—which is the starting-point of the process in the production and generation - of artificial things, and in which some part of the result is already existent—is - such that it can initiate its own motion, and in other cases it is not; and of the former - kind some can initiate motion in a particular way, and some cannot. For many things can - move themselves, but not in a particular way, e.g. so as to dance. It is impossible, then, for any things whose matter is of this - kind (e.g. stones) to be moved in this particular way except by something - else; but in that particular way it is possible. And it is so with fire.Stones can fall by themselves, but cannot by themselves - build a house; fire can rise by itself, but cannot boil a kettle. For this reason - some things cannot exist apart from the possessor of the art, and others can; because the motion can be initiated by those things - which do not indeed possess the art, but can themselves be moved either by other things - which do not possess the art, or by the motion from the part of the product which - pre-exists in them.e.g., health can be produced as - the result of the activity set up by heat in the body. It is clear also from what we - have said that in a sense all artificial things are generated either from something which - bears the same name (as is the case with natural objects) or from a part of themselves - which bears the same name as themselves (e.g. a house from a house, inasmuch as it is - generated by mind; for the art is the form), or from something which contains some part; - that is if the generation is not accidental; for the direct and independent cause of the - production is a part of the product. Heat in - the motion produces heat in the body; and either this is health or a part of health, or a - part of health or health accompanies it. And this is why heat is said to produce health, - because it produces that of which health is a concomitant and consequence. Therefore as - essence is the starting-point of everything in syllogisms (because syllogisms start from - the "what" of a thing), so too generation proceeds from it. And it is the same with natural formations - as it is with the products of art. For the seed produces just as do those things which - function by art. It contains the form potentially, and that from which the seed comes has in - some sense the same name as the product (for we must not expect that all should have the - same name in the sense that "man" is produced by "man"—since woman is also produced - by man); unless the product is a freak. This is why a mule is not produced by a - mule. Those - natural objects which are produced, like artificial objects, spontaneously, are those - whose matter can also initiate for itself that motion which the seed initiates. Those - whose matter cannot do this cannot be generated otherwise than by their proper - parents. It is not only with reference to substance that - our argument shows that the form is not generated; the same argument is common in its - application to all the primary divisions, i.e. quantity, quality and the other - categories. For just as the bronze sphere is - generated, but not the sphere nor the bronze; and as in the case of bronze, if it is - generated the form and matter are not (because they must always pre-exist), so it is too - with the "what" and the quality and quantity and the other categories similarly; for it is - not the quality that is generated, but the wood of that quality; nor is it the size, but - the wood or animal of that size. But a - peculiarity of substance may be gathered from this: that some other substance must - pre-exist in actuality which produces it; e.g. an animal, if an animal is being generated; - but a quality or quantity need not pre-exist otherwise than potentially. Since a definition is a formula, and every formula has parts; and - since the formula is related to the thing in the same way as the part of the formula to - the part of the thing, the questionThe questions - discussed in chs. 10-12 arise out of the consideration of essence as definition. - now arises: Must the formula of the parts be contained in the formula of the whole, or - not? It seems clear that it is so in some cases, but not in others. The formula of the circle does not include that of the - segments, but the formula of the syllable includes that of the letters. And yet the circle - is divisible into its segments in just the same way as the syllable into its - letters. Again, if the parts are prior to the whole, and - the acute angle is part of the right angle, and the finger part of the animal, the acute - angle will be prior to the right angle, and the finger to the man. But it is considered that the latter are prior; for in the - formula the parts are explained from them; and the wholes are prior also in virtue of - their ability to exist independently. The truth probably is that "part" has several - meanings, one of which is "that which measures in respect of quantity." However, let us - dismiss this question and consider of what, in the sense of parts, substance consists. - If then - matter, form, and the combination of the two are distinct, and if both matter and form and - their combination are substance, there is one sense in which even matter may be called - "part" of a thing; and another in which it is not, but the only parts are those elements - of which the formula of the form consists. E.g., flesh is not a part of concavity, because - flesh is the matter in which concavity is induced; but it is a part of snubness. And - bronze is part of the statue as a concrete whole, but not of the statue in the sense of - form. We may speak of the form (or the thing - as having a form) as an individual thing, but we may never so speak of that which is - material by itself. This is why the formula of the circle does not contain that of the - segments, whereas the formula of the syllable does contain that of the letters; for the - letters are parts of the formula of the form; they are not matter; but the segments are - parts in the sense of matter in which the form is induced. They approximate, however, more - closely to the form than does the bronze when roundness is engendered in bronze. But there is a sense in which not even all the letters - will be contained in the formula of the syllable; e.g. particular letters on waxi.e. written on a waxed tablet. or sounds in the - air; for these too are part of the syllable in the sense that they are its sensible - matter. For even if the line is divided and - resolved into its halves, or if the man is resolved into bones and muscles and - flesh, it does not follow that they are - composed of these as parts of their essence, but as their matter; and these are parts of - the concrete whole, but not of the form, or that to which the formula refers. Hence they - are not in the formulae. Accordingly in some - cases the formula will include the formula of such parts as the above, but in others it - need not necessarily contain their formula, unless it is the formula of the concrete - object. It is for this reason that some things are composed of parts in the sense of - principles into which they can be resolved, while others are not. All things which are concrete combinations of form and matter - (e.g. "the snub" or the bronze circle) can be resolved into form and matter, and the - matter is a part of them; but such as are not concrete combinations with matter, but are - without matter—whose formulae refer to the form only—cannot be resolved; - either not at all, or at least not in this way. Thus these material components are principles and parts of the - concrete objects, but they are neither parts nor principles of the form. For this reason - the clay statue can be resolved into clay, and the sphere into bronze, and Callias into - flesh and bones, and the circle too into segments, because it is something which is - combined with matter. For we use the same name for the absolute circle and for the particular - circle, since there is no special name for the particular circles. We have now stated the truth; - nevertheless let us recapitulate and state it more clearly. All constituents which are - parts of the formula, and into which the formula can be divided, are prior to their - wholes—either all or some of them. But the formula of the right angle is not - divisible into the formula of an acute angle, but vice versa; since in defining the acute - angle we use the right angle, because "the acute angle is less than a right - angle." It is the same with the circle and - the semicircle; for the semicircle is defined by means of the circle. And the finger is - defined by means of the whole body; for a finger is a particular kind of part of a man. - Thus such parts as are material, and into which the whole is resolved as into matter, are - posterior to the whole; but such as are parts in the sense of parts of the formula and of - the essence as expressed in the formula, are prior; either all or some of them. And since the soul of animals (which is the substance - of the living creature) is their substance in accordance with the formula, and the form - and essence of that particular kind of body (at least each part, if it is to be properly - defined, will not be defined apart from its function; and this will not belong to it apart - from perceptionWhich implies soul.); - therefore the parts of the soul are prior, either all or some of them, to the concrete - animal; and similarly in other individual cases. But the body and its parts are posterior - to this substance, and it is not the substance, but the concrete whole, which is resolved - into these parts as into matter. Therefore in one sense these parts are prior to the - concrete whole, and in another not; for they cannot exist in separation. A finger cannot - in every state be a part of a living animal; for the dead finger has only the name in - common with the living one. Some parts are - contemporary with the whole: such as are indispensable and in which the formula and the - essence are primarily present; e.g. the heart or perhaps the brain,Cf. Aristot. Met. 5.1.1. - for it does not matter which of them is of this nature. But "man" and "horse" and terms - which are applied in this way to individuals, but universally, are not substance, but a - kind of concrete whole composed of this particular formula and - this particular matter regarded as universal. But individually Socrates is - already composed of ultimate matter; and similarly in all other cases. A part, then, may be part of - the form (by form I mean essence), or of the concrete whole composed of form and matter, - or of the matter itself. But only the parts of the form are parts of the formula, and the - formula refers to the universal; for "circle" is the same as "essence of circle," and "soul" the - same as "essence of soul." But when we come - to the concrete thing, e.g. this circle—which is a particular individual, either - sensible or intelligible (by intelligible circles I mean those of mathematics,i.e., something very similar to the Platonic - "intermediates." Cf. Introduction. and by sensible those which are of bronze or - wood)—of these individuals there is no definition; we apprehend them by intelligence or perception; and when they have - passed from the sphere of actuality it is uncertain whether they exist or not, but they - are always spoken of and apprehended by the universal formula. But the matter is in itself - unknowable. Some matter is sensible and some intelligible; sensible, such as bronze and - wood and all movable matter; intelligible, that which is present in sensible things not - qua sensible, e.g. the objects of mathematics.See Aristot. Met. - 13.2, 3. We have now discussed the case of the whole and part, and of prior and - posterior. But we must answer the question, when we are asked which is prior—the - right angle and circle and animal, or that into which they are resolved and of which they - are composed, i.e. their parts—by saying that neither is absolutely - prior. For if the soul also is - the animal or living thing, or the soul of the individual is the individual, - and "being a circle" is the circle, and "being a right angle" or the essence - of the right angle is the right angle, then we must admit that the whole in - one sense is posterior to the part in one sense: e.g. to the parts in the formula and the parts of a particular right angle (since both the material right angle of bronze and - the right angle included by individual lines are posterior to their parts), but the - immaterial angle is posterior to the parts in the formula, but prior to the parts in the - individual. We must not give an unqualified answer. And if the soul is not the animal but - something else, even so we must say that some wholes are prior and some are not, as has - been stated. The question naturally presents itself, what sort of parts belong to the form and what - sort belong not to it but to the concrete object. Yet if this is not plain it is - impossible to define the particular; because the definition refers to the universal and - the form. Therefore if it is not clear what kind of parts are material and what kind are - not, the formula of the thing will not be clear either. In the case of things which can be seen to be induced in specifically - different materials, as, e.g., a circle is in bronze and stone and wood, it seems clear - that these things, the bronze and the stone, are in no sense part of the essential - substance of the circle, because it is separable from them. As for things which are not visibly separable, there is no reason why - the same should not apply to them; e.g., if all the circles that had ever been seen were - bronze; for - the bronze would be none the less no part of the form, but it is difficult to separate it - in thought. For example, the form of "man" is - always manifested in flesh and bones and elements of this kind; then are these actually - parts of the form and formula, or are they not so, but matter, though since the form is - not induced in other materials, we cannot separate it? Now since this seems to be possible, but it is not clear - when, some thinkersThe - Pythagoreans. are doubtful even in the case of the circle and the triangle, - considering that it is not proper to define them by lines and continuous space, but that - all these are to the circle or triangle as flesh or bone is to man, and bronze or stone to - the statue; and they reduce everything to numbers, and say that the formula of "line" is - the formula of 2. And of the exponents of the - Forms, some make 2 the Ideal line, and some the form of the lineThe distinction seems to be that given in Aristot. Met. 8.3.1. Some held that the line, considered absolutely, is simply - "twoness"; others that it is "twoness in length."; for they say that in some - cases the form and that of which it is the form, e.g. 2 and the form of 2, are the same; - but in the case of "line" this is no longer so. It follows, then, that there is one form of many things whose form is clearly different - (a consequence which confronted the Pythagoreans tooCf. Aristot. Met. 1.5.17.), and that it is - possible to make one supreme Form of everything, and not to regard the rest as - forms. In this way, however, all things would - be one. Now we - have stated that the question of definitions involves some difficulty, and have shown why - this is so. Hence to reduce everything in this way and to dispose of the matter is going - too far; for some things are presumably a particular form in particular matter, or - particular things in a particular state. And - the analogy in the case of the living thing which the younger SocratesA "disciple" of the great Socrates; one of the speakers - in the PoliticusPlat. Stat. and referred to in Plat. Theaet. 147c, Plat. - Soph. 218b. used to state is not a good one; for it leads one away from - the truth, and makes one suppose that it is possible for a man to exist without his parts, - as a circle does without the bronze. But the case is not similar; for the animal is - sensible and cannot be defined without motion, and hence not unless its parts are in some - definite condition; for it is not the hand in - any condition that is a part of a man, but only when it can perform its - function, and so has life in it. Without life in it it is not a part. And with respect to mathematical objects, why are the formulae of the parts - not parts of the formulae of the whole; e.g., why are the formulae of the semicircles not - parts of the formula of the circle? for they are not sensible. Probably this makes no difference; because there will be matter even - of some things which are not sensible. Indeed there will be matter in some sense in everything - which is not essence or form considered independently, but a particular thing. Thus the - semicircles will be parts not of the universal circle but of the particular circles, as we - said beforeAristot. - Met. 7.10.17.—for some matter is sensible, and some - intelligible. It is clear also that the - soul is the primary substance, and the body matter; and "man" or "animal" is the - combination of both taken universally. And " Socrates" or "Coriscus" has a double sense, - that is if the soul too can be called Socrates (for by Socrates some mean the soul and - some the concrete person); but if Socrates means simply this soul and - this body, the individual is composed similarly to the universal. Whether there is some - other material component of these substances besides their matter, and whether we should - look for some further substance in them, such as numbers or something of that kind, must - be considered later.In Books 13 and 14. It - is with a view to this that we are trying to determine the nature of sensible substances, - since in a sense the study of sensible substances belongs to physics or secondary - philosophy; for the physicist must know not only about the matter, but also about the - substance according to the formula; this is even more essential. And in the case of definitions, in what sense the elements in - the formula are parts of the definition, and why the definition is one formula (for the - thing is clearly one, but in virtue of what is - it one, seeing that it has parts?); this must be considered later.Aristot. Met. - 8.6. We have stated, then, in a general account which covers all cases, - what essence is, and how it is independent; and why the formula of the essence of some - things contains the parts of the thing defined, while that of others does not; and we have - shown that the material parts of a thing cannot be present in the formula of the substance - (since they are not even parts of the substance in that sense, but of the concrete - substance; and of this in one sense there is a formula, and in another sense there is - not. There is no formula involving the - matter, for this is indeterminate; but there is a formula in accordance with the primary - substance, e.g., in the case of a man, the formula of the soul; because the substance is - the indwelling form, of which and of the matter the so called concrete substance is - composed. E.g., concavity is such a form, since from this and "nose" is derived "snub - nose" and "snubness"—for "nose" will be present twice over in these - expressions); but in the concrete - substance, e.g. snub nose or Callias, matter will be present too.Chapters. 10-11; and cf. Aristot. Met. - 7.4. We have stated also that the essence and the individual are in some - cases the same, as in the case of the primary substances; e.g. crookedness and "essence of - crookedness," if this is primary. By primary - I mean that which does not imply the presence of something in something else as a material - substrate. But such things as are material or are compounded with matter are not the same - as their essence; not even if they are accidentally one, e.g. Socrates and "cultured"; for - these are only accidentally the same. Now let us first deal with definition, in so far as it has not - been dealt with in the Analytics; for the problem stated thereAristot. An. Post. 92a - 29. has a bearing upon our discussion of substance. The problem I mean - is this: what constitutes the unity of the thing of which we say that the formula is a - definition? E.g., in the case of man, "two-footed animal"; for let us take this as the - formula of "man." Why, then, is this a unity - and not a plurality, "animal" and "two-footed"? For in the case of "man" and "white" we - have a plurality when the latter does not refer to the former, but a unity when it does - refer to it, and the subject, "man," has an attribute; for then they become a unity and we - have "the white man." But in the case before - us one term does not partake of the other; the genus is not considered to partake of its - differentiae, for then the same thing would be partaking simultaneously of - contraries, since the differentiae by which - the genus is distinguished are contrary. And even if it does partake of them, the same - argument applies, since the differentiae are many; e.g. terrestrial, two-footed, - wingless. Why is it that these are a unity - and not a plurality? Not because they are present in one genus, for in that case all the - differentiae of the genus will form a unity. But all the elements in the definition must - form a unity, because the definition is a kind of formula which is one and defines - substance, so that it must be a formula of one particular thing; because the substance - denotes one thing and an individual, as we say. We must - firstThe other type of definition, that which - states the constituent parts of a thing, is not discussed here. examine - definitions which are reached by the process of division. For there is nothing else in the definition but the primary genus and - the differentiae; the other genera consist of the primary genus together with the - differentiae which are taken with it. E.g., the primary genus is "animal"; the next below - it, "two-footed animal"; and again, "two-footed wingless animal"; and similarly also if - the expression contains more terms still. In general - it does not matter whether it contains many or few terms, nor, therefore, whether it - contains few or two. Of the two one is differentia and the other genus; e.g., in - "two-footed animal" "animal" is genus, and the other term differentia. If, then, the genus absolutely does not exist apart from the - species which it includes, or if it exists, but only as matter (for speech is genus and - matter, and the differentiae make the species, i.e. the letters, out of it), obviously the - definition is the formula composed of the differentiae. But further we must also divide by the - differentia of the differentia. E.g., "having feet" is a differentia of "animal"; then in - turn we must discover the differentia of "animal having feet" qua - "having feet." Accordingly we should not say that of "that which has feet" one kind is - winged and another wingless, (that is if we are to speak correctly; if we say this it will - be through incapability), but only that one kind is cloven-footed and another not; because - these are differentiae of "foot," since cloven-footedness is a kind of - footedness. And thus we tend always to - progress until we come to the species which contain no differentiae. At this point there - will be just as many species of foot as there are differentiae, and the kinds of animals - having feet will be equal in number to the differentiae. Then, if this is so, obviously the ultimate differentia will be the substance - and definition of the thing, since we need not state the same things more than once in - definitions, because this is superfluous. However, it does happen; for when we say "footed two-footed animal" we have simply said - "animal having feet, having two feet." And if we divide this by its proper division, we - shall be stating the same thing several times, as many times as there are - differentiae. If, then, we keep on taking a differentia of a differentia, one of them, the last, will - be the form and the substance. But if we proceed with reference to accidental - qualities—e.g. if we divide "that which has feet" into white and black—there - will be as many differentiae as there are divisions. It is therefore obvious that the - definition is the formula derived from the differentiae, and strictly speaking from the - last of them. This will be clear if we change - the order of such definitions, e.g. that of man, saying "two-footed footed animal"; for - "footed" is superfluous when we have already said "two-footed." But there is no question - of order in the substance; for how are we to think of one part as posterior and the other - prior? With regard, then, to definitions by division, let - this suffice as a preliminary statement of their nature. Since the subject of our inquiry is - substance, let us return to it. Just as the substrate and the essence and the combination - of these are called substance, so too is the universal. With two of these we have already - dealt, i.e. with the essenceChs. 4-5.,10-12. - and the substrateCh. 3.; of the latter we - have said that it underlies in two senses—either being an individual thing (as the - animal underlies its attributes), or as matter underlies the actuality. The universal also is thought by someThe Platonists. to be in the truest sense a cause and a principle. - Let us therefore proceed to discuss this question too; for it seems impossible that any - universal term can be substance. First, the substance of an - individual is the substance which is peculiar to it and belongs to nothing else; whereas - the universal is common; for by universal we mean that which by nature appertains to - several things. Of what particular, then, will - the universal be the substance? Either of all or of none. But it cannot be the substance - of all; while, if it is to be the substance of one, the rest also will be that one; - because things whose substance is one have also one essence and are themselves - one. Again, substance means that which is not predicated - of a subject, whereas the universal is always predicated of some subject. But perhaps although the universal cannot be substance in the sense that - essence is, it can be present in the essence, as "animal" can be present in "man" and - "horse." Then clearly there is in some sense - a formula of the universal. It makes no difference even if there is not a formula of everything that is in the substance; for - the universal will be none the less the substance of something; e.g., "man" will be the - substance of the man in whom it is present. Thus the same thing will happen againi.e., the argument in ch. 3 will apply to this case - also.; e.g. "animal" will be the substance of that in which it is present as - peculiar to it. Again, it is impossible and absurd that the individual or substance, if it is composed - of anything, should be composed not of substances nor of the individual, but of a quality; - for then non-substance or quality will be prior to substance or the individual. Which is - impossible; for neither in formula nor in time nor in generation can the affections of - substance be prior to the substance, since then they would be separable. Again, a substance will be - present in "Socrates," who is a substance; so that it will be the substance of two things. - And in general it follows that if "man" and all terms used in this way are substance, none - of the elements in the formula is the substance of anything, nor can it exist apart from - the species or in anything else; I mean, e.g., that neither "animal" nor any other element - of the formula can exist apart from the particular species. If we look at the question from this - standpoint it is obvious that no universal attribute is substance; and it is also clear - from the fact that none of the common predicates means "so-and-so," but "such and-such." Otherwise - amongst many other awkward consequences we have the "third man."See note on Aristot. Met. - 1.9.3. Again, it is clear in this way too. Substance can not consist of - substances actually present in it; for that which is actually two can never be actually - one, whereas if it is potentially two it can be one. E.g., the double consists of two - halves—that is, potentially; for the actualization separates the halves. Thus if substance is one, it cannot consist of - substances present in it even in this sense, as Democritus rightly observes; he says that - it is impossible for two to come from one, or one from two, because he identifies - substance with the atoms.Cf. Aristot. De Caelo 303a 6, Aristot. De Gen. et Corr. 325a 35. Clearly then the same will also hold good in the case - of number (assuming that number is a composition of units, as it is said to be by some); - because either 2 is not 1, or there is not actually a unit in it. The consequence - involves a difficulty; for if no substance can consist of universals, because they mean - "of such a kind," and not a particular thing; and if no substance can be actually composed - of substances, every substance will be incomposite, and so there will be no formula of any - substance. But in point of fact it is - universally held, and has been previously stated,Aristot. Met. 7.5.5-7. that substance is the only or chief subject of definition; but - on this showing there is no definition even of substance. Then there can be no definition - of anything; or rather in a sense there can, and in a sense cannot. What this means will - be clearer from what follows later.Aristot. Met. 7.15, Aristot. Met. 8.6. From these same considerations it is clear also what - consequence follows for those who maintain that the Forms are substances and separable, - and who at the same time make the species consist of the genus and the differentiae. If - there are Forms, and if "animal" is present in the man and the horse, it is either - numerically one and the same with them, or not. (In formula they are clearly one; for in each case the speaker will enunciate the same - formula.) If, then, there is in some sense an Absolute Man, who is an individual and - exists separately, then the constituents, e.g. "animal" and "two-footed," must have an - individual meaning and be separable and substances. Hence there must be an Absolute Animal - too. (i) Then - if the "animal" which is in the horse and the man is one and the same, as you are one and - the same with yourself, how can the one which in things that exist separately be one, and why - should not this "animal" also be separated from itself? Again, if it is to partake of - "two-footed" and of "many-footed," an impossibility follows; for contrary attributes will - belong to it although it is one and individual. But if it does not, in what sense is it that one calls an animal "two-footed" or - "terrestrial"? Perhaps the terms are "combined" and "in contact" or "mixed." But all these - expressions are absurd. (2) "But there is a different - 'animal' in each species." Then there will be practically an infinity of things of which - "animal" is the substance, since it is not in an accidental sense that "man" is derived - from "animal." Again, the Absolute Animal will - be a plurality. For (a) the "animal" in each species will be the substance of that - species, since the species is called after it and no other thing. Otherwise "man" would be - derived from that other thing, which would be the genus of "man." (b) Further, all the - constituents of "man" will be Ideas. Then, since nothing can be the Idea of one thing and - the substance of another (for this is impossible), each and every "animal" in the various species will be the Absolute - Animal. Further, from what will these Forms be derived, - and how can they be derived from the Absolute Animal? Or how can "the animal," whose very - essence is "animal," exist apart from the Absolute Animal? And further, in the case of - sensible things both these and still more absurd consequences follow. If, then, these - consequences are impossible, clearly there are not Forms of sensible things in the sense - in which some hold that there are. Since substance is - of two kinds, the concrete thing and the formula (I mean that one kind of substance is the - formula in combination with the matter, and the other is the formula in its full sense), - substances in the former sense admit of destruction, for they also admit of generation. - But the formula does not admit of destruction in the sense that it is ever - being destroyed, since neither does it so admit of generation (for the - essence of house is not generated, but only the essence of this house); - formulae are , and are not, independently of generation and - destruction; for it has been shownCf. Aristot. Met. 7.8.3. that no one either - generates or creates them. For this reason - also there is no definition or demonstration of particular sensible substances, because - they contain matter whose nature is such that it can both exist and not exist. Hence all - the individual instances of them are perishable. If, then, the demonstration and definition of necessary truths - requires scientific knowledge, and if, just as knowledge cannot be sometimes knowledge and - sometimes ignorance (it is opinion that is of this nature), so too demonstration and - definition cannot vary (it is opinion that is concerned with that which can be otherwise - than it is)— then clearly there can be neither definition nor demonstration of - individual sensible substances. For (a) things - which perish are obscure to those who have knowledge of them when they are removed from - the sphere of their perception, and (b) even though their formulae are preserved in the - soul, there will no longer be either definition or demonstration of them. Therefore in - cases relating to definition, when we are trying to define any individual, we must not - fail to realize that our definition may always be upset; because it is impossible to - define these things. Nor, indeed, can any Idea be defined; for the Idea is an individual, - as they say, and separable; and the formula must consist of words, and the man who is - defining must not coin a word, because it would not be comprehensible. But the words which - are in use are common to all the things which they denote; and so they must necessarily - apply to something else as well. E.g., if a man were to define you, he would say that you - are an animal which is lean or white or has some other attribute, which will apply to - something else as well. And if it should be - said that there is no reason why all the attributes separately should not belong to - several things, and yet in combination belong to this alone, we must reply, (1.) that they - also belong to both the elements; e.g., "two-footed animal" belongs both to "animal" and - to "two-footed" (and in the case of eternal elements this is even necessarily so; since - they are prior to the compound, and parts of it. Indeed they are also separable, if the term "man" is - separable—for either neither can be separable, or both are so. If neither, the genus will not exist apart from the species, or - if it is so to exist, so will the differentia); (2.) that "animal" and "two-footed" are - prior in being to "two-footed animal," and that which is prior to something else is not - destroyed together with it. Again, if the Ideas are composed of Ideas (for constituents are less - composite than that which they compose), still the elements of which the Idea is composed - (e.g. "animal" and "two-footed") will have to be predicated of many particulars. - Otherwise, how can they be known? For there would be an Idea which cannot be predicated of - more than one thing. But this is not considered possible; every Idea is thought to admit - of participation. Thus, as we have said,The - statement has only been implied in the preceding arguments. the impossibility of - defining individuals is hard to realize when we are dealing with eternal entities, - especially in the case of such as are unique, e.g. the sun and moon. For people go wrong - not only by including in the definition attributes on whose removal it will still be - sun—e.g., "that which goes round the earth," or "night-hidden " (for they suppose - that if it stops or becomes visiblesc. in the - night. it will no longer be sun; but it is absurd that this should be so, since - "the sun "denotes a definite substance)—they also mention attributes which may apply - to something else; e.g., if another thing with those attributes comes into being, clearly - it will be a sun. The formula, then, is general; but the sun was supposed to be an - individual, like Cleon or Socrates. Why does - not one of the exponents of the Ideas produce a definition of them? If they were to try, - it would become obvious that what we have just said is true. It is obvious that even of those things - which are thought to be substances the majority are potentialities; both the parts of - living things (for none of them has a separate substantial existence; and when they are - separated, although they still exist, they exist as matter), and earth, fire and air; for - none of these is one thing —they are a mere aggregate before they are - digested and some one thing is generated from them. It might be supposed very reasonably that the parts of living things - and the corresponding parts of their vital principle are both, i.e. exist both actually - and potentially, because they contain principles of motion derived from something in their - joints; and hence some animalse.g. wasps, bees, - tortoises (P. Nat. 467a 18, 468a - 25). live even when they are divided. Nevertheless it is only - potentially that all of them will exist when they are one and continuous by nature and not - by force or concretion; for this sort of thing is malformation.i.e., it is only when they do not properly constitute a unity that parts - can be said to exist actually. And since "unity" has the same variety of senses as "being," - and the substance of Unity is one, and things whose substance is numerically one are - numerically one, evidently neither Unity nor Being can be the substance of things, just as - neither "being an element" or "principle" can be the substance; but we ask what the principle is so that we may refer to - something more intelligible.i.e., a thing is a - principle in relation to something else which it explains; therefore a principle is less - substantial than unity or being, which belong to a thing in itself. Now of these concepts Being and Unity are more nearly - substance than are principle, element and cause; but not even the former are quite - substance, since nothing else that is common is substance; for substance belongs to - nothing except itself and that which contains it and of which it is the - substance. Again, Unity cannot exist in many - places at the same time, but that which is common is present in many things at the same - time. Hence it is clear that no universal exists in separation apart from its particulars. - The exponents of the Forms are partly right in their account when they make the Forms - separate; that is, if the Forms are substances, but they are also partly wrong, since by - "Form" they mean the "one-over-many."i.e. - universal; cf. Aristot. Met. - 1.9.1. The reason for this is - that they cannot explain what are the imperishable substances of this kind which exist - besides particular sensible substances; so they make them the same in kind as perishable - things (for these we know); i.e., they make "Ideal Man" and "Ideal Horse," adding the word - "Ideal" to the names of sensible things. However, I presume that even if we had never seen the stars, none the less there would be - eternal substances besides those which we knew; and so in the present case even if we - cannot apprehend what they are, still there must be eternal substances of some - kind. It is clear, then, both that no universal term is - substance and that no substance is composed of substances. As for what and what sort of thing we - mean by substance, let us explain this by making, as it were, another fresh start. Perhaps - in this way we shall also obtain some light upon that kind of substance which exists in - separation from sensible substances. Since, then, substance is a kind of principle and - cause, we had better pursue our inquiry from this point. Now - when we ask why a thing is, it is always in the sense "why does A belong to B?" To ask why the cultured man is a cultured man is to - ask either, as we have said, why the man is cultured, or something else. Now to ask why a - thing is itself is no question; because when we ask the reason of a thing the fact must - first be evident; e.g., that the moon suffers eclipse; and "because it is itself" is the one explanation and reason which - applies to all questions such as "why is man man?" or "why is the cultured person - cultured?" (unless one were to say that each thing is indivisible from itself, and that - this is what "being one" really means); but - this, besides being a general answer, is a summary one.The argument is: The question "Why is the cultured man a cultured man?" - if it does not mean "Why is the man cultured?" can only mean "Why is a - thing itself?" But when we ask a question the fact must be obvious; and since it is - obvious that a thing is itself, "because it is itself" (or "because each thing is - indivisible from itself") is the one and only complete answer to all questions of this - type. Since this answer (in either form) is clearly unsatisfactory, the question which - it answers cannot be a proper question. We may, however, ask why a man is an - animal of such-and-such a kind. It is clear, - then, that we are not asking why he who is a man is a man; therefore we are asking why A, - which is predicated of B, belongs to B. (The fact that A does belong to B must be evident, - for if this is not so, the question is pointless.) E.g., "Why does it thunder?" means "why - is a noise produced in the clouds?" for the true form of the question is one thing - predicated in this way of another. Or again, - "why are these things, e.g. bricks and stones, a house?" Clearly then we are inquiring for - the cause (i.e., to speak abstractly, the essence); which is in the case of some things, - e.g. house or bed, the end , and in others the prime mover—for this - also is a cause. We look for the latter kind of cause in the case of generation and - destruction, but for the former also in the case of existence. What we are now looking for is - most obscure when one term is not predicated of another; e.g. when we inquire what man - is; because the expression is a simple one not analyzed into subject and attributes. We - must make the question articulate before we ask it; otherwise we get something which - shares the nature of a pointless and of a definite question. Now since we must know that the fact actually exists, it is surely - clear that the question is "why is the matter so-and-so?" e.g. "why are these - materials a house?" Because the essence of house is present in them. And this matter, or - the body containing this particular form, is man. Thus what we are seeking is the cause - (i.e. the form) in virtue of which the matter is a definite thing; and this is the - substance of the thing. Clearly then in the case of simple - entitiesPure forms which contain no matter; in - their case the method just described obviously will not apply. They can only be - apprehended intuitively (cf. Aristot. Met. - 9.10.). inquiry and explanation are impossible; in such cases there is a - different mode of inquiry. Now since that which is composed of something in such a way that the - whole is a unity; not as an aggregate is a unity, but as a syllable isThis sentence is not finished; the parenthesis which - follows lasts until the end of the chapter.—the syllable is not the - letters, nor is BA the same as B and A; nor is flesh fire and earth; because after - dissolution the compounds, e.g. flesh or the syllable, no longer exist; but the letters - exist, and so do fire and earth. Therefore the - syllable is some particular thing; not merely the letters, vowel and consonant, but - something else besides. And flesh is not merely fire and earth, or hot and cold, but - something else besides. Since then this - something else must be either an element or composed of elements, (a) if it is an element, the same argument applies again; for - flesh will be composed of this and fire and earth, and again of another - element, so that there will be an infinite regression. And (b) if it is composed of - elements, clearly it is composed not of one (otherwise it will itself be that element) but - of several; so that we shall use the same argument in this case as about the flesh or the - syllable. It would seem, however, that this - "something else" is something that is not an element, but is the cause that - this matter is flesh and that matter a syllable, and similarly - in other cases. And this is the substance of - each thing, for it is the primary cause of its existence. And since, although some things - are not substances, all substances are constituted in accordance with and by nature, - substance would seem to be this "nature," which is not an element but a principle.i.e. the formal cause. Cf. Aristot. Met. 5.4.4-6. An element is that - which is present as matter in a thing, and into which the thing is divided; e.g., A and B - are the elements of the syllable.

- - -

We must now draw our - conclusions from what has been said, and after summing up the result, bring our inquiry to - a close. We have saidCf. Aristot. Met. 7.1. that the objects of our - inquiry are the causes and principles and elements of substances. Now some substances are - agreed upon by all; but about others certain thinkers have stated individual - theories. Those about which there is - agreement are natural substances: e.g. fire, earth, water, air and all the other simple - bodies; next, plants and their parts, and animals and the parts of animals; and finally - the sensible universe and its parts; and certain thinkers individually include as - substances the Forms and the objects of mathematics.Cf. Aristot. Met. 7.2. And arguments show that there are yet other substances: the - essence and the substrate.Cf. Aristot. Met. 7.3-4. Again, from another point - of view, the genus is more nearly substance than the species, and the universal than the - particularsCf. Aristot. Met. 7.13.; and there is a close connection between the - universal and genus and the Ideas, for they are thought to be substance on the same - grounds.Cf. Aristot. Met. 7.14. And - since the essence is substance, and definition is the formula of the essence, we have - therefore systematically examined definition and essential predication.Cf. Aristot. Met. - 7.4-6, 12, 15. And since the definition is a formula, and the formula - has parts, we have been compelled to investigate - "parts," and to discover what things are parts of the substance, and what are not; and - whether the parts of the substance are also parts of the definition.Cf. Aristot. Met. 7.10, - 11. Further, then, neither the universal nor the genus is - substance.Cf. Aristot. Met. 7.13, 16. As - for the Ideas and the objects of mathematics (for some say that these exist apart from - sensible substances) we must consider them later.Books 13 and 14. But now let us proceed to discuss those substances which are - generally accepted as such. Now these are the sensible - substances, and all sensible substances contain matter. And the substrate is substance; in one sense matter (by matter I mean - that which is not actually, but is potentially, an individual thing); and in another the - formula and the specific shape (which is an individual thing and is theoretically - separable); and thirdly there is the combination of the two, which alone admits of - generation and destruction,Cf. Aristot. Met. 7.8. and is separable in an - unqualified sense—for of substances in the sense of formula some are separableIn point of fact the only form which is absolutely - separable is Mind or Reason. Cf. Aristot. Met. - 12.7, 9. and some are not. That matter is also substance is evident; for in all - opposite processes of change there is something that underlies those processes; e.g., if - the change is of place , that which is now in one place and subsequently in - another; and if the change is of magnitude , that which is now of - such-and-such a size, and subsequently smaller or greater; and if the change is of - quality , that which is now healthy and subsequently diseased. Similarly, if the change is in respect of being , - there is something which is now in course of generation, and subsequently in course of - destruction, and which is the underlying substrate, now as this individual - thing, and subsequently as deprived of its individuality. In this last process of change - the others are involved, but in either one or twoi.e., locomotion does not involve substantial change; alteration may or may not involve - it (in Aristot. Met. 9.8.17 we find that it does - not); increase or decrease does involve it. of the others it is not involved; for - it does not necessarily follow that if a thing contains matter that admits of change of - place, it also contains matter that is generable and destructible.e.g., the heavenly bodies, though imperishable, can move in space (Aristot. Met. 8.4.7, Aristot. Met. 12.2.4). The difference between absolute and qualified - generation has been explained in the Physics.Aristot. Phys. 225a 12-20; cf. - Aristot. De Gen. et Corr. 317a - 17-31. Since substance in the sense of substrate or matter is admittedly - substance, and this is potential substance, it remains to explain the nature of the actual - substance of sensible things. Now DemocritusCf. - Aristot. Met. 1.4.11. apparently assumes - three differences in substance; for he says that the underlying body is one and the same - in material, but differs in figure, i.e. shape; or inclination, i.e. position; or - intercontact, i.e. arrangement. But evidently - there are many differences; e.g. some things are defined by the way in which their - materials are combined, as, for example, things which are unified by mixture, as - honey-water; or by ligature, as a faggot; or by glue, as a book; or by clamping, as a - chest; or by more than one of these methods. Other things are defined by their position, - e.g. threshold and lintel (for these differ in being situated in a particular - way); and others by place <or - direction>, e.g. the winds; others by time, e.g. dinner and breakfast; and others by - the attributes peculiar to sensible things, e.g. hardness and softness, density and - rarity, dryness and humidity. Some are distinguished by some of these differences, and - others by all of them; and in general some by excess and some by defect. Hence it is clear that "is" has - the same number of senses; for a thing "is" a threshold because it is situated in a - particular way, and "to be a threshold" means to be situated in this particular way, and - "to be ice" means to be condensed in this particular way. Some things have their being - defined in all these ways: by being partly mixed, partly blended, partly bound, partly - condensed, and partly subjected to all the other different processes; as, for example, a - hand or a foot. We must therefore comprehend - the various kinds of differences—for these will be principles of being—i.e. - the differences in degree, or in density and rarity, and in other such modifications, for - they are all instances of excess and defect. And if anything differs in shape or in smoothness or roughness, all these are - differences in straightness and curvature. For some things mixture will constitute being, - and the - opposite state not-being. From this it is evident that if - substance is the cause of the existence of each thing, we must look among these - "differences" for the cause of the being of each thing. No one of them, nor the combination of any two of them, is substance, - but nevertheless each one of them contains something analogous to substance. And just as - in the case of substances that which is predicated of the matter is the actuality itself, - so in the other kinds of definition it is the nearest approximation to actuality. E.g., if - we have to define a threshold, we shall call it "a piece of wood or stone placed in - such-and-such a way"; and we should define a house as "bricks and timber arranged in - such-and-such a way"; or again in some cases - there is the final cause as well. And if we are defining ice, we shall describe it as - "water congealed or condensed in such-and-such a way"; and a harmony is "such-and-such a - combination of high and low"; and similarly in the other cases. From this it is evident that the actuality or formula is different in the - case of different matter; for in some cases it is a combination, in others a mixture, and - in others some other of the modes which we have described. Hence in defining the nature of a house, those who describe it as - stones, bricks and wood, describe the potential house, since these things are its matter; - those who describe it as "a receptacle for containing goods and bodies," or something else - to the same effect, describe its actuality; but those who combine these two definitions - describe the third kind of substance, that which is composed of matter and form. For it would seem that the formula which involves the - differentiae is that of the form and the actuality, while that which involves the constituent parts is rather that of the - matter. The same is true of the kind of definitions which ArchytasA celebrated Pythagorean, contemporary with Plato. used to accept; - for they are definitions of the combined matter and form. E.g., what is "windlessness?" - Stillness in a large extent of air; for the air is the matter, and the stillness is the - actuality and substance. What is a calm? - Levelness of sea. The sea is the material substrate, and the levelness is the actuality or - form. From the foregoing account it is clear what sensible - substance is, and in what sense it exists; either as matter, or as form and actuality, or - thirdly as the combination of the two. We must not fail to realize that sometimes it is doubtful - whether a name denotes the composite substance or the actuality and the form—e.g. - whether "house" denotes the composite thing, "a covering made of bricks and stones - arranged in such-and-such a way," or the actuality and form, "a covering"; and whether - "line" means "duality in length" or "duality"Cf. - Aristot. Met. 7.11.6.; and whether - "animal" means "a soul in a body" or "a soul"; for the soul is the substance and actuality - of some body. The term "animal" would be - applicable to both cases; not as being defined by one formula, but as relating to one - concept. These distinctions are of importance from another point of view, but unimportant - for the investigation of sensible substance; because the essence belongs to the form and - the actualization. Soul and essence of soul are - the same, but man and essence of man are not, unless the soul is also to be called man; - and although this is so in one sense, it is not so in another. It appears, then, upon inquiry into the matter,Cf. Plat. Theaet. 204aff. that - a syllable is not derived from the phonetic elements plus combination, nor is a house - bricks plus combination. And this is true; for the combination or mixture is not derived - from the things of which it is a combination or mixture, nor, similarly, is any other of the "differences." E.g., if the - threshold is defined by its position, the position is not derived from the threshold, but - rather vice versa. Nor, indeed, is man "animal" plus "two-footed"; there must - be something which exists besides these, if they are matter; but it is neither an element - nor derived from an element, but the substance; and those who offer the definition given - above are omitting this and describing the matter. If, then, this something else is the cause of a man's being, and this - is his substance, they will not be stating his actual substance. Now the substance must be either eternal or perishable without ever being - in process of perishing, and generated without ever being in process of generation. It has - been clearly demonstrated elsewhereCf. Aristot. Met. 7.8. that no one generates or - creates the form; it is the individual thing that is created, and the compound that is - generated. But whether the substances of - perishable things are separable or not is not yet at all clearCf. Aristot. Met. 8.1.6. - n..; only it is clear that this is impossible in some cases, i.e. in the case of all things which cannot exist apart - from the particular instances; e.g. house or implement.Cf. Aristot. Met. 7.8.6. - Probably, then, neither these things themselves, nor anything else which is not naturally - composed, are substances; for their nature is the only substance which one can assume in - the case of perishable things. Hence the - difficulty which perplexed the followers of AntisthenesCf. Aristot. Met. 5.29.4. - and others similarly unlearned has a certain application; I mean the difficulty that it is - impossible to define what a thing is (for the definition, they say, is a - lengthy formula), but it is possible actually to teach others what a thing - is like; e.g., we cannot say what silver is, but we can say - that it is like tin. Hence there can be - definition and formula of one kind of substance, i.e. the composite, whether it is - sensible or intelligible; but not of its primary constituents, since the defining formula - denotes something predicated of something, and this must be partly of the nature of matter - and partly of the nature of form. It is also obvious that, if numbers are in any sense substances, they - are such in this sense, and not, as someAristotle - is referring to the Pythagoreans and Platonists, but seems as usual to misrepresent - their views. His object in this section is to show that the relation of number to - substance is only one of analogy. Cf. Aristot. Met. - 13.6, 7, and see Introduction. describe them, aggregates of units. For - (a) the definition is a kind of number, since it is divisible, and divisible into - indivisible parts (for formulae are not infinite); and number is of this nature. And (b) just as when any element which composes the - number is subtracted or added, it is no longer the same number but a different one, - however small the subtraction or addition is; so neither the definition nor the essence - will continue to exist if something is subtracted from or added to it. And (c) a number - must be something in virtue of which it is a unity (whereas our opponents cannot say what - makes it one); that is, if it is a unity. For - either it is not a unity but a kind of aggregate, or if it is a unity, we must explain - what makes a unity out of a plurality. And the definition is a unity; but similarly they - cannot explain the definition either. This is a natural consequence, for the same reason - applies to both, and substance is a unity in the way which we have explained, and not as - some thinkers say: e.g. because it is a kind of unit or point; but each substance is a - kind of actuality and nature. Also (d) just as - a number does not admit of variation in degree, so neither does substance in the sense of - form; if any substance does admit of this, it is substance in combination with - matter.In Aristot. - Categories 3b 33-4a 9 Aristotle does not allow this exception. Let this suffice as a detailed account of the generation and - destruction of so-called substances, in what sense they are possible and in what sense - they are not; and of the reference of things to number. As regards material substance, we must not - fail to realize that even if all things are derived from the same primary cause, or from - the same things as primary causesi.e. from prime - matter or the four elements.; i.e. even if all things that are generated have the - same matter for their first principle, nevertheless each thing has some matter peculiar to - it; e.g., "the sweet" or "the viscous" is the proximate matter of mucus, and "the bitter" - or some such thing is that of bile— although probably mucus and bile are derived from the same ultimate matter. The result is that there is more than one matter of the - same thing, when one thing is the matter of the other; e.g., mucus is derived from "the - viscous"; and from "the sweet," if "the viscous" is derived from "the sweet"; and from - bile, by the analysis of bile into its ultimate matter. For there are two senses in which - X comes from Y; either because X will be found further on than Y in the process of - development, or because X is produced when Y is analyzed into its original - constituents. And different things can be - generated by the moving cause when the matter is one and the same, e.g. a chest and a bed - from wood. But some different things must necessarily have different matter; e.g., a saw - cannot be generated from wood, nor does this lie in the power of the moving cause, for it - cannot make a saw of wool or wood. If, then, it is possible to make the same thing from different matter, - clearly the art, i.e. the moving principle, is the same; for if both the matter and the - mover are different, so too is the product. So whenever we - inquire what the cause is, since there are causes in several senses, we must state all the - possible causes. E.g., what is the material - cause of a man? The menses. What is the moving cause? The semen. What is the formal cause? - The essence. What is the final cause? The end. (But perhaps both the latter are the same.) - We must, however, state the most proximate causes. What is the matter? Not fire or earth, - but the matter proper to man. Thus as regards generable natural substances we must proceed in this - manner, if we are to proceed correctly; that is, if the causes are these and of this - number, and it is necessary to know the causes. But in the case of substances which though - natural are eternal the principle is different. For presumably some of them have no - matter; or no matter of this kind, but only such as is spatially mobile.Cf. Aristot. Met. 8.1.8 - n. Moreover, things which - exist by nature but are not substances have no matter; their substrate is their substance. - E.g., what is the cause of an eclipse; what is its matter? It has none; it is the moon - which is affected. What is the moving cause which destroys the light? The earth. There is - probably no final cause. The formal cause is the formula; but this is obscure unless it - includes the efficient cause. E.g., what is an - eclipse? A privation of light; and if we add "caused by the earth's intervention," this is - the definition which includes the <efficient> cause. In the case of sleep it is not - clear what it is that is proximately affected. Is it the animal? Yes; but in respect of - what, and of what proximately? The heart, or some other part. Again, by what is it - affected? Again, what is the affection which affects that part, and not the whole animal? - A particular kind of immobility? Yes; but in - virtue of what affection of the proximate subject is it this? Since some things both are and are not, - without being liable to generation and destructionCf. Aristot. Met. 6.3.1, Aristot. Met. 7.8.3.—e.g. points,Cf. Aristot. Met. - 3.5.8, 9. if they exist at all; and in general the forms and shapes of - things (because white does not come to be, but the wood becomes white, since everything - which comes into being comes from something and becomes something)—not all the - contrariesi.e., we must distinguish "contraries" - in the sense of "contrary qualities" from "contraries" in the sense of "things - characterized by contrary qualities." can be generated from each other. White is - not generated from black in the same way as a white man is generated from a black man; nor - does everything contain matter, but only such things as admit of generation and - transformation into each other. And such things - as, without undergoing a process of change, both are and are not, have no - matter. There is a difficulty in the question how the - matter of the individual is related to the contraries. E.g., if the body is potentially - healthy, and the contrary of health is disease, is the body potentially both healthy and - diseased? And is water potentially wine and vinegar? Probably in the one case it is the - matter in respect of the positive state and form, and in the other case in respect of - privation and degeneration which is contrary to its proper nature. There is also a difficulty as - to why wine is not the matter of vinegar, nor potentially vinegar (though vinegar comes - from it), and why the living man is not potentially dead. In point of fact they are not; - their degeneration is accidental, and the actual matter of the living body becomes by - degeneration the potentiality and matter of the dead body, and water the matter of - vinegar; for the one becomes the other just as day becomes night. All things which change reciprocally in this way must return into the - matter; e.g., if a living thing is generated from a dead one, it must first become the - matter, and then a living thing; and vinegar must first become water, and then - wine. With - regard to the difficulty which we have describedAristot. Met. 7.12, Aristot. Met. 8.3.10, 11. in connection with - definitions and numbers, what is the cause of the unification? In all things which have a - plurality of parts, and which are not a total aggregate but a whole of some sort distinct - from the parts, there is some cause ; inasmuch as even in bodies sometimes - contact is the cause of their unity, and sometimes viscosity or some other such - quality. But a definition is one - account, not by connection, like the Iliad , but because it is a - definition of one thing. What is it, then, that makes "man" - one thing, and why does it make him one thing and not many, e.g. "animal" and - "two-footed," especially if, as some say, there is an Idea of "animal" and an Idea of - "two-footed"? Why are not these Ideas "man," - and why should not man exist by participation, not in any "man," but in two Ideas, those - of "animal" and "two-footed"? And in general - "man" will be not one, but two things—"animal" and "two-footed." Evidently if we - proceed in this way, as it is usual to define and explain, it will be impossible to answer - and solve the difficulty. But if, as we - maintain, man is part matter and part form—the matter being potentially, and the - form actually man—, the point which we are investigating will no longer seem to be a - difficulty. For this difficulty is just the same as we should have if the definition of - XLiterally "cloak"; cf. Aristot. Met. 7.4.7 n. were "round bronze"; - for this name would give a clue to the formula, so that the question becomes "what is the - cause of the unification of 'round' and 'bronze'?" The difficulty is no longer apparent, because the one is matter and - the other form. What then is it (apart from the active cause) which causes that which - exists potentially to exist actually in things which admit of generation? There - is no other cause of the potential sphere's being an actual sphere; this - was the essence of each.i.e., it was the essence of - the potential sphere to become the actual sphere, and of the actual sphere to be - generated from the potential sphere. Some matter is intelligible and some sensible, and part - of the formula is always matter and part actuality; e.g., the circle is a plane - figure.Even formulae contain matter in a sense - ("intelligible matter"); i.e. the generic element in the species. "Plane figure" is the - generic element of "circle." But such thingThe highest genera, or categories. as have no matter, neither intelligible nor - sensible, are ipso facto each one of them essentially something one; just as they are essentially - something existent: an individual substance, a quality, or a quantity. Hence neither - "existent" nor "one" is present in their definitions. And their essence is ipso facto - something one, just as it is something existent. Hence also there is no other cause of the unity of any of these things, or of their - existence; for each one of them is one and "existent" not because it is contained in the - genus "being" or "unity," nor because these genera exist separately apart from their - particulars, but ipso facto. It is because of this difficulty that some thinkersThe Platonists. speak of "participation," and - raise the question of what is the cause of participation, and what participation means; - and others speak of "communion"; e.g., LycophronA - sophist, disciple of Gorgias. says that knowledge is a communion of the soul with - "knowing"; and others call life a combination or connection of soul with body. The same argument, however, applies in every case; for - "being healthy" will be the "communion" or "connection" or "combination" of soul and - health; and "being a bronze triangle" a "combination" of bronze and triangle; and "being - white" a "combination" of surface and whiteness. The reason for this is that people look - for a unifying formula, and a difference, between potentiality and actuality. But, as we have said,Cf. sects. 4, 5. the proximate matter and the shape are one and - the same; the one existing potentially, and the other actually. Therefore to ask the cause of their unity is like asking the - cause of unity in general; for each individual thing is one, and the potential and the - actual are in a sense one. Thus there is no cause other than whatever initiates the - development from potentiality to actuality. And such things as have no matter are all, - without qualification, essential unities.

- - -

We have now - dealt with Being in the primary sense, to which all the other categories of being are - related; i.e. substance. For it is from the concept of substance that all the other modes - of being take their meaning; both quantity and quality and all other such terms; for they - will all involve the concept of substance, as we stated it in the beginning of our - discussion.Aristot. Met. 7.1. And since - the senses of being are analyzableCf. Aristot. Met. 6.2.1. not only into substance - or quality or quantity, but also in accordance with potentiality and actuality and - function, let us also gain a clear understanding about potentiality and actuality; and - first about potentiality in the sense which is most proper to the word, but not most - useful for our present purpose— for potentiality and actuality extend beyond the sphere - of terms which only refer to motion. When we - have discussed this sense of potentiality we will, in the course of our definitions of - actuality,Chs. 6-10. explain the others - also. We have made it plain elsewhereAristot. Met. - 5.12. that "potentiality" and "can" have several senses. All senses which are merely equivocal may be dismissed; - for some are used by analogy, as in geometry,Cf. - Aristot. Met. 5.12.11. and we call - things possible or impossible because they "are" or "are not" in some particular way. But - the potentialities which conform to the same type are all principles, and derive their - meaning from one primary sense of potency, which is the source of change in some other - thing, or in the same thing qua other. One kind of potentiality is the power of - being affected; the principle in the patient itself which initiates a passive change in it - by the action of some other thing, or of itself qua other. Another - is a positive state of impassivity in respect of deterioration or destruction by something - else or by itself qua something else; i.e. by a transformatory - principle—for all these definitions contain the formula of the primary sense of - potentiality. Again, all these potentialities - are so called either because they merely act or are acted upon in a particular way, or - because they do so well . Hence in their formulae also the formulae of - potentiality in the senses previously described are present in some degree. Clearly, then, in one sense the potentiality for acting and being - acted upon is one (for a thing is "capable" both - because it itself possesses the power of being acted upon, and also because something else - has the power of being acted upon by it); and - in another sense it is not; for it is partly in the patient (for it is because it contains - a certain principle, and because even the matter is a kind of principle, that the patient - is acted upon; i.e., one thing is acted upon by another: oily stuff is inflammable, and - stuff which yields in a certain way is breakable, and similarly in other - cases)— and partly in the agent; e.g. - heat and the art of building: the former in that which produces heat, and the latter in - that which builds. Hence in so far as it is a natural unity, nothing is acted upon by - itself; because it is one, and not a separate thing. "Incapacity" and "the incapable" is the privation contrary to "capacity" in this sense; - so that every "capacity" has a contrary incapacity for producing the same result in - respect of the same subject. Privation has several sensesCf. - Aristot. Met. 5.22.—it is applied - (1.) to anything which does not possess a certain attribute; (2.) to that which would - naturally possess it, but does not; either (a) in general, or (b) when it would naturally - possess it; and either (1) in a particular way, e.g. entirely, or (2) in any way at all. - And in some cases if things which would naturally possess some attribute lack it as the - result of constraint, we say that they are "deprived." Since some of these principles are - inherent in inanimate things, and others in animate things and in the soul and in the - rational part of the soul, it is clear that some of the potencies also will be irrational - and some rational. Hence all arts, i.e. the productive sciences, are potencies; because - they are principles of change in another thing, or in the artist himself qua other. Every rational potency admits equally of contrary results, but - irrational potencies admit of one result only. E.g., heat can only produce heat, but - medical science can produce disease and health. The reason of this is that science is a - rational account, and the same account explains both the thing and its privation, though - not in the same way; and in one sense it applies to both, and in another sense rather to - the actual fact. Therefore such sciences must - treat of contraries—essentially of the one, and non-essentially of the other; for - the rational account also applies essentially to the one, but to the other in a kind of - accidental way, since it is by negation and removal that it throws light on the contrary. - For the contrary is the primary privation,Cf. Aristot. Met. 10.4.7. and this is the removal - of that to which it is contrary.Literally "of the - other," i.e. the positive term. And - since contrary attributes cannot be induced in the same subject, and science is a potency - which depends upon the possession of a rational formula, and the soul contains a principle - of motion, it follows that whereas "the salutary" can only produce health, and "the - calefactory" only heat, and "the frigorific" only cold, the scientific man can produce both contrary results. For the rational account includes both, though not in the same - way; and it is in the soul, which contains a principle of motion, and will therefore, by - means of the same principle, set both processes in motion, by linking them with the same - rational account. Hence things which have a rational potency produce results contrary to - those of things whose potency is irrationalThe - meaning of this awkward sentence is clearly shown in the latter part of 4.; for - the results of the former are included under one principle, the rational - account. It is evident also that whereas the - power of merely producing (or suffering) a given effect is implied in the power of - producing that effect well , the contrary is not always true; for that which - produces an effect well must also produce it, but that which merely produces a given - effect does not necessarily produce it well. There are some, e.g. the Megaric school,Founded by Euclides of Megara, an enthusiastic admirer of Socrates. The Megarics adopted the - Eleatic system and developed it along dialectical lines. who say that a thing - only has potency when it functions, and that when it is not functioning it has no potency. - E.g., they say that a man who is not building cannot build, but only the man who is - building, and at the moment when he is building; and similarly in the other - cases. It is not difficult to see the absurd - consequences of this theory. Obviously a man will not be a builder unless he is building, - because "to be a builder" is "to be capable of building"; and the same will be true of the - other arts. If, therefore, it is impossible to - possess these arts without learning them at some time and having grasped them, and impossible not - to possess them without having lost them at some time (through forgetfulness or some - affection or the lapse of time; not, of course, through the destruction of the object of - the art,i.e. the form of "house." because it - exists always), when the artist ceases to practice his art, he will not possess - it; and if he immediately starts building - again, how will he have re-acquired the art? The same is - true of inanimate things. Neither the cold nor the hot nor the sweet nor in general any - sensible thing will exist unless we are perceiving it (and so the result will be that they - are affirming Protagoras' theoryCf. IV. v., - vi.). Indeed, nothing will have the faculty of sensation unless it is perceiving, - i.e. actually employing the faculty. If, then, - that is blind which has not sight, though it would naturally have it, and when it would - naturally have it, and while it still exists, the same people will be blind many times a - day; and deaf too. Further, if that which is deprived of its - potency is incapable, that which is not happening will be incapable of happening; and he - who says that that which is incapable of happening is or will - be, will be in error, for this is what "incapable" meant.i.e., we have just said that that which is incapable is deprived of its - potency—in this case, of its potency for happening. Thus these theories do away with both motion and generation; - for that which is standing will always stand, and that which is sitting will always sit; - because if it is sitting it will not get up, since it is impossible that anything which is - incapable of getting up should get up. Since, - then, we cannot maintain this, obviously potentiality and actuality are different. But - these theories make potentiality and actuality identical; hence it is no small thing that they are trying to abolish. Thus it is possible that a thing may be capable of being and yet not - be, and capable of not being and yet be; and similarly in the other categories that which - is capable of walking may not walk, and that which is capable of not walking may - walk. A thing is capable of doing something - if there is nothing impossible in its having the actuality of that of which it is said to - have the potentiality. I mean, e.g., that if a thing is capable of sitting and is not - prevented from sitting, there is nothing impossible in its actually sitting; and similarly - if it is capable of being moved or moving or standing or making to stand or being or - becoming or not being or not becoming. The term "actuality," with its implication of "complete - reality," has been extended from motions, to which it properly belongs, to other things; - for it is agreed that actuality is properly motion. Hence people do not invest non-existent things with motion, although - they do invest them with certain other predicates. E.g., they say that non-existent things - are conceivable and desirable, but not that they are in motion. This is because, although - these things do not exist actually, they will exist actually; for some non-existent things - exist potentially; yet they do not exist, because they do not exist in complete - reality. Now - if, as we have said, that is possible which does not involve an impossibility, obviously - it cannot be true to say that so-and-so is possible, but will not be, this view entirely - loses sight of the instances of impossibility.If it - is true to say that a thing which is possible will not be, anything may be possible, and - nothing impossible. I mean, suppose that someone—i.e. the sort of man who - does not take the impossible into account—were to say that it is possible to measure - the diagonal of a square, but that it will not be measured, because there is nothing to - prevent a thing which is capable of being or coming to be from neither being nor being - likely ever to be. But from our premisses this - necessarily follows: that if we are to assume that which is not, but is possible, to be or - to have come to be, nothing impossible must be involved. But in this case something - impossible will take place; for the measuring of the diagonal is impossible. The false is of course not the same as the impossible; for although - it is false that you are now standing, it is not impossible. At the same time it is also clear that if B must be real if A is, then - if it is possible for A to be real, it must also be possible for B to be real; for even if - B is not necessarily possible, there is nothing to prevent its being possible. Let A, - then, be possible. Then when A was possible, if A was assumed to be real, nothing - impossible was involved; but B was necessarily real too. But ex hypothesi B was impossible. Let B be impossible. Then if B is impossible, A must also be impossible. But A was - by definition possible. Therefore so is B. If, therefore, A - is possible, B will also be possible; that is if their relation was such that if A is - real, B must be real. Then if, A and B being - thus related, B is not possible on this condition, A and B will not be related as we - assumed; and if when A is possible B is necessarily possible, then if A is real B must be - real too. For to say that B must be possible if A is possible means that if A is real at - the time when and in the way in which it was assumed that it was possible for it to be - real, then B must be real at that time and in that way. Since all potencies are either innate, - like the senses, or acquired by practice, like flute-playing, or by study, as in the arts, - some—such as are acquired by practice or a rational formula—we can only - possess when we have first exercised themCf. Aristot. Met. 9.8.6, 7.; in the case of others - which are not of this kind and which imply passivity, this is not necessary. Since anything which is - possible is something possible at some time and in some way, and with any other - qualifications which are necessarily included in the definition; and since some things can - set up processes rationally and have rational potencies, while others are irrational and - have irrational potencies; and since the former class can only belong to a living thing, - whereas the latter can belong both to living and to inanimate things: it follows that as - for potencies of the latter kind, when the agent and the patient meet in accordance with - the potency in question, the one must act and the other be acted upon; but in the former - kind of potency this is not necessary, for whereas each single potency of the latter kind - is productive of a single effect, those of the former kind are productive of contrary - effects,Cf. Aristot. Met. 9.2.4, 5. so that one potency will produce at the same - time contrary effects.sc., if every potency must - act automatically whenever agent and patient meet. But this is impossible. Therefore there must be some other deciding - factor, by which I mean desire or conscious choice. For - whichever of two things an animal desires decisively it will do, when it is in - circumstances appropriate to the potency and meets with that which admits of being acted - upon. Therefore everything which is rationally capable, when it desires something of which - it has the capability, and in the circumstances in which it has the capability, must do - that thing. Now it has the capability when that - which admits of being acted upon is present and is in a certain state; otherwise it will - not be able to act. (To add the qualification "if nothing external prevents it" is no - longer necessary; because the agent has the capability in so far as it is a capability of - acting; and this is not in all, but in certain circumstances, in which external hindrances - will be excluded; for they are precluded by some - of the positive qualifications in the definition.) Hence even if it wishes or desires to do two things or contrary things - simultaneously, it will not do them, for it has not the capability to do them under these - conditions, nor has it the capability of doing things simultaneously, since it will only - do the things to which the capability applies and under the appropriate - conditions. Since we have now dealt with the kind of potency which is related to motion, let us now - discuss actuality; what it is, and what its qualities are. For as we continue our analysis - it will also become clear with regard to the potential that we apply the name not only to - that whose nature it is to move or be moved by something else, either without - qualification or in some definite way, but also in other senses; and it is on this account - that in the course of our inquiry we have discussed these as well. "Actuality" means the presence - of the thing, not in the sense which we mean by "potentially." We say that a thing is - present potentially as Hermes is present in the wood, or the half-line in the whole, - because it can be separated from it; and as we call even a man who is not studying "a - scholar" if he is capable of studying. That which is present in the opposite sense to this - is present actually. What we mean can be - plainly seen in the particular cases by induction; we need not seek a definition for every - term, but must comprehend the analogy: that as that which is actually building is to that - which is capable of building, so is that which is awake to that which is asleep; and that - which is seeing to that which has the eyes shut, but has the power of sight; and that - which is differentiated out of matter to the matter; and the finished article to the raw - material. Let actuality be defined by one - member of this antithesis, and the potential by the other. But things are not all said to exist actually in the same sense, but only by - analogy—as A is in B or to B, so is C in or to D; for the relation is either that of - motion to potentiality, or that of substance to some particular matter. Infinity and void and other - concepts of this kind are said to "be" potentially or actually in a different sense from - the majority of existing things, e.g. that which sees, or walks, or is seen. For in these latter cases the predication may sometimes - be truly made without qualification, since "that which is seen" is so called sometimes - because it is seen and sometimes because it is capable of being seen; but the Infinite - does not exist potentially in the sense that it will ever exist separately in actuality; - it is separable only in knowledge. For the fact that the process of division never ceases - makes this actuality exist potentially, but not separately.For Aristotle's views about infinity and void see Aristot. Physics 3.4-8, 4.6-9 - respectively. Since no action which has a limit is an end, but only a means to the - end, as, e.g., the process of thinning; and - since the parts of the body themselves, when one is thinning them, are in motion in the - sense that they are not already that which it is the object of the motion to make them, - this process is not an action, or at least not a complete one, since it is not an end; it - is the process which includes the end that is an action. E.g., at the same time we see and have seen, understand and have - understood, think and have thought; but we cannot at the same time learn and have learnt, - or become healthy and be healthy. We are living well and have lived well, we are happy and - have been happy, at the same time; otherwise the process would have had to cease at some - time, like the thinning-process; but it has not ceased at the present moment; we both are - living and have lived. Now of these processes we should call - the one type motions, and the other actualizations. Every motion is incomplete—the processes of thinning, learning, - walking, building—these are motions, and incomplete at that. For it is not the same - thing which at the same time is walking and has walked, or is building and has built, or - is becoming and has become, or is being moved and has been moved, but two different - things; and that which is causing motion is different from that which has caused - motion. But the same thing at the same time - is seeing and has seen, is thinking and has thought. The latter kind of process, then, is - what I mean by actualization, and the former what I mean by motion. What the actual is, then, and what it is like, may be regarded as - demonstrated from these and similar considerations. We must, however, distinguish when a - particular thing exists potentially, and when it does not; for it does not so exist at any - and every time. E.g., is earth potentially a man? No, but rather when it has already become - semen,This is inconsistent with Aristotle's - doctrine that the semen is the formal element in reproduction. Cf. Aristot. Met. 8.4.5, Aristot. Met. - 6.9.5. and perhaps not even then; just as not everything can - be healed by medicine, or even by chance, but there is some definite kind of thing which - is capable of it, and this is that which is potentially healthy. The definition of that which as - a result of thought comes, from existing potentially, to exist actually, is that, when it - has been willed, if no external influence hinders it, it comes to pass; and the condition - in the case of the patient, i.e. in the person who is being healed, is that nothing in him - should hinder the process. Similarly a house exists potentially if there is nothing in X, - the matter, to prevent it from becoming a house, i.e., if there is nothing which must be - added or removed or changed; then X is potentially a house; and similarly in all other cases where the generative principle is - external. And in all cases where the generative principle is contained in the thing - itself, one thing is potentially another when, if nothing external hinders, it will of - itself become the other. E.g., the semen is not yet potentially a man; for it must further - undergo a change in some other medium.This is - inconsistent with Aristotle's doctrine that the semen is the formal element in - reproduction. Cf. Aristot. Met. 8.4.5, - Aristot. Met. 9.6.5. But when, by its own generative principle, it - has already come to have the necessary attributes, in this state it is now potentially a - man, whereas in the former state it has need of another principle; just as earth is not yet potentially a statue, because it must - undergo a change before it becomes bronze. It seems that - what we are describing is not a particular thing, but a definite material; e.g., a box is - not wood, but wooden material,Cf. Aristot. Met. 7.7.10-12. and wood is not earth, but earthen material; and earth also is - an illustration of our point if it is similarly not some other thing, but a definite - material—it is always the latter term in this series which is, in the fullest sense, - potentially something else. E.g., a box is not - earth, nor earthen, but wooden; for it is this that is potentially a box, and this is the - matter of the box—that is, wooden material in general is the matter of "box" in - general, whereas the matter of a particular box is a particular piece of wood. If there is some primary stuff, which is not further called the - material of some other thing, this is primary matter. E.g., if earth is "made of air," and - air is not fire, but "made of fire," then fire is primary matter, not being an individual - thing. For the subject or substrate is - distinguishable into two kinds by either being or not being an individual thing. Take for - example as the subject of the attributes "man," or "body" or "soul," and as an attribute - "cultured" or "white." Now the subject, when culture is induced in it, is called not - "culture" but "cultured," and the man is called not whiteness but white; nor is he called - "ambulation" or "motion," but "walking" or "moving"; just as we said that things are of a - definite material. Thus where "subject" has - this sense, the ultimate substrate is substance; but where it has not this sense, and the - predicate is a form or individuality, the ultimate substrate is matter or material - substance. It is quite proper that both matter and attributes should be described by a - derivative predicate, since they are both indefinite. Thus it has - now been stated when a thing should be said to exist potentially, and when it should - not. Now since - we have distinguishedAristot. Met. 5.11. the several senses of - priority, it is obvious that actuality is prior to potentiality. By potentiality I mean - not that which we have defined as "a principle of change which is in something other than - the thing changed, or in that same thing qua other," but in general - any principle of motion or of rest; for nature also is in the same genus as potentiality, - because it is a principle of motion, although not in some other thing, but in the thing - itself qua itself.Cf. Aristot. Met. 5.4.1. To every potentiality of this kind actuality is prior, both in formula - and in substance; in time it is sometimes prior and sometimes not. That actuality is prior in formula is evident; for it is because it can be - actualized that the potential, in the primary sense, is potential, I mean, e.g., that the - potentially constructive is that which can construct, the potentially seeing that which - can see, and the potentially visible that which can be seen. The same principle holds in all other cases too, so that the formula - and knowledge of the actual must precede the knowledge of the potential. In time it is prior in this sense: the actual is prior to the potential - with which it is formally identical, but not to that with which it is identical - numerically. What I mean is this: that the matter and the seed and the thing which is - capable of seeing, which are potentially a man and corn and seeing, but are not yet so - actually, are prior in time to the individual man and corn and seeing subject which - already exist in actuality. But prior in time - to these potential entities are other actual entities from which the former are generated; - for the actually existent is always generated from the potentially existent by something - which is actually existent—e.g., man by man, cultured by cultured—there is - always some prime mover; and that which initiates motion exists already in - actuality. We have saidAristot. Met. 7.7, 8. in - our discussion of substance that everything which is generated is generated from something - and by something; and by something formally identical with itself. Hence it seems impossible that a man can be a builder if he has - never built, or a harpist if he has never played a harp; because he who learns to play the - harp learns by playing it, and similarly in all other cases. This was the origin of the sophists' quibble that a man who does not - know a given science will be doing that which is the object of that science, because the - learner does not know the science. But since something of that which is being generated is - already generated, and something of that which is being moved as a whole is already moved - (this is demonstrated in our discussion on MotionAristot. Physics, 6.6.), presumably the - learner too must possess something of the science. At any rate from this argument it is clear that actuality is prior to - potentiality in this sense too, i.e. in respect of generation and time. But it is also prior in substantiality; (a) because things which are - posterior in generation are prior in form and substantiality; e.g., adult is prior to - child, and man to semen, because the one already possesses the form, but the other does - not; and (b) because everything which is - generated moves towards a principle, i.e. its end . For the object of a thing - is its principle; and generation has as its object the end . And the - actuality is the end, and it is for the sake of this that the potentiality is acquired; - for animals do not see in order that they may have sight, but have sight in order that - they may see. Similarly men possess the art of - building in order that they may build, and the power of speculation that they may - speculate; they do not speculate in order that they may have the power of - speculation—except those who are learning by practice; and they do not really - speculate, but only in a limited sense, or about a subject about which they have no desire - to speculate. Further, matter exists potentially, because it - may attain to the form; but when it exists actually, it is then in the form. - The same applies in all other cases, including those where the end is motion. Hence, just as teachers think that they have achieved - their end when they have exhibited their pupil performing, so it is with nature. For if - this is not so, it will be another case of - "Pauson's Hermes"Probably a "trick" picture of some - kind. So Pauson is said to have painted a picture of a horse galloping which when - inverted showed the horse rolling on its back. Cf. Aelian, Var. - Hist. 14.15; Lucian, Demosth. Enc. 24; - Plut. Moralia, 396e; Pfuhl, Malerei und Zeichnung - der Griechen, 763.; it will be impossible to say whether the knowledge is - in the pupil or outside him, as in the case of the Hermes. For the activity - is the end, and the actuality is the activity; hence the term "actuality" is derived from - "activity," and tends to have the meaning of "complete reality." Now whereas in some cases the - ultimate thing is the use of the faculty, as, e.g., in the case of sight seeing is the - ultimate thing, and sight produces nothing else besides this; but in other cases something - is produced, e.g. the art of building produces not only the act of building but a house; - nevertheless in the one case the use of the faculty is the end, and in the other it is - more truly the end than is the potentiality. For the act of building resides in the thing - built; i.e., it comes to be and exists simultaneously with the house. Thus in all cases where the - result is something other than the exercise of the faculty, the actuality resides in the - thing produced; e.g. the act of building in the thing built, the act of weaving in the - thing woven, and so on; and in general the motion resides in the thing moved. But where - there is no other result besides the actualization, the actualization resides in the - subject; e.g. seeing in the seer, and speculation in the speculator, and life in the soul - (and hence also happiness, since - happiness is a particular kind of life). Evidently, therefore, substance or form is - actuality. Thus it is obvious by this argument that actuality is prior in substantiality - to potentiality; and that in point of time, as we have said, one actuality presupposes - another right back to that of the prime mover in each case. It is also prior in a deeper sense; - because that which is eternal is prior in substantiality to that which is perishable, and - nothing eternal is potential. The argument is as follows. Every potentiality is at the - same time a potentiality for the opposite.Cf. - 19. For whereas that which is incapable of happening cannot happen to anything, - everything which is capable may fail to be actualized. Therefore that which is capable of being may both be and not be. - Therefore the same thing is capable both of being and of not being. But that which is - capable of not being may possibly not be; and that which may possibly not be is - perishable; either absolutely, or in the particular sense in which it is said that it may - possibly not be; that is, in respect either of place or of quantity or of quality. - "Absolutely" means in respect of substance. Hence nothing which is absolutely imperishable is absolutely potential (although there - is no reason why it should not be potential in some particular respect; e.g. of quality or - place); therefore all imperishable things are actual. Nor can anything which is of - necessity be potential; and yet these things are primary, for if they did not exist, - nothing would exist. Nor can motion be - potential, if there is any eternal motion. Nor, if there is anything eternally in motion, - is it potentially in motion (except in respect of some starting-point or destination), and - there is no reason why the matter of such a thing should not exist. Hence the sun and stars and the whole visible heaven are always - active, and there is no fear that they will ever stop—a fear which the writerse.g. Empedocles; cf. Aristot. Met. 5.23.3 n. on physics entertain. Nor do the heavenly - bodies tire in their activity; for motion does not imply for them, as it does for - perishable things, the potentiality for the opposite, which makes the continuity of the - motion distressing; this results when the substance is matter and potentiality, not - actuality. Imperishable things are resembled in this respect by things which are always undergoing - transformation, such as earth and fire; for the latter too are always active, since they - have their motion independently and in themselves.Cf. Aristot. De Gen. et Corr. 337a 1-7. - Other potentialities, according to the distinctions already made,Aristot. Met. 9.5.2. all - admit of the opposite result; for that which is capable of causing motion in a certain way - can also cause it not in that way; that is if it acts rationally. The same irrational potentialities can only produce opposite - results by their presence or absence. Thus if there are any - entities or substances such as the dialecticiansFor - this description of the Platonists cf. Aristot. Met. - 1.6.7. describe the Ideas to be, there must be something which has much - more knowledge than absolute knowledge, and much more mobility than motion; for they will be in - a truer sense actualities, whereas knowledge and motion will be their potentialities.This is a passing thrust at the Ideal theory. "Absolute - knowledge" (the faculty of knowledge) will be a mere potentiality, and therefore - substantially posterior to its actualization in particular instances. Thus it is - obvious that actuality is prior both to potentiality and to every principle of - change. That a - good actuality is both better and more estimable than a good potentiality will be obvious - from the following arguments. Everything of which we speak as capable is alike capable of - contrary results; e.g., that which we call capable of being well is alike capable of being - ill, and has both potentialities at once; for the same potentiality admits of health and - disease, or of rest and motion, or of building and of pulling down, or of being built and - of falling down. Thus the capacity for two - contraries can belong to a thing at the same time, but the contraries cannot belong at the - same time; i.e., the actualities, e.g. health and disease, cannot belong to a thing at the - same time. Therefore one of them must be the good; but the potentiality may equally well - be both or neither. Therefore the actuality is better. Also in the case of evils the end or - actuality must be worse than the potentiality; for that which is capable is capable alike - of both contraries. Clearly, then, evil does not exist apart - from things ; for evil is by nature posterior to potentiality.The argument is presumably as follows (the fallacy, as - pointed out by Bonitz, is indicated in parenthesis): That which has a separate - substantial existence is actuality. Actuality is prior (substantially) to potentiality. - Potentiality is prior to evil (in the moral scale. But since by evil Aristotle means the - actualization of a potentiality for evil, potentiality is substantially posterior to - evil). Therefore that which has a separate substantial existence is prior to evil; i.e., - evil does not exist apart from particular instances of evil. The argument is directed - against the Platonic Idea of evil (Plat. Rep. - 476a); and the corollary which follows against the identification of Evil with - one of the principles of the universe (Aristot. Met. - 1.6.10, Aristot. Met. 12.10.6, Aristot. Met. 14.4.10, 11; cf. Plat. Laws 896e, Plat. Laws - 898c). Nor is there in things - which are original and eternal any evil or error, or anything which has been - destroyed—for destruction is an evil. Geometrical constructions, too, are discovered by an - actualization, because it is by dividing that we discover them. If the division were - already done, they would be obvious; but as it is the division is only there potentially. - Why is the sum of the interior angles of a triangle equal to two right angles? Because the - angles about one point <in a straight line> are equal to two right angles. If the - line parallel to the side had been already drawn, the answer would have been obvious at - sight.The figure, construction and proof are as - follows: *** Why is the angle in a - semicircle always a right angle? If three lines are equal, the two forming the base, and - the one set upright from the middle of the base, the answer is obvious to one who knows - the former proposition.Aristotle implies a proof - something after this fashion: FIGURE BAC is an angle in a semicircle. From D, the - mid-point of the diameter BC, draw a perpendicular DE to meet the circumference at E. - Join EB, EC.*** Thus it is evident that the potential constructions are - discovered by being actualized. The reason for this is that the actualization is an act of - thinking. Thus potentiality comes from actuality (and therefore it is by constructive - action that we acquire knowledge). <But this is true only in the abstract>, for the - individual actuality is posterior in generation to its potentiality.This whole passage (sects. 4, 5) should be compared - with Aristot. Met. 9.8.3-7, where it logically - belongs. The terms "being" and "not-being" are used not only with reference to - the types of predication, and to the potentiality or actuality, or non-potentiality and - non-actuality, of these types, but also (in the strictest senseThis appears to contradict Aristot. Met. - 6.4.3. But it is just possible to interpret kuriw/tata(with Jaeger) as "in the commonest sense.") to denote - truth and falsity. This depends, in the case of the objects, upon their being united or - divided; so that he who thinks that what is divided is divided, or that what is united is - united, is right; while he whose thought is contrary to the real condition of the objects - is in error. Then when do what we call truth and falsity exist or not exist? - We must consider what we mean by these terms. It is not because we are right in thinking that you - are white that you are white; it is because you are white that we are right in saying so. - Now if whereas some things are always united and cannot be divided, and others are always - divided and cannot be united, others again admit of both contrary states, then "to be" is - to be united, i.e. a unity; and "not to be" is to be not united, but a - plurality. Therefore as regards the class of - things which admit of both contrary states, the same opinion or the same statement comes - to be false and true, and it is possible at one time to be right and at another wrong; but - as regards things which cannot be otherwise the same opinion is not sometimes true and - sometimes false, but the same opinions are always true or always false. But with regard to incomposite - things, what is being or not-being, and truths or falsity? Such a thing is not composite, - so as to be when it is united and not to be when it is divided, like the proposition that "the wood is white," or "the diagonal - is incommensurable"; nor will truth and falsity apply in the same way to these cases as to - the previous ones. In point of fact, just as - truth is not the same in these cases, so neither is being. Truth and falsity are as - follows: contacti.e. direct and accurate - apprehension. and assertion are truth (for assertion is not the same as - affirmation), and ignorance is non-contact. I say ignorance, because it is impossible to - be deceived with respect to what a thing is, except accidentallyi.e. we cannot be mistaken with regard to a simple term X. We either - apprehend it or not. Mistake arises when we either predicate something wrongly of X, or - analyze X wrongly.; and the same - applies to incomposite substances, for it is impossible to be deceived about them. And - they all exist actually, not potentially; otherwise they would be generated and destroyed; - but as it is, Being itself is not generated (nor destroyed); if it were, it would be - generated out of something. With respect, then, to all things which are essences and - actual, there is no question of being mistaken, but only of thinking or not thinking - them. Inquiry as to what they - are takes the form of inquiring whether they are of such-and-such a nature or - not. As for being in the sense of truth, and not-being in - the sense of falsity, a unity is true if the terms are combined, and if they are not - combined it is false. Again, if the unity exists, it exists in a particular way, and if it - does not exist in that way, it does not exist at all. Truth means to think these objects, and there is no falsity or deception, but only - ignorance—not, however, ignorance such as blindness is; for blindness is like a - total absence of the power of thinking. And it is obvious that with regard to immovable - things also, if one assumes that there are immovable things, there is no deception in - respect of time. E.g., if we suppose that the - triangle is immutable, we shall not suppose that it sometimes contains two right angles - and sometimes does not, for this would imply that it changes; but we may suppose that one - thing has a certain property and another has not; e.g., that no even number is a prime, or - that some are primes and others are not. But about a single number we cannot be mistaken - even in this way, for we can no longer suppose that one instance is of such a nature, and - another not, but whether we are right or wrong, the fact is always the same.

- - -

That "one" has several meanings has been - already statedAristot. Met. 5.6. in our distinction of the various meanings of terms. - But although it has a number of senses, the things which are primarily and essentially - called one, and not in an accidental sense, may be summarized under four heads: (1.) That which is continuous, either absolutely or in particular that which is continuous by natural - growth and not by contact or ligature; and of these things those are more strictly and in - a prior sense one whose motion is more simple and indivisible. (2.) Of this kind in a still - higher degree is that which is a whole and has a definite shape or form, particularly that - which is such by nature and not by constraint (like things which are joined by glue or - nails or by being tied together), but which contains in itself the cause of its - continuity. A thing is of this kind if its - motion is one and indivisible in respect of place and time; so that clearly if a thing has - as its principle of motion the primary kind of motion (i.e. locomotion) in its primary - form (i.e. circular locomotion), it is in the primary sense one spatial - magnitude.This description applies to the - celestial spheres. Some things, then, are one in - this sense, qua continuous or whole; the other things which are one - are those whose formula is one. Such are the - things of which the concept is one, i.e. of which the concept is indivisible; and this is - indivisible when the object is indivisible (3.) in form or (4.) in number. Now in number - the individual is indivisible, and in form that which is indivisible in comprehension and - knowledge; so that that which causes the unity of substances must be one in the primary - sense. Such, then, in number are the meanings - of "one": the naturally continuous, the whole, the individual, and the universal. All - these are one because they are indivisible; some in motion, and others in concept or - formula. But we must recognize that the questions, "What sort of things are called one?" and - "What is essential unity, and what is the formula?" must not be taken to be the same. - "One" has these several meanings, and each - thing to which some one of these senses applies will be one; but essential unity will have - now one of these senses and now something else, which is still nearer to the - term one, whereas they are nearer to its denotation . This is - also true of "element" and "cause," supposing that one had to explain them both by - exhibiting concrete examples and by giving a definition of the term. There is a sense in which fire is an element (and no doubt so - too is "the indeterminate"The reference is - undoubtedly to Anaximander. or some other similar thing, of its own nature), and - there is a sense in which it is not; because "to be fire" and "to be an element" are not - the same. It is as a concrete thing and as a stuff that fire is an element; but the term - "element" denotes that it has this attribute: that something is made of it as a primary - constituent. The same is true of "cause" or - "one" and all other such terms. Hence "to be one" means "to - be indivisible" (being essentially a particular thing, distinct and separate in place or - form or thought), or "to be whole and indivisible"; but especially "to be the first - measure of each kind," and above all of quantity; for it is from this that it has been - extended to the other categories. Measure is that by which quantity is known, and - quantity qua quantity is known either by unity or by number, and - all number is known by unity. Therefore all quantity qua quantity - is known by unity, and that by which quantities are primarily known is absolute - unity. Thus unity is the starting point of - number qua number. Hence in other cases too "measure" means that by - which each thing is primarily known, and the measure of each thing is a unit—in - length, breadth, depth, weight and speed. (The - terms "weight" and "speed" are common to both contraries, for each of them has a double - meaning; e.g., "weight" applies to that which has the least amount of gravity and also to - that which has excess of it, and speed to that which has the least amount of motion and - also to that which has excess of it; for even the slow has some speed, and the light some - weight.) In - all these cases, then, the measure and starting-point is some indivisible unit (since even - in the case of lines we treat the "one-foot line" as indivisible). For everywhere we - require as our measure an indivisible unit; i.e., that which is simple either in quality - or in quantity. Now where it seems impossible - to take away or add, there the measure is exact. Hence the measure of number is most exact, - for we posit the unit as in every way indivisible; and in all other cases we follow this - example, for with the furlong or talent or in general with the greater measure an addition - or subtraction would be less obvious than with a smaller one. Therefore the first thing from which, according to our perception, - nothing can be subtracted is used by all men as their measure of wet and dry, weight and - magnitude; and they think that they know the quantity only when they know it in terms of - this measure. And they know motion too by simple motion and the most rapid, for this takes - least time. Hence in astronomy a unit of this - kind is the starting point and measure; for they assume that the motion of the heavens is - uniform and the most rapid, and by it they judge the others. In music the measure is the - quarter tone, because it is the smallest interval; and in language the letter. All these - are examples of units in this sense—not in the sense that unity is something common - to them all, but in the sense which we have described. The measure is not always numerically one, but sometimes more than - one; e.g., there are two quarter tones, distinguished not by our hearing but by their - theoretical ratiosi.e., the enharmonic (or - quarter-tone proper) and the chromatic, which was 1/3 of a tone (Aristoxenus 1.21, 2.51). There was also the DI/ESIS - H(MIOLI/A, which was 3/8 of a tone.; and the articulate sounds by - which we measure speech are more than one; and the diagonal of a square is measured by two - quantities,The meaning seems to be that the - diameter consists of two parts, one equal to the side, and the other representing its - excess over the side; the two parts being incommensurate are measured by different units - (Ross). KAI\ H( PLEURA/ must, I think, be a - gloss. and so are all magnitudes of this kind. Thus unity is the measure of all - things, because we learn of what the substance is composed by dividing it, in respect of either quantity or form. Hence unity is indivisible, because that which is - primary in each class of things is indivisible. But not every unit is indivisible in the - same sense—e.g. the foot and the arithmetical unit; but the latter is absolutely - indivisible, and the former must be classed as indivisible with respect to our power of - perception, as we have already stated; since presumably everything which is continuous is - divisible. The measure is always akin to the thing measured. The measure of magnitude is magnitude, - and in particular the measure of length is a length; of breadth, a breadth; of sounds, a - sound; of weight, a weight; of units, a unit; for this is the view that we must take, and - not that the measure of numbers is a number. The latter, indeed, would necessarily be - true, if the analogy held good; but the supposition is not analogous—it is as though - one were to suppose that the measure of units is units, and not a unit; for number is a - plurality of units. We also speak of knowledge or sense perception as a measure of things - for the same reason, because through them we come to know something; whereas really they - are measured themselves rather than measure other things. But our experience is as though - someone else measured us, and we learned our height by noticing to what extent he applied - his foot-rule to us. Protagoras says that "man - is the measure of all things," meaning, as it were, the scholar or the man of perception; - and these - because they possess, the one knowledge, and the other perception, which we hold to be the - measures of objects. Thus, while appearing to say something exceptional, he is really - saying nothing.What Protagoras really meant was - (apparently) that appearances are true relatively to the percipient. Cf. Aristot. Met. 4.4.27, and see Burnet, Greek - Philosophy (Part I. Thales to Plato), 92. Obviously, then, unity in the strictest - sense, if we make our definition in accordance with the meaning of the term, is a measure; - particularly of quantity, and secondarily of quality. Some things will be of this kind if - they are indivisible in quantity, and others if in quality. Therefore that which is one is - indivisible, either absolutely or qua one. We must inquire, with regard - to the substance and nature of unity, in which sense it exists. This is the same question - which we approached in our discussion of difficultiesAristot. Met. 3.4.24-27.: - what unity is, and what view we are to take of it; whether that unity - itself is a kind of substance—as first the Pythagoreans, and later Plato, both - maintain—or whether rather some nature underlies it, and we should give a more - intelligible account of it, and more after the manner of the physicists; for of them - oneEmpedocles. holds that the One is Love, - anotherAnaximenes. Air, and anotherAnaximander. the Indeterminate. Now if no universal can be a - substance (as we have stated in our discussionAristot. Met. 7.13. of substance and being), - and being itself cannot be a substance in the sense of one thing existing alongside the - many (since it is common to them), but only as a predicate, then clearly neither can unity be a substance; because being and unity are - the most universal of all predicates. Therefore - (a) genera are not certain entities and substances separate from other things; and (b) - unity cannot be a genus, for the same reasons that being and substance cannot.Cf. Aristot. Met. - 3.3.7. Further, the nature of unity must - be the same for all categories. Now being and - unity have the same number of meanings; so that since in the category of qualities unity - is something definite, i.e. some definite entity, and similarly in the category of - quantity, clearly we must also inquire in general what unity is, just as in the case of - being; since it is not enough to say that its nature is simply unity or being. But in the sphere of colors unity is a color, e.g. - white; that is if all the other colors are apparently derived from white and black, and - black is a privation of white, as darkness is of light. Thus if all existing things were - colors, all existing things would be a number; but of what? Clearly of colors. And unity would be some one color, e.g. white. - Similarly if all existing things were tunes, there would be a number—of - quarter-tones; but their substance would not be a number; and unity would be something - whose substance is not unity but a quarter-tone. Similarly in the case of sounds, existing - things would be a number of letters, and unity would be a vowel; and if existing things were right-lined figures, they would be a - number of figures, and unity would be a triangle. And the same principle holds for all - other genera. Therefore if in the categories of passivity and quality and quantity and - motion there is in every category a number and a unity, and if the number is of particular - things and the unity is a particular unity, and its substance is not unity, then the same - must be true in the case of substances, because the same is true in all cases. It is obvious, then, - that in every genus one is a definite entity, and that in no case is its nature merely - unity; but as in the sphere of colors the One-itself which we have to seek is one color, - so too in the sphere of substance the One-itself is one substance. And that in a sense unity means the same as being is clear (a) - from the fact that it has a meaning corresponding to each of the categories, and is - contained in none of them—e.g., it is contained neither in substance nor in quality, - but is related to them exactly as being is; (b) from the fact that in "one man" nothing - more is predicated than in "man"Cf. Aristot. Met. 4.2.6-8.(just as Being too does - not exist apart from some thing or quality or quantity); and (c) because "to be one" is - "to be a particular thing." "One" and "Many" are opposed - in several ways. Unity and Plurality are opposed as being indivisible and divisible; for - that which is divided or divisible is called a plurality, and that which is indivisible or - undivided is called one. Then since opposition is of four kinds, and one of the present - pairs of opposites is used in a privative sense, they must be contraries, and neither - contradictories nor relative terms. Unity is - described and explained by its contrary—the indivisible by the - divisible—because plurality, i.e. the divisible, is more easily perceptible than the - indivisible; and so in formula plurality is prior to the indivisible, on account of our - powers of perception. To Unity belong (as we showed by - tabulation in our distinction of the contrariesCf. - Aristot. Met. 4.2.9.) Identity, - Similarity and Equality; and to Plurality belong Otherness, Dissimilarity and - Inequality. "Identity"Or "the same." Cf. Aristot. Met. 5.9. has several meanings. (a) - Sometimes we speak of it in respect of number. (b) We call a thing the same if it is one - both in formula and in number, e.g., you are one with yourself both in form and in matter; - and again - (c) if the formula of the primary substance is one, e.g., equal straight lines are the - same, and equal quadrilaterals with equal angles, and there are many more examples; but in - these equality means unity. Things are "similar"Or "like." - Cf. Aristot. Met. 5.9.5.(a) if, while not - being the same absolutely or indistinguishable in respect of their concrete substance, - they are identical in form; e.g the larger square is similar to the smaller, and unequal - straight lines are similar. These are similar, but not absolutely the same. (b) If, having - the same form, and being capable of difference in degree, they have no difference of - degree. (c) If things have an attribute which - is the same and one in form—e.g. white—in different degrees, we say that they - are similar because their form is one. (d) If the respects in which they are the same are - more than those in which they differ, either in general or as regards their more prominent - qualities; e.g., tin is similar to silver, as being white; and gold to fire, as being - yellow or flame-colored. Thus it is obvious that "Other"Cf. Aristot. Met. 5.9.4. and "Unlike" - also have several meanings. (a) In one sense "other" is used in the sense opposite to "the - same"; thus everything in relation to every other thing is either "the same" or "other." - (b) In another sense things are "other" unless both their matter and their formula are - one; thus you are "other" than your neighbor. (c) The third sense is that which is found - in mathematics.sc. as opposed to "same" in sense - (a); 3 above. Therefore everything in relation to everything else is called - either "other" or "the same"; that is, in the case of things of which unity and being are - predicated; for "other" is not the contradictory of "the same," and so it is not - predicated of non-existent things (they are called "not the same"), but it is predicated - of all things which exist; for whatever is by nature existent and one is either one or not - one with something else. "Other" and "same," then, are - opposed in this way; but "difference"Cf. Aristot. Met. 5.9.4. is distinct from - "otherness." For that which is "other" than - something need not be other in a particular respect, since everything which is existent is - either "other" or "the same." But that which is different from something is different in - some particular respect, so that that in which they differ must be the same sort of thing; - i.e. the same genus or species. For everything - which is different differs either in genus or in species—in genus, such things as - have not common matter and cannot be generated into or out of each other, e.g. things - which belong to different categories; and in species, such things as are of the same genus - (genus meaning that which is predicated of both the different things alike in respect of - their substance). The contrariesCf. Aristot. Met. 5.10. are different, and - contrariety is a kind of difference. That this is rightly premissed is made clear by - induction; for the contraries are obviously all different, since they are not merely - "other," but some are other in genus, and others are in the same line of predication, - and so - are in the same genus and the same in genus. We have distinguished elsewhereAristot. Met. - 5.28.4. what sort of things are the same or other in genus. Since things which - differ can differ from one another in a greater or less degree, there is a certain maximum - difference, and this I call contrariety. That it is the maximum difference is shown by - induction. For whereas things which differ in genus have no means of passing into each - other, and are more widely distant, and are not comparable, in the case of things which - differ in species the contraries are the extremes from which generation takes - place; and the greatest distance is that - which is between the extremes, and therefore also between the contraries. But in every - class the greatest thing is complete. For (a) that is greatest which cannot be exceeded, - and (b) that is complete outside which nothing proper to it can be found. For complete - difference implies an end, just as all other things are called complete because they imply - an end. And there is nothing beyond the end; - for in everything the end is the last thing, and forms the boundary. Thus there is nothing - beyond the end, and that which is complete lacks nothing. From this argument, then, it is clear that contrariety is maximum difference; and since - we speak of contraries in various senses, the sense of completeness will vary in - accordance with the sense of contrariety which applies to the contraries. This being so, evidently one thing cannot have more than one contrary - (since there can be nothing more extreme than the extreme, nor can there be more than two - extremes of one interval); and in general this is evident, if contrariety is difference, - and difference (and therefore complete difference) is between two things. The other definitions of - contraries must also be true, for (1.) complete difference is the maximum difference; - since (a) we can find nothing beyond it, whether things differ in genus or in species (for - we have shown that difference in relation to things outside the genus is impossible; this - is the maximum difference between them); and (b) the things which differ most in the same - genus are contraries; for complete difference is the maximum difference between - these. (2.) The things which differ most in - the same receptive material are contraries; for contraries have the same matter. (3.) The - most different things which come under the same faculty are contraries; for one science - treats of one class of things, in which complete difference is the greatest. "Positive state" and - "Privation" constitute primary contrariety—not every form of privation (for it has - several senses), but any form which is complete. All other contraries must be so called - with respect to these; some because they possess these, others because they produce them - or are productive of them, and others because they are acquisitions or losses of these or - other contraries. Now if the types of - opposition are contradiction, privation, contrariety and relation, and of these the primary type - is contradiction, and an intermediate is impossible in contradiction but possible between - contraries, obviously contradiction is not the same as contrariety; and privation is a - form of contradiction; for it is either that - which is totally incapable of possessing some attribute,This is not a proper example of privation. Cf. Aristot. Met. 5.22. or that which would - naturally possess some attribute but does not, that suffers privation—either - absolutely or in some specified way. Here we already have several meanings, which we have - distinguished elsewhere. Thus privation is a kind of contradiction or incapacity which is - determinate or associated with the receptive material. This is why though there is no intermediate in contradiction there is - one in some kinds of privation. For everything is either equal or not equal, but not - everything is either equal or unequal; if it is, it is only so in the case of a material - which admits of equality. If, then, processes of material generation start from the - contraries, and proceed either from the form and the possession of the form, or from some - privation of the form or shape, clearly all contrariety must be a form of privation, - although presumably not all privation is contrariety. This is because that which suffers privation may suffer it in several - senses; for it is only the extremes from which changes proceed that are - contraries. This can also be shown by induction. Every - contrariety involves privation as one of its contraries, but not always in the same - way: inequality involves the privation of - equality, dissimilarity that of similarity, evil that of goodness. And the differences are as we have stated: one case is, if a - thing is merely deprived; another, if it is deprived at a certain time or in a certain - part—e.g. at a certain age or in the important part—or entirely. Hence in some - cases there is an intermediate (there are men who are neither good nor bad), and in others - there is not—a thing must be either odd or even. Again, some have a determinate subject, and others have not. Thus it - is evident that one of a pair of contraries always has a privative sense; but it is enough - if this is true of the primary or generic contraries, e.g. unity and plurality; for the - others can be reduced to them. Since one thing has one contrary, it might be asked in what sense - unity is opposed to plurality, and the equal to the great and to the small. For if we - always use the word "whether" in an antithesis—e.g., "whether it is white or black," - or "whether it is white or not" (but we do not ask "whether it is a man or white," unless - we are proceeding upon some assumption, and asking, for instance, whether it was Cleon who - came or Socrates. This is not a necessary - disjunction in any class of things, but is derived from the use in the case of - opposites—for it is only opposites that cannot be true at the same time—and we - have this same use here in the question "which of the two came?" for if both alternatives were - possible, the question would be absurd; but even so the question falls into an antithesis: - that of "one" or "many"—i.e., "whether both came, or one")— if, then, the question "whether" is always concerned with - opposites, and we can ask "whether it is greater or smaller, or equal," what is the nature - of the antithesis between "equal" and "greater or smaller"? It is contrary neither to one - only, nor to both: for (a) it is no more contrary to the greater than to the smaller; (b) - "equal" is contrary to "unequal," and thus it will be contrary to more than one - thing; (c) if "unequal" means the same as - both "greater" and "smaller" at the same time, "equal" must still be opposed to them both: - This difficulty supports the theoryHeld by the - Platonists. Cf. Aristot. Met. 14.1.4, 5. - that "the unequal" is a duality. But the result is that one thing is contrary to two; - which is impossible. Further, it is apparent that "equal" is intermediate between "great" - and "small," but it is not apparent that any contrariety is intermediate, nor can it be, - by definition; for it could not be complete if it were the intermediate of something, but - rather it always has something intermediate between itself and the other - extreme. It remains, then, that it is opposed either as - negation or as privation. Now it cannot be so opposed to one of the two, for it is no more - opposed to the great than to the small. Therefore it is a privative negation of both. For this reason we say "whether" with - reference to both, and not to one of the two—e.g., "whether it is greater or equal," - or "whether it is equal or smaller"; there are - always three alternatives. But it is not a necessary privation; for not everything is - equal which is not greater or smaller, but only things which would naturally have these - attributes. The equal, then, is that which is neither great nor small, but would naturally be either - great or small; and it is opposed to both as a privative negation, and therefore is - intermediate between them. And that which is neither good nor bad is opposed to both, but - it has no name (for each of these terms has several meanings, and there is no one material - which is receptive of both); that which is neither white nor black is better entitled to a - name, although even this has no single name, - but the colors of which this negation is privatively predicated are to a certain extent - limited; for it must be either grey or buff or something similar. Therefore those persons are - wrong in their criticism who imagine that all terms are used analogously, so that that - which is neither a shoe nor a hand will be intermediate between "shoe" and "hand," because - that which is neither good nor bad is intermediate between good and bad—as though - there must be an intermediate in all cases; but this does not necessarily - follow. For the one is a joint negation of - opposites where there is an intermediate and a natural interval; but in the other case there is - no question of difference, since the joint negation applies to things which are in - different genera, and therefore the substrate is not one.Cf. Aristot. Met. - 10.3.8 A similar question might be raised about "one" and "many." For if - "many" is absolutely opposed to "one," certain impossibilities result. (1) One will be - few; for "many" is also opposed to "few." (2) - Two will be many; since "twofold" is "manifold," and "twofold" is derived from two. - Therefore one will be few; for in what relation can two be many if not in relation to one, - which must therefore be few? for there can be nothing less. (3) If "much" and "little" are - in plurality what "long" and "short" are in length, and if whatever is "much" is also - "many," and "many" is "much" (unless indeed - there is a difference in the case of a plastic continuumi.e., a fluid, which cannot be described as "many."), "few" will - be a plurality. Therefore one will be a plurality, if it is few; and this necessarily - follows if two is many. Presumably, however, although "many" in a sense means "much," - there is a distinction; e.g., water is called "much" but not "many." To all things, however, which are divisible the term "many" is - applicable: in one sense, if there is a plurality which involves excess either absolutely - or relatively (and similarly "few" is a plurality involving defect); and in another in the - sense of number, in which case it is opposed to "one" only. For we say "one or many" just as if we were to say "one and ones," or - "white thing and white things," or were to compare the things measured with the - measure. Multiples, too, are spoken of in - this way; for every number is "many," because it consists of "ones," and because every - number is measurable by one; and also as being the opposite of one, and not of few. In - this sense even two is many; but as a plurality involving excess either relatively or - absolutely it is not many, but the first plurality. Two is, however, absolutely few; - because it is the first plurality involving defect (hence AnaxagorasCf. Aristot. Met. 1.3.9. was not right in leaving - the subject by saying "all things were together, infinite both in multitude and in - smallness"; instead of "in smallness" he should have said "in fewness,"sc. "and then the absurdity of his view would have been - apparent, for," etc. Aristotle assumes the Anaxagoras meant "smallness" (MIKRO/THS) to be the opposite of "multitude" (PLH=QOS); but he meant just what he said—that the - particles of which things consist are infinitely many and infinitely small. See Bowman - in Classical Review 30, 42-44. for things cannot be infinite in fewness), since - fewness is constituted not by one, as some hold, but by two. In the sphere of numbers "one" is opposed - to many as the measure to the measurable, i.e., as relative terms are opposed which are - not of their own nature relative. We have distinguished elsewhereAristot. Met. 5.15.8, 9. - that things are called relative in two senses—either as being contraries, or as - knowledge is related to the knowable, A being related to B because B is described in - relation to A. There is no reason why one should not be fewer than something, e.g. two; for if it is - fewer it is not therefore few. Plurality is, as it were, a genus of number, since number - is a plurality measurable by one. And in a sense one and number are opposed; not, however, - as being contrary, but as we have said some relative terms to be; for it is qua measure and measurable that they are opposed. (Hence not everything which is one is a number—e.g., a - thing which is indivisible.) But although the relation between knowledge and the knowable - is said to be similar to this, it turns out not to be similar. For it would seem that - knowledge is a measure, and the knowable that which is measurable by it; but it happens - that whereas all knowledge is knowable, the knowable is not always knowledge, because in a - way knowledge is measured by the knowable.Cf. Aristot. Met. 10.1.19. Plurality is contrary neither - to the few (whose real contrary is the many, as an excessive plurality to an exceeded - plurality) nor in all senses to one; but they are contrary in one sense (as - has been said) as being the one divisible and the other indivisible; and in another as - being relative (just as knowledge is relative to the knowable) if plurality is a number - and one is the measure. Since there can be, and in some cases is, an intermediate between - contraries, intermediates must be composed of contraries; for all intermediates are in the same genus as the things between which - they are intermediate. By intermediates we mean - those things into which that which changes must first change. E.g., if we change from the - highest string to the lowest by the smallest gradations we shall first come to the - intermediate notes; and in the case of colors if we change from white to black we shall - come to red and grey before we come to black; and similarly in other cases. But change from one genus into another is impossible - except accidentally; e.g., from color to shape. Therefore intermediates must be in the - same genus as one another and as the things between which they are intermediate. But all intermediates are between certain opposites, for it is only - from these per se that change is possible. Hence there can be no intermediate between things which are not opposites; for then - there would be change also between things which are not opposites. Of things which are - opposites, contradiction has no intermediate term (for contradiction means this: an - antithesis one term of which must apply to any given thing, and which contains no - intermediate term); of the remaining types of opposites some are relative, others - privative, and others contrary. Those relative - opposites which are not contrary have no intermediate. The reason for this is that they - are not in the same genus— for what is intermediate between knowledge and the - knowable?—but between great and small there is an intermediate. Now since - intermediates are in the same genus, as has been shown, and are between contraries, they - must be composed of those contraries. For the contraries must either belong to a genus or - not. And if there is a genus in such a way that - it is something prior to the contraries, then the differentiae which constitute the - contrary species (for species consist of genus and differentiae) will be contraries in a - prior sense. E.g., if white and black are - contraries, and the one is a penetrativeThis is - Plato's definition. Cf. Plat. Tim. 67d, e. and - the other a compressive color, these differentiae, "penetrative" and "compressive," are - prior, and so are opposed to each other in a prior sense. But it is the species which have contrary differentiae that are more - truly contraries; the other, i.e. intermediate, species will consist of genus and - differentiae. E.g., all colors which are intermediate between white and black should be - described by their genus (i.e. color) and by certain differentiae. But these differentiae will not be the primary contraries; - otherwise every thing will be either white or black. Therefore they will be different from - the primary contraries. Therefore they will be intermediate between them, and the primary - differentiae will be "the penetrative" and "the compressive." Thus we must first investigate the contraries which are not contained in a - genus, and discover of what their intermediates are composed. For things which are in the same genus must either be composed of - differentiae which are not compounded with the genus, or be incomposite. Contraries are - not compounded with one another, and are therefore first principles; but intermediates are - either all incomposite or none of them. Now from the contraries something is generated in - such a way that change will reach it before reaching the contraries themselves (for there - must be something which is less in degree than one contrary and greater than the other). - Therefore this also will be intermediate between the contraries. Hence all the other intermediates must be composite; for that which is - greater in degree than one contrary and less than the other is in some sense a compound of - the contraries of which it is said to be greater in degree than one and less than the - other. And since there is nothing else homogeneous which is prior to the contraries, all - intermediates must be composed of contraries. Therefore all the lower terms, both contraries and intermediates, must be composed of - the primary contraries. Thus it is clear that intermediates are all in the same genus, and - are between contraries, and are all composed of contraries. That which is "other in species" than - something else is "other" in respect of something and that something must apply to both. - E.g., if an animal is other in species than something else, they must both be animals. - Hence things which are other in species must be in the same genus. The sort of thing I - mean by "genus" is that in virtue of which two things are both called the same one thing; - and which - is not accidentally differentiated, whether regarded as matter or otherwise. For not only must the common quality belong to both, - e.g., that they are both animals, but the very animality of each must be different; e.g., - in one case it must be equinity and in the other humanity. Hence the common quality must - for one be other in species than that which it is for the other. They must be, then, of - their very nature, the one this kind of animal, and the other - that ; e.g., the one a horse and the other a man. Therefore this difference must be "otherness of genus" (I say - "otherness of genus" because by "difference of genus" I mean an otherness which makes the - genus itself other); this, then, will be a form of contrariety. This is obvious by - induction.Aristotle does not use induction to - prove his point; indeed he does not prove it at all. For all differentiation is - by opposites, and we have shownIn ch. 4. - that contraries are in the same genus, because contrariety was shown to be complete - difference. But difference in species is always difference from something in respect of - something; therefore this is the same thing, i.e. the genus, for both. (Hence too all contraries which differ in species but not in - genus are in the same line of predication,Or - "category." and are other than each other in the highest degree; for their - difference is complete, and they cannot come into existence simultaneously.) Hence the - difference is a form of contrariety. To be "other in - species," then, means this: to be in the same genus and involve contrariety, while being - indivisible (and "the same in species" - applies to all things which do not involve contrariety, while being - indivisible); for it is in the course of - differentiation and in the intermediate terms that contrariety appears, before we come to - the indivisibles.i.e., indivisible species and - individuals. Thus it is evident that - in relation to what is called genus no species is either the same or other in species (and - this is as it should be, for the matter is disclosed by negation, and the genus is the - matter of that of which it is predicated as genus; not in the sense in which we speak of - the genus or clan of the Heraclidae,Cf. Aristot. Met. 5.28.1. but as we speak of a - genus in nature); nor yet in relation to things which are not in the same genus. From the - latter it will differ in genus, but in species from things which are in the same genus. - For the difference of things which differ in species must be a contrariety; and this - belongs only to things which are in the same genus. The question might be raised as to why - woman does not differ in species from man, seeing that female is contrary to male, and - difference is contrariety; and why a female and a male animal are not other in species, - although this difference belongs to "animal" per se, and not as whiteness or blackness - does; "male" and "female" belong to it qua animal. This problem is practically the same as "why does one - kind of contrariety (e.g. "footed" and "winged") make things other in species, while - another (e.g. whiteness and blackness) does not?" The answer may be that in the one case - the attributes are peculiar to the genus, and in the other they are less so; and since one - element is formula and the other matter, contrarieties in the formula produce difference - in species, but contrarieties in the concrete whole do not. Hence the whiteness or blackness of a man does not produce this, nor - is there any specific difference between a white man and a black man; not even if one term - is assigned to each. For we are now regarding "man" as matter, and matter does not produce - difference; and for this reason, too, individual men are not species of "man," although - the flesh and bones of which this and that man consist are different. The concrete whole - is "other," but not "other in species," because there is no contrariety in the formula, - and this is the ultimate indivisible species. But Callias is definition and matter. Then so too is "white man," because - it is the individual, Callias, who is white. Hence "man" is only white accidentally. - Again, a bronze circle and a wooden one do not differ in species; and a bronze triangle - and a wooden circle differ in species not because of their matter, but because there is - contrariety in their formulae. But does not matter, when it is "other" in a particular way, make - things "other in species"? Probably there is a sense in which it does. Otherwise why is - this particular horse "other in species" than this particular man, although the - definitions involve matter? Surely it is because there is contrariety in the definition, - for so there also is in "white man" and "black horse"; and it is a contrariety in species, but not because one is white and the - other black; for even if they had both been white, they would still be "other in - species." "Male" and "female" are attributes peculiar to the animal, but not in virtue of its - substance; they ar material or physical. Hence the same semen may, as the result of some - modification, become either female or male. We have now - stated what "to be other in species" means, and why some things differ in species and - others do not. Since contraries are other in form,It appears that - in this chapter (apart from 5, which may be a later addition) the terms EI)=DOS and GE/NOS are used in - a non-technical sense. Cf. Ross on Aristot. Met. - 1058b 28. and "the perishable" and "imperishable" are contraries (for - privation is a definite incapacity), "the perishable" must be "other in kind" than "the - imperishable." But so far we have spoken only of the universal terms; and so it might - appear to be unnecessary that anything perishable and imperishable should be - "other in form," just as in the case of white and black. For the same thing may be both at the same time, if it is a universal - (e.g, "man" may be both white and black); and it may still be both if it is a particular, - for the same person may be white and black, although not at the same time. Yet white is - contrary to black. But although some contraries (e.g. those which we have just mentioned, and many others) can belong to certain things - accidentally, others cannot; and this applies to "the perishable" and "the imperishable." - Nothing is accidentally perishable; for that which is accidental may not be applicable; - but perishability is an attribute which applies necessarily when it is applicable at all. - Otherwise one and the same thing will be imperishable as well as perishable, if it is - possible for perishability not to apply to it. Thus perishability must be either the substance or in the substance of every perishable - thing. The same argument also applies to the imperishable; for both perishability and - imperishability are attributes which are necessarily applicable. Hence the characteristics - in respect of which and in direct consequence of which one thing is perishable and another - imperishable are opposed; and therefore they must be other in kind. Thus it is obvious that there cannot be Forms such as some - thinkers maintain; for then there would be both a perishable and an imperishable - "man."i.e., the individual man is perishable and - the Idea of man imperishable; and these must be other in kind (GE/NEI non-technical). But the Platonists hold that the Idea is the same in - species as the particular. This is impossible if it is other in genus (GE/NEI technical). Yet the Forms are said to be the same - in species as the particulars, and not merely to share a common predicate with them; but - things which are other in genus differ more widely than things which are other in - species.

- - -

That - wisdom is a science of first principles is clear from our Introductory remarks,Aristot. Met. - 1.3-10. in which we of raised objections to the statements of other - thinkers about the first principles. It might be - asked, however, whether we should regard Wisdom as one science or as more than one.Cf. Aristot. Met. - 3.1.5, Aristot. Met. 3.2.1-10. If - as one, it may be objected that the objects of one science are always contraries; but the - first principles are not contraries. And if it is not one, what sort of sciences are we to - suppose them to be? Again, is it the province of one science, or of more than one, to - study the principles of demonstration?Cf. Aristot. Met. 3.1.5, , Aristot. Met. 3.2.10-15, where the problem - takes a slightly different form. If of one, why of it rather than of any other? - And if of more than one, of what sort are we to suppose them to be? Again, are we to suppose that Wisdom deals with all substances or not?Cf. Aristot. Met. - 3.1.6, Aristot. Met. 3.2.15-17. If - not with all, it is hard to lay down with what kind it does deal; while if there is one - science of them all, it is not clear how the same science can deal with more than one - subject. Again, is this science concerned only with substances, or with attributes as well?Cf. Aristot. Met. - 3.1.8-10, Aristot. Met. 3.2.18-19. - For if it is a demonstration of attributes, it is not concerned with substances; and if - there is a separate science of each, what is each of these sciences, and which of them is - Wisdom? qua demonstrative, the science of attributes appears to be - Wisdom; but qua concerned with that which is primary, the science - of substances. Nor must we suppose that the science which we are seeking is concerned with the causes - described in the Physics.Aristot. Physics 2.3. It is not concerned with - the final cause; for this is the Good, and this belongs to the sphere of action and to - things which are in motion; and it is this which first causes motion (for the - end is of this nature); but there is no Prime Mover in the sphere of - immovable things. And in general it is a - difficult question whether the science which we are now seeking is concerned with sensible - substances, or not with sensible substances, but with some other kind.Cf. Aristot. Met. 3.1.7, Aristot. Met.3.2.20-30. If with another - kind, it must be concerned either with the Forms or with mathematical objects. Now clearly - the Forms do not exist. (But nevertheless, even if we posit them, it is a difficult - question as to why the same rule does not apply to the other things of which there are - Forms as applies to the objects of mathematics. I mean that they posit the objects of mathematics as intermediate between the Forms and - sensible things, as a third class besides the Forms and the things of our world; but there - is no "third man"This phrase has no technical sense - here; cf. Aristot. Met. 1.9.4. or "horse" - besides the Ideal one and the particulars. If on the other hand it is not as they make - out, what sort of objects are we to suppose to be the concern of the mathematician? Not - surely the things of our world; for none of these is of the kind which the mathematical - sciences investigate.) Nor indeed is the - science which we are now seeking concerned with the objects of mathematics; for none of - them can exist separately. But it does not deal with sensible substances either; for they - are perishable. In general the question might be raised, to - what science it pertains to discuss the problems concerned with the matteri.e., intelligible matter (cf. Aristot. Met. 7.10.18). This problem is not raised in - Book 3. of mathematical objects. It is - not the province of physics, because the whole business of the physicist is with things - which contain in themselves a principle of motion and rest; nor yet of the science which - inquires into demonstration and scientific - knowledge, for it is simply this sort of thing - which forms the subject of its inquiry. It remains, therefore, that it is the science - which we have set ourselves to find that treats of these subjects. One might consider the - question whether we should regard the science which we are now seeking as dealing with the - principles which by some are called elements.Cf. - Aristot. Met. 3.1.10, Aristot. Met. 3.3. But everyone assumes that - these are present in composite things; and it would seem rather that the science which we - are seeking must be concerned with universals, since every formula and every science is of - universals and not of ultimate species; so that in this case it must deal with the primary - genera. These would be Being and Unity; for - these, if any, might best be supposed to embrace all existing things, and to be most of - the nature of first principles, because they are by nature primary; for if they are - destroyed, everything else is destroyed with them, since everything exists and is - one. But inasmuch as, if Being and Unity are - to be regarded as genera, they must be predicable of their differentiae, whereas no genus - is predicable of any of its differentiae, from this point of view it would seem that they - should be regarded neither as genera nor as principles. Further, since the more simple is more nearly a principle than the - less simple, and the ultimate subdivisions of the genus are more simple than the genera - (because they are indivisible), and the genera are divided into a number of different - species, it would seem that species are more nearly a principle than genera. On the other hand, inasmuch as species are destroyed - together with their genera, it seems more likely that the genera are principles; - because - that which involves the destruction of something else is a principle. These and other - similar points are those which cause us perplexity. Again, ought we to assume the existence - of something else besides particular things, or are they the objects of the science which - we are seeking?Cf. Aristot. Met. 3.1.11, Aristot. Met. - 3.4.1-8. It is true that they are infinite in number; but then the - things which exist besides particulars are genera or species, and neither of these is the - object of the science which we are now seeking. We have explained - Aristot. Met. 11.1.11-13 - why this is impossible. Indeed, in - general it is a difficult question whether we should suppose that there is some substance - which exists separately besides sensible substances (i.e. the substances of our world), or - that the latter constitute reality, and that it is with them that Wisdom is concerned. It - seems that we are looking for some other kind of substance, and that this - is the object of our undertaking: I mean, to see whether there is anything which exists - separately and independently, and does not appertain to any sensible thing. But again, if there is another kind of substance - besides sensible substances, to what kind of sensible things are we to suppose that it - corresponds? Why should we suppose that it corresponds to men or horses rather than to - other animals, or even to inanimate objects in general? And yet to manufacture a set of - eternal substances equal in number to those which are sensible and perishable would seem - to fall outside the bounds of plausibility. Yet - if the principle which we are now seeking does not exist in separation from - bodies, what can we suppose it to be if not - matter? Yes, but matter does not exist actually, but only potentially. It might seem - rather that a more appropriate principle would be form or shape; but this is - perishableForms which are induced in matter are - perishable, although not subject to the process of destruction; they are at - one time and are not at another (cf. Aristot. Met. - 7.15.1). The only pure form (i.e., the only form which is independent of matter - in any and every sense) is the prime mover (Aristot. - Met. 12.7).; and so in general there is no eternal substance which - exists separately and independently. But this - is absurd, because it seems natural that there should be a substance and principle of this - kind, and it is sought for as existing by nearly all the most enlightened thinkers. For - how can there be any order in the universe if there is not something eternal and separate - and permanent? Again, if there is a substance and principle of such a nature as that which we are now - seeking, and if it is one for all things, i.e. the same for both eternal and perishable - things, it is a difficult question as to why, when the principle is the same, some of the - things which come under that principle are eternal, and others not; for this is - paradoxical.Cf. Aristot. Met. 3.1.12, Aristot. Met. - 3.4.11-23. But if there is - one principle of perishable things, and another of eternal things, if the principle of - perishable things is also eternal, we shall still have the same difficulty; because if the - principle is eternal, why are not the things which come under that principle eternal? And - if it is perishable, it must have another principle behind it, and that principle must - have another behind it; and the process will go on to infinity. On the other hand, if we posit - the principles which seem most unchangeable, Being and Unity,Cf. Aristot. Met. 3.1.13, Aristot. Met. 3.4.24-34.(a) unless each of - them denotes a particular thing and a substance, how can they be separate and independent? - but the eternal and primary principles for which we are looking are of this - nature. (b) If, however, each of them denotes - a particular thing and a substance, then all existing things are substances; for Being is - predicated of everything, and Unity also of some things. But that all things are substances is false. (c) As for those who - maintain that Unity is the first principle and a substance, and who generate number from - Unity and matter as their first product, and assert that it is a substance, how can their - theory be true? How are we to conceive of 2 and each of the other numbers thus composed, - as one? On this point they give no explanation; nor is it easy to give one. But if we posit lines - or the things derived from them (I mean surfaces in the primary sensei.e., intelligible surfaces, etc.) as - principles,Cf. Aristot. Met. 3.1.15, Aristot. Met. - 3.5. these at least are not separately existing substances, but sections - and divisions, the former of surfaces and the latter of bodies (and points are sections - and divisions of lines); and further they are limits of these same things. All these - things are integral parts of something else, and not one of them exists - separately. Further, how are we to suppose - that there is a substance of unity or a point? for in the case of every substancesc. which is liable to generation or - destruction. there is a process of generation, but - in the case of the point there is not; for the point is a division. It is a perplexing fact also - that whereas every science treats of universals and types, substance is not a universal - thing, but rather a particular and separable thing; so that if there is a science that - deals with first principles, how can we suppose that substance is a first principle?Cf. Aristot. Met. - 3.1.14, Aristot. Met. - 3.6.7-9. Again, is there anything besides the concrete whole (I mean the - matter and the form in combination) or not?This - section belongs to the problem discussed in 1-5 above. If not, all things in the - nature of matter are perishable; but if there is something, it must be the form or shape. - It is hard to determine in what cases this is possible and in what it is not; for in some - cases, e.g. that of a house, the form clearly does not exist in separation. Again, are the first principles formally or numerically the - same?Cf. Aristot. - Met. 3.1.12, Aristot. Met. - 3.4.8-10. If they are numerically one, all things will be the - same. Since - the science of the philosopher is concerned with Being qua Being - universally,This chapter corresponds to Aristot. Met. 4.1, 2, with which it should be - compared. and not with some part of it, and since the term Being has several - meanings and is not used only in one sense, if it is merely equivocal and has no common - significance it cannot fall under one science (for there is no one class in things of this - kind); but if it has a common significance it must fall under one science. Now it would seem that - it is used in the sense which we have described, like "medical" and "healthy," for we use - each of these terms in several senses; and each is used in this way because it has a reference, - one to the science of medicine, and another to health, and another to something else; but - each refers always to the same concept. A diagnosis and a scalpel are both called medical, - because the one proceeds from medical science and the other is useful to it. The same is true of "healthy"; one thing is so called - because it is indicative, and another because it is productive, of health; and the same - applies to all other cases. Now it is in this same way that everything which exists is - said to be ; each thing is said to be because it is a modification or - permanent or temporary state or motion or some other such affection of Being qua Being. And since - everything that is can be referred to some one common concept, each of the contrarieties - too can be referred to the primary differentiae and contrarieties of Being—whether - the primary differentiae of Being are plurality and unity, or similarity and - dissimilarity, or something else; for we may take them as already discussed.Cf. Aristot. Met. 4.2.9 - n. It makes no difference - whether that which is is referred to Being or Unity; for even if they are not - the same but different, they are in any case convertible, since that which is one also in - a sense is , and that which is is one. Now since the study of - contraries pertains to one and the same science, and each contrary is so called in virtue of privation (although indeed one might wonder - in what sense they can be called contraries in virtue of privation when they admit of a - middle term—e.g. "unjust" and "just"), in all such cases we must regard the - privation as being not of the whole definition but of the ultimate species. E.g., if the - just man is "one who is obedient to the laws in virtue of some volitional state," the - unjust man will not be entirely deprived of the whole definition, but will be "one who is - in some respect deficient in obedience to the laws"; and it is in this respect that the - privation of justice will apply to him (and the same holds good in all other - cases). And just as the mathematician makes a - study of abstractions (for in his investigations he first abstracts everything that is - sensible, such as weight and lightness, hardness and its contrary, and also heat and cold - and all other sensible contrarieties, leaving only quantity and continuity—sometimes - in one, sometimes in two and sometimes in three dimensions—and their affections qua quantitative and continuous, and does not study them with respect - to any other thing; and in some cases investigates the relative positions of things and - the properties of these, and in others their commensurability or incommensurability, and in others - their ratios; yet nevertheless we hold that there is one and the same science of all these - things, viz. geometry), so it is the same with regard to Being. For the study of its attributes in so far as it is Being, and of its - contrarietiesi.e., identity, otherness, - etc. - qua Being, belongs to no other science than Philosophy; for to - physics one would assign the study of things not qua Being but qua participating in motion, while dialectics and sophistry deal with - the attributes of existing things, but not of things qua Being, nor - do they treat of Being itself in so far as it is Being. Therefore it remains that the philosopher is the man who studies the - things which we have described, in so far as they are Being. And since everything that - is , although the term has several meanings, is so described in virtue of - some one common concept, and the same is true of the contraries (since they can be - referred to the primary contrarieties and differences of Being), and since things of this - kind can fall under one science, the difficulty which we stated at the beginningAristot. Met. - 11.1.1. may be regarded as solvedAlso the problem stated in ch. i. 3.—I mean the problem as to how there - can be one science of several things which are different in genus. Since even the mathematician - uses the common axioms only in a particular application, it will be the province of - Primary Philosophy to study the principles of these as well.This chapter corresponds to Aristot. Met. - 4.3.1-6, and answers the problem stated in Aristot. Met. 11.1.2. That when equals are taken from equals the - remainders are equal is an axiom common to all quantities; but mathematics isolates a - particular part of its proper subject matter and studies it separately; e.g. lines or - angles or numbers or some other kind of quantity, but not qua - Being, but only in so far as each of them is continuous in one, two or three dimensions. - But philosophy does not investigate particular things in so far as each of them has some - definite attribute, but studies that which is , in so far as each particular - thing is . The same applies to the - science of physics as to mathematics, for physics studies the attributes and first - principles of things qua in motion, and not qua Being; but Primary Science, as we have said, deals with these things only in - so far as the subjects which underlie them are existent, and not in respect of anything - else. Hence we should regard both physics and mathematics as subdivisions of - Wisdom. There - is a principle in existing things about which we cannot make a mistakeThis chapter corresponds to Aristot. Met. 4.3.7-4.31.; of which, on the - contrary, we must always realize the truth—viz. that the same thing cannot at one - and the same time be and not be, nor admit of any other similar pair of opposites. Of such - axioms although there is a proof ad hominem, there is no absolute proof; because there is no principle more convincing than the axiom - itself on which to base an argument, whereas there must be such a principle if there is to - be absolute proof. But he who wants to - convince an opponent who makes opposite statements that he is wrong must obtain from him - an admission which shall be identical with the proposition that the same thing cannot at - one and the same time be and not be, but shall seem not to be identical with it. This is - the only method of proof which can be used against one who maintains that opposite - statements can be truly made about the same subject. Now those who intend to join in discussion must understand one another - to some extent; for without this how can there be any common discussion between them? - Therefore each of the terms which they use must be intelligible and signify something; not - several things, but one only; or if it signifies more than one thing, it must be made - clear to which of these the term is applied. Now he who says that A is and is not denies what he asserts, and therefore denies that - the term signifies what it does signify. But this is impossible. Therefore if "to be - so-and-so" has a definite meaning, the opposite statement about the same subject cannot be - true. Again, if the term has a definite - significance and this is truly stated, it must of necessity be so.sect. 6=Aristot. Met. - 4.4.14-16. But that which of necessity is can never not be. Hence opposite - statements about the same subject cannot be true. Again, if - the assertion is no more true than the negation, it will be no more true to say "A is man" - than to say "A is not man."With this section cf. - Aristot. Met. 4.4.26-30. But it would also be admitted that it is more or at - least not less true to say that a man is not a horse than to say that he is not a man; and - therefore, since it was assumed that opposite statements are equally true, it will be true - to say that the same person is also a horse. It follows therefore, that the same person is - a man and a horse, or any other animal. Thus, although there is no absolute proof of these axioms, - there is an ad hominem proof where one's opponent makes these assumptions.sect. 8=Aristot. Met. - 4.3.10. Perhaps even Heraclitus himself, if he had been questioned on - these lines, would have been compelled to admit that opposite statements can never be true - of the same subjects; as it is, he adopted this theory through ignorance of what his - doctrine implied. In general,sect. 9-11=Aristot. - Met. 4.4.31. if what he says is true, not even this statement itself - (I mean - "that the same thing can at one and the same time be and not be") will be true; because just as, when they are separated, the - affirmation is no more true than the negation, so in the same way, if the complex - statement is taken as a single affirmation, the negation will be just as true as the whole - statement regarded as an affirmation. And - further, if nothing can be truly affirmed, then this very statement—that there is no - such thing as a true affirmation—will be false. But if there is such a thing, the - contentions of those who raise objections of this kind and utterly destroy rational - discourse may be considered to be refuted.Cf. Aristot. Met. 4.8.4, 5. Very similar to the views - which we have just mentioned is the dictum of ProtagorasThis chapter forms a summary of Aristot. - Met. 4.5-8. sect. 1-3=Aristot. Met. - 4.5.1-5.; for he said that man is the measure of all things, by which he - meant simply that each individual's impressions are positively true. But if this is so, it follows that the same thing is and is - not, and is bad and good, and that all the other implications of opposite statements are - true; because often a given thing seems beautiful to one set of people and ugly to - another, and that which seems to each individual is the measure. This difficulty - will be solved if we consider the origin of the assumption. It seems probable that it - arose in some cases from the doctrine of the natural philosophers, and in others from the - fact that everyone does not form the same opinion about the same things, but to some a - given thing seems sweet and to others the contrary. For that nothing comes from what is not, but everything from what is, - is a doctrine common to nearly all natural philosophers.With sect. 4, 5 cf. Aristot. Met. - 4.5.6. Since, then, a thing does not become white which was before - completely white and in no respect not-white, that which becomes white must come from what - was not-white. Hence according to this theory there would be generation from what is not, - unless the same thing were originally white and not-white. However, it is not hard to solve this difficulty. We have - explained in the PhysicsAristot. Physics 1.7-9. in what sense things - which are generated are generated from what is not, and in what sense from what - is. But to attach equal importance to the opinions and - impressions of opposing parties is foolish, because clearly one side or the other must be - wrong.sect. 5-7=Aristot. Met. 4.5.23-27. This is evident from what happens in the sphere of - sensation; for the same thing never seems to some people sweet and to others to the contrary unless - one of the parties has the organ of sense which distinguishes the said flavors injured or - impaired. Such being the case, the one party should be taken as the "measure," and the - other not. And I hold the same in the case of - good and bad, and of beautiful and ugly, and of all other such qualities. For to maintain - this viewi.e., that the same thing has contrary - qualities. is just the same as to maintain that what appears to us when we press - the finger below the eye and make a thing seem two instead of one must be two because it - appears to be so, and then afterwards that it must be one; because if we do not interfere - with our sight that which is one appears to be one. And in general it is absurd to form our opinion of the truth from the - appearances of things in this world of ours which are subject to change and never remain - in the same statesect. 8, 9 (first half)=Aristot. Met. 4.5.21, 22.; for it is by - reference to those things which are always the same state and undergo no change that we - should prosecute our search for truth. Of this - kind are the heavenly bodies; for these do not appear to be now of one nature and - subsequently of another, but are manifestly always the same and have no change of any - kind. Again, if there is motion there is also something - which is moved; and everything is moved from something and into something. Therefore that - which is moved must be in that from which it is to be moved, and must also not be in it; and must be moved into so-and-so and must also - come to be in it; but the contradictory statements cannot be true at the same time, as our - opponents allege. And if the things of our - world are in a state of continuous flux and motion in respect of quantity, and we assume - this although it is not true, why should they not be constant in respect of quality?Cf. Aristot. Met. - 4.5.20, 21. It appears that not the least reason why our opponents - predicate opposite statements of the same thing is that they start with the assumption - that quantity is not constant in the case of bodies; hence they say that the same thing is - and is not six feet long. But essence depends - upon quality, and this is of a determinate, whereas quantity is of an indeterminate - nature. Again, when the doctor orders them to adopt some - article of diet, why do they adopt it?Cf. Aristot. Met. 4.4.39-42. For on their view it - is no more true that a thing is bread than that it is not; and therefore it would make no - difference whether they ate it or not. But as it is, they adopt a particular food as - though they knew the truth about it and it were the food prescribed; yet they ought not to do so if there were no fixed and - permanent nature in sensible things and everything were always in a state of motion and - flux. Again, if we are always changing and never remain - the same, is it any wonder that to us, as to the diseased, things never appear the - same?With this section cf. Aristot. Met. 4.5.7-14. - For to the diseased, since they are not in the same - physical condition as when they were well, sensible qualities do not appear to be the - same; although this does not mean that the sensible things themselves partake of any - change, but that they cause different, and not the same, sensations in the diseased. - Doubtless the same must be true if the change which we have referred to takes place in - us. If, however, we do not change but remain - always the same, there must be something permanent. As for - those who raise the aforesaid difficulties on dialectical grounds,With this section cf. Aristot. Met. - 4.5.3, 4, Aristot. Met. - 4.6.1-3. it is not easy to find a solution which will convince them unless - they grant some assumption for which they no longer require an explanation; for every - argument and proof is possible only in this way. If they grant no assumption, they destroy - discussion and reasoning in general. Thus - there is no arguing with people of this kind; but in the case of those who are perplexed - by the traditional difficulties it is easy to meet and refute the causes of their - perplexity. This is evident from what has been already said. Thus from these considerations it is - obvious that opposite statements cannot be true of the same thing at one time; nor can - contrary statements, since every contrariety involves privation. This is clear if we - reduce the formulae of contraries to their first principles.Cf. Aristot. Met. 4.6.10, - 11. Similarly no middle term can be - predicated of one and the same thing of which - one of the contraries is predicated.Cf. Aristot. Met. 4.7 where, however, the point which is - proved is that there can be no intermediate between contradictories. If, when the subject is white, we say that it is - neither white nor black, we shall be in error; for it follows that it is and is not white, - because the first of the two terms in the complex statement will be true of the subject, - and this is the contradictory of white. Thus we cannot be - right in holding the views either of HeraclitusCf. - Aristot. Met. 11.5.8 or of - Anaxagoras.Cf. Aristot. Met. 4.7.8-8.5 If - we could, it would follow that contraries are predicable of the same subject; for when - heAnaxagoras. What he really meant was that even - the sweetest things contain some bitter particles. Cf. Anaxagoras Fr. 11 (Diels); Burnet, E.G.P. 129. says that in everything - there is a part of everything, he means that nothing is sweet any more than it is bitter, - and similarly with any of the other pairs of contraries; that is, if everything is present - in everything not merely potentially but actually and in differentiation. Similarly all - statements cannot be false, nor all true. Among many other difficulties which might be - adduced as involved by this supposition there is the objection that if all statements were - false, not even this proposition itself would be true; while if they were all true it - would not be false to say that they are all false. Every science inquires for certain - principles and causes with respect to every knowable thing which comes within its - scopeThis chapter corresponds to Aristot. Met. 6.1; cf. also Aristot. Met. 4.3.1-6 and ch. 4 above. It also - answers the problem stated in ch. 1.2.; e.g., the sciences of medicine and physical - culture do this, and so does each of the other productive and mathematical sciences. Each - one of these marks out for itself some class of objects, and concerns itself with this as - with something existent and real, but not qua real; it is another - science distinct from these which does this. Each of the said sciences arrives in some way at the essence in a particular class of - things, and then tries to prove the rest more or less exactly. Some arrive at the essence - through sense-perception, and some by hypothesis; hence it is obvious from such a process - of induction that there is no demonstration of the reality or essence. Now since there is a science - of nature, clearly it must be different from both practical and productive science. In a - productive science the source of motion is in the producer and not in the thing produced, - and is either an art or some other kind of potency; and similarly in a practical science - the motion is not in the thing acted upon but rather in the agent. But the science of the natural philosopher is concerned with - things which contain in themselves a source of motion. From this it is clear that natural - science must be neither practical nor productive, but speculative; since it must fall - under one of these classes. And since every - science must have some knowledge of the essence and must use it as a starting-point, we must be careful to observe how the natural - philosopher should define, and how he should regard the formula of essence—whether - in the same way as the term "snub," or rather as the term "concave." For of these the formula of "snub" is stated in conjunction - with the matter of the object, whereas that of "concave" is stated apart from the matter; - since snubness is only found in the nose, which is therefore included in the formula, for - "the snub" is a concave nose . Thus it is obvious that the formula of "flesh" - and "eye" and the other parts of the body must always be stated in conjunction with their - matter. Since - there is a science of Being qua Being and separately existent, we - must inquire whether this should be regarded as identical with natural science or rather - as a distinct branch of knowledge. Physics deals with things which contain a source of - motion in themselves, and mathematics is speculative and is a science which deals with - permanent things, but not with things which can exist separately. Hence there is a science distinct from both of these, which deals with - that which exists separately and is immovable; that is, if there really is a substance of - this kind—I mean separately existent and immovable—as we shall endeavor to - prove.Aristot. - Met. 12.6, 7. And if there is an entity of this kind in the world of - reality, here surely must be the Divine, and this must be the first and most fundamental - principle. Evidently, then, there are three kinds of - speculative science: physics, mathematics, and theology. The highest class of science is - the speculative, and of the speculative sciences themselves the highest is the last named, - because it deals with the most important side of reality; and each science is reckoned - higher or lower in accordance with the object of its study. The question might be raised as to whether the science of Being qua Being should be regarded as universal or not. Each of the mathematical sciences deals with some one class of things - which is determinate, but universal mathematics is common to all alike. If, then, natural - substances are the first of existing things, physics will be the first of the sciences; - but if there is some other nature and substance which exists separately and is immovable, - then the science which treats of it must be different from and prior to physics, and - universal because of its priority. Since the term Being in its unqualified sense is used with several - meanings, of which one is accidental Being, we must first consider Being in this - sense.Sections 1-9 of this chapter correspond to - Aristot. Met. 6.2-4. Clearly none of the - traditional sciences concerns itself with the accidental; the science of building does not - consider what will happen to the occupants of the house, e.g. whether they will find it unpleasant or the contrary to live in; nor - does the science of weaving or of shoemaking or of confectionery. Each of these sciences considers only what is proper to it, i.e. its - particular end. As for the question whether "the cultured" is also "the lettered," or the - quibbleThis is a different form of the "quibble" - in Aristot. Met. 6.2.4. Here the fallacy - obviously consists in the wrong application of the word A(/MA("at once" or "at the same time"). that "the man who is - cultured, when he has become lettered, will be both at once although he was not before; - but that which is but was not always so must have come to be; therefore he must have - become at the same time cultured and lettered" —none of the recognized sciences considers this, except sophistry. This is the - only science which concerns itself with the accidental, and hence Plato was not far wrong - in sayingPlat. Sop. - 254a. that the sophist spends his time in the study of unreality. But - that it is not even possible for there to be a science of the accidental will be apparent - if we try to see what the accidental really is. Of some things we say that they are so always and of - necessity (necessity having the sense not of compulsion, but that which we use in logical - demonstrationCf. Aristot. Met. 6.2.6.), and of others that they are so usually, but of - others that they are so neither usually nor always and of necessity, but fortuitously. - E.g., there might be a frost at midsummer, although this comes about neither always and of - necessity nor usually; but it might happen sometimes. The accidental, then, is that which comes about, but not always nor of necessity nor - usually. Thus we have now stated what the accidental is; and it is obvious why there can - be no science of such a thing, because every science has as its object that which is so - always or usually, and the accidental falls under neither of these descriptions. Clearly there can be no - causes and principles of the accidental such as there are of that which is per se; - otherwise everything would be of necessity. For if A is when B is, and B is when C is, and - C is not fortuitously but of necessity, then that of which C was the cause will also be of - necessity, and so on down to the last causatum , as it is called. (But this was assumed to be accidental.) Therefore - everything will be of necessity, and the element of chance, i.e. the possibility of a - thing's either happening or not, is entirely banished from the world of events. Even if we - suppose the cause not to exist already but to be coming to be, the result will be the - same; for everything will come to be of necessity. The eclipse tomorrow will come about if A does, and A will if B does, - and B if C does; and in this way if we keep on subtracting time from the finite time - between now and to-morrow, we shall at some point arrive at the present existing - condition. Therefore since this exists, - everything subsequent to it will happen of necessity, and so everything happens of - necessity. As - for "what is" in the sense of what is true or what is accidental - , the former depends upon a combination in thought, and is an affection of thought (hence - we do not look for the principles of Being in this sense, but only for those of objective - and separable Being) the latter is not necessary but indeterminate (I mean the - accidental); and of such a thing the causes are indefinite and cannot be reduced to a - system. Teleology is found in events which come about in the course of nature or as a result of - thought.This section is taken from Aristot. Physics 2.5, 6. It is "chance" <or - "luck"> when one of these comes about by accident; for a thing may be a cause, just as - it may exist, either per se or accidentally. Chance is an accidental cause of normally - purposive teleological events. Hence chance - and thought have the same sphere of action, for there is no purpose without thought. - Causes from which chance results may come about are indeterminate; hence chance is - inscrutable to human calculation, and is a cause only accidentally, but in the strictest - sense is a cause of nothing. It is "good" or - "bad luck" when the result is good or bad, and "good" or "bad fortune" when the result is on a large - scale. Since nothing accidental is prior to that which is - per se, neither are accidental causes prior. Therefore if chance or spontaneity is the - cause of the universe, mind and nature are prior causes.The argument is stated more fully and clearly in Aristot. Physics 2.6ff.. Chance produces indirectly - the effects produced directly by mind; and spontaneity is similarly related to nature. - But the indirect cause presupposes the direct. The argument is directed against the - Atomists. Cf. Aristot. Phys. 196a 24, Simplicius 327.24, Cicero De - Nat. Deor. 1.66 ("nulla cogente natura, sed concursu quodam - fortuito"). A thing may exist only actually or potentially, or actually and - potentially; it may be a substance or a quantity or one of the other categories. There is - no motionThe discussion of motion in this chapter - consists of extracts from Aristot. Physics - 3.1-3. apart from things, for change is always in accordance with the - categories of Beingi.e., change is substantial - (generation and destruction); quantitative (increase and decrease); qualitative - (alteration); spatial (locomotion). Cf. Aristot. Met. - 11.12.1, 2.; and there is nothing which is common to these and in no one - category. Each category belongs to all its members in two ways—e.g. substance, for - this is sometimes the form of the thing and sometimes its privation; and as regards quality there is white and black; and as regards - quantity, complete and incomplete; and as regards spatial motion there is up and down or - light and heavy—so that there are as many forms of motion and change as there are of - Being.This is inaccurate; see previous - note. Now since every kind of thing is divided into - the potential and the real, I call the actualization of the potential as such,What Aristotle means by this is explained more clearly - in the following sections, which may be summarized thus. The material substrate, e.g. - bricks, etc., which is potentially a house, may be regarded (a) as potential material; - in this sense it is actualized as bricks before building begins; (b) as potentially a - house; in this sense when it is actualized it is no longer buildable but built, i.e., it - is no longer potential; (c) as potentially buildable into a house. In this sense its - actualization is conterminous with the process of building, and is incomplete (sect.11), - and should not be described as E)NTELE/XEIA or "complete - reality." But Aristotle often uses this term as synonymous with the vaguer E)NE/RGEIA. motion. That this is a true statement will be clear from what follows. When - the "buildable" in the sense in which we call it such exists actually, it is being built; - and this is the process of building. The same is true of the processes of learning, - healing, walking, jumping, ageing, maturing. - Motion results when the complete reality itself exists, and neither sooner nor - later. The complete reality, then, of that - which exists potentially, when it is completely real and actual, not qua itself but qua movable, is motion. By qua I mean this. The bronze is potentially a statue; but nevertheless the complete - reality of the bronze qua bronze is not motion. To be bronze is not - the same as to be a particular potentiality; since if it were absolutely the same by - definition the complete reality of the bronze would be a kind of motion; but it is not the - same. (This is obvious in the case of - contraries; for the potentiality for health and the potentiality for illness are not the - same—for if they were, health and illness would be the same too—but the - substrate which becomes healthy or ill, whether it is moisture or blood, is one and the - same.) And since it is not the same, just as "color" and "visible" are not the same, it is - the complete reality of the potential qua potential that is - motion. It is evident that it is this, and - that motion results when the complete reality itself exists, and neither sooner nor later. - For - everything may sometimes be actual, and sometimes not; e.g. the "buildable" qua "buildable"; and the actualization of the "buildable" qua "buildable" is the act of building. For the actualization is either this—the act of - building—or a house. But when the house exists, it will no longer be buildable; the - buildable is that which is being built. Hence the actualization must be the - act of building, and the act of building is a kind of motion. The same argument applies to - the other kinds of motion. That this account is correct is clear from what the other authorities - say about motion, and from the fact that it is not easy to define it otherwise. For one - thing, it could not be placed in any other class; this is clear from the fact that some - peoplePythagoreans and Platonists. Cf. Aristot. Met. 1.5.6, Plat. - Soph. 256d. identify it with otherness and inequality and not-being, - none of which is necessarily moved; moreover - change is no more into these or out of them than into or out of their opposites.The criticism implied is: If motion is identified with - otherness, inequality, etc., then these concepts must be either (a) subjects of motion, - which is absurd, or (b) termini of motion, in which case the same must be true of their - contraries, since motion is between contraries. The reason for placing motion in - this class is that it is considered to be indeterminate, and the principles in one of the - columns of contraries are indeterminate, being privative; for none of them is a - determinate thing or quality or any of the other categories. The reason for considering motion to be indeterminate is that it - cannot be associated either with the potentiality or with the actuality of things; for - neither that which is potentially nor that which - is actually of a certain size is necessarily moved. And motion is considered to be a kind of actualization, but - incompleteCf. note on sect. 2 (end) above, and - Aristot. Met. 9.6.7-10.; the reason of - this is that the potential, of which it is the actualization, is incomplete. Thus it is difficult to comprehend what motion is; for we must - associate it either with privation or with potentiality or with absolute actuality; and - apparently none of these is possible. There - remains, then, the account which we have given; that it is an actuality, and an actuality - of the kind which we have described, which is hard to visualize but capable of - existing. That motion is in the movable is evident; for it - is the complete realization of the movable by that which is capable of causing motion, and - the actualization of that which is capable of causing motion is identical with that of the - movable. For it must be a complete - realization of them both; since a thing is capable of moving because it has the - potentiality, but it moves only when it is active; but it is upon the movable that it is - capable of acting. Thus the actuality of both alike is one; just as there is the same - interval from one to two as from two to one, and the hill up and the hill down are one, - although their being is not one; the case of the mover and the thing moved is - similar. This chapter consists of extracts from Aristot. Physics 3.4, 5, 7.The infinite is - either (a) that which cannot be traversed because it is not its nature to be traversed - (just as sound is by nature invisible); or (b) that which admits of an endless traverse; - or (c) scarcely admits of traverse; or (d) which, though it would naturally admit of - traverse or limit, does not do so. Further, it may be infinite in respect of addition or of - subtraction or of both. That the infinite should be a - separate independent entity,The Pythagorean and - Platonic view. and yet imperceptible, is impossible. For if it is neither magnitude nor plurality, but infinity itself is - the essence of it, and not merely an accident, it must be indivisible; because that which - is divisible is either magnitude or plurality. And if it is indivisible it cannot be - infinite, except in the same way as sound is invisible. But this is not what people mean - by infinite; and it is not the infinite in this sense that we are investigating, but the - infinite in the sense of the untraversable. Again, how can the infinite exist independently - unless number and magnitude, of which infinity is an attribute, also exist - independently?Aristotle has argued that they do - not in Aristot. Met. 1.9.16-25. And - further, if the infinite is accidental, it cannot, qua infinite, be - an element of things; just as the invisible is not an element of speech, although sound is - invisible. It is clear also that the infinite cannot exist actually. Otherwise any part of it which we might take would be infinite; - for infinity and the infinite are the same, if the infinite is substance and is not - predicated of a subject. Therefore it is either indivisible, or if it is partible, the - parts into which it is divisible are infinite. But the same thing cannot be many - infinites; for just as a part of air is air, so a part of the infinite will be infinite, - if the infinite is a substance and principle. Therefore it is impartible and indivisible. But this is impossible of the actually - infinite, because it must be some quantity. Therefore infinity is an accidental attribute. - But if so, as we have said, it cannot be it that - is a principle, but that of which it is an accident: airAccording to Anaximenes; cf. Theophrastus, Phys. - Opin. Fr. 2 (Ritter and Preller 26). or "the even."According to the Pythagoreans. Cf. Aristot. Met. 1.5.5. n The foregoing inquiry is general; but what follows will show that the - infinite does not exist in sensible things. If - the definition of a body is "that which is bounded by surfaces," then no body, whether - sensible or intelligible, can be infinite nor can there be any separate and infinite - number, since number or that which involves number is numerable. This is clearly shown by - the following concrete argument. The infinite can neither be composite nor simple. For (a) - it cannot be a composite body if the elements are limited in numberThis is proved in Aristot. Physics - 1.6.; for the contraries must - be equal, and no one of them must be infinite; for if the potency of one of the two - corporeal elements is in any way inferior, the finite element will be destroyed by the - infinite. And every element cannot be infinite, because body is that which has extension - in all directions, and the infinite is that which is extended without limit; so that if - the infinite is corporeal it will be infinite in all directions.sc. and so no other body can exist beside it. Nor (b) can the infinite be any simple body; neither, as - someAnaximander. It seems, however, that by - A)/PEIRON he meant "indeterminate" or - "undifferentiated," although he no doubt regarded this principle as "infinite" as well. - Cf. notes on Aristot. Met. 1.7.3, Aristot. Met. 12.2.3. hold, something which - is apart from the elements and from which they suppose the elements to be generated (for - there is no such body apart from the elements; everything can be resolved into that of - which it consists, but we do not see things resolved into anything apart from the simple - bodies), nor fire nor any other element. Apart from - the question of how any of them could be infinite, the All, even if it is finite, cannot - be or become any one of the elements, as Heraclitus saysCf. Hereclitus Fr. 20-22 - (Bywater). all things at certain times become fire. The same argument - applies as to the One which the physicists posit besides the elements; for all change - proceeds from the contrary, e.g. from hot to cold.The argument seems to be: Since all change is from contrary to contrary, and it is - impossible that either (a) one of the elements should be contrary to the rest, or (b) - one material principle should be contrary to all four elements, it follows that no one - element, and similarly that no one material principle apart from the elements, can be - the ultimate material principle of the universe. Again, a sensible body is in some - region, and the region of the whole and of the part (e.g. of the earth) is the same.i.e., the region of the universe which is proper to a - given element is proper also to any part of that element. The proper region of earth is - the center, of fire the circumference of the universe. Cf. Aristot. De Caelo 1.2. Therefore if the infinite body is homogeneous, - it will be immovable or will always be in motionRoss is evidently right in taking this to refer to the rest or motion of the parts. An - infinite body cannot move as a whole, because there is no space outside it.; but - this is impossible, for why should there be rest or motion below rather than above or in - any other region? E.g., if there were a clod, in what region would it move or be at - rest? The region proper to the body which - is homogeneous with the clod is infinite. Then will the clod occupy the whole of that - region? How can it? Then what of its rest or motion? It will either rest - everywhere—in which case it cannot move—or move everywhere; in which case it - cannot rest.If earth is an infinite body, its - region must be infinite. But the infinite has no center (cf. sect. 13). Therefore a - clod, which cannot occupy the whole region proper to earth, will have no region proper - to itself to which it can move or in which it can rest. And if the whole is not - alike throughout, the regions proper to its parts are unlike also; and (a) the body of the - whole is not one, except in virtue of contact; (b) the parts will be either finite or - infinite in kind. Finite they cannot be, for - then those of one kind would be infinitesc. in - quantity. If the universe is infinite in quantity, and the elements are limited in kind, - some of the elements (or at least one) must be infinite in quantity. But this is - impossible, just as it is impossible that all the elements should be infinite in - quantity. Cf. sect. 7 above and those of another would not (if the whole is - infinite); e.g., fire or water would be infinite. But such a condition would involve the destruction of the contraries. But if the parts - are infinitesc. in kind or number. and - simple, the regions proper to them are infinite and the elements will be infinite. And - since this is impossible,Cf. sect. 6 n. the - regions are finiteCf. sect. 14 n. and the - whole must be finite. In general, there cannot be an infinite body and a place - for bodies if every body which is sensible has either weight or lightness; for it will - have to move either towards the center or upwards, and the infinite—either the whole - or the half—cannot do either; for how can you divide it? How can the infinite be - part up and part down, or part extreme and part center? Further, every sensible body is in some place, and of place there are - six kinds,i.e., above and below, before and behind, - right and left (Aristot. Phys. 205b 31). - but these cannot exist in an infinite body. In general, if an infinite place is - impossible, so is an infinite body; because that which is in a place is somewhere, and - this means either up or down or one of the other kinds of place, and each of these is a - limit. The - infinite is not the same in the sense that it is one nature whether it applies to - magnitude or to motion or to time; the posterior is derived from the prior sense, e.g. - motion is called infinite in virtue of the magnitude involved when a thing is moved or - changed or increased, and time is so called on account of motion.Cf. Aristot. Met. 5.13.5. - That which changes - either changes accidentally, as when "the cultured" walks; or is said to change in general - because something in it changes, as in the case of things which change in their parts; the - body becomes healthy because the eye does. But - there is something which is moved directly per se, i.e. the essentially movable. The same - applies to that which moves, for it moves sometimes accidentally, sometimes partially, and - sometimes per se. There is something that moves directly, and something that is moved; and - also a time in which, and something from which, and something into which it is moved. But - the forms and modifications and place into which moving things are moved are immovable; - e.g. knowledge and warmth. It is not warmth that is motion, but the process of - warming. Non-accidental change is not found in all things, but only between contraries and - intermediates and contradictories. We can convince ourselves of this by means of - induction. That which changes changes either from positive into positive, or from negative - into negative, or from positive into negative, or from negative into positive. By "positive" I mean that which is denoted by an - affirmation. Thus there must be three forms of change; for that which is from negative into negative is not change, because they - are neither contraries nor contradictories, since they entail no opposition. The change - from the negative into its contradictory positive is generation—absolute change - absolute generation, and qualified change qualified generation; and the change from the - positive to the negative is destruction—absolute change absolute destruction, and - qualified change qualified destruction.The change - from positive to positive is omitted here (but cf. sect. 7). Aristotle no doubt intended - to use it as an example of non-substantial change, e.g. from "poor man" to "rich man"; - but since this can be regarded as change from "poor man " to "not-poor man," or - "not-rich man" to "rich man," he includes it as a qualified type of substantial - change. Now if "what is not" has - several meanings, and neither that which implies a combination or separation of - terms,i.e., falsity. Cf. Aristot. Met. 9.10.1. nor that which relates - to potentiality and is opposed to unqualified Being, admits of motion ("not-white" or - "not-good," however, admits of motion accidentally, because "not-white" may be a man; but - that which is "not so-and-so" in an absolute sense does not admit of it at all), then - "what is not" cannot be moved. If this is so, generation cannot be motion; for it is "what - is not" that is generated. For even if the - generation is in the highest degree accidental, still it is true to say that not-being is - predicable of that which is generated absolutely. And the argument applies similarly to - rest. Thus not only do these difficult conclusions follow, but also that everything which - is moved is in a place, whereas "what is not" is not in a place; for then it would - be somewhere. Nor is destruction motion; for the contrary of motion is - motion or rest, but the contrary of destruction is generation. And since every motion is a kind of change, and the three kinds of - change are those which we have described,sect. - 3. and of these those which relate to generation and destruction are not motions, - and these are the changes between contradictories, the change from positive to positive - must alone be motion. The subjects are either contraries or intermediates (for privative - terms may also be regarded as contraries) and are denoted by a positive term—e.g. - "naked" or "toothless" or "black." Now since the categories are distinguished as substance, - quality, place, activity or passivity, relation and quantity,Aristotle generally distinguishes eight categories (originally ten, but - he seems to have abandoned KEI=SQAI"position" and - E)/XEIN"state" at an early date); here he omits "time" - as being relative to motion (it is that by which motion can be numerically estimated; - cf. Aristot. Met. 12.6.2, Aristot. Phys. 219b 1) and therefore neither the - subject nor the terminus of motion. Cf. Ross ad loc. there must be three kinds of - motion, in respect of quality, quantity and place. There is no motionThere is, however, change in respect of substance - (generation and destruction), but this is between contradictories and is not motion in - the strict sense. Cf. Aristot. Met. 11.11.6, and - sect. 4 below. The distinction between motion and change is not always - maintained. in respect of substance, because substance has no contrary; nor of - the relative, because it is possible that when one of two related things changes the - relation to it of the other thing, even though the thing itself does not change, may - become untrue; therefore the motion of these related things is accidental. Nor is there motion of the agent or patient, or of the - mover and the thing moved, because there is no motion of motion nor no generation of - generation, nor in general is there change of change. There are two ways in which there - might be motion of motion: (1) Motion might be the subject of motion, as, e.g., a man is - moved because he changes from white to black; in this way motion might be heated or cooled - or might change its place or increase. But this is impossible, because the - change is not a subject. Or (2) some other subject might change from change to some other - form of existence, as, e.g., a man changes from sickness to health. But this is also - impossible except accidentally. Every motion - is a change from one thing into something else; and the same is true of generation and - destruction, except that these are changes into opposites in one sense,sc. contradictories. while the other, i.e. - motion, is a change into opposites in another sense.sc. contraries. Hence a thing changes at the same time from health to sickness, - and from this change itself into another. Now - clearly if it has fallen ill it will be already changed (for it cannot remain at rest) - into that other change, whatever it may be; and further this cannot be, in any given case, - any chance change; and it also must be from something into something else. Therefore it - will be the opposite change, viz. becoming healthy. But this is so accidentally; just as - there is change from recollecting to forgetting because the subject changes, - now in the direction of knowledge and now in that of ignorance. Further, we shall have an - infinite series if there is to be change of change and becoming of becoming, because if - the latter of two becomings comes to be from the former, the former must come to be too. - E.g., if - simple becoming was once coming to be, that which comes to be something was also once - coming to be. Therefore that which simply comes to be was not yet, but there was already - something coming to be coming to be something. But this too was at one time coming to be, and therefore it was not at that time coming - to be something. But in infinite series there is no first term, and therefore in this - series the first term cannot exist, nor can any subsequent term. Therefore nothing can be - either generated or moved or changed. Further, the same - thing which admits of motion admits also of the contrary motion and of rest, and that - which admits of generation admits also of destruction. Therefore that which comes to be, when it has come to be coming to be, - is then in course of perishingsc. which is - absurd.; for it does not perish as soon as it is coming to be coming to be, nor - afterwards, because that which is perishing must exist .That which comes to be must cease to be, and it can - cease to be only when it exists. Therefore if that which comes to be comes to be coming - to be, it must cease to be when it is coming to be; before this it does not - exist, but is only coming to be coming to be, and after this it is not "that which comes - to be" but "that which has come to be." Further, - there must be some matter underlying that which is coming to be or changing. What then - will it be? What is it that becomes motion or generation in the same way as it is body or - soul that undergoes change? And moreover what is that which is the terminus of the motion? - For that which we are considering must be a motion or generation of A - from B into C. How - then can these conditions be fulfilled? There can be no learning of learning, and - therefore there can be no generation of generation. Since - there is no motion of substance or of the relative or of activity and passivity, it - remains that there is motion in respect of quality, quantity and place; for each of these - admits of contrariety. By "quality" I mean not that which is in the substance (for indeed - even the differentia is a quality), but the - passive quality in virtue of which a thing is said to be acted upon or to be immune from - being acted upon.Cf. Aristot. Met. 5.14. The immovable is either that which is wholly incapable of being - moved, or that which is scarcely moved in the course of a long time or is slow in - starting, or that which would naturally be moved but cannot be moved at the time when and - from the place whence and in the way in which it would naturally be moved. This last is - the only kind of immovable thing which I recognize as being at rest; for rest is contrary - to motion, and so must be a privation of that which admits of motion. Things are "together in - place" which are in the primary sensei.e., when - they occupy one place to the exclusion of anything else. Cf. Aristot. Phys. 209a 33-b 1. in one place, and - "separate" which are in different places. "Contrary in place" is that which is at a - maximum distance in a straight line.I have - transferred this sentence from the end of the section, where it is placed in the text, - on the ground that it fits more naturally here. I suspect that it, like the displaced - portion of sect. 13, was originally a marginal note which was later inserted in the body - of the text, but in the wrong position. Things are said to be "in contact" whose - extremes are together in place. An "intermediate" is that at which a changing thing which - changes continuously in accordance with its nature naturally arrives before it arrives at - the extreme into which it is changing. Since all change takes place between opposites, and - these are either contraries or contradictories, and contradictories have no middle term, - clearly it is to the sphere of contraries that the intermediate belongs.I have followed Prantl's suggestion in transferring - this sentence from the end of sect. 13. "Successive" is that which comes after the beginning (the order being - determined by position or form or in some other way) and has nothing of the same class - between itself and that which it succeeds; e.g. lines in the case of a line, and units in - that of a unit, and a house in the case of a house (but there is nothing to prevent - something else from coming between). For that which is successive is a thing which is - successive and posterior to some other thing. 1 is not successive to 2, nor is the new - mooni.e., the first day of the month. to - the second day of the month. "Contiguous" is - that which is successive and in contact. The "continuous" is a species of the - contiguous. I call two things continuous - when their respective boundaries, by which they are kept together in contact, become one - and the same; hence clearly the continuous belongs to the sphere of things whose nature it - is to become one by contiguity. Clearly "successive" is the - most ultimate term; for the successive need not be in contact, but contact implies - succession; and if there is continuity there is contact, but if there is contact there is - not necessarily continuity; and where there - is no contact there is no coalescence. Therefore a point is not the same as a unit; for - points admit of contact, whereas units do not, but only of succession; and between points - there is something intermediate, but between units there is not.

- - -

Our - inquiry is concerned with substance; for it is the principles and causes of substances - that we are investigating. Indeed if the universe is to be regarded as a whole, substance is its first part; and if it is to be regarded - as a succession,Cf. Aristot. Met. 12.10.14, Aristot. Met. 14.3.9. even so substance is - first, then quality, then quantity. Moreover, the latter hardly exist at all in the full - sense, but are merely qualifications and affections of Being. Otherwise "not-white" and - "not-straight" would also exist; at any rate we say that they too "are," e.g., "it is not - white." Further, none of the other categories - is separately existent. Even the ancients in effect testify to this, for it was of - substance that they sought the principles and elements and causes. Present-day - thinkersPlatonists. tend to regard - universals as substance, because genera are universal, and they hold that these are more - truly principles and substances because they approach the question theoretically; but the - ancients identified substance with particular things, e.g. fire and earth, and not with - body in general. Now there are three kinds of substance. One is sensible (and may be either - eternali.e., the celestial bodies. or - perishable; the latter, e.g. plants and animals, is universally recognized); of this we - must apprehend the elements, whether they are one or many. Another is immutable , which certain thinkers hold to - exist separately; some dividing it into two classes, others combining the Forms and the - objects of mathematics into a single class, and others recognizing only the objects of - mathematics as of this nature.These three views - were held respectively by Plato, Xenocrates and Speusippus. Cf. Aristot. Met. 7.2.3, 4; Aristot. Met. 13.1.4, and see - Introduction. The first two kinds of substance come within the scope of physics, - since they involve motion; the last belongs to some other science, if there is no - principle common to all three. Sensible substance is liable to change. Now if change proceeds from - opposites or intermediates—not however from all opposites (for speech is not white), - but only from the contraryCf. Aristot. Met. 10.7.—then there must be - something underlying which changes into the opposite contrary; for the contrariesi.e., contrary qualities. Cf. Aristot. Met. 8.5.1. do not change. Further, something - persists, whereas the contrary does not persist. Therefore besides the contraries there is - some third thing, the matter . Now if change is of four kinds, in respect - either of substance or of quality or of quantity or of place, and if change of substance - is generation or destruction in the simple sense, and change of quantity is increase or - decrease, and change of affection is alteration, and change of place is locomotion, then - changes must be in each case into the corresponding contrary state. It must be the matter, then, which admits of both contraries, - that changes. And since "that which is" is twofold, everything changes from that which is - potentially to that which is actually; e.g. from potentially white to actually white. The - same applies to increase and decrease. Hence not only may there be generation accidentally - from that which is not, but also everything is generated from that which is, but is potentially and is not actually. And this is the "one" of Anaxagoras; for his "all - things were together,"Anaxagoras Fr. 1 (Diels). and the "mixture" of Empedocles and - Anaximander and the doctrine of Democritus would be better expressed as "all things were - together potentially, but not actually."In this - passage I follow Ross's punctuation and interpretation, which seem to me to be certainly - right. Anaxagoras's undifferentiated infinity of homoeomerous particles (although - contrasted with the unifying principle of Mind, cf. Aristot. Met. 1.8.14) can be regarded as in a sense a unity. Again, MI=GMA(as Ross points out) in its Aristotelian sense of - "complete fusion" is a fair description of Anaximander's "indeterminate." The general - meaning of the passage is that in each of the systems referred to the material principle - in its elemental state should have been described as existing only - potentially. Hence these thinkers - must have had some conception of matter. All things which change have matter, but - different things have different kinds; and of eternal things such as are not generable but - are movable by locomotion have matter; matter, however, which admits not of generation, - but of motion from one place to another.Cf. Aristot. Met. 12.1.3, Aristot. Met. 8.1.7, 8. One might raise the question from what sort of "not-being" generation takes - place; for not-being has three senses.(1) the - negation of a category, (2) falsity, (3) unrealized potentiality. Cf. Aristot. Met. 14.2.10. If a thing exists - through a potentiality, nevertheless it is not through a potentiality for any chance - thing; different things are derived from different things. Nor is it satisfactory to say that "all things were together," for - they differ in their matter, since otherwise why did they become an infinity and not one? - For Mind is one; so that if matter is also one, only that could have come to be in - actuality whose matter existed potentially. The causes and principles, then, are three; - two being the pair of contraries, of which one is the formula or form and the other the - privation, and the third being the matter.This - classification is found in Aristot. Physics 1.6, 7, - but is foreign to the main treatise of the Metaphysics. See - Introduction. We must next observeSee - Introduction. that neither matter nor form (I mean in the proximate sense) is - generated. All change is of some subject by some agent into some object. The agent is the - immediate mover; the subject is the matter; and the object is the form. Thus the process - will go on to infinity if not only the bronze comes to be round, but also roundness or - bronze comes to be; there must, then, be some stopping-point. We must next observe that every substance - is generated from something which has the same name ("substances" including not only - natural but all other products). Things are generated either by art or by nature or by - chance or spontaneously. Art is a generative principle in something else; nature is a - generative principle in the subject itselfIn - natural reproduction the generative principle is obviously in the parent. But the - offspring is in a sense a part of the parent, and so Aristotle identifies the - two.(for man begets man); the other causes are privations of these.Cf. Aristot. Met. - 11.8.12 n. There are three kinds of substance: (1.) matter, which exists - individually in virtue of being apparentAristotle - is contrasting proximate with primary matter. Fire, the primary matter of a man, is a - simple undifferentiated element which cannot be perceived as such, and has no - individuality. The head, and the other parts of the body, considered merely as in - contact and not as forming an organic unity, are the proximate matter of a man; they are - perceptible and individual. Flesh (in general) represents the matter in an intermediate - stage.(for everything which is characterized by contact and so not by coalescence - is matter and substrate; e.g. fire, flesh and head; these are all matter, and the last is the matter of a substance in the - strictest sense); (2.) the "nature"i.e., - form.(existing individually)—i.e. a kind of positive state which is the - terminus of motion; and (3.) the particular combination of these, e.g. Socrates or - Callias. In some cases the individuality does not exist apart from the composite substance - (e.g., the form of a house does not exist separately, except as the art of - building; nor are these forms liable to - generation and destruction; there is a distinct sense in which "house" and "health" and - every artificial product, considered in the abstract, do or do not existi.e., in the mind of the architect or doctor.); - if it does so at all, it does so in the case of natural objects. Hence Plato was not far - wrong in sayingSee Introduction. that there - are as many Forms as there are kinds of natural objects; that is if there are Forms - distinct from the things of our world. Moving causes are causes in the sense of pre-existent things, - but formal causes coexist with their effects. For it is when the man becomes healthy that - health exists, and the shape of the bronze sphere comes into being simultaneously with the - bronze sphere. Whether any form remains also - afterwards is another question. In some cases there is nothing to prevent this, e.g. the - soul may be of this nature (not all of it, but the intelligent part; for presumably all of - it cannot be). Clearly then there is no need on these grounds for the Ideas to exist; for - man begets man, the individual begetting the particular person. And the same is true of - the arts, for the art of medicine is the formula of health. In one sense the causes and principles - are different for different things; but in another, if one speaks generally and - analogically, they are the same for all. For the question might be raised whether the - principles and elements of substances and of relations are the same or different; and - similarly with respect to each of the other categories. But it is absurd that they should - be the same for all; for then relations and substance would have the same constituents. - What then can their common constituent - be? For there is nothing common to and yet distinct from substance and the other - predicable categories, yet the element is prior to that of which it is an element. - Moreover substance is not an element of relations, nor is any of the latter an element of - substance. Further, how can all the categories have the same elements? For no element can be the same as that which is composed of - elements; e.g., neither B nor A can be the same as BA (nor indeed can any of the - "intelligibles,"Unity and Being are called - intelligibles as being the most universal predicates and as contrasted with particulars, - which are sensible. e.g. Unity or Being, be an element; for these apply in every - case, even to composite things); hence no element can be either substance or relation. But - it must be one or the other. Therefore the categories have not all the same - elements. The - truth is that, as we say, in one sense all things have the same elements and in another - they have not. E.g., the elements of sensible bodies are, let us say, (1) as form, the - hot, and in another sense the cold, which is the corresponding privation; as matter, that - which directly and of its own nature is potentially hot or cold. And not only these are - substances, but so are (2) the compoundsThis - apparently refers to the elements; fire and air are hot matter, water and earth cold - matter. of which they are principles, and (3) any unity which is generated from - hot and cold, e.g. flesh or bone; for the product of hot and cold must be distinct from - them. These things, then, have the same - elements and principles, although specifically different things have specifically - different elements; we cannot, however, say that all things have the same elements in this - sense, but only by analogy: i.e., one might say that there are three principles, form, - privation and matter. But each of these is - different in respect of each class of things, e.g., in the case of color they are white, black, surface; or again there is light, - darkness and air, of which day and night are composed. And since not only things which are - inherent in an object are its causes, but also certain external things, e.g. the moving - cause, clearly "principle" and "element" are not the same; but both are causes. Principles - are divided into these two kinds, and that which moves a thing or brings it to rest is a - kind of principle and substance. Thus - analogically there are three elements and four causes or principles; but they are - different in different cases, and the proximate moving cause is different in different - cases. Health, disease, body; and the moving cause is the art of medicine. Form, a - particular kind of disorder, bricks; and the moving cause is the art of - building. And since in the sphere of natural - objects the moving cause of man is man, while in the sphere of objects of thought the - moving cause is the form or its contrary, in one sense there are three causes and in - another four. For in a sense the art of medicine is health, and the art of building is the - form of a house, and man begets man; but besides these there is that which as first of all - things moves all things.For the first time the - ultimate efficient cause is distinguished from the proximate. Aristotle is leading up to - the description of the Prime Mover which occupies the latter half of the - book. Now since some things can exist in separation and others cannot, it is the former that are - substances. And therefore all things have the same causes, because without substance there can be no - affections and motions. Next we shall seeSee - Introduction. that these causes are probably soul and body, or mind, appetite and - body.Aristotle is thinking of animals and human - beings, which are substances in the truest sense. Again, there is another sense - in which by analogy the principles are the same viz. actuality and potentiality; but these - are different for different things, and apply to them in different ways. For in some cases the same thing exists now actually and now - potentially; e.g. wine or flesh or man (actuality and potentiality also fall under the - causes as already described; for the form exists actually if it is separable, and so does - the compound of form and matter, and the privation, e.g. darkness or disease; and the - matter exists potentially, for it is this which has the potentiality of becoming bothi.e., of acquiring either of the contrary qualities - distinguished by the form and the privation; but the distinction in virtue of actuality and potentiality applies in - a different sense to cases where the matter of cause and effect is not the same, in some - of which the form is not the same but different. E.g., the cause of a man is (i) his - elements: fire and earth as matter, and the particular form; (2) some external formal - cause, viz. his father; and besides these (3) the sun and the ecliptic,The sun, moving in the ecliptic, approaches nearer to - the earth in summer, causing generation, and recedes farther from the earth in winter, - causing destruction. Cf. Aristot. Met. 12.6.10 - n., Aristot. De Gen. et Corr. 336a - 32. which are neither matter nor form nor privation nor identical in form - with him, but cause motion. Further, we must observe that - some causes can be stated universally, but others cannot. The proximate principles of all things are the proximate actual - individual and another individual which exists potentially.i.e., the proximate efficient cause and proximate - matter. Therefore the proximate - principles are not universal. For it is the particular that is the principle of - particulars; "man" in general is the principle of "man" in general, but there is no such - person as "man," whereas Peleus is the principle of Achilles and your father of you, and - this particular B of this particular BA; but B in general is the principle of BA regarded - absolutely. Again, even if the causes of - substances are universal, still, as has been said,Aristot. Met. 12.4.6. different - things, i.e. things which are not in the same genus, as colors, sounds, substances and - quantity, have different causes and elements, except in an analogical sense; and the - causes of things which are in the same species are different, not in species, but because - the causes of individuals are different: your matter and form and moving cause being - different from mine, although in their universal formula they are the same. As for the question - what are the principles or elements of substances and relations and qualities, whether - they are the same or different, it is evident that when the terms "principle" and - "element" are used with several meanings they are the same for everything; but when the - meanings are distinguished, they are not the same but different; except that in a certain - sense they are the same for all. In a certain sense they are the same or analogous, - because (a) everything has matter, form, privation and a moving cause; (b) the causes of - substances may be regarded as the causes of all things, since if substances are destroyed - everything is destroyed; and further (c) that which is first in complete realityi.e., the prime mover. is the cause of all - things. In another sense, however, proximate - causes are different; there are as many proximate causes as there are contraries which are - predicated neither as genera nor with a variety of meaningsi.e., individual forms and privations of individual things.; and - further the particular material causes are different. Thus we have stated what the principles of - sensible things are, and how many they are, and in what sense they are the same and in - what sense different. Since we have seenAristot. Met. 12.1.3, 4. that there are - three kinds of substance, two of which are natural and one immutable, we must now discuss - the last named and show that there must be some substance which is eternal and immutable. - Substances are the primary reality, and if they are all perishable, everything is - perishable. But motion cannot be either generated or destroyed, for it always existedCf. Aristot. Physics - 8.1-3; nor can time, because there can be no priority or posteriority if - there is no time.The argument seems to be: If we - assume that time was generated, it follows that before that there was no time; but the - very term "before" implies time. The same applies to the destruction of - time. Hence as time is continuous, so - too is motion; for time is either identical with motion or an affection of it.Cf. Aristot. Met. - 11.12.1 n. But there is no continuous motion except that which is - spatial, of spatial motion only that which is circular.These statements are proved inAristot. Physics - 8.8, 9. But even if we are to suppose that - there is something which is kinetic and productive although it does not actually move or - produce, there will not necessarily be motion; for that which has a potentiality may not - actualize it. Thus it will not help matters if - we posit eternal substances, as do the exponents of the Forms, unless there is in them - some principle which can cause change.As there is - not, according to Aristotle; cf. Aristot. Met. - 1.7.4. And even this is not enough, nor is it enough if there is another - substance besides the Forms; for unless it actually functions there will not be - motion. And it will still not be enough even - if it does function, if its essence is potentiality; for there will not be eternal motion, - since that which exists potentially may not exist. Therefore there must be a principle of this kind whose essence is - actuality. Furthermore these substancesAristotle is - now thinking not only of the prime mover (God or Mind) but also of the movers of the - celestial spheres. Cf. Aristot. Met. - 12.8.14. must be immaterial; for they must be eternal if anything is. - Therefore they are actuality. There is a difficulty, however; for it seems that everything which - actually functions has a potentiality, whereas not everything which has a potentiality - actually functions; so that potentiality is prior. But if this is so, there need be no - reality; for everything may be capable of existing, but not yet existent. Yet if we accept the statements of the cosmologists who - generate everything from Night,Cf. Hes. WD 17, Hes. Th. 116ff. - or the doctrine of the physicists that "all things were together,"Cf. Aristot. Met. 12.2.3. - we have the same impossibility; for how can there be motion if there is no actual cause? - Wood will not move itself—carpentry must act upon it; nor will the menses or the - earth move themselves—the seeds must act upon the earth, and the semen on the - menses. Hence some, e.g. LeucippusCf. Aristot. Met. - 1.4.12, Aristot. De Caelo 300b 8, and - see Burnet, E.G.P. 178. and Plato,Cf. - Plat. Tim. 30a, and sect. 8 below. posit - an eternal actuality, for they say that there is always motion; but why there is, and what - it is, they do not say; nor, if it moves in this or that particular way, what the cause - is. For nothing is moved at haphazard, but in every case there must be some reason - present; as in point of fact things are moved in one way by nature, and in another by - force or mind or some other agent. And further, what kind of motion is primary? For this - is an extremely important point. Again, Plato at - least cannot even explain what it is that he sometimes thinks to be the source of motion, - i.e., that which moves itself; for according to him the soul is posterior to motion and - coeval with the sensible universe.Aristotle refers - to Plato's rather inconsistent account in Plat. Tim. - 30-34. Now to suppose that potentiality is prior to actuality is in one - sense right and in another wrong; we have explainedThe reference is probably to 5 above, but cf. Aristot. - Met. 9.8. the distinction. But that actuality is prior is testified by Anaxagoras (since mind is actuality), and by - Empedocles with his theory of Love and Strife, and by those who hold that motion is - eternal, e.g. Leucippus. Therefore Chaos or Night did not - endure for an unlimited time, but the same things have always existed, either passing - through a cycle or in accordance with some other principle—that is, if actuality is - prior to potentiality. Now if there is a - regular cycle, there must be somethingThe sphere of - the fixed stars, Aristot. Met. 12.8.9; cf. Aristot. De Gen. et Corr. 336a 23ff. which - remains always active in the same way; but if there is to be generation and destruction, - there must be something elseThe sun, which has its - own yearly orbit in the ecliptic, and a daily rotation round the earth, which is - explained most economically with reference to the rotation of the sphere of the fixed - stars. Cf. Aristot. Met. 12.5.3 n., Aristot. De Gen. et Corr. 336a 23ff. which is - always active in two different ways. Therefore this must be active in one way - independently, and in the other in virtue of something else, i.e. either of some third - active principle or of the first. It must, - then, be in virtue of the first; for this is in turn the cause both of the third and of - the second. Therefore the first is preferable, since it was the cause of perpetual regular - motion, and something else was the cause of variety; and obviously both together make up - the cause of perpetual variety. Now this is just what actually characterizes motions; - therefore why need we seek any further principles? Since (a) this is a possible explanation, - and (b) if it is not true, we shall have to regard everything as coming from "Night" - Aristot. Met. 12.6.6 - and "all things together" and "not-being,"Aristot. Met. 12.2.2, 3. these difficulties may be considered to be solved. There - is something which is eternally moved with an unceasing motion, and that circular motion. - This is evident not merely in theory, but in fact. Therefore the "ultimate heaven" must be - eternal. Then there is also something which moves it. And since that which is moved while it moves is intermediate, there is - something which moves without being moved; something eternal which is both substance and - actuality. Now it moves in the following manner. The - object of desire and the object of thought move without being moved. The primary objects - of desire and thought are the same. For it is the apparent good that is the object of - appetite, and the real good that is the object of the rational will.This shows that desire in general (of which appetite - and will are the irrational and rational aspects) has as its object the good. - Desire is the result of opinion rather than opinion that of desire; it is the act of - thinking that is the starting-point. Now - thought is moved by the intelligible, and one of the series of contrariesAristotle himself recognizes two series, lists or - columns of contraries, similar to those of the Pythagoreans (Aristot. Met. 1.5.6). One, the positive, contains - being, unity, substance, etc.; the other is negative and contains not-being, plurality, - non-substance, etc. The negative terms are intelligible only in reference to the - positive. Cf. Aristot. Met. 4.2.21. is - essentially intelligible. In this series substance stands first, and of substance that - which is simple and exists actually. (The one and the simple are not the same; for one - signifies a measure,Cf Aristot. Met. 5.6.17. whereas "simple" means - that the subject itself is in a certain state.) But the Good, and that which is in itself desirable, are also in the same series; - and that - which is first in a class is always best or analogous to the best. That the final cause may apply to immovable things is shown by the - distinction of its meanings. For the final cause is not only "the good for - something," but also "the good which is the end of some action." In - the latter sense it applies to immovable things, although in the former it does not; and - it causes motion as being an object of love, whereas all other things cause motion because - they are themselves in motion. Now if a thing - is moved, it can be otherwise than it is. Therefore if the actuality of "the heaven" is - primary locomotion, then in so far as "the heaven" is moved, in this respect at least it - is possible for it to be otherwise; i.e. in respect of place, even if not of - substantiality. But since there is something—X—which moves while being itself - unmoved, existing actually, X cannot be otherwise in any respect. For the primary kind of change is locomotion,Proved in Aristot. Physics 8.7. - and of locomotion circular locomotion - Aristot. Physics 8.9 - ; and this is the motion which X induces. Thus X is necessarily existent; and qua necessary it is good, and is in this sense a first - principle.The argument is: X (the prime mover), - since it imparts the primary motion, cannot be liable to motion (or change) of any kind. - Therefore it exists of necessity, and must be good (cf. Aristot. Met. 5.5.6); and it is qua good, i.e., the - object of desire, that X is a first principle. For the necessary has all these - meanings: that which is by constraint because it is contrary to impulse; and that without - which excellence is impossible; and that which cannot be otherwise, but is absolutely - necessary.Cf. Aristot. Met. 5.5 Such, then, is the - first principle upon which depend the sensible universe and the world of nature. And its life is like the best which we temporarily - enjoy. It must be in that state always (which for us is impossible), since its actuality - is also pleasure.For the relation of pleasure to - actuality or activity see Aristot. Nic. Eth. - 10.4.(And for this reason waking, sensation and thinking are most - pleasant, and hopes and memories are pleasant because of them.) Now thinking in itself is - concerned with that which is in itself best, and thinking in the highest sense with that - which is in the highest sense best.Since the prime - mover is pure actuality, and has or rather is the highest form of life, Aristotle - identifies it with the highest activity—pure thinking. And thought thinks - itself through participation in the object of thought; for it becomes an object of thought - by the act of apprehension and thinking, so that thought and the object of thought are the - same, because that which is receptive of the object of thought, i.e. essence, is thought. - And it actually functions when it possesses this object.In actualization the subject and object of thought (like those of - perception, Aristot. De Anima 3.2.) are - identical. Hence it is actuality rather than potentiality that is held to be the - divine possession of rational thought, and its active contemplation is that which is most - pleasant and best. If, then, the happiness - which God always enjoys is as great as that which we enjoy sometimes, it is marvellous; - and if it is greater, this is still more marvellous. Nevertheless it is so. Moreover, life - belongs to God. For the actuality of thought is life, and God is that actuality; and the - essential actuality of God is life most good and eternal. We hold, then, that God is a - living being, eternal, most good; and therefore life and a continuous eternal existence - belong to God; for that is what God is. Those who suppose, as do the Pythagoreans and Speusippus,The view is referred to again in Aristot. Met. 12.10.6, Aristot. Met. 14.4.2, 3, Aristot. Met. 14.5.1. that perfect beauty and - goodness do not exist in the beginning (on the ground that - whereas the first beginnings of plants and animals are causes, it is in the products of - these that beauty and perfection are found) are mistaken in their views. For seed comes from prior creatures which are perfect, - and that which is first is not the seed but the perfect creature. E.g., one might say that prior - to the seed is the man—not he who is produced from the seed, but another man from - whom the seed comes.Cf. Aristot. Met. 9.8.4, 5. Thus it is evident from the - foregoing account that there is some substance which is eternal and immovable and separate - from sensible things; and it has also been shown that this substance can have no - magnitude, but is impartible and indivisible (for it causes motion for infinite time, and - nothing finite has an infinite potentialityCf.Aristot. Physics 266a24-b6.; and therefore - since every magnitude is either finite or infinite, it cannot have finite - magnitude, and it cannot have infinite - magnitude because there is no such thing at all); and moreover that it is impassive and - unalterable; for all the other kinds of motion are posterior to spatial motion. Thus it is - clear why this substance has these attributes. We must not disregard the question whether we should - hold that there is one substance of this kind or more than one, and if more than one, how - many; we must review the pronouncements of other thinkers and show that with regard to the - number of the substances they have said nothing that can be clearly stated. The theory of the Ideas contains no peculiar treatment - of the question; for the exponents of the theory call the Ideas numbers, and speak of the - numbers now as though they were unlimited and - now as though they were limited by the number 10Cf. - Aristot. Met. 13.8.17, 20. This was a - Pythagorean survival, cf. Vol. I. Introduction. xvi.; but as for why there should - be just so many numbers, there is no explanation given with demonstrative - accuracy. We, however, must discuss the - question on the basis of the assumptions and distinctions which we have already - made. The first principle and primary reality is - immovable, both essentially and accidentally, but it excites the primary form of motion, - which is one and eternal. Now since that which - is moved must be moved by something, and the prime mover must be essentially immovable, - and eternal motion must be excited by something eternal, and one motion by some one thing; - and since we can see that besides the simple spatial motion of the universei.e., the (apparent) diurnal revolution of the - heavens.(which we hold to be excited by the primary immovable substance) there - are other spatial motions—those of the planets—which are eternal (because a - body which moves in a circle is eternal and is never at rest—this has been proved in - our physical treatisesAristot. Physics 8.8, 9, Aristot. De Caelo 1.2, - 2.3-8.); then each of these spatial motions must also be excited by a - substance which is essentially immovable and eternal. For the nature of the heavenly bodies is eternal, being a kind of - substance; and that which moves is eternal and prior to the moved; and that which is prior - to a substance must be a substance. It is therefore clear that there must be an equal - number of substances, in nature eternal, essentially immovable, and without magnitude; for - the reason already stated.Aristot. Met. 12.7.12, 13. - Thus it is clear that - the movers are substances, and that one of them is first and another second and so on in - the same order as the spatial motions of the heavenly bodies. As regards the number of these motions, we have now reached a question - which must be investigated by the aid of that branch of mathematical science which is most - akin to philosophy, i.e. astronomy; for this has as its object a substance which is - sensible but eternal, whereas the other mathematical sciences, e.g. arithmetic and - geometry, do not deal with any substance. That there are more spatial motions than there - are bodies which move in space is obvious to those who have even a moderate grasp of the - subject, since each of the non-fixed stars has more than one spatial motion. As to how many these spatial motions actually are we - shall now, to give some idea of the subject, quote what some of the mathematicians say, in - order that there may be some definite number for the mind to grasp; but for the rest we - must partly investigate for ourselves and partly learn from other investigators, and if - those who apply themselves to these matters come to some conclusion which clashes with - what we have just stated, we must appreciate both views, but follow the more - accurate. EudoxusOf Cnidus (circa 408 -355 - B.C.). He was a pupil of Plato, and a distinguished mathematician. held that the - motion of the sun and moon involves in either case three spheres,For a full discussion of the theories of Eudoxus and Callipus see Dreyer, - Planetary Systems 87-114; Heath,Aristarchus of <placeName - key="perseus,Samos City">Samos</placeName>190-224. of which the - outermost is that of the fixed stars,Not identical - with that of the fixed stars, but having the same motion. the second revolves in - the circle which bisects the zodiac,i.e., revolves - with its equator in the ecliptic. and - the third revolves in a circle which is inclined across the breadth of the zodiaci.e., has the plane of its equator inclined to the - plane of the ecliptic. This sphere carries the sun (or moon) fixed to a point in its - equator.; but the circle in which the moon moves is inclined at a greater angle - than that in which the sun moves. And he held - that the motion of the planets involved in each case four spheres; and that of these the - first and second are the sameNot the same, but - having the same motion. as before (for the sphere of the fixed stars is that - which carries round all the other spheres, and the sphere next in order, which has its - motion in the circle which bisects the zodiac, is common to all the planets); the third - sphere of all the planets has its poles in the circle which bisects the zodiac; and the - fourth sphere moves in the circle inclined to the equator of the third. In the case of the - third sphere, while the other planets have their own peculiar poles, those of Venus and - Mercury are the same. Callippusof Cyzicus (fl. 380 B.C.). - Simplicius says (Simplicius 493.5-8) that he corrected and - elaborated Eudoxus's theory with Aristotle's help while on a visit to him at Athens. assumed the same arrangement of the - spheres as did Eudoxus (that is, with respect to the order of their intervals), but as - regards their number, whereas he assigned to Jupiter and Saturn the same number of spheres - as Eudoxus, he considered that two further spheres should be added both for the sun and - for the moon, if the phenomena are to be accounted for, and one for each of the other - planets. But - if all the spheres in combination are to account for the phenomena, there must be for each of the - other planets other spheres, one less in number than those already mentioned, which - counteract these and restore to the same position the first sphere of the star which in - each case is next in order below.Aristotle is - trying to establish a mechanical relation between the spheres, which Eudoxus and - Callipus did not attempt to do. In this way only can the combination of forces - produce the motion of the planets. Therefore - since the forces by which the planets themselves are moved are 8 for Jupiter and Saturn, - and 25 for the others, and since of these the only ones which do not need to be - counteracted are those by which the lowest planetThe moon. is moved, the counteracting spheres for the first two planets will be - 6, and those of the remaining four will be 16; and the total number of spheres, both those - which move the planets and those which counteract these, will be 55. If we do not invest the moon and the sun with the additional - motions which we have mentioned,In sect. 11. - there will be 47 (?)Either Aristotle has made a - slip in his calculations, or we should read E)NNE/A(Sosigenes) for E(PTA/; this would - give 49, which appears to be the correct total. For alternative explanations of an error - in calculation see Ross ad loc. spheres in all. This, then, may be taken to be the number of the spheres; and thus it is reasonable to - suppose that there are as many immovable substances and principles,i.e., the movers of the spheres.—the statement of logical - necessity may be left to more competent thinkers. If there can be no spatial motion which is not - conducive to the motion of a star, and if - moreover every entity and every substance which is impassive and has in itself attained to - the highest good should be regarded as an end, then there can be no other entity besides - these,See previous note. and the number of - the substances must be as we have said. For if there are other substances, they must move - something, since they are the end of spatial motion. But there can be no other spatial motions besides those already - mentioned. This is a reasonable inference from a general consideration of spatial motion. - For if everything which moves exists for the sake of that which is moved, and every motion - for the sake of something which is moved, no motion can exist for the sake of itself or of - some other motion, but all motions must exist for the sake of the stars. For if we are to suppose that one motion is for the - sake of another, the latter too must be for the sake of something else; and since the - series cannot be infinite, the end of every motion must be one of the divine bodies which - are moved through the heavens. It is evident that there is - only one heaven.This paragraph seems to belong to - an earlier period of Aristotle's thought. At any rate the argument that plurality - involves matter is inconsistent with the view that there are 55 immaterial - movers. For if there is to be a plurality of heavens (as there is of men), the - principle of each must be one in kind but many in number. But all things which are many in number have matter (for one and the - same definition applies to many individuals, e.g. that of "man"; but Socrates is oneThe definition or form is one and universal; it is the - combination of form with matter that constitutes an individual. Thus a plurality of - individuals is caused by the combination of the same form with different - matter.), but the primary essence has no matter, because it is complete reality. - Therefore the prime mover, which is immovable, is one both in formula and in number; and - therefore so also is that which is eternally and continuously in motion. Therefore there - is only one heaven. A tradition has been handed down by the ancient thinkers of very early times, and - bequeathed to posterity in the form of a myth, to the effect that these heavenly bodies - are gods,This statement is not literally true. The - planets do not seem to have been associated with the gods of popular mythology until the - fourth century B.C. (see Burnet, E.G.P. p. 23 n.). But Aristotle's general meaning seems - to be that the gods were identified with the primary natural forces; and this is - substantially true. and that the Divine pervades the whole of nature. The rest of their tradition has been added later in a - mythological form to influence the vulgar and as a constitutional and utilitarian - expedientCf. Aristot. Met. 2.3.1.; they say that these gods are human in shape or - are like certain other animals,e.g. the Egyptian - deities. Zoomorphism in Greek religion is a doubtful quantity. and make other - statements consequent upon and similar to those which we have mentioned. Now if we separate these statements and accept only - the first, that they supposed the primary substances to be gods, we must regard it as an - inspired saying and reflect that whereas every art and philosophy has probably been - repeatedly developed to the utmost and has perished again, these beliefs of theirs have - been preserved as a relic of former knowledge. To this extent only, then, are the views of - our forefathers and of the earliest thinkers intelligible to us. The subject of Mind involves - certain difficulties. Mind is held to be of all phenomena the most supernatural; but the - question of how we must regard it if it is to be of this nature involves certain - difficulties. If Mind thinks nothing, where is its dignity? It is in just the same state - as a man who is asleep. If it thinks, but something else determines its thinking, then - since that which is its essence is not thinking but potentiality,i.e., if its thinking is determined by something else, Mind is only a - potentiality, and not (as described in Aristot. Met. - 12.7.1-9) the highest actuality. it cannot be the best reality; because it derives its excellence from the - act of thinking. Again, whether its essence is - thought or thinking, what does it think? It must think either itself or something else; - and if something else, then it must think either the same thing always, or different - things at different times. Then does it make any difference, or not, whether it thinks - that which is good or thinks at random? Surely - it would be absurd for it to think about some subjects. Clearly, then, it thinks that - which is most divine and estimable, and does not change; for the change would be for the - worse, and anything of this kind would immediately imply some sort of motion. Therefore if - Mind is not thinking but a potentiality, (a) it is reasonable to suppose that the - continuity of its thinking is laboriousCf. Aristot. Met. 9.8.18.; (b) clearly there must - be something else which is more excellent than Mind; i.e. the object of thought; for both thought and the act of thinking will belong - even to the thinker of the worst thoughts.If Mind - is a potentiality, since a potentiality is of contraries, Mind may think that which is - worst. Therefore if this is to be avoided (as it is, since it is better not to - see some things than to see them), thinking cannot be the supreme good. Therefore Mind - thinks itself, if it is that which is best; and its thinking is a thinking of - thinking. Yet it seems that knowledge and perception and - opinion and understanding are always of something else, and only incidentally of - themselves. And further, if to think is not - the same as to be thought, in respect of which does goodness belong to thought? for the - act of thinking and the object of thought have not the same essence. The answer is that in some - cases the knowledge is the object. In the productive sciences, if we disregard the matter, - the substance, i.e. the essence, is the object; but in the speculative sciences the - formula or the act of thinking is the object. Therefore since thought and the object of - thought are not different in the case of things which contain no matter, they will be the - same, and the act of thinking will be one with the object of thought. There still remains the - question whether the object of thought is composite; for if so, thought would change in - passing from one part of the whole to another. The answer is that everything which - contains no matter is indivisible. Just as the human mind, or rather the mind of composite - beings,i.e., beings composed of matter as well as - form. Such beings are contrasted with the divine Mind, which is pure form. is in - a certain space of timeThe meaning of this sentence - is shown by the definition of Happiness in Aristot. Nic. Eth. 1098a 16-20. It takes the human mind a lifetime of the - highest intellectual activity of which it is capable to attain to happiness; but the - divine Mind is always happy. Cf. Aristot. Met. - 12.7.9.(for it does not possess the good at this or at that moment, but - in the course of a certain whole period it attains to the supreme good, which is other - than itself), so is absolute self-thought throughout all eternity. We must also consider in - which sense the nature of the universe contains the good or the supreme good; whether as - something separate and independent, or as the orderly arrangement of its parts. Probably in both senses, as an army does; for the - efficiency of an army consists partly in the order and partly in the general; but chiefly - in the latter, because he does not depend upon the order, but the order depends upon him. - All things, both fishes and birds and plants, are ordered together in some way, but not in - the same way; and the system is not such that there is no relation between one thing and - another; there is a definite connection. Everything is ordered together to one end; but the arrangement is like that in a - household, where the free persons have the least liberty to act at random, and have all or most of their actions preordained for - them, whereas the slaves and animals have little common responsibility and act for the - most part at random; for the nature of each class is a principle such as we have - described.The free persons correspond to the - heavenly bodies, whose movements are fixed by necessity; the servile class to human - beings. Each class acts in accordance with its nature, a principle which "produces - obedience to duty in the higher creatures, caprice in the lower" ( - Ross). I mean, for example, that - everything must at least come to dissolution; and similarly there are other respects in - which everything contributes to the good of the whole. We - must not fail to observe how many impossibilities and absurdities are involved by other - theories, and what views the more enlightened thinkers hold, and what views entail the - fewest difficulties. All thinkers maintain - that all things come from contraries; but they are wrong both in saying "all things"Because there is an eternal substance, which is not - derived from contraries (Aristot. Met. - 12.6.1). and in saying that they come from contraries,Things are derived from a substrate as well (Aristot. Met. 12.2.1). nor do they explain - how things in which the contraries really are present come from the contraries; for the - contraries cannot act upon each other. For us, however, this problem is satisfactorily - solved by the fact that there is a third factor. Other thinkers make one of the two - contraries matter; e.g., this is done by thoseSee - on Aristot. Met. 14.1.4. who make the - Unequal matter for the Equal, or the Many matter for the One. But this also is disposed of in the same way; for the one matter of - two contraries is contrary to nothing. Further, on their view everything except Unity - itself will partake of evil; for "the Bad"The "Bad" - was identified with the unequal; cf. Aristot. Met. - 1.6.10. is itself one of the elements. The other schoolSee Aristot. Met. - 12.7.10 does not even regard the Good and the Bad as principles; yet the - Good is in the truest sense a principle in all things. The former school is right in - holding that the Good is a principle, but they do not explain how it is a principle— - whether - as an end or as a moving cause or as form. Empedocles theory is also absurd, for he identifies - the Good with Love.Cf. Aristot. Met. 1.4.3. This is a principle both - as causing motion (since it combines) and as matter (since it is part of the - mixture).Empedocles Fr. 17 - (Diels), 18-20. Now even if it so happens that the same thing is a - principle both as matter and as causing motion, still the essence of the two principles is - not the same. In which respect, then, is Love a principle? And it is also absurd that - Strife should be imperishable; strife is the very essence of evil.Cf. Aristot. Met. - 9.9.3. Anaxagoras makes the Good a principle as causing motion; for Mind - moves things, but moves them for some end, and therefore there must be some other - GoodMotion presupposes a final cause, which was - not what Anaxagoras meant by "Mind." Cf. Aristot. Met. - 1.7.5.—unless it is as we say; for on our view the art of medicine - is in a sense health.Aristotle identifies the - efficient cause, in a sense, with the final cause. Cf. Aristot. Met. 7.9.3. It is absurd also not to provide a contrary for - the Good, i.e. for Mind.In Aristot. Met. 1.6.10 Aristotle describes Anaxagoras as - a recognizing contrary principles of good and evil. Moreover, on Aristotle's own - showing, evil cannot be a principle (Aristot. Met. - 9.9.3). But all those who recognize the contraries fail to make use of - the contraries, unless we systematize their theories. And none of them explains why some things are perishable and others - imperishable; for they make all existing things come from the same first principles.Cf. Aristot. Met. - 3.4.11-20. Again, someCf. Aristot. Met. 12.2.2, 3. make existing - things come from not-being, while others,The - Eleatics. Cf. Aristot. Met. 1.5.10-13. to - avoid this necessity, make all things one. Again, no one explains why there must always be - generation, and what the cause of generation is. Moreover, those who posit two principles must admit - another superior principle,i.e., an efficient - cause. and so must the exponents of the Forms; for what made or makes particulars - participate in the Forms? And on all other views - it follows necessarily that there must be something which is contrary to Wisdom or supreme - knowledge, but on ours it does not. For there is no contrary to that which is - primary, since all contraries involve - matter, and that which has matter exists potentially; and the ignorance which is contrary - to Wisdom would tend towards the contrary of the object of Wisdom; but that which is - primary has no contrary. Further, if there is to be nothing - else besides sensible things, there will be no first principle, no order, no generation, - and no celestial motions, but every principle will be based upon another,If there is nothing but what is sensible or potential, - there can be no prime mover (which is actuality) to excite motion in the universe, and - no teleology in causation. For the cosmologists on causation see Aristot. Met. 3.3.11-13. as in the accounts of - all the cosmologists and physicists. And if - the Forms or numbers are to exist, they will be causes of nothing; or if not of nothing, - at least not of motion. Further, how can extension, i.e. a - continuum, be produced from that which is unextended? Number cannot, either as a moving or - as a formal cause, produce a continuum. Moreover, no contrary can be essentially - productive and kinetic, for then it would be possible for it not to exist; and further, the act of production would in any case - be posterior to the potentiality. Therefore the world of reality is not eternal. But there - are real objects which are eternal. Therefore one of these premisses must be rejected. We - have described how this may be done.By assuming an - eternal actual mover (Aristot. Met. - 12.6.4). Further, in virtue of what the - numbers, or soul and body, or in general the form and the object, are one, no one attempts - to explain; nor is it possible to do so except on our theory, that it is the moving cause - that makes them one.Cf.Aristot. Met. 8.6. As for thoseSpeusippus and his - followers; cf. Aristot. Met. 7.2.4, Aristot. Met. 14.3.8. who maintain that - mathematical number is the primary reality, and so go on generating one substance after - another and finding different principles for each one, they make the substance of the - universe incoherent (for one substance in no way affects another by its existence or - non-existence) and give us a great many governing principles. But the world must not be - governed badly: The rule of many is not good; let one be the - ruler.Hom. - Il.2.204.

- - -

We have already - explained what the substance of sensible things is, dealing in our treatise on - physicsThe reference is presumably to Aristot. Physics 1. with the material substrate, and - subsequently with substance as actuality.In Books - 7-9. Now since we are inquiring - whether there is or is not some immutable and eternal substance besides sensible - substances, and if there is, what it is, we must first examine the statements of other - thinkers, so that if they have been mistaken in any respect, we may not be liable to the - same mistakes; and if there is any view which is common to them and us, we may not feel - any private self-irritation on this score. For we must be content if we state some points - better than they have done, and others no worse. There are two views on this subject. Some say that - mathematical objects, i.e. numbers and lines, are substances; and others again that the - Ideas are substances. Now since someThis was the orthodox Platonist view; cf. Aristot. Met. 1.6.4. recognize these as two - classes— the Ideas and the mathematical - numbers—and othersXenocrates and his - followers. regard both as having one nature, and yet othersThe Pythagoreans and Speusippus. hold that only - the mathematical substances are substances, we must first consider the mathematical - objects, without imputing to them any other characteristic—e.g. by asking whether - they are really Ideas or not, or whether they are principles and substances of existing - things or not—and merely inquire whether as mathematical objects they exist or not, - and if they do, in what sense; then after this we must separately consider the Ideas - themselves, simply and in so far as the accepted procedure requires; for most of the - arguments have been made familiar already by the criticisms of other thinkers. And further, the greater part of our discussion must - bear directly upon this second question—viz. when we are considering whether the - substances and first principles of existing things are numbers and Ideas; for after we - have dealt with the Ideas there remains this third question. Now if the objects of mathematics exist, - they must be either in sensible things, as some hold; or separate from them (there are - some also who hold this view); or if they are neither the one nor the other, either they - do not exist at all, or they exist in some other way. Thus the point which we shall have - to discuss is concerned not with their existence, but with the mode of their - existence. That the objects of mathematics cannot be in sensible things, and that moreover the theory - that they are is a fabrication, has been observed already in our discussion of - difficultiesCf. Aristot. Met. 3.2.23-30. - —the - reasons being (a) that two solids cannot occupy the same space, and (b) that on this same - theory all other potentialities and characteristics would exist in sensible things, and - none of them would exist separately. This, then, has been already stated; but in addition to this it is clearly impossible on - this theory for any body to be divided. For it must be divided in a plane, and the plane - in a line, and the line at a point; and therefore if the point is indivisible, so is the - line, and so on. For what difference does it - make whether entities of this kind are sensible objects, or while not being the objects - themselves, are yet present in them? the consequence will be the same, for either they - must be divided when the sensible objects are divided, or else not even the sensible - objects can be divided. Nor again can entities of this kind - exist separately. For if besides sensible - solids there are to be other solids which are separate from them and prior to sensible - solids, clearly besides sensible planes there must be other separate planes, and so too - with points and lines; for the same argument applies. And if these exist, again besides - the planes, lines and points of the mathematical solid, there must be others which are - separate; for the incomposite is prior to the - composite, and if prior to sensible bodies there are other non-sensible bodies, then by the same argument the planes which exist - independently must be prior to those which are present in the immovable solids. Therefore - there will be planes and lines distinct from those which coexist with the - separately-existent solids; for the latter coexist with the mathematical solids, but the - former are prior to the mathematical solids. Again, in these planes there will be lines, and by the same argument there must be other - lines prior to these; and prior to the points which are in the prior lines there must be - other points, although there will be no other points prior to these. Now the accumulation becomes absurd; because whereas we get - only one class of solids besides sensible solids, we get three classes of planes besides - sensible planes—those which exist separately from sensible planes, those which exist - in the mathematical solids, and those which exist separately from those in the - mathematical solids—four classes of lines, and five of points; with which of these, then, will the mathematical sciences deal? - Not, surely, with the planes, lines and points in the immovable solid; for knowledge is - always concerned with that which is prior. And the same argument applies to numbers; for - there will be other units besides each class of points, and besides each class of existing - things, first the sensible and then the intelligible; so that there will be an infinite - number of kinds of mathematical numbers. Again, there are the problems which we enumerated in our - discussion of difficultiesAristot. Met. 3.2.23-27.: how can they be - solved? For - the objects of astronomy will similarly be distinct from sensible things, and so will - those of geometry; but how can a heaven and its parts (or anything else which has motion) - exist apart from the sensible heaven? And similarly the objects of optics and of harmonics - will be distinct, for there will be sound and sight apart from the sensible and particular - objects. Hence clearly the other senses and - objects of sense will exist separately; for why should one class of objects do so rather - than another? And if this is so, animals too will exist separately, inasmuch as the senses - will. Again, there are certain general mathematical - theorems which are not restricted to these substances. Here, then, we shall have yet another kind of substance intermediate - between and distinct from the Ideas and the intermediates, which is neither number nor - points nor spatial magnitude nor time. And if this is impossible, clearly it is also - impossible that the aforesaid substances should exist separately from sensible - objects. In - general, consequences result which are contrary both to the truth and to received opinion - if we thus posit the objects of mathematics as definite separately-existent entities. For - if they exist in this way, they must be prior to sensible spatial magnitudes, whereas in - truth they must be posterior to them; for the incomplete spatial magnitude is in point of - generation prior, but in point of substantiality posterior, as the inanimate is to the animate. Again, in virtue of what can we possibly - regard mathematical magnitudes as one? Things in this world of ours may be reasonably - supposed to be one in virtue of soul or part of the soul, or some other influence; apart - from this they are a plurality and are disintegrated. But inasmuch as the former are - divisible and quantitative, what is the cause of their unity and cohesion? Again, the ways in which the objects of mathematics are generated - prove our point; for they are generated first - in the dimension of length, then in that of breadth, and finally in that of depth, - whereupon the process is complete. Thus if that which is posterior in generationi.e., in the natural order of development. Thus - "generation" (GE/NESIS) is used in two different senses - in this argument, which therefore becomes invalid (Bonitz). is prior in - substantiality, body will be prior to plane and line, and in this sense it will also be - more truly complete and whole, because it can become animate; whereas how could a line or - plane be animate? The supposition is beyond our powers of apprehension. Further, body is a kind of - substance, since it already in some sense possesses completeness; but in what sense are - lines substances? Neither as being a kind of form or shape, as perhaps the soul is, nor as - being matter, like the body; for it does not appear that anything can be composed either - of lines or of planes or of points, whereas if - they were a kind of material substance it would be apparent that things can be so - composed. Let it be granted that they are prior in formula; yet not everything which is prior in - formula is also prior in substantiality. Things are prior in substantiality which when - separated have a superior power of existence; things are prior in formula from whose - formulae the formulae of other things are compounded. And these characteristics are not - indissociable. For if attributes, such as - "moving" or "white," do not exist apart from their substances, "white" will be prior in - formula to "white man," but not in substantiality; for it cannot exist in separation, but - always exists conjointly with the concrete whole—by which I mean "white - man." Thus it is obvious that neither is the - result of abstraction prior, nor the result of adding a determinant posterior—for - the expression "white man" is the result of adding a determinant to "white." Thus we have sufficiently shown (a) that the objects of mathematics - are not more substantial than corporeal objects; (b) that they are not prior in point of - existence to sensible things, but only in formula; and (c) that they cannot in any way - exist in separation. And since we have - seensect. 1-3 above. that they cannot - exist in sensible things, it is clear that either they do not exist at all, or they exist - only in a certain way, and therefore not absolutely; for "exist" has several - senses. The - general propositions in mathematics are not concerned with objects which exist separately - apart from magnitudes and numbers; they are concerned with magnitudes and - numbers, but not with them as possessing - magnitude or being divisible. It is clearly possible that in the same way propositions and - logical proofs may apply to sensible magnitudes; not qua sensible, - but qua having certain characteristics. For just as there can be many propositions about things merely qua movable, without any reference to the essential nature of each - one or to their attributes, and it does not necessarily follow from this either that there - is something movable which exists in separation from sensible things or that there is a - distinct movable nature in sensible things; so too there will be propositions and sciences - which apply to movable things, not qua movable but qua corporeal only; and again qua planes only - and qua lines only, and qua divisible, and - qua indivisible but having position, and qua indivisible only. Therefore since - it is true to say in a general sense not only that things which are separable but that - things which are inseparable exist, e.g., that movable things exist, it is also true to - say in a general sense that mathematical objects exist, and in such a form as - mathematicians describe them. And just as it is - true to say generally of the other sciences that they deal with a particular - subject—not with that which is accidental to it (e.g. not with "white" if "the - healthy" is white, and the subject of the science is "the healthy"), but with that which - is the subject of the particular science; with the healthy if it treats of things qua healthy, and with man if qua man—so this is also - true of geometry. If the things of which it treats are accidentally sensible although it - does not treat of them qua sensible, it does not follow that the - mathematical sciences treat of sensible things—nor, on the other hand, that they - treat of other things which exist independently apart from these. Many attributes are essential - properties of things as possessing a particular characteristic; e.g., there are attributes - peculiar to an animal qua female or qua - male, although there is no such thing as female or male in separation from animals. Hence - there are also attributes which are peculiar to things merely qua - lines or planes. And in proportion as the - things which we are considering are prior in formula and simpler, they admit of greater - exactness; for simplicity implies exactness. Hence we find greater exactness where there - is no magnitude, and the greatest exactness where there is no motion; or if motion is - involved, where it is primary, because this is the simplest kind; and the simplest kind of - primary motion is uniform motion.Aristot. Met. 12.7.6. The same principle applies to - both harmonics and optics, for neither of these sciences studies objects qua sight or qua sound, but qua - lines and numbersOptics studies lines and harmonics - numbers because these sciences are subordinate to geometry and arithmetic (Aristot. An. Post. 75b 15).; yet the latter are - affections peculiar to the former. The same is also true of mechanics. Thus if we regard objects - independently of their attributes and investigate any aspect of them as so regarded, we - shall not be guilty of any error on this account, any more than when we draw a diagram on - the ground and say that a line is a foot long when it is not; because the error is not in the premisses.Cf. Aristot. Met. 14.2.9, - 10. The best way to conduct an investigation in every case is to take that - which does not exist in separation and consider it separately; which is just what the - arithmetician or the geometrician does. For - man, qua man, is one indivisible thing; and the arithmetician - assumes man to be one indivisible thing, and then considers whether there is any attribute - of man qua indivisible. And the geometrician considers man neither - qua man nor qua indivisible, but qua something solid. For clearly the attributes which would have - belonged to "man" even if man were somehow not indivisible can belong to man - irrespectively of his humanity or indivisibility. Hence for this reason the geometricians are right in what they - maintain, and treat of what really exists; i.e., the objects of geometry really exist. For - things can exist in two ways, either in complete reality or as matter.i.e., potentially. And since goodness is distinct from beauty (for it is always in actions that goodness is - present, whereas beauty is also in immovable things), theyCf. Aristot. Met. 3.2.4. - are in error who assert that the mathematical sciences tell us nothing about beauty or - goodness; for they describe and manifest - these qualities in the highest degree, since it does not follow, because they manifest the - effects and principles of beauty and goodness without naming them, that they do not treat - of these qualities. The main species of beauty are orderly arrangement, proportion, and - definiteness; and these are especially manifested by the mathematical sciences. And inasmuch as it is evident that these (I mean, - e.g., orderly arrangement and definiteness) are causes of many things, obviously they must - also to some extent treat of the cause in this sense, i.e. the cause in the sense of the - Beautiful. But we shall deal with this subject more explicitly elsewhere.There is no obvious fulfilment of this - promise. As regards the objects of mathematics, then, the foregoing account may be taken as - sufficient to show that they exist, and in what sense they exist, and in what sense they - are prior and in what they are not. But as regards the Ideas we must first consider the - actual theory in relation to the Idea, without connecting it in any way with the nature of - numbers, but approaching it in the form in which it was originally propounded by the first - exponentsIt seems quite obvious that Aristotle - intends this vague phrase to refer to Plato. Cf. Aristot. - Met. 1.6.1-3, with which the following sections 2-5 should be compared. On the - whole subject see Introduction. of the Ideas. The theory of Forms occurred to those who - enunciated it because they were convinced as to the true nature of reality by the doctrine - of Heraclitus, that all sensible things are always in a state of flux; so that if there is - to be any knowledge or thought about anything, there must be certain other entities, - besides sensible ones, which persist. For there can be no knowledge of that which is in - flux. Now Socrates devoted his attention to - the moral virtues, and was the first to seek a general definition of these (for of the Physicists Democritus gained only a - superficial grasp of the subjectCf. Aristot. Phys. 194a 20, Aristot. De Part. Anim. 642a 24. and defined, after a fashion, "the - hot" and "the cold"; while the PythagoreansCf. - Aristot. Met. 1.5.2, 16. at an earlier - date had arrived at definitions of some few things—whose formulae they connected - with numbers—e.g., what "opportunity" is, or "justice" or "marriage"); and he - naturally inquired into the essence of things; for he was trying to reason logically, and the starting-point of all logical reasoning - is the essence. At that time there was as yet no such proficiency in Dialectic that men - could study contraries independently of the essence, and consider whether both contraries - come under the same science. There are two - innovationsThis is perhaps too strong a word. - What Aristotle means is that Socrates was the first thinker who attached importance to - general definitions and systematically used arguments from analogy in order to arrive at - them. The Greeks as a whole were only too readily impressed by analogy; Socrates merely - developed an already prevalent tendency. For an example of his method see the reference - at Aristot. Met. 5.29.5 n. which, may - fairly be ascribed to Socrates: inductive reasoning and general definition. Both of these - are associated with the starting-point of scientific knowledge. But whereas Socrates regarded neither universals nor definitions as - existing in separation, the Idealists gave them a separate existence, and to these - universals and definitions of existing things they gave the name of Ideas.Cf. Introduction. Hence on their view it followed by virtually the same argument that - there are Ideas of all terms which are predicated universallyWith sect. 6-13 cf. Aristot. Met. - 1.9.1-8, which are almost verbally the same. See Introduction.; and the - result was very nearly the same as if a man who wishes to count a number of things were to - suppose that he could not do so when they are few, and yet were to try to count them when - he has added to them. For it is hardly an exaggeration to say that there are more Forms - than there are particular sensible things (in seeking for whose causes these thinkers were led on - from particulars to Ideas); because corresponding to each thing there is a synonymous - entity, apart from the substances (and in the case of non-substantial things there is a - One over the Many) both in our everyday world and in the realm of eternal - entities. Again, not one of the ways in which it is attempted to prove that the Forms exist - demonstrates their point; from some of them no necessary conclusion follows, and from - others it follows that there are Form of things of which they hold that there are no - Forms. For according to the arguments from - the sciences, there will be Forms of all things of which there are sciences; and according - to the "One-over-Many" argument, of negations too; and according to the argument that "we - have some conception of what has perished" there will be Forms of perishable things, - because we have a mental picture of these things. Further, of the most exact arguments - some establish Ideas of relations, of which the Idealists deny that there is a separate - genus, and others state the "Third Man." And in - general the arguments for the Forms do away with things which are more important to the - exponents of the Forms than the existence of the Ideas; for they imply that it is not the - Dyad that is primary, but Number; and that the relative is prior to number, and therefore - to the absolute; and all the other conclusions in respect of which certain persons by - following up the views held about the Forms have gone against the principles of the - theory. Again, according to the assumption by which they hold that the Ideas exist, there will be Forms not only of substances but of many - other things (since the concept is one not only in the case of substances but in the case - of non-substantial things as well; and there can be sciences not only of substances but - also of other things; and there are a thousand other similar consequences); but it follows necessarily from the views generally - held about them that if the Forms are participated in, there can only be Ideas of - substances, because they are not participated in accidentally; things can only participate - in a Form in so far as it is not predicated of a subject. I mean, e.g., that if a thing participates in absolute doubleness, it - participates also in something eternal, but only accidentally; because it is an accident - of "doubleness" to be eternal. Thus the Ideas will be substance. But the same terms denote - substance in the sensible as in the Ideal world; otherwise what meaning will there be in - saying that something exists besides the particulars, i.e. the unity comprising their - multiplicity? If the form of the Ideas and - of the things which participate in them is the same, they will have something in common - (for why should duality mean one and the same thing in the case of perishable 2's and the - 2's which are many but eternal, and not in the case of absolute duality and a particular 2?). - But if the form is not the same, they will simply be homonyms; just as though one were to - call both Callias and a piece of wood "man," without remarking any property common to - them. sect. 14, 15 have no counterpart in Book 1.And - if we profess that in all other respects the common definitions apply to the Forms, e.g. - that "plane figure" and the other parts of the definition apply to the Ideal circle, only - that we must also state of what the Form is a Form, we must beware lest this is a quite - meaningless statement.The suggestion is that the - definition of an Ideal circle is the same as that of a particular circle, except that it - must have added to it the statement of what particular the Idea is an - Idea. For to what element of the - definition must the addition be made? to "center," or "plane" or all of them? For all the - elements in the essence of an Idea are Ideas; e.g. "animal" and "two-footed."sc. in the definition or essence of "Ideal man." - Further, it is obvious that "being an Idea," just like "plane," must be a definite - characteristic which belongs as genus to all its species.i.e., "being an idea" will be a characteristic common to all ideas, and - so must be itself an Idea. This chapter corresponds - almost verbally to Aristot. Met. 1.9.9-15. Cf. - note on Aristot. Met. 13.4.6.Above all we - might examine the question what on earth the Ideas contribute to sensible things, whether - eternal or subject to generation and decay; for they are not the cause of any motion or - change in them. Moreover they are no help - towards the knowledge of other things (for they are not the substance of particulars, - otherwise they would be in particulars) or to their existence (since they are - not present in the things which participate in them. If they were, they might perhaps seem - to be causes, in the sense in which the admixture of white causes a thing to be - white. But this theory, which was stated first by Anaxagoras and later by - Eudoxus in his discussion of difficulties, and by others also, is very readily refuted; - for it is easy to adduce plenty of impossibilities against such a view). Again, other - things are not in any accepted sense derived from the Forms. To say that the Forms are patterns, and that other things participate - in them, is to use empty phrases and poetical metaphors; for what is it that fashions - things on the model of the Ideas? Besides, anything may both be and come to be without - being imitated from something else; thus a man may become like Socrates whether Socrates - exists or not, and even if Socrates were - eternal, clearly the case would be the same. Also there will be several "patterns" (and - therefore Forms) of the same thing; e.g., "animal" and "two-footed" will be patterns of - "man," and so too will the Idea of man. Further, the Forms will be patterns not only of sensible things but of Ideas; e.g. the - genus will be the pattern of its species; hence the same thing will be pattern and copy. - Further, it would seem impossible for the substance and that of which it is the substance - to exist in separation; then how can the Ideas, if they are the substances of things, exist in - separation from them? In thePhaedoPlat. Phaedo - 100d. this statement is made: that the Forms are causes both of being and - of generation. Yet assuming that the Forms exist, still there is no generation unless - there is something to impart motion; and many other things are generated (e.g. house and - ring) of which the Idealists say that there are no Forms. Thus it is clearly possible that those things of which they say that - there are Ideas may also exist and be generated through the same kind of causes as those - of the things which we have just mentioned, and not because of the Forms. Indeed, as - regards the Ideas, we can collect against them plenty of evidence similar to that which we - have now considered; not only by the foregoing methods, but by means of more abstract and - exact reasoning. Now that we have dealt with the problems concerning the Ideas, we had better - re-investigate the problems connected with numbers that follow from the theory that - numbers are separate substances and primary causes of existing things. Now if number is a - kind of entity, and has nothing else as its substance, but only number itself, as some - maintain; then either (a) there must be some one part of number which is primary, and some - other part next in succession, and so on, each part being specifically differentThis statement bears two meanings, which Aristotle - confuses: (i) There must be more than one number-series, each series being different in - kind from every other series; (2) All numbers are different in kind, and inaddible. - Confusion (or textual inaccuracy) is further suggested by the fact that Aristotle offers - no alternative statement of the nature of number in general, such as we should expect - from his language. In any case the classification is arbitrary and - incomplete.— and this applies - directly to units, and any given unit is inaddible to any other given unit; or (b) theyThe - units. are all directly successive, and any units can be added to any other - units, as is held of mathematical number; for in mathematical number no one unit differs - in any way from another. Or (c) some units must - be addible and others not. E.g., 2 is first after 1, and then 3, and so on with the other - numbers; and the units in each number are addible, e.g. the units in the firsti.e., Ideal or natural.2 are addible to one - another, and those in the first 3 to one another, and so on in the case of the other - numbers; but the units in the Ideal 2 are inaddible to those in the Ideal 3; and similarly in the case of the other successive - numbers. Hence whereas mathematical number is counted thus: after 1, 2 (which consists of - another 1 added to the former) and 3 (which consists of another 1 added to these two) and - the other numbers in the same way, Ideal number is counted like this: after 1, a distinct - 2 not including the original 1; and a 3 not including the 2, and the rest of the numbers - similarly. Or (d) one kind of number must be - such as we first described, and another or such as the mathematicians maintain, and that - which we have last described must be a third kind. Again, - these numbers must exist either in separation from things, or not in separation, but in - sensible things (not, however, in the way which we first considered,In Aristot. Met. - 13.2.1-3. but in the sense that sensible things are composed of numbers - which are present in themThe Pythagorean - number-atomist view; See Introduction.)—either some of them and not others, - or all of them.i.e., either all numbers are - material elements of things, or some are and others are not. These are of necessity the only ways in which the numbers can - exist. Now of those who say that unity is the beginning and substance and element of all - things, and that number is derived from it and something else, almost everyone has - described number in one of these ways (except that no one has maintained that all units - are inaddibleCf. sect. 2.); and this is natural enough, because there can be no - other way apart from those which we have mentioned. Some hold that both kinds of number - exist, that which involves priority and posteriority being identical with the Ideas, and - mathematical number being distinct from Ideas and sensible things, and both kinds being - separable from sensible thingsCf. Aristot. Met. 1.6.4.; others hold that - mathematical number alone exists,Cf. Aristot. Met. 12.10.14. being the primary - reality and separate from sensible things. The Pythagoreans also believe in one kind of - number—the mathematical; only they maintain that it is not separate, but that - sensible substances are composed of it. For they construct the whole universe of numbers, - but not of numbers consisting of abstract units; they suppose the units to be extended—but as for how the first extended unit was - formed they appear to be at a loss.Cf. Aristot. Met. 13.8.9, 10, Aristot. Met. 14.3.15, Aristot. Met. 14.5.7, and see - Introduction. Another thinker holds that primary or Ideal number alone exists; and - someCf. 10ff., Aristot. Met. 13.1.4. identify this with mathematical number. The same applies in the case of lines, planes and solids. SomePlato. distinguish mathematical objects from those which "come after the - Ideas"i.e., the (semi-)Ideal lines, planes, etc. - Cf. Aristot. Met. 1.9.30.; and of those who - treat the subject in a different manner someSpeusippus; cf. sect. 7 above. speak of the mathematical objects and in a - mathematical way—viz. those who do not regard the Ideas as numbers, nor indeed hold - that the Ideas exist—and othersXenocrates. - For his belief in indivisible lines see Ritter and Preller 362. Aristotle ascribes the - doctrine to Plato in Aristot. Met. - 1.9.25. speak of the mathematical objects, but not in a mathematical way; - for they deny that every spatial magnitude is divisible into extended magnitudes, or that - any two given units make 2. But all who hold - that Unity is an element and principle of existing things regard numbers as consisting of - abstract units, except the Pythagoreans; and they regard number as having spatial - magnitude, as has been previously stated.sect. - 8. It is clear from the foregoing account (1.) in - how many ways it is possible to speak of numbers, and that all the ways have been - described. They are all impossible, but doubtless somesc. the view of Xenocrates (cf. Aristot. - Met. 13.8.8). are more so than others. First, then, we must inquire whether the - limits are addible or inaddible; and if inaddible, in which of the two ways which we have - distinguished.Aristot. Met. 13.6.2, 3. For it is possible either (a) that any one - unit is inaddible to any other, or (b) that the units in the Ideal 2 are inaddible to - those in the Ideal 3, and thus that the units in each Ideal number are inaddible to those - in the other Ideal numbers. Now if all units are addible and do not differ in kind, we get one - type of number only, the mathematical, and the Ideas cannot be the numbers thus - produced; for how can we regard the Idea of - Man or Animal, or any other Form, as a number? There is one Idea of each kind of thing: - e.g. one of Humanity and another one of Animality; but the numbers which are similar and - do not differ in kind are infinitely many, so that this is no more the Idea of Man than - any other 3 is. But if the Ideas are not numbers, they cannot exist at all; for from what principles can the Ideas be derived? - Number is derived from Unity and the indeterminate dyad, and the principles and elements - are said to be the principles and elements of number, and the Ideas cannot be placed - either as prior or as posterior to numbers.Since - the only principles which Plato recognizes are Unity and the Dyad, which are numerical - (Aristotle insists on regarding them as a kind of 1 and 2), and therefore clearly - principles of number; and the Ideas can only be derived from these principles if they - (the Ideas) are (a) numbers (which has been proved impossible) or (b) prior or posterior - to numbers (i.e., causes or effects of numbers, which they cannot be if they are - composed of a different kind of units); then the Ideas are not derived from any - principle at all, and therefore do not exist. But if the units are inaddible in the - sense that any one unit is inaddible to any other, the number so composed can be neither - mathematical number (since mathematical number consists of units which do not - differ, and the facts demonstrated of it fit - in with this character) nor Ideal number. For on this view 2 will not be the first number - generated from Unity and the indeterminate dyad, and then the other numbers in succession, - as theyThe Platonists. say 2, 3, because the - units in the primary 2 are generated at the same time,This was the orthodox Platonist view of the generation of ideal numbers; - or at least Aristotle is intending to describe the orthodox view. Plato should not have - regarded the Ideal numbers as composed of units at all, and there is no real reason to - suppose that he did (see Introduction). But Aristotle infers from the fact that the - Ideal 2 is the first number generated (and then the other Ideal numbers in the natural - order) that the units of the Ideal 2 are generated simultaneously, and then goes on to - show that this is incompatible with the theory of inaddible units. whether, as - the originator of the theory held, from unequalsi.e., the Great-and-Small, which Aristotle wrongly understands as two unequal things. - It is practically certain that Plato used the term (as he did that of "Indeterminate - Dyad") to describe indeterminate quantity. See Introduction.(coming into being - when these were equalized), or otherwise— since if we regard the one unit as prior to the other,This is a necessary implication of the theory of inaddible units (cf. - Aristot. Met. 13.6.1, 2). it will be - prior also to the 2 which is composed of them; because whenever one thing is prior and - another posterior, their compound will be prior to the latter and posterior to the - former.So the order of generation will be: (i) - Unity (ungenerated); (2) first unit in 2; (3) second unit in 2; and the Ideal 2 will - come between (2) and (3). Further, since the Ideal 1 is first, and then comes a particular 1 - which is first of the other 1's but second after the Ideal 1, and then a third 1 which is - next after the second but third after the first 1, it - follows that the units will be prior to the numbers after which they are called; e.g., - there will be a third unit in 2 before 3 exists, and a fourth and fifth in 3 before these - numbers exist.This is a corollary to the previous - argument, and depends upon an identification of "ones" (including the Ideal One or - Unity) with units. It is true that nobody has represented the units of numbers as - inaddible in this way; but according to the principles held by these thinkers even this - view is quite reasonable, although in actual fact it is untenable. For assuming that there is a first unit or first 1,i.e., the Ideal One. it is reasonable that the - units should be prior and posterior; and similarly in the case of 2's, if there is a first - 2. For it is reasonable and indeed necessary that after the first there should be a - second; and if a second, a third; and so on with the rest in sequence. But the two statements, that there is after 1 a first and a - second unit, and that there is a first 2, are incompatible. These thinkers, however, - recognize a first unit and first 1, but not a second and third; and they recognize a first - 2, but not a second and third. It is also evident that if - all units are inaddible, there cannot be an Ideal 2 and 3, and similarly with the other - numbers; for whether the units are - indistinguishable or each is different in kind from every other, numbers must be produced - by addition; e.g. 2 by adding 1 to another 1, and 3 by adding another 1 to the 2, and 4 - similarly.This is of course not true of the - natural numbers. This being so, - numbers cannot be generated as these thinkers try to generate them, from Unity and the - dyad; because 2 becomes a part of 3,i.e., 3 is - produced by adding 1 to 2. and 3 of 4, and the same applies to the following numbers. But according to them 4 was generated from the first 2 and the - indeterminate dyad, thus consisting of two 2's apart from the Ideal 2.Cf. sect. 18. Otherwise 4 will consist of the - Ideal 2 and another 2 added to it, and the Ideal 2 will consist of the Ideal 1 and another - 1; and if this is so the other element cannot be the indeterminate dyad, because it - produces one unit and not a definite 2.The general - argument is: Numbers are produced by addition; but this is incompatible with the belief - in the Indeterminate Dyad as a generative principle, because, being duplicative, it - cannot produce single units. Again, how can there be other 3's and 2's besides the Ideal - numbers 3 and 2, and in what way can they be composed of prior and posterior units? All - these theories are absurd and fictitious, and there can be no primary 2 and Ideal 3. Yet - there must be, if we are to regard Unity and the indeterminate dyad as elements.i.e., if numbers are not generated by addition, there - must be Ideal (or natural) numbers. But if the consequences are impossible, the principles cannot be of this nature. If, then, any one unit differs in kind from any other, these and - other similar consequences necessarily follow. If, on the other hand, while the units in - different numbers are different, those which are in the same number are alone - indistinguishable from one another, even so the consequences which follow are no less - difficult. For example, in the Ideal number 10 - there are ten units, and 10 is composed both of these and of two 5's. Now since the Ideal - 10 is not a chance number,I think Ross's - interpretation of this passage must be right. The Ideal 10 is a unique number, and the - numbers contained in it must be ideal and unique; therefore the two 5's must be - specifically different, and so must their units—which contradicts the view under - discussion. and is not composed of chance 5's, any more than of chance units, the - units in this number 10 must be different; for - if they are not different, the 5's of which the 10 is composed will not be different; but - since these are different, the units must be different too. Now if the units are - different, will there or will there not be other 5's in this 10, and not only the two? If - there are not, the thing is absurdi.e., it is only - reasonable to suppose that other 5's might be made up out of different combinations of - the units.; whereas if there are, what sort of 10 will be composed of them? for - there is no other 10 in 10 besides the 10 itself: Again, it must also be true that 4 is not composed of - chance 2's. For according to them the indeterminate dyad, receiving the determinate dyad, - made two dyads; for it was capable of duplicating that which it received.Cf. Introduction. Again, how is it possible that 2 can be - a definite entity existing besides the two units, and 3 besides the three units? Either by - participation of the one in the other, as "white man" exists besides "white" and "man," - because it partakes of these concepts; or when the one is a differentia of the other, as - "man" exists besides "animal" and "two-footed." Again, some - things are one by contact, others by mixture, and others by position; but none of these - alternatives can possibly apply to the units of which 2 and 3 consist. Just as two men do - not constitute any one thing distinct from both of them, so it must be with the - units. The fact that the units are - indivisible will make no difference; because points are indivisible also, but nevertheless - a pair of points is not anything distinct from the two single points. Moreover we must not fail to realize this: that on this theory it follows - that 2's are prior and posterior, and the other numbers similarly. Let it be granted that the 2's in 4 are contemporaneous; yet - they are prior to those in 8, and just as the <determinate> 2 produced the 2's in 4, - soIn each case the other factor is the - indeterminate dyad (cf. sect. 18). they produced the 4's in 8. Hence if the - original 2 is an Idea, these 2's will also be Ideas of a sort. And the same argument applies to the units, because the units in the - original 2 produce the four units in 4; and so all the units become Ideas, and an Idea - will be composed of Ideas. Hence clearly those things also of which these things are Ideas - will be composite; e.g., one might say that animals are composed of animals, if there are - Ideas of animals. In general, to regard units as different in any way whatsoever is - absurd and fictitious (by "fictitious" I mean "dragged in to support a hypothesis"). For - we can see that one unit differs from another neither in quantity nor in quality; and a - number must be either equal or unequal—this applies to all numbers, but especially - to numbers consisting of abstract units. Thus - if a number is neither more nor less, it is equal; and things which are equal and entirely - without difference we assume, in the sphere of number, to be identical. Otherwise even the - 2's in the Ideal 10 will be different, although they are equal; for if anyone maintains - that they are not different, what reason will he be able to allege? Again, if every unit plus - another unit makes 2, a unit from the Ideal 2 plus one from the Ideal 3 will make - 2—a 2 composed of different unitsWhich - conflicts with the view under discussion.; will this be prior or posterior to 3? - It rather seems that it must be prior, because one of the units is contemporaneous with 3, - and the other with 2.The implication seems to be, - as Ross says, that the Platonists will refuse to admit that there is a number between 2 - and 3. We assume that in general 1 - and 1, whether the things are equal or unequal, make 2; e.g. good and bad, or man and - horse; but the supporters of this theory say that not even two units make 2. If the number of the Ideal 3 is not greater than that of the Ideal - 2, it is strange; and if it is greater, then - clearly there is a number in it equal to the 2, so that this number is not different from - the Ideal 2. But this is impossible, if there - is a first and second number.i.e., if numbers are - specifically different. Cf. Aristot. Met. - 13.6.1. Nor will the Ideas be numbers. For on this particular point they - are right who claim that the units must be different if there are to be Ideas, as has been - already stated.sect. 2-4 above. For the form - is unique; but if the units are undifferentiated, the 2's and 3's will be - undifferentiated. Hence they have to say - that when we count like this, l, 2, we do not add to the already existing number; for if - we do, (a) number will not be generated from the indeterminate dyad, and (b) a number - cannot be an Idea; because one Idea will pre-exist in another, and all the Forms will be - parts of one Form.i.e., the biggest - number. Thus in relation to their - hypothesis they are right, but absolutely they are wrong, for their view is very - destructive, inasmuch as they will say that this point presents a difficulty: whether, - when we count and say "1, 2, 3," we count by addition or by enumerating distinct - portions.This is Apelt's interpretation of - KATA\ MERI/DAS. For this sense of the word he quotes - Plut. Mor. 644c. The meaning then is: If you - count by addition, you regard number as exhibited only in concrete instances; if you - treat each number as a "distinct portion" (i.e. generated separately), you admit another - kind of number besides the mathematical. Aristotle says that number can be regarded in - both ways. But we do both; and therefore it is ridiculous to refer this point to - so great a difference in essence. First of all it would be well to define the differentia of a number; - and of a unit, if it has a differentia. Now units must differ either in quantity or in - quality; and clearly neither of these alternatives can be true. "But units may differ, as - number does, in quantity." But if units also differed in quantity, number would differ - from number, although equal in number of units. Again, are the first units greater or smaller, and do the later units increase in size, - or the opposite? All these suggestions are absurd. Nor can units differ in quality; for no - modification can ever be applicable to them, because these thinkers hold that even in - numbers quality is a later attribute than quantity.Numbers have quality as being prime or composite, "plane" or "solid" (i.e., products of - two or three factors); but these qualities are clearly incidental to quantity. Cf. Aristot. Met. 5.14.2. Further, the units cannot derive quality either from unity or from - the dyad; because unity has no quality, and the dyad produces quantity, because its nature - causes things to be many. If, then, the units differ in some other way, they should most - certainly state this at the outset, and explain, if possible, with regard to the - differentia of the unit, why it must exist; or failing this, what differentia they - mean. Clearly, then, if the Ideas are numbers, the units cannot all be addible, nor can they all be inaddible in either sense. Nor again is the - theory sound which certain other thinkersCf. Aristot. Met. 13.1.4. hold concerning - numbers. These are they who do not believe in - Ideas, either absolutely or as being a kind of numbers, but believe that the objects of - mathematics exist, and that the numbers are the first of existing things, and that their - principle is Unity itself. For it is absurd that if, as they say, there is a 1 which is - first of the 1's,i.e., Speusippus recognized unity - or "the One" as a formal principle, but admitted no other ideal numbers. Aristotle - argues that this is inconsistent. there should not be a 2 first of the 2's, nor a - 3 of the 3's; for the same principle applies to all cases. Now if this is the truth with regard to number, and we posit only - mathematical number as existing, Unity is not a principle. For the Unity which is of this - nature must differ from the other units; and if so, then there must be some 2 which is - first of the 2's; and similarly with the other numbers in succession. But if Unity is a principle, then the truth about numbers must - rather be as Plato used to maintain; there must be a first 2 and first 3, and the numbers - cannot be addible to each other. But then again, if we assume this, many impossibilities - result, as has been already stated.Aristot. Met. 13.7.1-8.3. Moreover, the truth - must lie one way or the other; so that if neither view is sound, number cannot have a separate - abstract existence. From these considerations it is also clear that the third - alternativeCf. Aristot. Met. 13.6.7.—that Ideal number and mathematical number - are the same—is the worst; for two errors have to be combined to make one theory. - (1.) Mathematical number cannot be of this nature, but the propounder of this view has to - spin it out by making peculiar assumptions; (2.) his theory must admit all the - difficulties which confront those who speak of Ideal number. The Pythagorean view in one way contains - fewer difficulties than the view described above, but in another way it contains further - difficulties peculiar to itself. By not regarding number as separable, it disposes of many - of the impossibilities; but that bodies should be composed of numbers, and that these - numbers should be mathematical, is impossible.See - Introduction. For (a) it is not true - to speak of indivisible magnitudesThis is proved in - Aristot. De Gen. et. Corr. 315b 24-317a - 17.; (b) assuming that this view is perfectly true, still units at any - rate have no magnitude; and how can a magnitude be composed of indivisible parts? Moreover - arithmetical number consists of abstract units. But the Pythagoreans identify number with - existing things; at least they apply mathematical propositions to bodies as though they - consisted of those numbers.See - Introduction. Thus if number, if it is a - self-subsistent reality, must be regarded in one of the ways described above, and if it - cannot be regarded in any of these ways, clearly number has no such nature as is invented - for it by those who treat it as separable. Again, does each unit come from the Great and the - Small, when they are equalizedCf. Aristot. Met. 13.7.5 n. Aristotle is obviously - referring to the two units in the Ideal 2.; or does one come from the Small and - another from the Great? If the latter, each thing is not composed of all the elements, nor - are the units undifferentiated; for one contains the Great, and the other the Small, which - is by nature contrary to the Great. Again, - what of the units in the Ideal 3? because there is one over. But no doubt it is for this - reason that in an odd number they make the Ideal One the middle unit.Cf. DieIs, Vorsokratiker 270. 18. - If on the other hand each of the units comes from both Great and Small, when they are - equalized, how can the Ideal 2 be a single entity composed of the Great and Small? How - will it differ from one of its units? Again, the unit is prior to the 2; because when the - unit disappears the 2 disappears. Therefore - the unit must be the Idea of an Idea, since it is prior to an Idea, and must have been - generated before it. From what, then? for the indeterminate dyad, as we have seen,Aristot. Met. - 13.7.18. causes duality. Again, number - must be either infinite or finite (for they make number separable, so that one of these - alternatives must be true).The point seems to be - that if number is self-subsistent it must be actually finite or infinite. - Aristotle himself holds that number is infinite only potentially; i.e., however high you - can count, you can always count higher. Now it is obvious that it cannot be infinite, because infinite number - is neither odd nor even, and numbers are always generated either from odd or from even - number. By one process, when 1 is added to an even number, we get an odd number; by - another, when 1 is multiplied by 2, we get ascending powers of 2; and by another, when - powers of 2 are multiplied by odd numbers, we get the remaining even numbers. Again, if every Idea - is an Idea of something, and the numbers are Ideas, infinite number will also be an Idea - of something, either sensible or otherwise. This, however, is impossible, both - logicallyi.e., as implying an actual - infinite. and on their own assumption,i.e., as inconsistent with the conception of an Idea as a determining principle. - since they regard the Ideas as they do. If, on the other - hand, number is finite, what is its limit? In reply to this we must not only assert the - fact, but give the reason. Now if number only - goes up to 10, as some hold,Cf. Aristot. Met. 12.8.2. The Platonists derived this - view from the Pythagoreans; see Introduction. in the first place the Forms will - soon run short. For example, if 3 is the Idea of Man, what number will be the Idea of - Horse? Each number up to 10 is an Idea; the Idea of Horse, then, must be one of the - numbers in this series, for they are substances or Ideas. But the fact remains that they will run short, because the different - types of animals will outnumber them. At the same time it is clear that if in this way the - Ideal 3 is the Idea of Man, so will the other 3's be also (for the 3's in the same - numbersRobin is probably right in taking this to - mean that the 3 which is in the ideal 4 is like the 3 which is in the 4 which is in a - higher ideal number, and so on (La Theorie platonicienne des Idees et des Nombres - d'apres Aristote, p. 352). are similar), so that there will be an infinite number of men; and if each 3 is an Idea, - each man will be an Idea of Man; or if not, they will still be men. And if the smaller number is part of the greater, when it is - composed of the addible units contained in the same number, then if the Ideal 4 is the - Idea of something, e.g. "horse" or "white," then "man" will be part of "horse," if "man" - is 2. It is absurd also that there should be an Idea of 10 and not of 11, nor of the - following numbers. Again, some things exist and come into being of which there are no - FormsCf. Aristot. Met. 13.4.7, 8; Aristot. Met. 1.9.2, - 3.; why, then, are there not Forms of these too? It follows that the - Forms are not the causes of things. Again, it is absurd that - number up to 10 should be more really existent, and a Form, than 10 itself; although the - former is not generated as a unity, whereas the latter is. However, they try to make out - that the series up to 10 is a complete number; at least they generate the derivatives, e.g. the void, proportion, the odd, etc., from - within the decad. Some, such as motion, rest, good and evil, they assign to the first - principles; the rest to numbers.From the Dyad were - derived void (Theophrastus, Met. 312.18-313.3) - and motion (cf. Aristot. Met. 1.9.29, Aristot. Met. 11.9.8). Rest would naturally be - derived from unity. For good and evil see Aristot. Met. - 1.6.10. Proportion alone of the "derivatives" here mentioned appears to be - derived from number. As Syrianus says, the three types of proportion can be illustrated - by numbers from within the decad—arithmetical 1. 2. 3, geometrical 1. 2. 4, - harmonic 2. 3. 6. Hence they - identify the odd with Unity; because if oddness depended on 3, how could 5 be odd?sc. because (on their theory) 3 is not contained in 5. - Thus oddness had to be referred to not a number but a - principle—unity. Again, they hold that - spatial magnitudes and the like have a certain limit; e.g. the first or indivisible line, then the - 2, and so on; these too extending up to 10.The - "indivisible line" or point was connected with 1, the line with 2, the plane with 3 and - the solid with 4 (Aristot. Met. 14.3.9); and - 1+2+3+4=10. Again, if number is separable, the - question might be raised whether Unity is prior, or 3 or 2. Now if we regard number as composite, Unity is prior; but if we regard - the universal or form as prior, number is prior, because each unit is a material part of - number, while number is the form of the units. And there is a sense in which the right - angle is prior to the acute angle—since it is definite and is involved in the - definition of the acute angle—and another sense in which the acute angle is prior, - because it is a part of the other, i.e., the right angle is divided into acute - angles. Thus regarded as matter the acute - angle and element and unit are prior; but with respect to form and substance in the sense - of formula, the right angle, and the whole composed of matter and form, is prior. For the - concrete whole is nearer to the form or subject of the definition, although in generation - it is posterior.Cf. Aristot. Met. 7.10, 11. In what sense, - then, is the One a first principle? Because, they say, it is indivisible. But the universal and the part or element are also - indivisible. Yes, but they are prior in a different sense; the one in formula and the - other in time. In which sense, then, is the One a first principle? for, as we have just - said, both the right angle seems to be prior to the acute angle, and the latter prior to - the former; and each of them is one. Accordingly the Platonists make the One a first principle in both senses. But this is - impossible; for in one sense it is the One qua form or - essence, and in the other the One qua part or matter, that is primary. There is a sense in which both - number and unit are one; they are so in truth potentially—that is, if a number is - not an aggregate but a unity consisting of units distinct from those of other numbers, as - the Platonists hold— but each of the - twoAristotle takes the number two as an example, - but the principle is of course universal. In a sense both number and unit are one; but - if the number exists as an actual unity, the unit can only exist potentially. - units is not one in complete reality. The cause of the error which befell the Platonists - was that they were pursuing their inquiry from two points of view—that of - mathematics and that of general definition—at the same time. Hence as a result of - the former they conceived of the One or first principle as a point, for the unit is a - point without position. (Thus they too, just like certain others, represented existing things as composed of that which is - smallest.)Perhaps the Atomists; but cf. Aristot. Met. 1.8.3, 4. We get, then, that the - unit is the material element of numbers, and at the same time is prior to the number 2; - and again we get that it is posterior to 2 regarded as a whole or unity or form. On the - other hand, through looking for the universal, they were led to speak of the unity - predicated of a given number as a part in the formal sense also. But these two - characteristics cannot belong simultaneously to the same thing. And if Unity itself must only - be without positionIf the text is sound (and no - convincing emendation has been suggested), it seems best to understand A)/QETON in a rather wider sense than the semi-technical one - put forward by Ross. "Without position"=not localized, i.e. abstract. Unity as a - principle has no concrete instance.(for it differs only in that it is a - principle) and 2 is divisible whereas the unit is not, the unit will be more nearly akin - to Unity itself; and if this is so, Unity itself will also be more nearly akin to the unit - than to 2. Hence each of the units in 2 will be prior to 2. But this they deny; at least - they make out that 2 is generated first.Cf. Aristot. Met. 13.7.5. - Further, if - 2 itself and 3 itself are each one thing, both together make 2. From what, then, does this - 2 come? Since - there is no contact in numbers, but units which have nothing between them—e.g. those - in 2 or 3—are successive, the question might be raised whether or not they are - successive to Unity itself, and whether of the numbers which succeed it 2 or one of the - units in 2 is prior. We find similar difficulties in the case of the genera posterior to - numberCf. Aristot. Met. 13.6.10.—the line, plane and solid. Some derive - these from the species of the Great and Small; viz. lines from the Long and Short, planes - from the Broad and Narrow, and solids from the Deep and Shallow. These are species of the - Great and Small. As for the geometrical first - principle which corresponds to the arithmetical One, different Platonists propound - different views.Cf. Aristot. Met. 3.4.34, Aristot. Met. - 14.3.9. In these too we can see innumerable impossibilities, fictions - and contradictions of all reasonable probability. For (a) we get that the geometrical - forms are unconnected with each other, unless their principles also are so associated that - the Broad and Narrow is also Long and Short; and if this is so, the plane will be a line - and the solid a plane. Moreover, how can angles and figures, etc., be explained? And (b) the - same result follows as in the case of number; for these concepts are modifications of - magnitude, but magnitude is not generated from them, any more than a line is generated - from the Straight and Crooked, or solids from the Smooth and Rough. Common to all these Platonic - theories is the same problem which presents itself in the case of species of a genus when - we posit universals—viz. whether it is the Ideal animal that is present in the - particular animal, or some other "animal" distinct from the Ideal animal. This question - will cause no difficulty if the universal is not separable; but if, as the Platonists say, - Unity and the numbers exist separately, then it is not easy to solve (if we should apply - the phrase "not easy" to what is impossible). For when we think of the one in 2, or in number generally, are we thinking of an Idea or - of something else? These thinkers, then, generate - geometrical magnitudes from this sort of material principle, but othersThe reference is probably to Speusippus; Plato and - Xenocrates did not believe in points (Aristot. Met. - 1.9.25, Aristot. Met. 13.5.10 n). generate them from the - point (they regard the point not as a unity but as similar to Unity) and another material - principle which is not plurality but is similar to it; yet in the case of these principles - none the less we get the same difficulties. For - if the matter is one, line, plane and solid will be the same; because the product of the - same elements must be one and the same. If on the other hand there is more than one kind of - matter—one of the line, another of the plane, and another of the solid—either - the kinds are associated with each other, or they are not. Thus the same result will - follow in this case also; for either the plane will not contain a line, or it will be a - line. Further, no attempt is made to explain how number can be generated from unity and - plurality; but howsoever they account for this, they have to meet the same difficulties as - those who generate number from unity and the indeterminate dyad. The one school generates - number not from a particular plurality but from that which is universally predicated; the - other from a particular plurality, but the first; for they hold that the dyad is the first - plurality.Aristotle again identifies the - indeterminate dyad with the number 2. Thus there is practically no difference between the two views; the same difficulties will - be involved with regard to mixture, position, blending, generation and the other similar - modes of combination.sc. of the elements of - number. We might very well ask the further - question: if each unit is one, of what it is composed; for clearly each unit is not - absolute unity. It must be generated from absolute unity and either plurality or a part of - plurality. Now we cannot hold that the unit - is a plurality, because the unit is indivisible; but the view that it is derived from a - part of plurality involves many further difficulties, because (a) each part must be - indivisible; otherwise it will be a plurality and the unit will be divisible, and unity and plurality will not be its elements, - because each unit will not be generated from pluralitysc. but from an indivisible part of plurality—which is not a - plurality but a unity. and unity. (b) - The exponent of this theory merely introduces another number; because plurality is a - number of indivisible parts.i.e., to say that - number is derived from plurality is to say that number is derived from - number—which explains nothing. Again, we must - inquire from the exponent of this theory whether the numbersc. which plurality has been shown to be. is infinite or - finite. There was, it appears, a finite - plurality from which, in combination with Unity, the finite units were generated; and - absolute plurality is different from finite plurality. What sort of plurality is it, then, - that is, in combination with unity, an element of number? We - might ask a similar question with regard to the point, i.e. the element out of which they - create spatial magnitudes. This is surely not - the one and only point. At least we may ask from what each of the other points comes; it - is not, certainly, from some interval and the Ideal point. Moreover, the parts of the - interval cannot be indivisible parts, any more than the parts of the plurality of which - the units are composed; because although number is composed of indivisible parts, spatial - magnitudes are not. All these and other similar considerations make it clear that number - and spatial magnitudes cannot exist separately. Further, the fact that the leading - authoritiesAlexander preferred the reading - PRW/TOUS, interpreting it in this sense; and I do not - see why he should not be followed. Ross objects that PRW=TOS is used in the chronological sense in 16., but this is really no - argument. For a much more serious (although different) inconsistency in the use of terms - cf. Aristot. Met. 12.3.1. disagree about - numbers indicates that it is the misrepresentation of the facts themselves that produces - this confusion in their views. ThoseSpeusippus and his followers. who recognize only - the objects of mathematics as existing besides sensible things, abandoned Ideal number and - posited mathematical number because they perceived the difficulty and artificiality of the - Ideal theory. Others,Xenocrates and his - followers. wishing to maintain both Forms and numbers, but not seeing how, if one - posits theseUnity and the indeterminate dyad; for - the difficulty see Aristot. Met. 13.7.3, - 4. as first principles, mathematical number can exist besides Ideal - number, identified Ideal with mathematical number,—but only in theory, since - actually mathematical number is done away with, because the hypotheses which they state - are peculiar to them and not mathematical.Cf. Aristot. Met. 13.6.10. And hePlato. who - first assumed that there are Ideas, and that the Ideas are numbers, and that the objects - of mathematics exist, naturally separated them. Thus it happens that all are right in some - respect, but not altogether right; even they themselves admit as much by not agreeing but - contradicting each other. The reason of this is that their assumptions and first - principles are wrong; and it is difficult to - propound a correct theory from faulty premisses: as Epicharmus says, "no sooner is it said - than it is seen to be wrong."Epicharmus, Fr. 14, Diels. We have now examined and analyzed the questions concerning numbers to a - sufficient extent; for although one who is already convinced might be still more convinced - by a fuller treatment, he who is not convinced - would be brought no nearer to conviction. As - for the first principles and causes and elements, the views expressed by those who discuss - only sensible substance either have been described in the PhysicsAristot. Physics - 1.4-6. or have no place in our present inquiry; but the views of those - who assert that there are other substances besides sensible ones call for investigation - next after those which we have just discussed. Since, then, some thinkers hold that the Ideas and - numbers are such substances, and that their elements are the elements and principles of - reality, we must inquire what it is that they hold, and in what sense they hold - it. ThoseThe Pythagoreans and Speusippus. who - posit only numbers, and mathematical numbers at that, may be considered laterAristot. Met. - 14.2.21, Aristot. Met. 14.3.2-8, 15, - 16.; but as for those who speak of the Ideas, we can observe at the same - time their way of thinking and the difficulties which befall them. For they not only treat - the Ideas as universal substances, but also as separable and particular. (That this is impossible has been already shownAristot. Met. - 3.6.7-9. by a consideration of the difficulties involved.) The reason - why those who hold substances to be universal combined these two views was that they did - not identify substances with sensible things. They considered that the particulars in the - sensible world are in a state of flux, and that none of them persists, but that the - universal exists besides them and is something distinct from them. This theory, as we have said in an earlier passage,Aristot. Met. - 13.4, and cf. Aristot. Met. 1.6. - was initiated by Socrates as a result of his definitions, but he did not separate - universals from particulars; and he was right in not separating them. This is evident from - the facts; for without the universal we cannot acquire knowledge, and the separation of - the universal is the cause of the difficulties which we find in the Ideal - theory. Others,The Platonists. regarding it as necessary, if there are to be any - substances besides those which are sensible and transitory, that they should be separable, - and having no other substances, assigned separate existence to those which are universally - predicated; thus it followed that universals and particulars are practically the same kind - of thing. This in itself would be one difficulty in the view which we have just - described.See Introduction. Let us now mention a - point which presents some difficulty both to those who hold the Ideal theory and to those - who do not. It has been stated already, at the beginning of our treatise, among the - problems.Cf. Aristot. Met. 3.4.8-10, Aristot. Met. - 3.6.7-9. If we do not suppose substances to be separate, that is in the - way in which particular things are said to be separate, we shall do away with substance in - the sense in which we wish to maintain it; but if we suppose substances to be - separable, how are we to regard their elements - and principles? If they are particular and not - universal, there will be as many real things as there are elements, and the elements will - not be knowable. For let us suppose that the syllables in speech are substances, and that - their letters are the elements of substances. Then there must be only one BA, and only one - of each of the other syllables; that is, if they are not universal and identical in form, - but each is numerically one and an individual, and not a member of a class bearing a - common name. (Moreover, the Platonists assume - that each Ideal entity is unique.) Now if this is true of the syllables, it is also true - of their letters. Hence there will not be more than one A, nor more than one of any of the - other letters,This is, as a matter of fact, the - assumption upon which the whole argument rests; Aristotle is arguing in a circle. - on the same argument by which in the case of the syllable there cannot be more than one - instance of the same syllable. But if this is so, there will be no other things besides - the letters, but only the letters. Nor again will the elements be knowable; for they will not be - universal, and knowledge is of the universal. This can be seen by reference to proofs and - definitions; for there is no logical conclusion that a given triangle has its angles equal - to two right angles unless every triangle has its angles equal to two right angles, or - that a given man is an animal unless every man is an animal. On the other hand, if the first - principles are universal, either the substances composed of them will be universal too, or - there will be a non-substance prior to substance; because the universal is not substance, - and the element or first principle is universal; and the element or first principle is - prior to that of which it is an element or first principle. All this naturally follows when they compose the Ideas of elements and - assert that besides the substances which have the same form there are also Ideas each of - which is a separate entity. But if, as in the case of the - phonetic elements, there is no reason why there should not be many A's and B's, and no "A - itself" or "B itself" apart from these many, then on this basis there may be any number of - similar syllables. The doctrine that all knowledge is of the universal, and hence that - the principles of existing things must also be universal and not separate substances, - presents the greatest difficulty of all that we have discussed; there is, however, a sense - in which this statement is true, although there is another in which it is not - true. Knowledge, like the verb "to know," - has two senses, of which one is potential and the other actual. The potentiality being, as - matter, universal and indefinite, has a universal and indefinite object; but the actuality - is definite and has a definite object, because it is particular and deals with the - particular. It is only accidentally that - sight sees universal color, because the - particular color which it sees is color; and the particular A which the grammarian studies - is an A. For if the first principles must be universal, that which is derived from them - must also be universal, as in the case of logical proofs"Because A)PO/DEICIS" (logical or - syllogistic proof) "must be in the first figure (Aristot. - An. Post. 1.14), and in that figure universal premises always give a universal - conclusion." (Ross.); and if this is so there will be nothing which has a - separate existence; i.e. no substance. But it is clear that although in one sense - knowledge is universal, in another it is not.

- - -

With - regard to this kind of substance,i.e., the Platonic - Ideas or numbers, which they regarded as unchangeable substances. There is, however, no - definite transition to a fresh subject at this point. The criticisms of the Ideas or - numbers as substances, and of the Platonic first principles, have not been grouped - systematically in Books 13 and 14. Indeed there is so little distinction in subject - matter between the two books that in some Mss. 14 was made to begin at 13.9.10. - (Syrianus ad loc.). See Introduction. then, let the foregoing account suffice. - All thinkers make the first principles contraries; as in the realm of natural objects, so - too in respect of the unchangeable substances. Now if nothing can be prior to the first principle of all things, that first principle - cannot be first principle if it is an attribute of something else. This would be as absurd - as to say that "white" is the first principle, not qua anything - else but qua white, and yet that it is predicable of a subject, and - is white because it is an attribute of something else; because the latter will be prior to - it. Moreover, all things are generated from - contraries as from a substrate, and therefore contraries must most certainly have a - substrate. Therefore all contraries are predicated of a subject, and none of them exists - separately. But there is no contrary to substance; not only is this apparent, but it is - borne out by reasoned consideration.Cf. Aristot. Categories 3b 24-27 Thus none of the - contraries is strictly a first principle; the first principle is something - different. But the Platonists treat one of the contraries as matter, some opposing "the unequal" to - Unity (on the ground that the former is of the nature of plurality) and others - plurality. For according to some,Plato; cf. Aristot. - Met. 13.7.5. numbers are generated from the unequal dyad of the Great - and Small; and according to another,Probably - Speusippus. from plurality; but in both cases they are generated by the essence - of unity. For he who speaks of "the unequal" and Unity as elements, and describes the - unequal as a dyad composed of Great and Small, speaks of the unequal, i.e. the Great and - Small, as being one; and does not draw the distinction that they are one in formula but - not in number.This shows clearly that by the - Great-and Small Plato meant a single principle, i.e., indeterminate quantity. Aristotle - admits this here because he is contrasting the Great-and Small with the One; but - elsewhere he prefers to regard the Platonic material principle as a duality. See - Introduction. Again, they state the first principles, which they call elements, - badly; some say that the Great and the Small, together with Unity (making 3Cf. previous note. in all), are the elements of - numbers; the two former as matter, and Unity as form. Others speak of the Many and Few, - because the Great and the Small are in their nature more suited to be the principles of - magnitude; and others use the more general term which covers these—"the exceeding" - and "the exceeded." But none of these - variations makes any appreciable difference with respect to some of the consequences of - the theory; they only affect the abstract - difficulties, which these thinkers escape because the proofs which they themselves employ - are abstract. There is, however, this - exception: if "the exceeding" and "the exceeded" are the first principles, and not the - Great and the Small, on the same principle number should be derived from the elements - before 2 is derived; for as "the exceeding and the exceeded" is more universal than the - Great and Small, so number is more universal than 2. But in point of fact they assert the - one and not the other. Others oppose "the different" or - "other" to Unity; and others contrast Plurality and Unity. Now if, as they maintain, existing things are derived from contraries, - and if there is either no contrary to unity, or if there is to be any contrary it is - plurality; and if the unequal is contrary to the equal, and the different to the same, and - the other to the thing itself then those who oppose unity to plurality have the best claim - to credibility—but even their theory is inadequate, because then unity will be few. - For plurality is opposed to paucity, and many to few. That "unity" denotes a measureCf. Aristot. Met. - 5.6.17, 18, Aristot. Met. 10.1.8, - 21. is obvious. And in every case there is something else which underlies - it; e.g., in the scale there is the quarter-tone; in spatial magnitude the inch or foot or - some similar thing; and in rhythms the foot or syllable. Similarly in the case of gravity - there is some definite weight. Unity is predicated of all things in the same way; - of - qualities as a quality, and of quantities as a quantity. (The measure is indivisible, in the former case in kind, and in the - latter to our senses.) This shows that unity is not any independent substance. And this is - reasonable; because unity denotes a measure of some plurality, and number denotes a - measured plurality and a plurality of measures. (Hence too it stands to reason that unity - is not a number; for the measure is not measures, but the measure and unity are - starting-points.) The measure must always be - something which applies to all alike; e.g., if the things are horses, the measure is a - horse; if they are men, the measure is a man; and if they are man, horse and god, the - measure will presumably be an animate being, and the number of them animate - beings. If the things are "man," "white" and - "walking," there will scarcely be a number of them, because they all belong to a subject - which is one and the same in number; however, their number will be a number of genera, or - some other such appellation. ThoseCf. sect. 5. who - regard the unequal as a unity, and the dyad as an indeterminate compound of great and - small, hold theories which are very far from being probable or possible. For these terms - represent affections and attributes, rather than substrates, of numbers and - magnitudes—"many" and "few" applying to number, and "great" and "small" to - magnitude— just as odd and even, smooth - and rough, straight and crooked, are attributes. Further, in addition to this error, "great" and "small" and all other - such terms must be relative. And the relative is of all the categories in the least degree - a definite entity or substance; it is posterior to quality and quantity. The relative is - an affection of quantity, as we have said, and not its matter; since there is something - else distinct which is the matter both of the relative in general and of its parts and - kinds. There is nothing great or small, many - or few, or in general relative, which is many or few, great or small, or relative to - something else without having a distinct nature of its own. That the relative is in the - lowest degree a substance and a real thing is shown by the fact that of it aloneCf. Aristot. Met. - 11.12.1. There Aristotle refers to seven categories, but here he omits - "activity" and "passivity" as being virtually identical with motion. there is - neither generation nor destruction nor change in the sense that in respect of quantity - there is increase and decrease, in respect of quality, alteration, in respect of place, - locomotion, and in respect of substance, absolute generation and destruction. There is no real change in respect of the relative; - for without any change in itself, one term will be now greater, now smaller or equal, as - the other term undergoes quantitative change. Moreover, the matter of every thing, and - therefore of substance, must be that which is potentially of that nature; but the relative - is neither potentially substance nor actually. It is absurd, then, or rather impossible, to - represent non-substance as an element of substance and prior to it; for all the other - categories are posterior to substance. And further, the elements are not predicated of - those things of which they are elements; yet "many" and "few" are predicated, both - separately and together, of number; and "long" and "short" are predicated of the line, and - the Plane is both broad and narrow. If, then, - there is a plurality of which one term, viz. "few," is always predicable, e.g. 2 (for if 2 - is many, 1 will be fewCf. Aristot. Met. 10.6.1-3.), then there will be - an absolute "many"; e.g., 10 will be many (if there is nothing more than 10Cf. Aristot. Met. - 13.8.17.), or 10,000. How, then, in this light, can number be derived - from Few and Many? Either both ought to be predicated of it, or neither; but according to - this view only one or the other is predicated. But we must inquire in general whether eternal things - can be composed of elements. If so, they will have matter; for everything which consists - of elements is composite. Assuming, then, that - that which consists of anything, whether it has always existed or it came into being, must - come into being <if at all> out of that of which it consists; and that everything - comes to be that which it comes to be out of that which is it potentially (for it could - not have come to be out of that which was not potentially such, nor could it have - consisted of it); and that the potential can either be actualized or not; then however everlasting number or anything else which has - matter may be, it would be possible for it not to exist, just as that which is any number - of years old is as capable of not existing as that which is one day old. And if this is - so, that which has existed for so long a time that there is no limit to it may also not - exist. Therefore things which contain matter - cannot be eternal, that is, if that which is capable of not existing is not eternal, as we - have had occasion to say elsewhere.Aristot. Met. 9.8.15-17, Aristot. De Caelo 1.12. Now if what we have just - been saying—that no substance is eternal unless it is actuality—is true - universally, and the elements are the matter of substance, an eternal substance can have - no elements of which, as inherent in it, it consists. There are some who, while making the - element which acts conjointly with unity the indeterminate dyad, object to "the unequal," - quite reasonably, on the score of the difficulties which it involves. But they are rid - only of those difficultiesCf. Aristot. Met. 14.1.14-17. which necessarily - attend the theory of those who make the unequal, i.e. the relative, an element; all the - difficulties which are independent of this view must apply to their theories also, whether - it is Ideal or mathematical number that they construct out of these elements. There are many causes - for their resorting to these explanations, the chief being that they visualized the problem in an - archaic form. They supposed that all existing things would be one, absolute Being, unless - they encountered and refuted Parmenides' dictum: It will - ne'er be proved that things which are not, are,Parmenides Fr. 7 (Diels). i.e., that they must show that that which is not, is; for only so—of - that which is, and of something else—could existing things be composed, if they are - more than one.Cf. Plat. - Soph. 237a, 241d, 256e. However, (i) in the first place, if "being" has several - meanings (for sometimes it means substance, sometimes quality, sometimes quantity, and so - on with the other categories), what sort of unity will all the things that are constitute, - if not-being is not to be? Will it be the substances that are one, or the affections (and - similarly with the other categories), or all the categories together? in which case the - "this" and the "such" and the "so great," and all the other categories which denote some - sense of Being, will be one. But it is absurd, - or rather impossible, that the introduction of one thing should account for the fact that - "what is" sometimes means "so-and-so," sometimes "such-and-such," sometimes "of - such-and-such a size," sometimes "in such-and-such a place." (2) Of what sort of not-being and Being - do real things consist? Not-being, too, has several senses, inasmuch as Being has; and - "not-man" means "not so-and-so," whereas "not straight" means "not such-and-such," and - "not five feet long" means "not of such-and-such a size." What sort of Being and - not-being, then, make existing things a plurality? This thinker means by the - not-being which together with Being makes existing things a plurality, falsity and - everything of this naturePlat. Soph. 237a, 240; but Aristotle's statement assumes too much.; and - for this reason also it was saidPresumably by some - Platonist. that we must assume something which is false, just as geometricians - assume that a line is a foot long when it is not. But this cannot be so; for (a) the geometricians do not assume - anything that is false (since the proposition is not part of the logical inferencei.e., the validity of a geometrical proof does not - depend upon the accuracy of the figure.), and (b) existing things are not - generated from or resolved into not-being in this sense. But not only has "not-being" in - its various cases as many meanings as there are categories, but moreover the false and the - potential are called "not-being"; and it is from the latter that generation takes - place—man comes to be from that which is not man but is potentially man, and white - from that which is not white but is potentially white; no matter whether one thing is - generated or many. Clearly the point at issue is how "being" in the sense of the - substances is many; for the things that are generated are numbers and lines and bodies. It - is absurd to inquire how Being as substance is many, and not how qualities or quantities - are many. Surely the indeterminate dyad or the - Great and Small is no reason why there should be two whites or many colors or flavors or - shapes; for - then these too would be numbers and units. But if the Platonists had pursued this inquiry, - they would have perceived the cause of plurality in substances as well; for the causeMatter, according to Aristotle; and there is matter, or - something analogous to it, in every category. Cf. Aristot. Met. 12.5. is the same, or analogous. This deviation of theirs was - the reason why in seeking the opposite of Being and unity, from which in combination with - Being and unity existing things are derived, they posited the relative (i.e. the unequal), - which is neither the contrary nor the negation of Being and unity, but is a single - characteristic of existing things, just like substance or quality. They should have - investigated this question also; how it is that relations are many, and not one. As it is, they inquire how it is that there are many - units besides the primary unity, but not how there are many unequal things besides the - Unequal. Yet they employ in their arguments and speak of Great and Small, Many and Few (of - which numbers are composed), Long and Short (of which the line is composed), Broad and - Narrow (of which the plane is composed), Deep and Shallow (of which solids are composed); - and they mention still further kinds of relation.Cf. Aristot. Met. 14.1.6, 18, Aristot. Met. 1.9.23. Now what is the - cause of plurality in these relations? We must, then, as I say, presuppose in the case of each thing - that which is it potentially. The authorPlato. of this theory further explained what it is that is potentially a - particular thing or substance, but is not per se existent—that it is the relative - (he might as well have said "quality"); which is neither potentially unity or Being, nor a - negation of unity or Being, but just a - particular kind of Being. And it was still - more necessary, as we have said,sect. 11. - that, if he was inquiring how it is that things are many, he should not confine his - inquiry to things in the same category, and ask how it is that substances or qualities are - many, but that he should ask how it is that things in general are many; for some things - are substances, some affections, and some relations. Now in the case of the other categories there is an additional - difficulty in discovering how they are many. For it may be said that since they are not - separable, it is because the substrate becomes or is many that qualities and quantities - are many; yet there must be some matter for each class of entities, only it cannot be - separable from substances. In the case of - particular substances, however, it is explicable how the particular thing can be many, if - we do not regard a thing both as a particular substance and as a certain - characteristic.This, according to Aristotle, is - how the Platonists regard the Ideas. See Introduction. The real difficulty which - arises from these considerations is how substances are actually many and not - one. Again, even if a particular thing and a quantity are - not the same, it is not explained how and why existing things are many, but only how - quantities are many; for all number denotes - quantity, and the unit, if it does not mean a measure, means that which is quantitatively - indivisible. If, then, quantity and substance are different, it is not explained whence or - how substance is many; but if they are the same, he who holds this has to face many logical - contradictions. One might fasten also upon the question - with respect to numbers, whence we should derive the belief that they exist. For onePlato - and his orthodox followers. who posits Ideas, numbers supply a kind of cause for - existing things; that is if each of the numbers is a kind of Idea, and the Idea is, in - some way or other, the cause of existence for other things; for let us grant them this - assumption. But as for himSpeusippus. who does not hold this belief, - because he can see the difficulties inherent in the Ideal theory (and so has not this - reason for positing numbers), and yet posits mathematical number, what grounds have we for - believing his statement that there is a number of this kind, and what good is this number - to other things? He who maintains its existence does not claim that it is the cause of - anything, but regards it as an independent entity; nor can we observe it to be the cause - of anything; for the theorems of the arithmeticians will all apply equally well to - sensible things, as we have said.Aristot. Met. 13.3.1. Those, then, who posit the - Ideas and identify them with numbers, by their assumption (in accordance with their method - of abstracting each general term from its several concrete examples) that every general - term is a unity, make some attempt to explain why number exists.I have followed Ross's text and interpretation of this sentence. For the - meaning cf. Aristot. Met. 14.2.20. Since, - however, their arguments are neither necessarily true nor indeed possible, there is no justification on this ground for maintaining - the existence of number. The Pythagoreans, on - the other hand, observing that many attributes of numbers apply to sensible bodies, - assumed that real things are numbers; not that numbers exist separately, but that real - things are composed of numbers.See - Introduction. But why? Because the attributes of numbers are to be found in a - musical scale, in the heavens, and in many other connections.Cf. Aristot. Met. - 14.6.5. As for those who hold that mathematical number alone exists,Cf. Aristot. Met. - 14.2.21. they cannot allege anything of this kindi.e., that things are composed of numbers. consistently with their - hypotheses; what they did say was that the sciences could not have sensible things as - their objects. But we maintain that they can; as we have said before. And clearly the - objects of mathematics do not exist in separation; for if they did their attributes would - not be present in corporeal things. Thus in - this respect the Pythagoreans are immune from criticism; but in so far as they construct - natural bodies, which have lightness and weight, out of numbers which have no weight or - lightness, they appear to be treating of another universe and other bodies, not of - sensible ones.See Introduction. But those who treat number as separable assume that it - exists and is separable because the axioms will not apply to sensible objects; whereas the - statements of mathematics are true and appeal to the soul.The statements of mathematics appeal so strongly to our intelligence that - they must be true; therefore if they are not true of sensible things, there must be some - class of objects of which they are true. - The same - applies to mathematical extended magnitudes. It is clear, then, both that the contrary theoryThe Pythagorean theory, which maintains that numbers - not only are present in sensible things but actually compose them, is in itself an - argument against the Speusippean view, which in separating numbers from sensible things - has to face the question why sensible things exhibit numerical attributes. can - make out a case for the contrary view, and that those who hold this theory must find a - solution for the difficulty which was recently raisedsect. 3.—why it is that while numbers are in no way present - in sensible things, their attributes are present in sensible things. There are someProbably Pythagoreans. - Cf. Aristot. Met. 7.2.2, Aristot. Met. 3.5.3. who think that, because - the point is the limit and extreme of the line, and the line of the plane, and the plane - of the solid, there must be entities of this kind. We must, then, examine this argument also, and see whether it is not - exceptionally weak. For (1.) extremes are not substances; rather all such things are - merely limits. Even walking, and motion in general, has some limit; so on the view which - we are criticizing this will be an individual thing, and a kind of substance. But this is - absurd. And moreover (2.) even if they are substances, they will all be substances of - particular sensible things, since it was to these that the argument applied. Why, then, - should they be separable? Again, we may, if we are not unduly acquiescent, further object with - regard to all number and mathematical objects that they contribute nothing to each other, - the prior to the posterior. For if number does not exist, none the less spatial magnitudes - will exist for those who maintain that only the objects of mathematics exist; and if the - latter do not exist, the soul and sensible bodies will exist.That the criticism is directed against Speusippus is clear from Aristot. Met. 7.2.4. Cf. Aristot. Met. 12.10.14. But it does not appear, to judge from the observed - facts, that the natural system lacks cohesion, like a poorly constructed drama. ThoseXenocrates - (that the reference is not to Plato is clear from sect. 11). who posit the Ideas - escape this difficulty, because they construct spatial magnitudes out of matter and a - number—2 in the case of lines, and 3, presumably, in that of planes, and 4 in that - of solids; or out of other numbers, for it makes no difference. But are we to regard these magnitudes as Ideas, or what is their mode - of existence? and what contribution do they make to reality? They contribute nothing; just - as the objects of mathematics contribute nothing. Moreover, no mathematical theorem - applies to them, unless one chooses to interfere with the principles of mathematics and - invent peculiar theoriese.g. that of "indivisible - lines." of one's own. But it is not difficult to take any chance hypotheses and - enlarge upon them and draw out a long string of conclusions. These thinkers, then, are quite wrong in - thus striving to connect the objects of mathematics with the Ideas. But those who first - recognized two kinds of number, the Ideal and the mathematical as well, neither have - explained nor can explain in any way how mathematical number will exist and of what it - will be composed; for they make it intermediate between Ideal and sensible - number. For if it is composed of the Great - and Small, it will be the same as the former, i.e. Ideal, number. But of what other Great - and Small can it be composed? for Plato makes spatial magnitudes out of a Great and - Small.This interpretation (Ross's second - alternative, reading TI/NOS for TINOS) seems to be the most satisfactory. For the objection cf. Aristot. Met. 3.4.34. - And if he - speaks of some other component, he will be maintaining too many elements; while if some - one thing is the first principle of each kind of number, unity will be something common to - these several kinds. We must inquire how it is - that unity is these many things, when at the same time number, according to him, cannot be - derived otherwise than from unity and an indeterminate dyad.The argument may be summarized thus. If mathematical number cannot be - derived from the Great-and-Small or a species of the Great-and-Small, either it has a - different material principle (which is not economical) or its formal principle is in - some sense distinct from that of the Ideal numbers. But this implies that unity is a - kind of plurality, and number or plurality can only be referred to the dyad or material - principle. All these views are irrational; they - conflict both with one another and with sound logic, and it seems that in them we have a - case of Simonides' "long storyThe exact reference - is uncertain, but Aristotle probably means Simonides of Ceos. Cf. Simonides Fr. 189 - (Bergk)."; for men have recourse to the "long story," such as slaves tell, - when they have nothing satisfactory to say. The very elements too, the Great and Small, seem to protest at being dragged in; for - they cannot possibly generate numbers except rising powers of 2.Assuming that the Great-and-Small, or indeterminate dyad, is duplicative - (Aristot. Met. 13.7.18). It is absurd also, or rather it is one of the impossibilities of - this theory, to introduce generation of things which are eternal. There is no reason to doubt whether the Pythagoreans do or do - not introduce it; for they clearly state that when the One had been - constituted—whether out of planes or superficies or seed or out of something that - they cannot explain—immediately the nearest part of the Infinite began to be drawn - in and limited by the Limit.Cf. Aristot. Physics 3.4, Aristot. Physics 4.6, and Burnet, E.G.P. sect. 53. However, since they are here explaining the construction of - the universe and meaning to speak in terms of physics, although we may somewhat criticize - their physical theories, it is only fair to - exempt them from the present inquiry; for it is the first principles in unchangeable - things that we are investigating, and therefore we have to consider the generation of this - kind of numbers. TheyThe Platonists. say that there is no - generation of odd numbers,This statement was - probably symbolical. "They described the odd numbers as ungenerated because they likened - them to the One, the principle of pure form" (Ross ad loc.). which clearly - implies that there is generation of even ones; and some hold that the even is constructed - first out of unequals—the Great and Small—when they are equalized.Cf. Aristot. Met. - 13.7.5. Therefore the inequality must apply to them before they are - equalized. If they had always been equalized they would not have been unequal before; for - there is nothing prior to that which has always been. Hence evidently it is not for the sake of a logical theory that they - introduce the generation of numbers A difficulty, and a - discredit to those who make light of the difficulty, arises out of the question how the - elements and first principles are related to the the Good and the Beautiful. The - difficulty is this: whether any of the elements is such as we mean when weAristotle speaks as a Platonist. See - Introduction. speak of the Good or the Supreme Good, or whether on the contrary - these are later in generation than the elements. It would seem that there is an agreement between the mythologists and some present-day - thinkers,The Pythagoreans and Speusippus; cf. - Aristot. Met. 12.7.10. who deny that - there is such an element, and say that it was only after some evolution in the natural - order of things that both the Good and the Beautiful appeared. They do this to avoid a - real difficulty which confronts those who hold, as some do, that unity is a first - principle. This difficulty arises not from ascribing - goodness to the first principle as an attribute, but from treating unity as a principle, - and a principle in the sense of an element, and then deriving number from unity. The early - poets agree with this view in so far as they assert that it was not the original - forces—such as Night, Heaven, Chaos or Ocean—but Zeus who was king and - ruler. It was, however, on the ground of the - changing of the rulers of the world that the poets were led to state these theories; - because those of them who compromise by not describing everything in mythological - language—e.g. PherecydesOf Syros (circa 600-525 B.C.). He made Zeus one of the three primary beings - (Diels,Vorsokratiker201, 202). and certain others—make the - primary generator the Supreme Good; and so do the Magi,The Zoroastrian priestly caste. and some of the later philosophers - such as Empedocles and Anaxagoras: the one making Love an element,Cf. Aristot. Met. 3.1.13. - and the other making Mind a first principle.Cf. - Aristot. Met. 1.3.16. And of those who hold that unchangeable substances exist, - somePlato; cf. Aristot. Met. 1.6.10. identify absolute unity with absolute goodness; - but they considered that the essence of goodness was primarily unity. This, then, is the problem: which of these two views we should - hold. Now it is remarkable if that which is - primary and eternal and supremely self-sufficient does not possess this very quality, viz. - self-sufficiency and immunity, in a primary degree and as something good. Moreover, it is - imperishable and self-sufficient for no other reason than because it is good. Hence it is probably true to say that the first - principle is of this nature. But to say that - this principle is unity, or if not that, that it is an element, and an element of numbers, - is impossible; for this involves a serious difficulty, to avoid which some thinkersSpeusippus and his followers; cf. sect. 3. have - abandoned the theory (viz. those who agree that unity is a first principle and element, - but of mathematical number). For on this view all units become identical with - some good, and we get a great abundance of goods.If - unity is goodness, and every unit is a kind of unity, every unit must be a kind of - goodness—which is absurd. Further, if the Forms are numbers, all Forms become identical with some good. Again, let - us assume that there are Ideas of anything that we choose. If there are Ideas only of - goods, the Ideas will not be substancesBecause they - are Ideas not of substances but of qualities.; and if there are Ideas of - substances also, all animals and plants, and all things that participate in the Ideas, - will be goods.Because the Ideas are - goods. Not only do these absurdities follow, but it also follows that the contrary element, - whether it is plurality or the unequal, i.e. the Great and Small, is absolute badness. - Hence one thinkerSpeusippus. avoided - associating the Good with unity, on the ground that since generation proceeds from - contraries, the nature of plurality would then necessarily be bad. OthersPlato and - Xenocrates. hold that inequality is the nature of the bad. It follows, then, that - all things partake of the Bad except one—absolute unity; and that numbers partake of - it in a more unmitigated form than do spatial magnitudesAs being more directly derived from the first principles. Cf. Aristot. Met. 1.9.23 n.; and that the Bad is the - province for the activity of the Good, and partakes of and tends towards that which is - destructive of the Good; for a contrary is destructive of its contrary. And if, as we said,Aristot. Met. 14.1.17. the matter of each - thing is that which is it potentially—e.g., the matter of actual fire is that which - is potentially fire—then the Bad will be simply the potentially Good. Thus all these objections follow because (1.) they make every - principle an element; (2.) they make contraries principles; (3.) they make unity a - principle; and (4.) they make numbers the primary substances, and separable, and - Forms. If, - then, it is impossible both not to include the Good among the first principles, and to - include it in this way, it is clear that the first principles are not being rightly - represented, nor are the primary substances. Nor is a certain thinkerEvidently Speusippus; cf. Aristot. Met. 14.4.3. right in his assumption - when he likens the principles of the universe to that of animals and plants, on the ground - that the more perfect forms are always produced from those which are indeterminate and - imperfect, and is led by this to assert that this is true also of the ultimate principles; - so that not even unity itself is a real thing.Speusippus argued that since all things are originally imperfect, unity, which is the - first principle, must be imperfect, and therefore distinct from the good. Aristotle - objects that the imperfect does not really exist, and so Speusippus deprives his first - principle of reality. He is wrong; - for even in the natural world the principles from which these things are derived are - perfect and complete—for it is man that begets man; the seed does not come - first.Cf. Aristot. Met. 9.8.5. It is absurd also to generate space simultaneously - with the mathematical solids (for space is peculiar to particular things, which is why - they are separable in space, whereas the objects of mathematics have no - position) and to say that they must be - somewhere, and yet not explain what their spatial position is. Those who assert that reality - is derived from elements, and that numbers are the primary realities, ought to have first - distinguished the senses in which one thing is derived from another, and then explained in - what way number is derived from the first principles. Is it by mixture? But (a) not - everything admits of mixturee.g. to admit of - mixture a thing must first have a separate existence, and the Great-and-Small, which is - an affection or quality of number (Aristot. Met. - 14.1.14) cannot exist separately.; (b) the result of mixture is - something different; and unity will not be separable,sc. when it has once been mixed. Cf. Aristot. De Gen. et Corr. 327b 21-26. nor will it be a distinct entity, - as they intend it to be. Is it by composition, - as we hold of the syllable? But (a) this necessarily implies position; (b) in thinking of - unity and plurality we shall think of them separately. This, then, is what number will - be—a unit plus plurality, or unity plus the - Unequal. And since a thing is derived from elements either - as inherent or as not inherent in it, in which way is number so derived? Derivation from - inherent elements is only possible for things which admit of generation.And numbers are supposed to be eternal. Cf. Aristot. Met. 14.2.1-3. Is it derived as from - seed? But nothing can be emitted from that - which is indivisible.i.e., unity, being - indivisible, cannot contribute the formal principle of generation in the way that the - male parent contributes it. Is it derived from a contrary which does not persist? - But all things which derive their being in this way derive it also from something else - which does persist. Since, therefore, one thinkerSpeusippus: Plato. Cf. Aristot. Met. - 14.1.5. regards unity as contrary to plurality, and another (treating it as - the Equal) as contrary to the Unequal, number must be derived as from - contraries. Hence there is something else - which persists from which, together with one contrary, number is or has been derived.The objection is directed against the Platonist - treatment of the principles as contraries (cf. Aristot. - Met. 14.4.12), and may be illustrated by Aristot. Met. 12.1.5-2.2. Plurality, as the contrary of unity, is privation, - not matter; the Platonists should have derived numbers from unity and some other - principle which is truly material. Further, why on - earth is it that whereas all other things which are derived from contraries or have - contraries perish, even if the contrary is exhausted in producing them,Because it may be regarded as still potentially - present. number does not perish? Of this no explanation is given; yet whether it - is inherent or not, a contrary is destructive; e.g., Strife destroys the mixture.According to Empedocles Fr. 17 - (Diels). It should not, however, do this; because the mixture is not its - contrary. Nor - is it in any way defined in which sense numbers are the causes of substances and of Being; - whether as bounds,The theories criticized from this - point onwards to Aristot. Met. 14.6.11 are - primarily Pythagorean. See Introduction. e.g. as points are the bounds of spatial - magnitudes,e.g. the line by 2 points, the - triangle (the simplest plane figure) by 3, the tetrahedron (the simplest solid figure) - by 4. and as EurytusDisciple of Philolaus; - he "flourished" in the early fourth century B.C. determined which number belongs - to which thing—e.g. this number to man, and this to horse—by using pebbles to - copy the shape of natural objects, like those who arrange numbers in the form of - geometrical figures, the triangle and the square.cf. Burnet, E.G.P. sect. 47. Or is - it because harmony is a ratio of numbers, and so too is man and everything else? But in - what sense are attributes—white, and sweet, and hot—numbers?This is an objection to the view that numbers are - causes as bounds. And clearly numbers are not the essence of things, nor are they - causes of the form; for the ratioOr - "formula." is the essence, and numberIn - the sense of a number of material particles. is matter. E.g. the essence of flesh or bone is number only in the sense that it - is three parts of fire and two of earth.Cf. Empedocles Fr. 96 (Diels). And the number, whatever it is, is always a number of something; of - particles of fire or earth, or of units. But the essence is the proportion of one quantity - to another in the mixture; i.e. no longer a number, but a ratio of the mixture of numbers, - either of corporeal particles or of any other kind. Thus number is not an efficient - cause—neither number in general, nor that which consists of abstract units—nor - is it the matter, nor the formula or form of things. Nor again is it a final - cause. The - question might also be raised as to what the good is which things derive from numbers - because their mixture can be expressed by a number, either one which is easily - calculable,i.e., a simple ratio. or an odd - number.It is hard to see exactly what this means. - If the terms of a ratio are rational, one of them must be odd. Alexander says a ratio - like 1 : 3 is meant. Oddness was associated with goodness (cf. Aristot. Met. 1.5.6). For in point of fact - honey-water is no more wholesome if it is mixed in the proportion "three times three"Apparently the Pythagoreans meant by this "three parts - of water to three of honey." Aristotle goes on to criticize this way of expressing - ratios.; it would be more beneficial mixed in no particular proportion, provided - that it be diluted, than mixed in an arithmetical proportion, but strong. Again, the ratios of mixtures are expressed by the - relation of numbers, and not simply by numbers; e.g., it is 3 : 2, not 3 X 2Cf. previous note.; for in products of - multiplication the units must belong to the same genus. Thus the product of 1 x 2 x 3 must - be measurable by 1, and the product of 4 X 5 x 7 by 4. Therefore all products which - contain the same factor must be measurable by that factor. Hence the number of fire cannot - be 2 X 5 X 3 X 7 if the number of water is 2 x 3.sc. because if so, a particle of fire would simply equal 35 particles of water. - If all things must - share in number, it must follow that many things are the same; i.e., that the same number - belongs both to this thing and to something else. Is number, then, a cause; i.e., is it - because of number that the object exists? Or is this not conclusive? E.g., there is a - certain number of the sun's motions, and again of the moon's,5 in each case, according to Aristotle; cf. Aristot. Met. 12.7.9, 11. and indeed of the - life and maturity of every animate thing. What reason, then, is there why some of these - numbers should not be squares and others cubes, some equal and others double? There is no reason; all things must fall within this - range of numbers if, as was assumed, all things share in number, and different things may - fall under the same number. Hence if certain things happened to have the same number, on - the Pythagorean view they would be the same as one another, because they would have the - same form of number; e.g., sun and moon would be the same.Cf. previous note. But - why are these numbers causes? There are seven vowels,In the Greek alphabet. seven strings to the scale,In the old heptachord; cf. note on Aristot. Met. 5.11.4. seven Pleiads; most - animals (though not allCf. Aristot. Hist. An. 576a 6.) lose their teeth in - the seventh year; and there were seven heroes who attacked Thebes. Is it, then, because the number 7 is such as it is that there were - seven heroes, or that the Pleiads consist of seven stars? Surely there were seven heroes - because of the seven gates, or for some other reason, and the Pleiads are seven because we - count them so; just as we count the Bear as 12, whereas others count more stars in - both. Indeed, they assert also that *C, *Y - and *Z are concords,According to Alexander Z was connected with the fourth, - C with the fifth, and Y with the octave. and that because there are three concords, there - are three double consonants. They ignore the fact that there might be thousands of double - consonants—because there might be one symbol for *G*R. But if they say that each of these letters is double any of the others, - whereas no other is,Q, - F, and X are aspirated, not double, - consonants. and that the reason is that there are three regionsPalate, lips, and teeth. of the mouth, and that - one consonant is combined with S in each region, it is for - this reason that there are only three double consonants, and not because there are three - concords—because there are really more than three; but there cannot be more than - three double consonants. Thus these thinkers are like the ancient Homeric scholars, who see - minor similarities but overlook important ones. Some say - that there are many correspondences of this kind; e.g., the middle notesi.e., the ME/SH(fourth) - and PARAME/SH(fifth), whose ratios can be expressed as 8 - : 6, 9 : 6. of the octave are respectively 8 and 9, and the epic hexameter has - seventeen syllables, which equals the sum of these two; and the line scans in the - first half with nine syllables, and in the second with eight.i.e., a dactylic hexameter whose sixth foot is always a spondee or - trochee has nine syllables in the first three feet and eight in the last three. For - TO\ DECIO/N meaning "the first part" of a metrical - system see Bassett,Journal of Classical Philology - 11.458-460. And they point out that - the interval from A to W - in the alphabet is equal to that from the lowest note of a flute to the highest, whose - number is equal to that of the whole system of the universe.Alexander suggests that the number 24 may have been made up of the 12 - signs of the zodiac, the 8 spheres (fixed stars, five planets, sun and moon) and 4 - elements. We must realize that no one would find any difficulty either in - discovering or in stating such correspondences as these in the realm of eternal things, - since they occur even among perishable things. As for the celebrated characteristics of number, and - their contraries, and in general the mathematical properties, in the sense that some - describe them and make them out to be causes of the natural world, it would seem that if - we examine them along these lines, they disappear; for not one of them is a cause in any - of the senses which we distinguished with until respect to the first Principles.Cf. Aristot. Met. - 1.3.1, Aristot. Met. 5.1, - 2. - There is a sense, however, in which these - thinkers make it clear that goodness is predicable of numbers, and that the odd, the - straight, the equal-by-equal,i.e., square. - and the powersProbably their "power" of being - represented as regular figures; e.g. the triangularity of 3 or 6. of certain - numbers, belong to the series of the Beautiful.Cf. - Aristot. Met. 1.5.6. For the seasons are - connected with a certain kind of numberi.e., - 4.; and the other examples which they adduce from mathematical theorems all have - the same force. Hence they would seem to be - mere coincidences, for they are accidental; but all the examples are appropriate to each - other, and they are one by analogy. For there is analogy between all the categories of - Being—as "straight" is in length, so is - "level" in breadth, perhaps "odd" in number, and "white" in color. Again, it is not the Ideal - numbers that are the causes of harmonic relations, etc. (for Ideal numbers, even when they - are equal, differ in kind, since their units also differ in kind)Aristotle has argued (Aristot. Met. - 13.6-8.) that if the Ideal numbers differ in kind, their units must differ in - kind. Hence even equal numbers, being composed of different units, must be different in - kind. In point of fact, since each ideal number is unique, no two of them could be - equal.; so on this ground at least we need not posit Forms. Such, then, are the - consequences of the theory, and even more might be adduced. But the mere fact that the - Platonists find so much trouble with regard to the generation of Ideal numbers, and can in - no way build up a system, would seem to be a proof that the objects of mathematics are not - separable from sensible things, as some maintain, and that the first principles are not - those which these thinkers assume.

- - - - + + + +The Metaphysics +Aristotle +Hugh Tredennick + +William Heinemann Ltd. +London +Harvard University Press +Cambridge, MA +1933-1935 +1-2 + + + +Loeb Classical Library + +Internet Archive +Internet Archive + + + + + + + +

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All men naturally desire knowledge. An indication of this is our esteem for the senses; for apart from their use we esteem them for their own sake, and most of all the sense of sight. Not only with a view to action, but even when no action is contemplated, we prefer sight, generally speaking, to all the other senses.

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The reason of this is that of all the senses sight best helps us to know things, and reveals many distinctions.

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Now animals are by nature born with the power of sensation, and from this some acquire the faculty of memory, whereas others do not. Accordingly the former are more intelligent and capable of learning than those which cannot remember.

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Such as cannot hear sounds (as the bee, and any other similar type of creature) are intelligent, but cannot learn; those only are capable of learning which possess this sense in addition to the faculty of memory.

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Thus the other animals live by impressions and memories, and have but a small share of experience; but the human race lives also by art and reasoning.

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It is from memory that men acquire experience, because the numerous memories of the same thing eventually produce the effect of a single experience. Experience seems very similar to science and art,

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but actually it is through experience that men acquire science and art; for as Polus rightly says, experience produces art, but inexperience chance. Plat. Gorgias 448c, Plat. Gorg. 462b-c. Art is produced when from many notions of experience a single universal judgement is formed with regard to like objects.

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To have a judgement that when Callias was suffering from this or that disease this or that benefited him, and similarly with Socrates and various other individuals, is a matter of experience; but to judge that it benefits all persons of a certain type, considered as a class, who suffer from this or that disease (e.g. the phlegmatic or bilious when suffering from burning fever) is a matter of art.

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It would seem that for practical purposes experience is in no way inferior to art; indeed we see men of experience succeeding more than those who have theory without experience.

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The reason of this is a that experience is knowledge of particulars, but art of universals; and actions and the effects produced are all concerned with the particular. For it is not man that the physician cures, except incidentally, but Callias or Socrates or some other person similarly named, who is incidentally a man as well.

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So if a man has theory without experience, and knows the universal, but does not know the particular contained in it, he will often fail in his treatment; for it is the particular that must be treated.

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Nevertheless we consider that knowledge and proficiency belong to art rather than to experience, and we assume that artists are wiser than men of mere experience (which implies that in all cases wisdom depends rather upon knowledge);

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and this is because the former know the cause, whereas the latter do not. For the experienced know the fact, but not the wherefore; but the artists know the wherefore and the cause. For the same reason we consider that the master craftsmen in every profession are more estimable and know more and are wiser than the artisans, because they know the reasons of the things which are done; but we think that the artisans, like certain inanimate objects, do things, but without knowing what they are doing (as, for instance, fire burns);

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only whereas inanimate objects perform all their actions in virtue of a certain natural quality, artisans perform theirs through habit. Thus the master craftsmen are superior in wisdom, not because they can do things, but because they possess a theory and know the causes.

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In general the sign of knowledge or ignorance is the ability to teach, and for this reason we hold that art rather than experience is scientific knowledge; for the artists can teach, but the others cannot.

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Further, we do not consider any of the senses to be Wisdom. They are indeed our chief sources of knowledge about particulars, but they do not tell us the reason for anything, as for example why fire is hot, but only that it is hot.

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It is therefore probable that at first the inventor of any art which went further than the ordinary sensations was admired by his fellow-men, not merely because some of his inventions were useful, but as being a wise and superior person.

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And as more and more arts were discovered, some relating to the necessities and some to the pastimes of life, the inventors of the latter were always considered wiser than those of the former, because their branches of knowledge did not aim at utility.

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Hence when all the discoveries of this kind were fully developed, the sciences which relate neither to pleasure nor yet to the necessities of life were invented, and first in those places where men had leisure. Thus the mathematical sciences originated in the neighborhood of Egypt, because there the priestly class was allowed leisure.Cf. Plat. Phaedrus 274, Hdt. 2.109.

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The difference between art and science and the other kindred mental activities has been stated in theEthicsAristot. Nic. Eth. 6.1139b 14-1141b 8.; the reason for our present discussion is that it is generally assumed that what is called Wisdomi.e. Metaphysics. is concerned with the primary causes and principles, so that, as has been already stated, the man of experience is held to be wiser than the mere possessors of any power of sensation, the artist than the man of experience, the master craftsman than the artisan; and the speculative sciences to be more learned than the productive. Thus it is clear that Wisdom is knowledge of certain principles and causes.

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Since we are investigating this kind of knowledge, we must consider what these causes and principles are whose knowledge is Wisdom. Perhaps it will be clearer if we take the opinions which we hold about the wise man.

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We consider first, then, that the wise man knows all things, so far as it is possible, without having knowledge of every one of them individually; next, that the wise man is he who can comprehend difficult things, such as are not easy for human comprehension (for sense-perception, being common to all, is easy, and has nothing to do with Wisdom); and further that in every branch of knowledge a man is wiser in proportion as he is more accurately informed and better able to expound the causes.

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Again among the sciences we consider that that science which is desirable in itself and for the sake of knowledge is more nearly Wisdom than that which is desirable for its results, and that the superior is more nearly Wisdom than the subsidiary; for the wise man should give orders, not receive them; nor should he obey others, but the less wise should obey him.

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Such in kind and in number are the opinions which we hold with regard to Wisdom and the wise. Of the qualities there described the knowledge of everything must necessarily belong to him who in the highest degree possesses knowledge of the universal, because he knows in a sense all the particulars which it comprises. These things, viz. the most universal, are perhaps the hardest for man to grasp, because they are furthest removed from the senses.

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Again, the most exact of the sciences are those which are most concerned with the first principles; for those which are based on fewer principles are more exact than those which include additional principles; e.g., arithmetic is more exact than geometry.

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Moreover, the science which investigates causes is more instructive than one which does not, for it is those who tell us the causes of any particular thing who instruct us. Moreover, knowledge and understanding which are desirable for their own sake are most attainable in the knowledge of that which is most knowable. For the man who desires knowledge for its own sake will most desire the most perfect knowledge, and this is the knowledge of the most knowable, and the things which are most knowable are first principles and causes; for it is through these and from these that other things come to be known, and not these through the particulars which fall under them.

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And that science is supreme, and superior to the subsidiary, which knows for what end each action is to be done; i.e. the Good in each particular case, and in general the highest Good in the whole of nature.

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Thus as a result of all the above considerations the term which we are investigating falls under the same science, which must speculate about first principles and causes; for the Good, i.e. the end , is one of the causes.

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That it is not a productive science is clear from a consideration of the first philosophers.

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It is through wonder that men now begin and originally began to philosophize; wondering in the first place at obvious perplexities, and then by gradual progression raising questions about the greater matters too, e.g. about the changes of the moon and of the sun, about the stars and about the origin of the universe.

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Now he who wonders and is perplexed feels that he is ignorant (thus the myth-lover is in a sense a philosopher, since myths are composed of wonders); therefore if it was to escape ignorance that men studied philosophy, it is obvious that they pursued science for the sake of knowledge, and not for any practical utility.

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The actual course of events bears witness to this; for speculation of this kind began with a view to recreation and pastime, at a time when practically all the necessities of life were already supplied. Clearly then it is for no extrinsic advantage that we seek this knowledge; for just as we call a man independent who exists for himself and not for another, so we call this the only independent science, since it alone exists for itself.

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For this reason its acquisition might justly be supposed to be beyond human power, since in many respects human nature is servile; in which case, as SimonidesSimon. Fr. 3 (Hiller). says, God alone can have this privilege, and man should only seek the knowledge which is within his reach.

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Indeed if the poets are right and the Deity is by nature jealous, it is probable that in this case He would be particularly jealous, and all those who excel in knowledge unfortunate. But it is impossible for the Deity to be jealous (indeed, as the proverbCf. Solon, Fr. 26 (Hiller); Leutsch and Schneidwin, Paroemiographi, 1.371. says, poets tell many a lie), nor must we suppose that any other form of knowledge is more precious than this; for what is most divine is most precious.

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Now there are two ways only in which it can be divine. A science is divine if it is peculiarly the possession of God, or if it is concerned with divine matters. And this science alone fulfils both these conditions; for (a) all believe that God is one of the causes and a kind of principle, and (b) God is the sole or chief possessor of this sort of knowledge. Accordingly, although all other sciences are more necessary than this, none is more excellent.

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The acquisition of this knowledge, however, must in a sense result in something which is the reverse of the outlook with which we first approached the inquiry. All begin, as we have said, by wondering that things should be as they are, e.g. with regard to marionettes, or the solstices, or the incommensurabilityi.e. the fact that the diagonal of a square cannot be rationally expressed in terms of the side. of the diagonal of a square; because it seems wonderful to everyone who has not yet perceived the cause that a thing should not be measurable by the smallest unit.

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But we must end with the contrary and (according to the proverb)i.e. δευτέρον ἀμεινόνων(second thoughts are better). Leutsch and Schneidwin 1.62. the better view, as men do even in these cases when they understand them; for a geometrician would wonder at nothing so much as if the diagonal were to become measurable.

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Thus we have stated what is the nature of the science which we are seeking, and what is the object which our search and our whole investigation must attain.

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It is clear that we must obtain knowledge of the primary causes, because it is when we think that we understand its primary cause that we claim to know each particular thing. Now there are four recognized kinds of cause. Of these we hold that one is the essence or essential nature of the thing (since the reason why of a thing is ultimately reducible to its formula, and the ultimate reason why is a cause and principle); another is the matter or substrate; the third is the source of motion; and the fourth is the cause which is opposite to this, namely the purpose or good;

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for this is the end of every generative or motive process. We have investigated these sufficiently in the PhysicsPhys. 2.3, Phys. 2.7; however, let us avail ourselves of the evidence of those who have before us approached the investigation of reality and philosophized about Truth. For clearly they too recognize certain principles and causes, and so it will be of some assistance to our present inquiry if we study their teaching; because we shall either discover some other kind of cause, or have more confidence in those which we have just described.

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Most of the earliest philosophers conceived only of material principles as underlying all things. That of which all things consist, from which they first come and into which on their destruction they are ultimately resolved, of which the essence persists although modified by its affections—this, they say, is an element and principle of existing things. Hence they believe that nothing is either generated or destroyed, since this kind of primary entity always persists. Similarly we do not say that Socrates comes into being absolutely when he becomes handsome or cultured, nor that he is destroyed when he loses these qualities; because the substrate, Socrates himself, persists.

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In the same way nothing else is generated or destroyed; for there is some one entity (or more than one) which always persists and from which all other things are generated.

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All are not agreed, however, as to the number and character of these principles. Thales,Thales of Miletus, fl. 585 B.C. the founder of this school of philosophy,That of the Ionian monists, who sought a single material principle of everything. says the permanent entity is water (which is why he also propounded that the earth floats on water). Presumably he derived this assumption from seeing that the nutriment of everything is moist, and that heat itself is generated from moisture and depends upon it for its existence (and that from which a thing is generated is always its first principle). He derived his assumption, then, from this; and also from the fact that the seeds of everything have a moist nature, whereas water is the first principle of the nature of moist things.

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There are someCf. Plat. Crat. 402b, Plat. Theaet. 152e, Plat. Theaet. 180c,d. who think that the men of very ancient times, long before the present era, who first speculated about the gods, also held this same opinion about the primary entity. For theycf. Hom. Il. 14. 201, Hom. Il. 14.246. represented Oceanus and Tethys to be the parents of creation, and the oath of the gods to be by water— Styx,Cf. Hom. Il. 2.755, Hom. Il. 14.271, Hom. Il.15.37. as they call it. Now what is most ancient is most revered, and what is most revered is what we swear by.

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Whether this view of the primary entity is really ancient and time-honored may perhaps be considered uncertain; however, it is said that this was Thales’ opinion concerning the first cause. (I say nothing of Hippo,Hippo of Samos, a medical writer and eclectic philosopher who lived in the latter half of the fifth century B.C. Cf.Aristot. De Anima 405b 2. because no one would presume to include him in this company, in view of the paltriness of his intelligence.)

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AnaximenesThe third Milesian monist; fl. circa 545 B.C. and DiogenesDiogenes of Apollonia, an eclectic philosopher roughly contemporary with Hippo. held that air is prior to water, and is of all corporeal elements most truly the first principle. HippasusA Pythagorean, probably slightly junior to Heraclitus. of Metapontum and HeraclitusFl. about 500 B.C. of Ephesus hold this of fire; and EmpedoclesOf Acragas; fl. 450 B.C.—adding earth as a fourth to those already mentioned—takes all four. These, he says, always persist, and are only generated in respect of multitude and paucity, according as they are combined into unity or differentiated out of unity.Cf. Empedocles, Fr. 17 (Diels), R.P. 166; Burnet, E.G.P. 108-109.

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Anaxagoras of Clazomenae—prior to Empedocles in point of age, but posterior in his activities—says that the first principles are infinite in number. For he says that as a general rule all things which are, like fire and water,This is Aristotle’s illustration; apparently Anaxagoras did not regard the elements as homoeomerous (i.e. composed of parts which are similar to one another and to the whole). Cf. Aristot. De Caelo 302a 28, Aristot. De Gen. et Corr. 314a 24. homoeomerous, are generated and destroyed in this sense only, by combination and differentiation; otherwise they are neither generated nor destroyed, but persist eternally.Cf. Anaxagoras Fr. 4 (Diels); and see Burnet, E.G.P. 130.

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From this account it might be supposed that the only cause is of the kind called material. But as men proceeded in this way, the very circumstances of the case led them on and compelled them to seek further; because if it is really true that all generation and destruction is out of some one entity or even more than one, why does this happen, and what is the cause?

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It is surely not the substrate itself which causes itself to change. I mean, e.g., that neither wood nor bronze is responsible for changing itself; wood does not make a bed, nor bronze a statue, but something else is the cause of the change. Now to investigate this is to investigate the second type of cause: the source of motion, as we should say.

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Those who were the very first to take up this inquiry, and who maintained that the substrate is one thing, had no misgivings on the subject; but some of thosei.e. the Eleatic school. who regard it as one thing, being baffled, as it were, by the inquiry, say that that one thing (and indeed the whole physical world) is immovable in respect not only of generation and destruction (this was a primitive belief and was generally admitted) but of all other change. This belief is peculiar to them.

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None of those who maintained that the universe is a unity achieved any conception of this type of cause, except perhaps ParmenidesFounder of the above; fl. about 475.; and him only in so far as he admits, in a sense, not one cause only but two.i.e. in the Δόξα. Parmenides Fr. 8 (Diels); R.P. 121.

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But those who recognize more than one entity, e.g. hot and cold, or fire and earth, are better able to give a systematic explanation, because they avail themselves of fire as being of a kinetic nature, and of water, earth, etc., as being the opposite.Aristotle is probably thinking of Empedocles. Cf. Aristot. Met. 4.8.

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After these thinkers and the discovery of these causes, since they were insufficient to account for the generation of the actual world, men were again compelled (as we have said) by truth itself to investigate the next first principle.

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For presumably it is unnatural that either fire or earth or any other such element should cause existing things to be or become well and beautifully disposed; or indeed that those thinkers should hold such a view. Nor again was it satisfactory to commit so important a matter to spontaneity and chance.

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Hence when someoneAnaxagoras. said that there is Mind in nature, just as in animals, and that this is the cause of all order and arrangement, he seemed like a sane man in contrast with the haphazard statements of his predecessors.Cf. Plat. Phaedo 97b-98b.

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We know definitely that Anaxagoras adopted this view; but HermotimusA semi-mythical person supposed to have been a preincarnation of Pythagoras. of Clazomenae is credited with having stated it earlier. Those thinkers, then, who held this view assumed a principle in things which is the cause of beauty, and the sort of cause by which motion is communicated to things.

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It might be inferred that the first person to consider this question was Hesiod, or indeed anyone else who assumed Love or Desire as a first principle in things; e.g. Parmenides. For he says, where he is describing the creation of the universe, Love sheProbably Aphrodite (so Simplicius, Plutarch). created first of all the gods . . . Parmenides Fr. 13 (Diels)And Hesiod says,Hes. Th. 116-20. The quotation is slightly inaccurate. First of all things was Chaos made, and then/Broad-bosomed Earth . . ./And Love, the foremost of immortal beings, thus implying that there must be in the world some cause to move things and combine them.

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The question of arranging these thinkers in order of priority may be decided later. Now since it was apparent that nature also contains the opposite of what is good, i.e. not only order and beauty, but disorder and ugliness; and that there are more bad and common things than there are good and beautiful: in view of this another thinker introduced Love and StrifeEmpedocles Fr. 17, 26 (Diels); R.P. 166. Cf. Burnet, E.G.P. 108 ff. as the respective causes of these things—

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because if one follows up and appreciates the statements of Empedocles with a view to his real meaning and not to his obscure language, it will be found that Love is the cause of good, and Strife of evil. Thus it would perhaps be correct to say that Empedocles in a sense spoke of evil and good as first principles, and was the first to do so—that is, if the cause of all good things is absolute good.

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These thinkers then, as I say, down to the time of Empedocles, seem to have grasped two of the causes which we have defined in the PhysicsAristot. Phys. 2.3, 7.: the material cause and the source of motion; but only vaguely and indefinitely. They are like untrained soldiers in a battle, who rush about and often strike good blows, but without science; in the same way these thinkers do not seem to understand their own statements, since it is clear that upon the whole they seldom or never apply them.

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Anaxagoras avails himself of Mind as an artificial device for producing order, and drags it in whenever he is at a loss to explain some necessary result; but otherwise he makes anything rather than Mind the cause of what happens.Cf. Plat. Phaedo 98b, Plat. Laws 967b; also Aristot. Met. 7.5. Again, Empedocles does indeed use causes to a greater degree than Anaxagoras, but not sufficiently; nor does he attain to consistency in their use.

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At any rate Love often differentiates and Strife combines: because whenever the universe is differentiated into its elements by Strife, fire and each of the other elements are agglomerated into a unity; and whenever they are all combined together again by Love, the particles of each element are necessarily again differentiated.

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Empedocles, then, differed from his predecessors in that he first introduced the division of this cause, making the source of motion not one but two contrary forces.

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Further, he was the first to maintain that the so-called material elements are four—not that he uses them as four, but as two only, treating fire on the one hand by itself, and the elements opposed to it—earth, air and water—on the other, as a single nature.Cf. 3.14. This can be seen from a study of his writings.e.g. Empedocles, Fr. 62 (Diels).

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Such, then, as I say, is his account of the nature and number of the first principles.

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Leucippus,Of Miletus; fl. circa 440 (?) B.C. See Burnet, E.G.P. 171 ff. however, and his disciple DemocritusOf Abdera; fl. circa 420 B.C. E.G.P loc. cit. hold that the elements are the Full and the Void—calling the one what is and the other what is not. Of these they identify the full or solid with what is, and the void or rare with what is not (hence they hold that what is not is no less real than what is,For the probable connection between the Atomists and the Eleatics see E.G.P. 173, 175, and cf. De Gen. et Corr. 324b 35-325a 32. because Void is as real as Body); and they say that these are the material causes of things.

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And just as those who make the underlying substance a unity generate all other things by means of its modifications, assuming rarity and density as first principles of these modifications, so these thinkers hold that the differencesi.e., of the atoms. are the causes of everything else.

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These differences, they say, are three: shape, arrangement, and position; because they hold that what is differs only in contour, inter-contact, and inclination .Cf. R.P. 194.(Of these contour means shape, inter-contact arrangement, and inclination position.) Thus, e.g., A differs from N in shape, AN from NA in arrangement, and Z from NThese letters will convey Aristotle’s point better to the English reader, but see critical note. in position.

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As for motion, whence and how it arises in things, they casually ignored this point, very much as the other thinkers did. Such, then, as I say, seems to be the extent of the inquiries which the earlier thinkers made into these two kinds of cause.

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At the same time, however, and even earlier the so-calledAristotle seems to have regarded Pythagoras as a legendary person. Pythagoreans applied themselves to mathematics, and were the first to develop this sciencePythagoras himself (fl. 532 B.C.) is said by Aristoxenus (ap. Stobaeus 1.20.1) to have been the first to make a theoretical study of arithmetic.; and through studying it they came to believe that its principles are the principles of everything.

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And since numbers are by nature first among these principles, and they fancied that they could detect in numbers, to a greater extent than in fire and earth and water, many analoguesCf. Aristot. Met. 14.6ff.. of what is and comes into being—such and such a property of number being justice ,Apparently (cf. infra, Aristot. Met. 1.17) they identified these not only with properties of number but with numbers themselves. Thus justice (properly=squareness)=4, the first square number; soul or mind=1, opportunity=7 (Alexander). and such and such soul or mind , another opportunity , and similarly, more or less, with all the rest—and since they saw further that the properties and ratios of the musical scales are based on numbers,Pythagoras himself is credited with having discovered the ratios of the octave (2 : 1), the fifth (3 : 2) and the fourth (4 : 3). Burnet, E.G.P. 51. and since it seemed clear that all other things have their whole nature modelled upon numbers, and that numbers are the ultimate things in the whole physical universe, they assumed the elements of numbers to be the elements of everything, and the whole universe to be a proportionOr harmony. Cf. Aristot. De Caelo 2.9, and E.G.P. 152. or number. Whatever analogues to the processes and parts of the heavens and to the whole order of the universe they could exhibit in numbers and proportions, these they collected and correlated;

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and if there was any deficiency anywhere, they made haste to supply it, in order to make their system a connected whole. For example, since the decad is considered to be a complete thing and to comprise the whole essential nature of the numerical system, they assert that the bodies which revolve in the heavens are ten; and there being only nineEarth, sun, moon, five planets, and the sphere of the fixed stars. that are visible, they make the antichthoni.e. counter-earth; a planet revolving round the central fire in such a way as to be always in opposition to the earth. the tenth.

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We have treated this subject in greater detail elsewhereIn the lost work On the Pythagoreans; but cf. Aristot. De Caelo 2.13.; but the object of our present review is to discover from these thinkers too what causes they assume and how these coincide with our list of causes.

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Well, it is obvious that these thinkers too consider number to be a first principle, both as the materialSee Burnet, E.G.P 143-146. of things and as constituting their properties and states.i.e., as a formal principle. Cf. Ross ad loc. The elements of number, according to them, are the Even and the Odd. Of these the former is limited and the latter unlimited; Unity consists of both (since it is both odd and even)Either because by addition it makes odd numbers even and even odd (Alexander, Theo Smyrnaeus) or because it was regarded as the principle of both odd and even numbers (Heath).; number is derived from Unity; and numbers, as we have said, compose the whole sensible universe.

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OthersZeller attributes the authorship of this theory to Philolaus. of this same school hold that there are ten principles, which they enunciate in a series of corresponding pairs: (1.) Limit and the Unlimited; (2.) Odd and Even; (3.) Unity and Plurality; (4.) Right and Left; (5.) Male and Female; (6.) Rest and Motion; (7.) Straight and Crooked; (8.) Light and Darkness; (9.) Good and Evil; (10.) Square and Oblong.

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Apparently Alcmaeon of Croton speculated along the same lines, and either he derived the theory from them or they from him; for [Alcmaeon was contemporary with the old age of Pythagoras, and]This statement is probably true, but a later addition. his doctrines were very similar to theirs.He was generally regarded as a Pythagorean. He says that the majority of things in the world of men are in pairs; but the contraries which he mentions are not, as in the case of the Pythagoreans, carefully defined, but are taken at random, e.g. white and black, sweet and bitter, good and bad, great and small.

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Thus Alcmaeon only threw out vague hints with regard to the other instances of contrariety, but the Pythagoreans pronounced how many and what the contraries are. Thus from both these authoritiesThe section of Pythagoreans mentioned in 6, and Alcmaeon. we can gather thus much, that the contraries are first principles of things; and from the former, how many and what the contraries are.

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How these can be referred to our list of causes is not definitely expressed by them, but they appear to reckon their elements as material; for they say that these are the original constituents of which Being is fashioned and composed.

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From this survey we can sufficiently understand the meaning of those ancients who taught that the elements of the natural world are a plurality. Others, however, theorized about the universe as though it were a single entity; but their doctrines are not all alike either in point of soundness or in respect of conformity with the facts of nature.

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For the purposes of our present inquiry an account of their teaching is quite irrelevant, since they do not, while assuming a unity, at the same time make out that Being is generated from the unity as from matter, as do some physicists, but give a different explanation; for the physicists assume motion also, at any rate when explaining the generation of the universe; but these thinkers hold that it is immovable. Nevertheless thus much is pertinent to our present inquiry.

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It appears that Parmenides conceived of the Unity as one in definition,His argument was Everything that is is one, if what is has one meaning (πάντα ἕν, εἰ τὸ ὂν ἓν σημαίνει, Aristot. Phys. 187a 1); but he probably believed, no less than Melissus, in the material unity of reality. Cf. Melissus Fr. 8 (Diels). It has been suggested, however (by the Rev. C. F. Angus), that he was simply trying to convey in figurative language a conception of absolute existence. but MelissusOf Samos; defeated the Athenian fleet in 441 B.C. as materially one. Hence the former says that it is finite,Melissus Fr. 8, ll. 32-3, 42-3. and the latter that it is infinite.Melissus Fr. 3. But Xenophanes,Of Colophon, b. 565 (?) B.C. Criticized and ridiculed most of the views of his day, especially the anthropomorphic conception of the gods. Burnet, E.G.P. 55 ff., esp. 61-62. Cf. Xenophanes Fr. 23 (Diels). the first exponent of the Unity (for Parmenides is said to have been his disciple), gave no definite teaching, nor does he seem to have grasped either of these conceptions of unity; but regarding the whole material universe he stated that the Unity is God.

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This school then, as we have said, may be disregarded for the purposes of our present inquiry; two of them, Xenophanes and Melissus, may be completely ignored, as being somewhat too crude in their views. Parmenides, however, seems to speak with rather more insight. For holding as he does that Not-being, as contrasted with Being, is nothing, he necessarily supposes that Being is one and that there is nothing else (we have discussed this point in greater detail in the Physics Aristot. Phys. 1.3 ); but being compelled to accord with phenomena, and assuming that Being is one in definition but many in respect of sensation, he posits in his turn two causes, i.e. two first principles, Hot and Cold; or in other words, Fire and Earth. Of these he ranks Hot under Being and the other under Not-being.Cf. note on Aristot. Met. 3.13.

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From the account just given, and from a consideration of those thinkers who have already debated this question, we have acquired the following information. From the earliest philosophers we have learned that the first principle is corporeal (since water and fire and the like are bodies); some of them assume one and others more than one corporeal principle, but both parties agree in making these principles material. Others assume in addition to this cause the source of motion, which some hold to be one and others two.

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Thus down to and apart from the ItalianThe Pythagoreans; so called because Pythagoras founded his society at Croton. philosophers the other thinkers have expressed themselves vaguely on the subject, except that, as we have said, they actually employ two causes, and one of these—the source of motion —some regard as one and others as two. The Pythagoreans, while they likewise spoke of two principles, made this further addition, which is peculiar to them: they believed, not that the Limited and the Unlimited are separate entities, like fire or water or some other such thing, but that the Unlimited itself and the One itself are the essence of those things of which they are predicated, and hence that number is the essence of all things.

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Such is the nature of their pronouncements on this subject. They also began to discuss and define the what of things; but their procedure was far too simple. They defined superficially, and supposed that the essence of a thing is that to which the term under consideration first applies—e.g. as if it were to be thought that double and 2 are the same, because 2 is the first number which is double another.

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But presumably to be double a number is not the same as to be the number 2. Otherwise, one thing will be many—a consequence which actually followed in their system.i.e., the same number might be the first to which each of several definitions applied; then that number would be each of the concepts so defined. This much, then, can be learned from other and earlier schools of thought.

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The philosophies described above were succeeded by the system of Plato,Compare Aristot. Met. 12.4.2-5. which in most respects accorded with them, but contained also certain peculiar features distinct from the philosophy of the Italians.

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In his youth Plato first became acquainted with CratylusCf. Aristot. Met. 4.5.18. and the Heraclitean doctrines—that the whole sensible world is always in a state of flux,Plat. Crat. 402a (fr. 41 Bywater). and that there is no scientific knowledge of it—and in after years he still held these opinions. And when Socrates, disregarding the physical universe and confining his study to moral questions, sought in this sphere for the universal and was the first to concentrate upon definition, Plato followed him and assumed that the problem of definition is concerned not with any sensible thing but with entities of another kind; for the reason that there can be no general definition of sensible things which are always changing.

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These entities he called Ideas,I have translated ἰδέα by Idea and εἶδος by Form wherever Aristotle uses the words with reference to the Platonic theory. Plato apparently uses them indifferently, and so does Aristotle in this particular connection, but he also uses εἶδος in the sense of form in general. For a discussion of the two words see Taylor, Varia Socratica, 178-267, and Gillespie, Classical Quarterly, 6.179-203. and held that all sensible things are named afterFor this interpretation of παρὰ ταῦτα see Ross’s note ad loc. them sensible and in virtue of their relation to them; for the plurality of things which bear the same name as the Forms exist by participation in them. (With regard to the participation, it was only the term that he changed; for whereas the Pythagoreans say that things exist by imitation of numbers, Plato says that they exist by participation—merely a change of term.

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As to what this participation or imitation may be, they left this an open question.)

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Further, he states that besides sensible things and the Forms there exists an intermediate class, the objects of mathematics,i.e. arithmetical numbers and geometrical figures. which differ from sensible things in being eternal and immutable, and from the Forms in that there are many similar objects of mathematics, whereas each Form is itself unique.

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Now since the Forms are the causes of everything else, he supposed that their elements are the elements of all things. Accordingly the material principle is the Great and Small, and the essence <or formal principle> is the One, since the numbers are derived from the Great and Small by participation in the the One.

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In treating the One as a substance instead of a predicate of some other entity, his teaching resembles that of the Pythagoreans, and also agrees with it in stating that the numbers are the causes of Being in everything else; but it is peculiar to him to posit a duality instead of the single Unlimited, and to make the Unlimited consist of the Great and Small. He is also peculiar in regarding the numbers as distinct from sensible things, whereas they hold that things themselves are numbers, nor do they posit an intermediate class of mathematical objects.

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His distinction of the One and the numbers from ordinary things (in which he differed from the Pythagoreans) and his introduction of the Forms were due to his investigation of logic (the earlier thinkers were strangers to Dialectic)See Aristot. Met. 4.2.19-20, and cf. Aristot. Met. 8.4.4.; his conception of the other principle as a duality to the belief that numbers other than primesἔξω τῶν πρώτων is very difficult, but it can hardly be a gloss, and no convincing emendation has been suggested. Whatever the statement means, it is probably (as the criticism which follows is certainly) based upon a misunderstanding. From Plat. Parm. 143c, it might be inferred that the Great and Small (the Indeterminate Dyad) played no part in the generation of numbers; but there the numbers are not Ideal, as here they must be. In any case Aristotle is obsessed with the notion that the Dyad is a duplicative principle (Aristot. Met. 13.8.14), which if true would imply that it could generate no odd number. Hence Heinze proposed reading περιττῶν(odd) for πρώτων(which may be right, although the corruption is improbable) and Alexander tried to extract the meaning of odd from πρώτων by understanding it as prime to 2. However, as Ross points out (note ad loc.), we may keep πρώτων in the sense of prime if we suppose Aristotle to be referring either (a) to the numbers within the decad (Aristot. Met. 13.8.17) and forgetting 9—the other odd numbers being primes; or (b) to numbers in general, and forgetting the entire class of compound odd numbers. Neither of these alternatives is very satisfactory, but it seems better to keep the traditional text. can be readily generated from it, as from a matrix.For a similar use of the word ἐκμαγεῖον cf. Plat. Tim. 50c.

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The fact, however, is just the reverse, and the theory is illogical; for whereas the Platonists derive multiplicity from matter although their Form generates only once,Aristotle’s objection is that it is unreasonable that a single operation of the formal upon the material principle should result in more than one product; i.e. that the material principle should be in itself duplicative. it is obvious that only one table can be made from one piece of timber, and yet he who imposes the form upon it, although he is but one, can make many tables. Such too is the relation of male to female: the female is impregnated in one coition, but one male can impregnate many females. And these relations are analogues of the principles referred to.

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This, then, is Plato’s verdict upon the question which we are investigating. From this account it is clear that he only employed two causesPlato refers several times in the dialogues to an efficient cause (e.g. the Demiurgus,Plat. Soph. 265b-d, Plat. Tim. 28c ff.) and a final cause (e.g. Plat. Phil. 20d, 53e, Plat. Tim. 29d ff.); but Aristotle does not seem to take these allusions seriously.: that of the essence, and the material cause; for the Forms are the cause of the essence in everything else, and the One is the cause of it in the Forms.

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He also tells us what the material substrate is of which the Forms are predicated in the case of sensible things, and the One in that of the Forms—that it is this the duality, the Great and Small. Further, he assigned to these two elements respectively the causation of goodCf. Plat. Phil. 25e-26b. and of evil; a problem which, as we have said,Aristot. Met. 3.17; 4.3. had also been considered by some of the earlier philosophers, e.g. Empedocles and Anaxagoras.

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We have given only a concise and summary account of those thinkers who have expressed views about the causes and reality, and of their doctrines. Nevertheless we have learned thus much from them: that not one of those who discuss principle or cause has mentioned any other type than those which we we have distinguished in the Physics. Aristot. Phys. 2.3 Clearly it is after these types that they are groping, however uncertainly.

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Some speak of the first principle as material, whether they regard it as one or several, as corporeal or incorporeal: e.g. Plato speaks of the Great and Small; the ItaliansSee note on Aristot. Met. 5.15. of the Unlimited; Empedocles of Fire, Earth, Water and Air; Anaxagoras of the infinity of homoeomeries.

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All these have apprehended this type of cause; and all those too who make their first principle air or water or something denser than fire but rarer than airThe various references in Aristotle to material principles intermediate between certain pairs of elements have been generally regarded as applying to Anaximander’s ἄπειρον or Indeterminate; but the references are so vague (cf. Aristot. Met. 7.6, Aristot. Phys.187a 14, 189b 3, 203a 18) that it seems better to connect them with later and minor members of the Milesian school. Cf. Ross’s note ad loc.(for some have so described the primary element). These, then, apprehended this cause only, but others apprehended the source of motion—e.g. all such as make Love and Strife, or Mind, or Desire a first principle.

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As for the essence or essential nature, nobody has definitely introduced it; but the inventors of the Forms express it most nearly. For they do not conceive of the Forms as the matter of sensible things (and the One as the matter of the Forms), nor as producing the source of motion (for they hold that they are rather the cause of immobility and tranquillity); but they adduce the Forms as the essential nature of all other things, and the One as that of the Forms.

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The end towards which actions, changes and motions tend they do in a way treat as a cause, but not in this sense, i.e. not in the sense in which it is naturally a cause. Those who speak of Mind or Love assume these causes as being something good; but nevertheless they do not profess that anything exists or is generated for the sake of them, but only that motions originate from them.Cf. Aristot. Met. 3.17.

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Similarly also those who hold that Unity or Being is an entity of this kind state that it is the cause of existence, but not that things exist or are generated for the sake of it. So it follows that in a sense they both assert and deny that the Good is a cause; for they treat it as such not absolutely, but incidentally.

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It appears, then, that all these thinkers too (being unable to arrive at any other cause) testify that we have classified the causes rightly, as regards both number and nature. Further, it is clear that all the principles must be sought either along these lines or in some similar way.

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Let us next examine the possible difficulties arising out of the statements of each of these thinkers, and out of his attitude to the first principles.

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All those who regard the universe as a unity, and assume as its matter some one nature, and that corporeal and extended, are clearly mistaken in many respects. They only assume elements of corporeal things, and not of incorporeal ones, which also exist. They attempt to state the causes of generation and destruction, and investigate the nature of everything; and at the same time do away with the cause of motion.

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Then there is their failure to regard the essence or formula as a cause of anything; and further their readiness to call any one of the simple bodies—except earth—a first principle, without inquiring how their reciprocal generation is effected. I refer to fire, water, earth and air. Of these some are generated from each other by combination and others by differentiation;

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and this difference is of the greatest importance in deciding their relative priority. In one way it might seem that the most elementary body is that from which first other bodies are produced by combination; and this will be that body which is rarest and composed of the finest particles.

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Hence all who posit Fire as first principle will be in the closest agreement with this theory. However, even among the other thinkers everyone agrees that the primary corporeal element is of this kind. At any rate none of the Monists thought earth likely to be an element—obviously on account of the size of its particles—

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but each of the other three has had an advocate; for some name fire as the primary element, others water, and others air.Cf. Aristot. Met. 3.5, 8. And yet why do they not suggest earth too, as common opinion does? for people say Everything is earth.

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And Hesiod too saysCf. Aristot. Met. 4.1. that earth was generated first of corporeal things—so ancient and popular is the conception found to be. Thus according to this theory anyone who suggests any of these bodies other than fire, or who assumes something denser than air but rarer than water,Cf. Aristot. Met. 7.3 n. will be wrong.

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On the other hand if what is posterior in generation is prior in nature, and that which is developed and combined is posterior in generation, then the reverse will be the case; water will be prior to air, and earth to water. So much for those who posit one cause such as we have described.

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The same will apply too if anyone posits more than one, as e.g. Empedocles says that matter consists of four bodies;

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objections must occur in his case also, some the same as before, and some peculiar to him. First, we can see things being generated from each other in a way which shows that fire and earth do not persist as the same corporeal entity. (This subject has been treated in my works on Natural Science.Aristot. De Caelo, 3.7; Aristot. De Gen. et Corr. 2.6.) Again with regard to the cause of motion in things, whether one or two should be assumed, it must not be thought that his account is entirely correct or even reasonable.Cf. Aristot. Met. 4.6.

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And in general those who hold such views as these must of necessity do away with qualitative alteration; for on such a theory cold will not come from hot nor hot from cold, because to effect this there must be something which actually takes on these contrary qualities: some single element which becomes both fire and water—which Empedocles denies.

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If one were to infer that Anaxagoras recognized twoMind, and the mixture of homoeomerous particles. elements, the inference would accord closely with a view which, although he did not articulate it himself, he must have accepted as developed by others.

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To say that originally everything was a mixture is absurd for various reasons, but especially since (a) it follows that things must have existed previously in an unmixed state; (b) it is contrary to nature for anything to mix with anything ; (c) moreover affections and attributes would then be separable from their substances (because what is mixed can also be separated). At the same time, if one were to follow his doctrine carefully and interpret its meaning, perhaps it would be seen to be more up-to-date;

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because when nothing was yet differentiated, obviously nothing could be truly predicated of that substance—e.g. that it was white or black or buff or any other color. It must necessarily have been colorless, since otherwise it would have had one of these colors.

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Similarly by the same argument it had no taste or any other such attribute; for it cannot have had any quality or magnitude or individuality. Otherwise some particular form would have belonged to it; but this is impossible on the assumption that everything was mixed together, for then the form would have been already differentiated, whereas he says that everything was mixed together except Mind, which alone was pure and unmixed.Anaxagoras. Fr. 12 (Diels).

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It follows from this that he recognizes as principles the One (which is simple and unmixed) and the Other, which is such as we suppose the Indeterminate to be before it is determined and partakes of some form. Thus his account is neither correct nor clear, but his meaning approximates to more recent theories and what is now more obviously true.

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However, these thinkers are really concerned only with the theories of generation and destruction and motion (for in general it is only with reference to this aspect of reality that they look for their principles and causes).

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Those, however, who make their study cover the whole of reality, and who distinguish between sensible and non-sensible objects, clearly give their attention to both kinds; hence in their case we may consider at greater length what contributions, valuable or otherwise, they make to the inquiry which is now before us.

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The so-called Pythagoreans employ abstruser principles and elements than the physicists. The reason is that they did not draw them from the sensible world; for mathematical objects, apart from those which are connected with astronomy, are devoid of motion.

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Nevertheless all their discussions and investigations are concerned with the physical world. They account for the generation of the sensible universe, and observe what happens in respect of its parts and affections and activities, and they use up their principles and causes in this connection, as though they agreed with the others—the physicists—that reality is just so much as is sensible and is contained in the so-called heavens.

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All the same, as we have said,Aristot. Met. 1.8.17. the causes and principles which they describe are capable of application to the remoter class of realities as well, and indeed are better fitted to these than to their physical theories.

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But as to how there is to be motion, if all that is premissed is Limit and the Unlimited, and Odd and Even, they do not even hint; nor how, without motion and change, there can be generation and destruction, or the activities of the bodies which traverse the heavens.

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And further, assuming that it be granted to them or proved by them that magnitudeAristotle uses the word μέγεθος both of magnitude in general and of spatial magnitude or extension. Here the meaning seems to be the former. Numbers obviously have magnitude, and might be regarded as causing it; but (except on the Number-Atomism theory,) they are no more the cause of extension than that of gravity. is composed of these factors, yet how is it to be explained that some bodies are light, and others have weight? For in their premisses and statements they are speaking just as much about sensible as about mathematical objects; and this is why they have made no mention of fire or earth or other similar bodies, because, I presume, they have no separate explanation of sensible things.

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Again, how are we to understand that number and the modifications of number are the causes of all being and generation, both in the beginning and now, and at the same time that there is no other number than the number of which the universe is composed?i.e., how can number be both reality and the cause of reality?

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Because when they make out that Opinion and Opportunity are in such and such a region, and a little above or below them Injustice and Separation or Mixture, and when they state as proof of this that each of these abstractions is a number; and that also in this region there is already a plurality of the magnitudes composed of number, inasmuch as these modifications of number correspond to these several regions,—is the number which we must understand each of these abstractions to be the same number which is present in the sensible universe, or another kind of number?The point seems to be this. The Pythagoreans say that Opinion is a number, 3 (or 2, according to another version), and is located in a certain region of the universe because that region is proper to a corporeal magnitude composed of the number 3 (air was so composed according to Syrianus). Are we to understand, says Aristotle, that the abstract number identified with Opinion is the same as the concrete number of which air consists? The difficulty is probably due to an attempt to combine two different Pythagorean views of number.

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Plato at least says that it is another. It is true that he too supposes that numbers are both these magnitudes and their causes; but in his view the causative numbers are intelligible and the others sensible.

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The Pythagoreans, then, may be dismissed for the present, for it is enough to touch upon them thus briefly. As for those who posit the Forms as causes,For a discussion of the Ideal theory and Aristotle’s conception of it see Introduction; and with the whole contents of Aristot. Met. 9.1-15 cf. Aristot. Met. 13.4.6-5. in the first place in their attempt to find the causes of things in our sensible world, they introduced an equal number of other entities—as though a man who wishes to count things should suppose that it would be impossible when they are few, and should attempt to count them when he has added to them. For the Forms are as many as, or not fewer than, the things in search of whose causes these thinkers were led to the Forms; because corresponding to each thing there is a synonymous entity apart from the substances (and in the case of non-substantial things there is a One over the ManyAn Idea which represents their common denominator.), both in our everyday world and in the realm of eternal entities.The heavenly bodies.

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Again, not one of the arguments by which weAristotle is here speaking as a Platonist. Contrast the language of Aristot. Met. 13.4.7ff., and see Introduction. try to prove that the Forms exist demonstrates our point: from some of them no necessary conclusion follows, and from others it follows that there are Forms of things of which we hold that there are no Forms.

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For according to the arguments from the sciencesScientific knowledge must have a permanent object (cf. Aristot. Met. 1.4.2. there will be Forms of all things of which there are sciencesIncluding artificial products; cf. Aristot. Met. 1.15.; and according to the One-over-Many argument,The fact that several particulars can have a common quality or nature implies a single Idea of which they all partake (Plat. Rep. 596a). of negations too; and according to the argument that we have some conception of what has perished, of perishable things; because we have a mental picture of these things.The theory always admitted Ideas of perishable things, e.g. man. The objection here is that if the memory of dead men establishes the Idea of man, the memory of a dead individual establishes an Idea of that (perishable) individual. Again, of Plato’s more exact arguments some establish Ideas of relations,Plat. Phaedo 74a-77a, Plat. Rep. 479a-480a. which we do not hold to form a separate genus;

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and others state the Third Man. Several arguments bore this name. Here the reference is probably to the following: If X is a man because he resembles the Idea of Man, there must be a third man in whom the humanity of these two is united. Cf.Plat. Parm. 132a-133a. And in general the arguments for the Forms do away with things which are more important to us exponents of the Forms than the existence of the Ideas; for they imply that it is not the Dyad that is primary, but NumberThe Indeterminate Dyad, being to Aristotle a glorified 2, falls under the Idea of Number, which is therefore prior to it.; and that the relative is prior to the absoluteThis seems to be a development of the same objection. Number, which is relative, becomes prior to the supposedly self-subsistent Dyad.; and all the other conclusions in respect of which certain persons, by following up the views held about the Ideas, have gone against the principles of the theory.

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Again, according to the assumption by which we hold that the Ideas exist, there will be Forms not only of substances but of many other things (since the concept is one not only in the case of substances, but also in the case of all other things; and there are sciences not only of substances but of other things as well; and there are a thousand other similar consequences); but according to logical necessity, and from the views generally held about them, it follows that if the Forms are participated in, then there can only be Ideas of substances. For they are not participated in qua accidents; each Form can only be participated in in so far as it is not predicated of a subject.

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I mean, e.g., that if anything participates in absolute Doubleness it participates also in eternal, but only accidentally; because it is an accident of Doubleness to be eternal.Sensible double things are not eternal; therefore they do not, in the proper sense of participation, participate in the Idea of Doubleness qua having the accidental attribute eternal. Therefore Ideas, qua participated in, are not attributes but substances.

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Thus the Forms must be substance. But the same names denote substance in the sensible as in the Ideal world; otherwise what meaning will there be in saying that something exists beside the particulars, i.e. the unity comprising their multiplicity?

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If the form of the Ideas and of the things which participate in them is the same, they will have something in common (for why should Duality mean one and the same thing in the case of perishable twosi.e. pairs of sensible objects. and the twos which are many but eternal,i.e. mathematical 2s. and not in the case of the Idea of Duality and a particular two?); but if the form is not the same, they will simply be homonyms; just as though one were to call both Callias and a piece of wood man, without remarking any property common to them.The argument of 7-8 is: Ideas are substances. The common name which an idea shares with its particulars must mean the same of both; otherwise participation is merely homonymy. But as applied to Ideas it denotes substance; therefore particulars must be substances.

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Above all we might examine the question what on earth the Forms contribute to sensible things, whether eternal or subject to generation and decay; for they are not the cause of any motion or change in them.

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Again, they are no help towards the knowledge of other thingsThis objection, like the next, is chiefly directed against the transcendence of the Ideas. It is anticipated by Plato in Plat. Parm. 134d.(for they are not the substance of things, otherwise they would be in things), nor to their existence, since they are not present in the things which partake of them. If they were, it might perhaps seem that they are causes, in the sense in which the admixture of white causes a thing to be white;

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but this theory, which was first stated by AnaxagorasAnaxagoras Fr. 12ad fin. and later by EudoxusSee note on Aristot. Met. 12.8.9. Apparently he was a Platonist who regarded the Ideas as immanent in particulars. and others, is very readily refutable, for it is easy to adduce plenty of impossibilities against such a view. Again, other things are not in any accepted sense derived from the Forms.

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To say that the Forms are patterns, and that other things participate in them, is to use empty phrases and poetical metaphors; for what is it that fashions things on the model of the IdeasPlato says the Demiurgus?Plat. Tim. 28c, Plat. Tim. 29a. Besides, anything may both be and become like something else without being imitated from it; thus a man may become just like Socrates whether Socrates exists or not,

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and even if Socrates were eternal, clearly the case would be the same. Also there will be several patterns, and hence Forms, of the same thing; e.g. animal and two-footed will be patterns of man, and so too will the Idea of Man.Why this consequence is objectionable is not quite clear. Perhaps it is on the ground that to account for appearances in this way is not economical.

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Further, the Forms will be patterns not only of sensible things but of themselves (e.g. genus in the sense of genus of species), and thus the same thing will be both pattern and copy.The species will be the pattern of individuals, and the genus of the species. Further, it would seem impossible that the substance and the thing of which it is the substance exist in separation; hence how can the Ideas, if they are the substances of things, exist in separation from them?Cf. Aristot. Met. 1.10. It is stated in the PhaedoPlat. Phaedo 100d. that the Forms are the causes both of existence and of generation.

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Yet, assuming that the Forms exist, still the things which participate in them are not generated unless there is something to impart motion; while many other things are generated (e.g. house, ring) of which we hold that there are no Forms. Thus it is clearly possible that all other things may both exist and be generated for the same causes as the things just mentioned.

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Further, if the Forms are numbers, in what sense will they be causes? Is it because things are other numbers, e.g. such and such a number Man, such and such another Socrates, such and such another Callias? then why are those numbers the causes of these? Even if the one class is eternal and the other not, it will make no difference.

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And if it is because the things of our world are ratios of numbers (e.g. a musical concord), clearly there is some one class of things of which they are ratios. Now if there is this something, i.e. their matter , clearly the numbers themselves will be ratios of one thing to another.

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I mean, e.g., that if Callias is a numerical ratio of fire, earth, water and air, the corresponding Idea too will be a number of certain other things which are its substrate. The Idea of Man, too, whether it is in a sense a number or not, will yet be an arithmetical ratio of certain things, and not a mere number; nor, on these grounds, will any Idea be a number.The point, which is not very clearly expressed, is that the Ideas will not be pure numerical expressions or ratios, but will have a substrate just as particulars have.

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Again, one number can be composed of several numbers, but how can one Form be composed of several Forms? And if the one number is not composed of the other numbers themselves, but of their constituents (e.g. those of the number 10,000), what is the relation of the units? If they are specifically alike, many absurdities will result, and also if they are not (whether (a) the units in a given number are unlike, or (b) the units in each number are unlike those in every other number).That the words in brackets give the approximate sense seems clear from Aristot. Met. 13.6.2-3, Aristot. Met. 13.7.15; but it is difficult to get it out of the Greek. For in what can they differ, seeing that they have no qualities? Such a view is neither reasonable nor compatible with our conception of units.

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Further, it becomes necessary to set up another kind of number (with which calculation deals), and all the objects which are called intermediate by some thinkers.Cf. vi. 4. But how or from what principles can these be derived? or on what grounds are they to be considered intermediate between things here and Ideal numbers? Further, each of the units in the number 2 comes from a prior 2; but this is impossible.i.e., if 2 is derived from a prior 2 (the Indeterminate Dyad; Aristotle always regards this as a number 2), and at the same time consists of two units or 1s, 2 will be prior both to itself and to 1.

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Further, why should a number <of units>, taken together, be one thing? And further, in addition to the above objections, if the units are unlike, they should be treated as the thinkers who assume two or four elements treat those elements; for not one of them applies the term element to the common substrate, e.g. body, but to fire and earth—whether there is a common substrate (i.e. body) or not.In the Aristot. De Gen. et Corr. 320b 23Aristotle says that there is not.

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As it is, the One is spoken of as though it were homogeneous, like fire or water. But if this is so, the numbers will not be substances. And if there is an absolute One which is a principle, clearly the term one is ambiguous; otherwise this is impossible.This last sentence shows that in what goes before A. has been regarding the Platonic One as a unit. If this is so, he says, substance cannot be composed of it. If on the other hand the One is something different from the unit, they ought to make this clear.

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When we wish to refer substances to their principles we derive linesThe lines, planes, and solids here discussed are probably the Ideal lines, etc., which are immediately posterior to the Idea-Numbers. Cf. 30, Aristot. Met. 13.6.10, Aristot. Met. 13.9.2, and see Introduction. from Long and Short, a kind of Great and Small; and the plane from Wide and Narrow, and the solid body from Deep and Shallow. But in this case how can the plane contain a line,

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or the solid a line and a plane? for Wide and Narrow and Deep and Shallow are different genera. Nor is Number contained in these objects (because Many and Few is yet another class); and in the same way it is clear that none of the other higher genera will be contained in the lower. Nor, again, is the Broad the genus of which the Deep is a species; for then body would be a kind of plane.

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Further, how will it be possible for figures to contain points?Lines, planes, and solids are generated from varieties of the Great and Small, but points cannot be, having no magnitude; how, then, can the latter be present in the former? Plato steadily rejected this class of objects as a geometrical fiction, but he recognized the beginning of a line, and he frequently assumed this latter class, i.e. the indivisible lines. That Plato denied the existence of the point and asserted that of indivisible lines is not directly stated elsewhere, but the same views are ascribed to Xenocrates, and were attacked in the treatise Xenocrates De lineis insecabilibus. See Ross ad loc. But these must have some limit; and so by the same argument which proves the existence of the line, the point also exists.Sc. if the point is the limit of the line.

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In general, although Wisdom is concerned with the cause of visible things, we have ignored this question (for we have no account to give of the cause from which change arises),Cf. Aristot. Met. 7.5 and Aristot. Met. 1.9. and in the belief that we are accounting for their substance we assert the existence of other substances; but as to how the latter are the substances of the former, our explanation is worthless—for participation, as we have said before,Aristot. Met. 1.12. means nothing.

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And as for that which we can see to be the cause in the sciences, and through which all mind and all nature works—this causeThe final cause. Cf. Aristot. Met. 1.6.9-10. which we hold to be one of the first principles—the Forms have not the slightest bearing upon it either. Philosophy has become mathematics for modern thinkers,e.g. Speusippus, for whom see Aristot. Met. 7.2.4. although they professCf. Plat. Rep.531c-d that mathematics is only to be studied as a means to some other end.

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Further, one might regard the substance which they make the material substrate as too mathematical, and as being a predicate and differentia of substance or matter rather than as matter itself, I mean the Great and Small, which is like the Rare and Dense of which the physicists speak,Cf. iv. 10. holding that they are the primary differentiae of the substrate; because these qualities are a species of excess and defect.

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Also with regard to motion, if the Great and Small is to constitute motion, obviously the Forms will be moved; if not, whence did it come? On this view the whole study of physics is abolished. And what is supposed to be easy, to prove that everything is One, does not follow; because from their expositionThe word ἔκθεσις has various technical meanings. The process referred to here apparently consisted in taking, e.g., particular men, and reducing them with reference to their common nature to a single unit or universal, man; then taking man, horse, dog, etc. and treating them in the same way, until a unit is reached which embraces everything (Alexander). it does not follow, even if you grant them all their assumptions that everything is One, but only that there is an absolute One—

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and not even this, unless you grant that the universal is a class; which is impossible in some cases.Probably those of relative or negative terms. Cf. Aristot. Met. 1.3. Nor is there any explanation of the lines, planes and solids which come after the NumbersSee note on Aristot. Met. 1.23.: neither as to how they exist or can exist, nor as to what their importance is. They cannot be Forms (since they are not numbers) or Intermediates (which are the objects of mathematics) or perishables; clearly they form yet another fourth class.

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In general, to investigate the elements of existing things without distinguishing the various senses in which things are said to exist is a hopeless task; especially when one inquires along these lines into the nature of the elements of which things are composed. For (a) we cannot surely conceive of the elements of activity or passivity or straightness; this is possible, if at all, only in the case of substances. Hence to look for, or to suppose that one has found, the elements of everything that exists, is a mistake.

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(b) How can one apprehend the elements of everything ? Obviously one could not have any previous knowledge of anything; because just as a man who is beginning to learn geometry can have previous knowledge of other facts, but no previous knowledge of the principles of that science or of the things about which he is to learn, so it is in the case of all other branches of knowledge.

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Hence if there is a science which embraces everythinge.g. Plato’s Dialectic.(as some say), the student of it can have no previous knowledge at all. But all learning proceeds, wholly or in part, from what is already known; whether it is through demonstration or through definition—since the parts of the definition must be already known and familiar. The same is true of induction.

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On the other hand, assuming that this knowledge should turn out to be innate,Cf. the doctrine of ἀνάμνησις (recollection), Plat. Meno 81c, Plat. Phaedo 72e. it is astonishing that we should possess unawares the most important of the sciences. Further, how is one to know of what elements things consist? how is it to be established?

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Even this presents a difficulty, because the facts might be disputed, as happens in the case of certain syllables—for some say that ZA is composed of S, D and A, while others say that it is a distinct sound and not any one of those which are familiar to us.στοιχεῖον means both an element and a letter of the alphabet; hence letters are often used as analogues of the material elements. The point here is: Is Z or rather the Greek ζ) a στοιχεῖον, or is it further analyzable? Since this can be disputed, we must expect differences of opinion about the elements in general.

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Further, how can one gain knowledge of the objects of a particular sense-perception without possessing that sense? Yet it should be possible, that if the elements of which all things consist, as composite sounds consist of their peculiar Peculiar to them as sounds, not as individual sounds. If sights and sounds had the same elements, sight, which knows those elements as composing sights, would know them as composing sounds; i.e., we could see sounds. elements, are the same.

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Thus it is obvious, from the statements of earlier thinkers also, that all inquiry is apparently directed towards the causes described in the Physics,Aristot. Phys. 2.3, 7. and that we cannot suggest any other cause apart from these. They were, however, only vaguely conceived; and although in one sense they have all been stated before, in another they have not been stated at all.

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For the earliest philosophy speaks falteringly, as it were, on all subjects; being new and in its infancy. Even Empedocles says that bone exists by virtue of its ratio,Empedocles Fr. 96, 98 (Diels), Ritter and Preller 175. Aristotle says that Empedocles had some idea of the essence or formal cause, but did not apply it generally. which is the definition or essence of a thing.

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But by similar reasoning both flesh and every other thing, or else nothing at all, must be ratio; for it must be because of this, and not because of their matter—which he calls fire, earth, water and air—that flesh and bone and every other thing exists.

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If anyone else had stated this, he would necessarily have agreed, but his own statement was not clear.

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These and similar points have been explained already. We will now return to the difficulties which might be raised about these same questions, for they may throw some light upon subsequent difficulties.The reference is to Book 3. See Introduction.

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The study of Truth is in one sense difficult, in another easy. This is shown by the fact that whereas no one person can obtain an adequate grasp of it, we cannot all fail in the attempt; each thinker makes some statement about the natural world, and as an individual contributes little or nothing to the inquiry; but a combination of all conjectures results in something considerable.

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Thus in so far as it seems that Truth is like the proverbial door which no one can miss,Leutsch and Schneidewin, Paroemiographi, 2.678. in this sense our study will be easy; but the fact that we cannot, although having some grasp of the whole, grasp a particular part, shows its difficulty. However, since difficulty also can be accounted for in two ways, its cause may exist not in the objects of our study but in ourselves:

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just as it is with bats’ eyes in respect of daylight, so it is with our mental intelligence in respect of those things which are by nature most obvious.

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It is only fair to be grateful not only to those whose views we can share but also to those who have expressed rather superficial opinions. They too have contributed something; by their preliminary work they have formed our mental experience.

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If there had been no Timotheus,Of Miletus, 446 (?)—357 B.C. we should not possess much of our music; and if there had been no Phrynis,Of Mytilene; he is referred to as still alive in Aristoph. Cl. 971. Both Phrynis and Timotheus are criticized in the fragment of Pherecrates Chirontranslated by Rogers in the appendix to his ed. of the Clouds. there would have been no Timotheus. It is just the same in the case of those who have theorized about reality: we have derived certain views from some of them, and they in turn were indebted to others.

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Moreover, philosophy is rightly called a knowledge of Truth. The object of theoretic knowledge is truth, while that of practical knowledge is action; for even when they are investigating how a thing is so, practical men study not the eternal principle but the relative and immediate application.

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But we cannot know the truth apart from the cause. Now every thing through which a common quality is communicated to other things is itself of all those things in the highest degree possessed of that quality (e.g. fire is hottest, because it is the cause of heat in everything else); hence that also is most true which causes all subsequent things to be true.

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Therefore in every case the first principles of things must necessarily be true above everything else—since they are not merely sometimes true, nor is anything the cause of their existence, but they are the cause of the existence of other things,—and so as each thing is in respect of existence, so it is in respect of truth.

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Moreover, it is obvious that there is some first principle, and that the causes of things are not infinitely many either in a direct sequence or in kind. For the material generation of one thing from another cannot go on in an infinite progression (e.g. flesh from earth, earth from air, air from fire, and so on without a stop); nor can the source of motion (e.g. man be moved by air, air by the sun, the sun by Strife,Aristotle is evidently thinking of Empedocles’ system. with no limit to the series).

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In the same way neither can the Final Cause recede to infinity—walking having health for its object, and health happiness, and happiness something else: one thing always being done for the sake of another.

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And it is just the same with the Formal Cause. For in the case of all intermediate terms of a series which are contained between a first and last term, the prior term is necessarily the cause of those which follow it; because if we had to say which of the three is the cause, we should say the first. At any rate it is not the last term, because what comes at the end is not the cause of anything. Neither, again, is the intermediate term, which is only the cause of one

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(and it makes no difference whether there is one intermediate term or several, nor whether they are infinite or limited in number). But of series which are infinite in this way, and in general of the infinite, all the parts are equally intermediate, down to the present moment. Thus if there is no first term, there is no cause at all.

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On the other hand there can be no infinite progression downwards (where there is a beginning in the upper direction) such that from fire comes water, and from water earth, and in this way some other kind of thing is always being produced. There are two senses in which one thing comes from another—apart from that in which one thing is said to come after another, e.g. the Olympian fromἐκ means not only from but after; Aristotle dismisses this latter meaning. The Isthmian fell alternatively in the same year as the Olympian festival; when this happened the former was held in the spring and the latter in the summer. Cf. Aristot. Met. 5.24.5. the Isthmian games—either as a man comes from a child as it develops, or as air comes from water.

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Now we say that a man comes from a child in the sense that that which has become something comes from that which is becoming: i.e. the perfect from the imperfect. (For just as becoming is always intermediate between being and not-being, so is that which is becoming between what is and what is not. The learner is becoming informed, and that is the meaning of the statement that the informed person comes from the learner.)

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On the other hand A comes from B in the sense that water comes from air by the destruction of B. Hence the former class of process is not reversible (e.g. a child cannot come from a man, for the result of the process of becoming is not the thing which is becoming, but that which exists after the process is complete. So day comes from early dawn, because it is after dawn; and hence dawn does not come from day). But the other class is reversible.

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In both cases progression to infinity is impossible; for in the former the intermediate terms must have an end, and in the second the process is reversible, for the destruction of one member of a pair is the generation of the other. At the same time the first cause, being eternal, cannot be destroyed; because, since the process of generation is not infinite in the upper direction, that cause which first, on its destruction, became something else, cannot possibly be eternal.The argument is elliptical and confused. The meaning is this: Since there is an upward limit, there is a first cause which is eternal, being independent of any other cause. Therefore this cause cannot cause other things by its destruction, in the manner just described.

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Further, the Final cause of a thing is an end , and is such that it does not happen for the sake of some thing else, but all other things happen for its sake. So if there is to be a last term of this kind, the series will not be infinite; and if there is no such term, there will be no Final cause. Those who introduce infinity do not realize that they are abolishing the nature of the Good (although no one would attempt to do anything if he were not likely to reach some limit);

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nor would there be any intelligence in the world, because the man who has intelligence always acts for the sake of something, and this is a limit, because the end is a limit.

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Nor again can the Formal cause be referred back to another fuller definition;

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for the prior definition is always closer, and the posterior is not; and where the original definition does not apply, neither does the subsequent one. Further, those who hold such a view do away with scientific knowledge, for on this view it is impossible to know anything until one comes to terms which cannot be analyzed.

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Understanding, too, is impossible; for how can one conceive of things which are infinite in this way? It is different in the case of the line, which, although in respect of divisibility it never stops, yet cannot be conceived of unless we make a stop (which is why, in examining an infinitei.e. infinitely divisible. line, one cannot count the sections).It does not follow that we can apprehend that which is infinite because we can apprehend a line which is infinitely divisible. We can only really apprehend the line by setting a limit to its divisibility and regarding it simply as divisible into a very great (but not infinite) number of sections. An infinite number of sections can neither be apprehended nor counted.

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Even matter has to be conceived under the form of something which changes,Matter too, which is infinite in its varieties, can only be apprehended in the form of concrete sensible objects which are liable to change. This seems to be the meaning of the text, but Ross’s reading and interpretation may be right: see his note ad loc. and there can be nothing which is infinite.i.e. not actually, but only potentially. In any case the concept of infinity is not infinite.Cf. the third note above.

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Again, if the kinds of causes were infinite in number it would still be impossible to acquire knowledge; for it is only when we have become acquainted with the causes that we assume that we know a thing; and we cannot, in a finite time, go completely through what is additively infinite.

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The effect of a lecture depends upon the habits of the listener; because we expect the language to which we are accustomed, and anything beyond this seems not to be on the same level, but somewhat strange and unintelligible on account of its unfamiliarity; for it is the familiar that is intelligible. The powerful effect of familiarity is clearly shown by the laws, in which the fanciful and puerile survivals prevail, through force of habit, against our recognition of them.

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Thus some people will not accept the statements of a speaker unless he gives a mathematical proof; others will not unless he makes use of illustrations; others expect to have a poet adduced as witness. Again, some require exactness in everything, while others are annoyed by it, either because they cannot follow the reasoning or because of its pettiness; for there is something about exactness which seems to some people to be mean, no less in an argument than in a business transaction.

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Hence one must have been already trained how to take each kind of argument, because it is absurd to seek simultaneously for knowledge and for the method of obtaining it; and neither is easy to acquire. Mathematical accuracy is not to be demanded in everything, but only in things which do not contain matter.

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Hence this method is not that of natural science, because presumably all nature is concerned with matter. Hence we should first inquire what nature is; for in this way it will become clear what the objects of natural science are [and whether it belongs to one science or more than one to study the causes and principles of things].These words have evidently been inserted to form a kind of link with the subject matter of the Metaphysics. The book is almost certainly part of a quite independent treatise; see Introduction.

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It is necessary, with a view to the science which we are investigating, that we first describe the questions which should first be discussed. These consist of all the divergent views which are held about the first principles; and also of any other view apart from these which happens to have been overlooked.

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Now for those who wish to get rid of perplexities it is a good plan to go into them thoroughly; for the subsequent certainty is a release from the previous perplexities, and release is impossible when we do not know the knot. The perplexity of the mind shows that there is a knot in the subject; for in its perplexity it is in much the same condition as men who are fettered: in both cases it is impossible to make any progress.

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Hence we should first have studied all the difficulties, both for the reasons given and also because those who start an inquiry without first considering the difficulties are like people who do not know where they are going; besides, one does not even know whether the thing required has been found or not. To such a man the end is not clear; but it is clear to one who has already faced the difficulties.

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Further, one who has heard all the conflicting theories, like one who has heard both sides in a lawsuit, is necessarily more competent to judge.

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The first difficulty is concerned with the subjectsThe principles and causes referred to in Book I. which we discussed in our prefatory remarks. (1.) Does the study of the causes belong to one science or to more than one?The problem is discussed Aristot. Met. 3.2.1-10, and answered Aristot. Met. 4.1.(2.) Has that science only to contemplate the first principles of substance, or is it also concerned with the principles which all use for demonstration—e.g. whether it is possible at the same time to assert and deny one and the same thing, and other similar principles?Discussed Aristot. Met. 3.2.10-15; answered Aristot. Met. 4.2.

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And if it is concerned with substance, (3.) is there one science which deals with all substances, or more than one; and if more than one, are they all cognate, or should we call some of them kinds of Wisdom and others something different?Discussed Aristot. Met. 3.2.15-17; answered Aristot. Met. 4.2.9-10, Aristot. Met. 6.1.

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This too is a question which demands inquiry: (iv.) should we hold that only sensible substances exist, or that there are other besides? And should we hold that there is only one class of non-sensible substances, or more than one (as do those who posit the Forms and the mathematical objects as intermediate between the Forms and sensible things)?Discussed Aristot. Met. 3.2.20-30 answered Aristot. Met. 12.6-10, and also by the refutation of the Platonic Ideas and Intermediates in Books 13 and 14.

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These questions, then, as I say, must be considered; and also (v.) whether our study is concerned only with substances, or also with the essential attributes of substance;

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and further, with regard to Same and Other, and Like and Unlike and Contrariety, and Prior and Posterior, and all other such terms which dialecticians try to investigate, basing their inquiry merely upon popular opinions; we must consider whose province it is to study all of these.

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Further, we must consider all the essential attributes of these same things, and not merely what each one of them is, but also whether each one has one oppositeDiscussed Aristot. Met. 3.2.18-19; answered Aristot. Met. 4.2.8-25.; and (vi.) whether the first principles and elements of things are the genera under which they fall or the pre-existent parts into which each thing is divided; and if the genera, whether they are those which are predicated ultimately of individuals, or the primary genera—e.g., whether animal or man is the first principle and the more independent of the individual.DiscussedAristot. Met. 3.3; answered Aristot. Met. 7.10, 12-13

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Above all we must consider and apply ourselves to the question (7.) whether there is any other cause per se besides matter, and if so whether it is dissociable from matter, and whether it is numerically one or several; and whether there is anything apart from the concrete thing (by the concrete thing I mean matter together with whatever is predicated of it) or nothing; or whether there is in some cases but not in others; and what these cases are.Discussed iv. 1-8. For answers to these questions see Aristot. Met. 7.8, 13-14; Aristot. Met. 12.6-10; Aristot. Met. 13.10.

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Further, (8.) we must ask whether the first principles are limited in number or in kindDiscussed Aristot. Met. 3.4.8-10; answered Aristot. Met. 12.4-5, Aristot. Met. 13.10.—both those in the definitions and those in the substrate—and (ix.) whether the principles of perishable and of imperishable things are the same or different; and whether all are imperishable, or those of perishable things are perishable.Discussed Aristot. Met. 3.4.11-23; for Aristotle’s general views on the subject see Aristot. Met. 7.7-10, Aristot. Met. 12.1-7.

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Further, there is the hardest and most perplexing question of all: (x.) whether Unity and Being (as the Pythagoreans and Plato maintained) are not distinct, but are the substance of things; or whether this is not so, and the substrate is something distinctDiscussed Aristot. Met. 3.4.24-34; answered Aristot. Met. 7.16.3-4, Aristot. Met. 10.2.(as Empedocles holds of Love,Actually Love was no more the universal substrate than was any other of Empedocles’ elements; Aristotle appears to select it on account of its unifying function. another thinkerHeraclitus. of fire, and another Thales. of water or airAnaximenes.);

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and (xi.) whether the first principles are universal or like individual thingsDiscussed Aristot. Met. 3.6.7-9; for the answer see Aristot. Met. 7.13-15, Aristot. Met. 13.10.; and (12.) whether they exist potentially or actually; and further whether their potentiality or actuality depends upon anything other than motionDiscussed Aristot. Met. 3.6.5-6; for the relation of potentiality to actuality see Aristot. Met. 9.1-9; for actuality and motion see Aristot. Met. 12.6-7.; for these questions may involve considerable difficulty.

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Moreover we must ask (13.) whether numbers and lines and figures and points are substances in any sense, or not; and if they are, whether they are separate from sensible things or inherent in them.Discussed Aristot. Met. 3.5; answered Aristot. Met. 13.1-3, 6-9; Aristot. Met. 14.1-3, 5, 6. With regard to these problems not only is it difficult to attain to the truth, but it is not even easy to state all the difficulties adequately.For another statement of the problems sketched in this chapter see Aristot. Met. 9.1, 2.

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(1.) Firstly, then, with respect to the first point raised: whether it is the province of one science or of more than one to study all the kinds of causes. How can one science comprehend the first principles unless they are contraries? Again, in many things they are not all present.

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How can a principle of motion be in immovable things? or the nature of the Good? for everything which is good in itself and of its own nature is an end and thus a cause, because for its sake other things come to be and exist; and the end and purpose is the end of some action, and all actions involve motion; thus it would be impossible either for this principle to exist in motionless things or for there to be any absolute Good.

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Hence in mathematics too nothing is proved by means of this cause, nor is there any demonstration of the kind because it is better or worse; indeed no one takes any such consideration into account.

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And so for this reason some of the sophists, e.g. Aristippus,Founder of the Cyrenaic school in the early fourth century. spurned mathematics, on the ground that in the other arts, even the mechanical ones such as carpentry and cobbling, all explanation is of the kind because it is better or worse, while mathematics takes no account of good and bad.For a defense of mathematics see Aristot. Met. 13.3.10-12.

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On the other hand if there are several sciences of the causes, and a different one for each different principle, which of them shall we consider to be the one which we are seeking, or whom of the masters of these sciences shall we consider to be most learned in the subject which we are investigating?

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For it is possible for all the kinds of cause to apply to the same object; e.g. in the case of a house the source of motion is the art and the architect; the final cause is the function; the matter is earth and stones, and the form is the definition. Now to judge from our discussion some time agoCf. Aristot. Met. 1.2.5-6. as to which of the sciences should be called Wisdom, there is some case for applying the name to each of them.

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Inasmuch as Wisdom is the most sovereign and authoritative kind of knowledge, which the other sciences, like slaves, may not contradict, the knowledge of the end and of the Good resembles Wisdom (since everything else is for the sake of the end ); but inasmuch as it has been defined as knowledge of the first principles and of the most knowable, the knowledge of the essence will resemble Wisdom.

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For while there are many ways of understanding the same thing, we say that the man who recognizes a thing by its being something knows more than he who recognizes it by its not being something; and even in the former case one knows more than another, and most of all he who knows what it is, and not he who knows its size or quality or natural capacity for acting or being acted upon.

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Further, in all other cases too, even in such as admit of demonstration, we consider that we know a particular thing when we know what it is (e.g. what is the squaring of a rectangle? answer, the finding of a mean proportional to its sides; and similarly in other instances); but in the case of generations and actions and all kinds of change, when we know the source of motion.

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This is distinct from and opposite to the end . Hence it might be supposed that the study of each of these causes pertained to a different science.See Aristot. Met. 4.1

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(2.) Again, with respect to the demonstrative principles as well, it may be disputed whether they too are the objects of one sciencesc. the science which studies the four causes. or of several.Cf. Aristot. Met. 3.1.5.

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By demonstrative I mean the axioms from which all demonstration proceeds, e.g. everything must be either affirmed or denied, and it is impossible at once to be and not to be, and all other such premisses. Is there one science both of these principles and of substance, or two distinct sciences? and if there is not one, which of the two should we consider to be the one which we are now seeking?

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It is not probable that both subjects belong to one science; for why should the claim to understand these principles be peculiar to geometry rather than to any other science? Then if it pertains equally to any science, and yet cannot pertain to all, comprehension of these principles is no more peculiar to the science which investigates substances than to any other science.

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Besides, in what sense can there in be a science of these principles? We know already just what each of them is; at any rate other sciences employ them as being known to us.sc. and so there can be no science which defines them. If, however there is a demonstrative science of them, there will have to be some underlying genus, and some of the principles will be derived from axioms, and others will be unproved

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(for there cannot be demonstration of everything), since demonstration must proceed from something, and have some subject matter, and prove something. Thus it follows that there is some one genus of demonstrable things; for all the demonstrative sciences employ axioms.

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On the other hand, if the science of substance is distinct from the science of these principles, which is of its own nature the more authoritative and ultimate?

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The axioms are most universal, and are the first principles of everything. And whose province will it be, if not the philosopher’s, to study truth and error with respect to them?For the answer see Aristot. Met. 4.3.

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(3.) And in general, is there one science of all substances, or more than one?Cf. Aristot. Met. 3.1.6. if there is not one, with what sort of substance must we assume that this science is concerned?

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On the other hand, it is not probable that there is one science of all substances; for then there would be one demonstrative of all attributes—assuming that every demonstrative science proceeds from accepted beliefs and studies the essential attributes concerned with some definite subject matter.

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Thus to study the essential attributes connected with the same genus is the province of the same science proceeding from the same beliefs. For the subject matter belongs to one science, and so do the axioms, whether to the same science or to a different one; hence so do the attributes, whether they are studied by these sciences themselves or by one derived from them.For the answer see Aristot. Met. 4.2.9-10, Aristot. Met. 6.1.

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(v.) Further, is this study concerned only with substances, or with their attributes as well?Cf. Aristot. Met. 3.1.8-10. I mean, e.g., if the solid is a kind of substance, and so too lines and planes, is it the province of the same science to investigate both these and their attributes, in every class of objects about which mathematics demonstrates anything, or of a different science?

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If of the same, then the science of substance too would be in some sense demonstrative; but it does not seem that there is any demonstration of the what is it? And if of a different science, what will be the science which studies the attributes of substance? This is a very difficult question to answer.This problem, together with the appendix to it stated in Aristot. Met. 3.1.9-10, is answered in Aristot. Met. 4.2.8-25.

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(iv.) Further, are we to say that only sensible substances exist, or that others do as well? and is there really only one kind of substance, or more than one (as they hold who speak of the Forms and the Intermediates, which they maintain to be the objects of the mathematical sciences)?

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In what sense we Platonists hold the Forms to be both causes and independent substances has been statedAristot. Met. 1.6. in our original discussion on this subject. But while they involve difficulty in many respects, not the least absurdity is the doctrine that there are certain entities apart from those in the sensible universe, and that these are the same as sensible things except in that the former are eternal and the latter perishable.As it stands this is a gross misrepresentation; but Aristotle’s objection is probably directed against the conception of Ideas existing independently of their particulars. See Introduction.

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For Platonists say nothing more or less than that there is an absolute Man, and Horse, and Health; in which they closely resemble those who state that there are Gods, but of human form; for as the latter invented nothing more or less than eternal men, so the former simply make the Forms eternal sensibles.

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Again, if anyone posits Intermediates distinct from Forms and sensible things, he will have many difficulties;

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because obviously not only will there be lines apart from both Ideal and sensible lines, but it will be the same with each of the other classes.sc. of objects of mathematical sciences. Thus since astronomy is one of the mathematical sciences, there will have to be a heaven besides the sensible heaven, and a sun and moon, and all the other heavenly bodies.

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But how are we to believe this? Nor is it reasonable that the heaven should be immovable; but that it should move is utterly impossible.The reference is to the supposed intermediate heaven. A heaven (including heavenly bodies) without motion is unthinkable; but a non-sensible heaven can have no motion. It is the same with the objects of optics and the mathematical theory of harmony; these too, for the same reasons, cannot exist apart from sensible objects. Because if there are intermediate objects of sense and sensations, clearly there will also be animals intermediate between the Ideal animals and the perishable animals.If there are intermediate, i.e. non-sensible, sights and sounds, there must be intermediate faculties of sight and hearing, and intermediate animals to exercise these faculties; which is absurd.

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One might also raise the question with respect to what kind of objects we are to look for these sciences. For if we are to take it that the only difference between mensuration and geometry is that the one is concerned with things which we can perceive and the other with things which we cannot, clearly there will be a science parallel to medicine (and to each of the other sciences), intermediate between Ideal medicine and the medicine which we know.

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Yet how is this possible? for then there would be a class of healthy things apart from those which are sensible and from the Ideally healthy. Nor, at the same time, is it true that mensuration is concerned with sensible and perishable magnitudes; for then it would perish as they do. Nor, again, can astronomy be concerned with sensible magnitudes or with this heaven of ours;

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for as sensible lines are not like those of which the geometrician speaks (since there is nothing sensible which is straight or curved in that sense; the circlei.e., the visible circle which we draw. Like the ruler, it is geometrically imperfect; thus they touch at more than one point. touches the ruler not at a point, but <along a line> as Protagoras used to say in refuting the geometricians), so the paths and orbits of our heaven are not like those which astronomy discusses, nor have the symbols of the astronomer the same nature as the stars.

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Some, however, say that these so-called Intermediates between Forms and sensibles do exist: not indeed separately from the sensibles, but in them. It would take too long to consider in detail all the impossible consequences of this theory, but it will be sufficient to observe the following.

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On this view it is not logical that only this should be so; in clearly it would be possible for the Forms also to be in sensible things; for the same argument applies to both. Further, it follows necessarily that two solids must occupy the same space; and that the Forms cannot be immovable, being present in sensible things, which move.

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And in general, what is the object of assuming that Intermediates exist, but only in sensible things? The same absurdities as before will result: there will be a heaven besides the sensible one, only not apart from it, but in the same place; which is still more impossible.The problem is dealt with partly in Aristot. Met. 12.6-10, where Aristotle describes the eternal moving principles, and partly in Books 13 and 14, where he argues against the Platonic non-sensible substances.

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Thus it is very difficult to say, not only what view we should adopt in the foregoing questions in order to arrive at the truth, but also in the case of the first principles (vi.) whether we should assume that the genera, or the simplest constituents of each particular thing, are more truly the elements and first principles of existing things. E.g., it is generally agreed that the elements and first principles of speech are those things of which, in their simplest form, all speech is composed; and not the common term speech; and in the case of geometrical propositions we call those the elementsCf. Aristot. Met. 5.3.3. whose proofs are embodied in the proofs of all or most of the rest.

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Again, in the case of bodies, both those who hold that there are several elements and those who hold that there is one call the things of which bodies are composed and constituted first principles. E.g., Empedocles states that fire and water and the other things associated with them are the elements which are present in things and of which things are composed; he does not speak of them as genera of things.

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Moreover in the case of other things too, if a man wishes to examine their nature he observes, e.g., of what parts a bed consists and how they are put together; and then he comprehends its nature. Thus to judge from these arguments the first principles will not be the genera of things.

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But from the point of view that it is through definitions that we get to know each particular thing, and that the genera are the first principles of definitions, the genera must also be the first principles of the things defined.

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And if to gain scientific knowledge of things is to gain it of the species after which things are named, the genera are first principles of the species. And apparently some even of thoseThe Pythagoreans and Plato. who call Unity or Being or the Great and Small elements of things treat them as genera.

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Nor again is it possible to speak of the first principles in both senses.

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The formula of substance is one; but the definition by genera will be different from that which tells us of what parts a thing is composed.

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Moreover, assuming that the genera are first principles in the truest sense, are we to consider the primary genera to be first principles, or the final terms predicated of individuals? This question too involves some dispute.

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For if universals are always more truly first principles, clearly the answer will be the highest genera, since these are predicated of everything. Then there will be as many first principles of things as there are primary genera, and so both Unity and Being will be first principles and substances, since they are in the highest degree predicated of all things.

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But it is impossible for either Unity or Being to be one genus of existing things. For there must be differentiae of each genus, and each differentia must be onei.e., each differentia must have Being and Unity predicated of it.; but it is impossible either for the species of the genus to be predicated of the specific differentiae, or for the genus to be predicated without its species.The reasons are given in Aristot. Topica, 144a 36-b11. Hence if Unity or Being is a genus, there will be no differentia Being or Unity.

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But if they are not genera, neither will they be first principles, assuming that it is the genera that are first principles. And further, the intermediate terms, taken together with the differentiae, will be genera, down to the individuals; but in point of fact, although some are thought to be such, others are not. Moreover the differentiae are more truly principles than are the genera; and if they also are principles, we get an almost infinite number of principles, especially if one makes the ultimate genus a principle.

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Moreover, if Unity is really more of the nature of a principle, and the indivisible is a unity, and every thing indivisible is such either in quantity or in kind, and the indivisible in kind is prior to the divisible, and the genera are divisible into species, then it is rather the lowest predicate that will be a unity (for man is not the genussc. but the species. of individual men).

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Further, in the case of things which admit of priority and posteriority, that which is predicated of the things cannot exist apart from them. E.g., if 2 is the first number, there will be no Number apart from the species of number; and similarly there will be no Figure apart from the species of figures. But if the genera do not exist apart from the species in these cases, they will scarcely do so in others; because it is assumed that genera are most likely to exist in these cases.

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In individuals, however, there is no priority and posteriority. Further, where there is a question of better or worse, the better is always prior; so there will be no genus in these cases either.

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From these considerations it seems that it is the terms predicated of individuals, rather than the genera, that are the first principles. But again on the other hand it is not easy to say in what sense we are to understand these to be principles;

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for the first principle and cause must be apart from the things of which it is a principle, and must be able to exist when separated from them. But why should we assume that such a thing exists alongside of the individual, except in that it is predicated universally and of all the terms? And indeed if this is a sufficient reason, it is the more universal concepts that should rather be considered to be principles; and so the primary genera will be the principles.For partial solutions to the problem see Aristot. Met. 7.10, 12-13.

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In this connection there is a difficulty which is the hardest and yet the most necessary of all to investigate, and with which our inquiry is now concerned. (7.) If nothing exists apart from individual things, and these are infinite in number, how is it possible to obtain knowledge of the numerically infinite? For we acquire our knowledge of all things only in so far as they contain something universal, some one and identical characteristic.

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But if this is essential, and there must be something apart from individual things, it must be the genera; either the lowest or the highest; but we have just concluded that this is impossible.In Aristot. Met. 3.3.

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Further, assuming that when something is predicated of matter there is in the fullest sense something apart from the concrete whole, if there is something, must it exist apart from all concrete wholes, or apart from some but not others, or apart from none?

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If nothing exists apart from individual things, nothing will be intelligible; everything will be sensible, and there will be no knowledge of anything—unless it be maintained that sense-perception is knowledge. Nor again will anything be eternal or immovable, since sensible things are all perishable and in motion.

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Again, if nothing is eternal, even generation is impossible; for there must be something which becomes something, i.e. out of which something is generated, and of this series the ultimate term must be ungenerated; that is if there is any end to the series and generation cannot take place out of nothing.

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Further, if there is generation and motion, there must be limit too. For (a) no motion is infinite, but every one has an end; (b) that which cannot be completely generated cannot begin to be generated, and that which has been generated must be as soon as it has been generated.

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Further, if matter exists apart in virtue of being ungenerated, it is still more probable that the substance, i.e. that which the matter is at any given time becoming, should exist. And if neither one nor the other exists, nothing will exist at all. But if this is impossible, there must be something, the shape or form, apart from the concrete whole.

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But again, if we assume this, there is a difficulty: in what cases shall we, and in what shall we not, assume it? Clearly it cannot be done in all cases; for we should not assume that a particular house exists apart from particular houses. Moreover, are we to regard the essence of all things, e.g. of men, as one? This is absurd; for all things whose essence is one are one.

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Then is it many and diverse? This too is illogical. And besides, how does the matter become each individual one of these things, and how is the concrete whole both matter and form?For answers to these questions see Aristot. Met. 7.8, 13-14; Aristot. Met. 12.6-10; Aristot. Met. 13.10.

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(8.) Further, the following difficulty might be raised about the first principles. If they are one in kind, none of them will be one in number, not even the Idea of Unity or of Being. And how can there be knowledge unless there is some universal term?If the principles are one in kind only, particular things cannot be referred to the same principle but only to like principles; i.e., there will be no universal terms, without which there can be no knowledge.

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On the other hand if they are numerically one, and each of the principles is one, and not, as in the case of sensible things, different in different instances (e.g. since a given syllable is always the same in kind, its first principles are always the same in kind, but only in kind, since they are essentially different in number)—if the first principles are one, not in this sense, but numerically, there will be nothing else apart from the elements; for numerically one and individual are identical in meaning. This is what we mean by individual: the numerically one; but by universal we mean what is predicable of individuals.

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Hence just as, if the elements of languageOr letters of the alphabet. Cf. Aristot. Met. 1.9.36n. were limited in number, the whole of literature would be no more than those elements—that is, if there were not two nor more than two of the same <so it would be in the case of existing things and their principles>.For the answer to the problem see Aristot. Met. 12.4-5, Aristot. Met. 13.10.

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(ix.) There is a difficulty, as serious as any, which has been left out of account both by present thinkers and by their predecessors: whether the first principles of perishable and imperishable things are the same or different. For if they are the same, how is it that some things are perishable and others imperishable, and for what cause?

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The school of Hesiod, and all the cosmologists, considered only what was convincing to themselves, and gave no consideration to us. For they make the first principles Gods or generated from Gods, and say that whatever did not taste of the nectar and ambrosia became mortal—clearly using these terms in a sense significant to themselves;

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but as regards the actual applications of these causes their statements are beyond our comprehension. For if it is for pleasure that the Gods partake of them, the nectar and ambrosia are in no sense causes of their existence; but if it is to support life, how can Gods who require nourishment be eternal?

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However, it is not worth while to consider seriously the subtleties of mythologists; we must ascertain by cross-examining those who offer demonstration of their statements why exactly things which are derived from the same principles are some of an eternal nature and some perishable. And since these thinkers state no reason for this view, and it is unreasonable that things should be so, obviously the causes and principles of things cannot be the same.

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Even the thinker who might be supposed to speak most consistently, Empedocles, is in the same case; for he posits Strife as a kind of principle which is the cause of destruction, but none the less Strife would seem to produce everything except the One; for everything except GodThe expressions the One and God refer to Empedocles’ Sphere: the universe as ordered and united by Love. Cf. Empedocles, Fr. 26-29 (Diels). proceeds from it.

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At any rate he says

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From which grew all that was and is and shall be

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In time to come: the trees, and men and women,

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The beasts and birds and water-nurtured fish,

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And the long-living Gods.Empedocles, Fr. 21. 9-12.

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And it is obvious even apart from this; for if there had not been Strife in things, all things would have been one, he says; for when they came together then Strife came to stand outermost. Empedocles, Fr. 36. 7. Hence it follows on his theory that God, the most blessed being, is less wise than the others, since He does not know all the elements; for He has no Strife in Him, and knowledge is of like by like:

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By earth (he says) we earth perceive, by water water,

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By air bright air, by fire consuming fire,

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Love too by love, and strife by grievous strife.Empedocles, Fr. 109.

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But—and this is the point from which we started—thus much is clear: that it follows on his theory that Strife is no more the cause of destruction than it is of Being. Nor, similarly, is Love the cause of Being; for in combining things into one it destroys everything else.Cf. Aristot. Met. 1.4.6.

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Moreover, of the actual process of change he gives no explanation, except that it is so by nature:

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But when Strife waxing great among the membersi.e., of the Sphere.

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Sprang up to honor as the time came round

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Appointed them in turn by a mighty oath,Empedocles, Fr. 30.

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as though change were a necessity; but he exhibits no cause for the necessity.

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However, thus much of his theory is consistent: he does not represent some things to be perishable and others imperishable, but makes everything perishable except the elements. But the difficulty now being stated is why some things are perishable and others not, assuming that they are derived from the same principles.

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The foregoing remarks may suffice to show that the principles cannot be the same.

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If however they are different, one difficulty is whether they too are to be regarded as imperishable or as perishable. For if they are perishable, it is clearly necessary that they too must be derived from something else, since everything passes upon dissolution into that from which it is derived. Hence it follows that there are other principles prior to the first principles;

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but this is impossible, whether the series stops or proceeds to infinity. And further, how can perishable things exist if their principles are abolished? On the other hand if the principles are imperishable, why should some imperishable principles produce perishable things, and others imperishable things? This is not reasonable; either it is impossible or it requires much explanation.

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Further, no one has so much as attempted to maintain different principles; they maintain the same principles for everything. But they swallow down the difficulty which we raised firsti.e., whether all things have the same principles. as though they took it to be trifling.For Aristotle’s views about the principles of perishable and imperishable things see Aristot. Met. 7.7-10, Aristot. Met. 12.1-7.

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But the hardest question of all to investigate and also the most important with a view to the discovery of the truth, is whether after all Being and Unity are substances of existing things, and each of them is nothing else than Being and Unity respectively, or whether we should inquire what exactly Being and Unity are, there being some other nature underlying them.

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Some take the former, others the latter view of the nature of Being and Unity. Plato and the Pythagoreans hold that neither Being nor Unity is anything else than itself, and that this is their nature, their essence being simply Being and Unity.

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But the physicists, e.g. Empedocles, explain what Unity is by reducing it to something, as it were, more intelligible—or it would seem that by Love Empedocles means Unity; at any rate Love is the cause of Unity in all things. Others identify fire and others air with this Unity and Being of which things consist and from which they have been generated.

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Those who posit more numerous elements also hold the same view; for they too must identify Unity and Being with all the principles which they recognize. And it follows that unless one assumes Unity and Being to be substance in some sense, no other universal term can be substance; for Unity and Being are the most universal of all terms,

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and if there is no absolute Unity or absolute Being, no other concept can well exist apart from the so-called particulars. Further, if Unity is not substance, clearly number cannot be a separate characteristic of things; for number is units, and the unit is simply a particular kind of one.

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On the other hand, if there is absolute Unity and Being, their substance must be Unity and Being; for no other term is predicated universally of Unity and Being, but only these terms themselves. Again, if there is to be absolute Being and absolute Unity, it is very hard to see how there can be anything else besides these; I mean, how things can be more than one.

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For that which is other than what is, is not; and so by Parmenides’ argumentBy τὸ ὄν Parmenides meant what is, i.e. the real universe, which he proved to be one thing because anything else must be what is not, or non-existent. The Platonists meant by it being in the abstract. Aristotle ignores this distinction. it must follow that all things are one, i.e. Being. In either case there is a difficulty; for whether Unity is not a substance or whether there is absolute Unity, number cannot be a substance.

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It has already been stated why this is so if Unity is not a substance; and if it is, there is the same difficulty as about Being. For whence, if not from the absolute One or Unity, can there be another one? It must be not-one; but all things are either one, or many of which each is one. Further, if absolute Unity is indivisible, by Zeno’s axiom it will be nothing.

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For that which neither when added makes a thing greater nor when subtracted makes it smaller is not an existent thing, he saysCf. Zeno, Fr. 2, and see Burnet, E.G.P. sects. 157 ff.; clearly assuming that what exists is spatial magnitude. And if it is a spatial magnitude it is corporeal, since the corporeal exists in all dimensions, whereas the other magnitudes, the plane or line, when added to a thing in one way will increase it, but when added in another will not; and the point or unit will not increase a thing in any way whatever.

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But since Zeno’s view is unsound, and it is possible for a thing to be indivisible in such a way that it can be defended even against his argument (for such a thinge.g., a point is indivisible and has no magnitude, yet added to other points it increases their number. when added will increase a thing in number though not in size)—still how can a magnitude be composed of one or more such indivisible things? It is like saying that the line is composed of points.

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Moreover, even if one supposes the case to be such that number is generated, as some say, from the One itself and from something else which is not one, we must none the less inquire why and how it is that the thing generated will be at one time number and at another magnitude, if the not-one was inequality and the same principle in both cases.The reference is to the Platonists. Cf. Aristot. Met. 14.1.5, 6; Aristot. Met. 14.2.13, 14. For it is not clear how magnitude can be generated either from One and this principle, or from a number and this principle.For the answer to this problem see Aristot. Met. 7.16.3, 4; Aristot. Met. 10.2; and cf. Aristot. Met. 13.8.

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(13.) Out of this arises the question whether numbers, bodies, planes and points are substances or not. If not, the question of what Being is, what the substances of things are, baffles us; for modifications and motions and relations and dispositions and ratios do not seem to indicate the substance of anything; they are all predicated of a substrate, and none of them is a definite thing.

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As for those things which might be especially supposed to indicate substance—water, earth, fire and air, of which composite bodies are composed— their heat and cold and the like are modifications, not substances; and it is only the body which undergoes these modifications that persists as something real and a kind of substance.

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Again, the body is less truly substance than the plane, and the plane than the line, and the line than the unit or point; for it is by these that the body is defined, and it seems that they are possible without the body, but that the body cannot exist without them.

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This is why the vulgar and the earlier thinkers supposed that substance and Being are Body, and everything else the modifications of Body; and hence also that the first principles of bodies are the first principles of existing things; whereas later thinkers with a greater reputation for wisdom supposed that substance and Being are numbers.

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As we have said, then, if these things are not substance, there is no substance or Being at all; for the attributes of these things surely have no right to be called existent things. On the other hand, if it be agreed that lines and points are more truly substance than bodies are, yet unless we can see to what kind of bodies they belong (for they cannot be in sensible bodies) there will still be no substance.

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Further, it is apparent that all these lines are divisions of Body, either in breadth or in depth or in length. Moreover every kind of shape is equally present in a solid, so that if Hermes is not in the stone,Apparently a proverbial expression. neither is the half-cube in the cube as a determinate shape.

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Hence neither is the plane; for if any kind of plane were in it, so would that plane be which defines the half-cube. The same argument applies to the line and to the point or unit. Hence however true it may be that body is substance, if planes, lines and points are more truly substance than Body is, and these are not substance in any sense, the question of what Being is and what is the substance of things baffles us.

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Because, in addition to the above arguments, absurd results follow from a consideration of generation and destruction; for it seems that if substance, not having existed before, now exists, or having existed before, subsequently does not exist it suffers these changes in the process of generation and destruction. But points, lines and planes, although they exist at one time and at another do not, cannot be in process of being either generated or destroyed;

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for whenever bodies are joined or divided, at one time, when they are joined one surface is instantaneously produced, and at another, when they are divided, two. Thus when the bodies are combined the surface does not exist but has perished; and when they are divided, surfaces exist which did not exist before. (The indivisible point is of course never divided into two.) And if they are generated and destroyed, from what are they generated?

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It is very much the same with the present moment in time. This too cannot be generated and destroyed; but nevertheless it seems always to be different, not being a substance. And obviously it is the same with points, lines and planes, for the argument is the same; they are all similarly either limits or divisions.For arguments against the substantiality of numbers and mathematical objects see Aristot. Met. 13.1-3, 6-9; Aristot. Met. 14.1-3, 5, 6.

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In general one might wonder why we should seek for other entities apart from sensible things and the Intermediates:Cf. Aristot. Met. 3.2.20ff.. e.g., for the Forms which we Platonists assume.

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If it is for the reason that the objects of mathematics, while differing from the things in our world in another respect, resemble them in being a plurality of objects similar in form, so that their principles cannot be numerically determined (just as the principles of all language in this world of ours are determinate not in number but in kind—unless one takes such and such a particular syllable or sound, for the principles of these are determinate in number too—

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and similarly with the Intermediates, for in their case too there is an infinity of objects similar in form), then if there is not another set of objects apart from sensible and mathematical objects, such as the Forms are said to be, there will be no substance which is one both in kind and in number, nor will the principles of things be determinate in number, but in kind only.

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Thus if this is necessarily so, it is necessary for this reason to posit the Forms also. For even if their exponents do not articulate their theory properly, still this is what they are trying to express, and it must be that they maintain the Forms on the ground that each of them is a substance, and none of them exists by accident.

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On the other hand, if we are to assume that the Forms exist, and that the first principles are one in number but not in kind, we have already statedAristot. Met. 3.4.9, 10. the impossible consequences which must follow.This problem is not stated in ch. 1., but is akin to problems 5. and 8., which see.

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(12.) Closely connected with these questions is the problem whether the elements exist potentially or in some other sense.

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If in some other sense, there will be something else prior to the first principles. For the potentiality is prior to the actual cause, and the potential need not necessarily always become actual. On the other hand, if the elements exist potentially, it is possible for nothing to exist; for even that which does not yet exist is capable of existing. That which does not exist may come to be, but nothing which cannot exist comes to be.For the relation of potentiality to actuality see Aristot. Met. 9.1-9. The second point raised in this connection in ch. 1 is not discussed here; for actuality and motion see Aristot. Met. 12.6, 7.

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(xi.) Besides the foregoing problems about the first principles we must also raise the question whether they are universal or such as we describe the particulars to be. For if they are universal, there will be no substances; for no common term denotes an individual thing, but a type; and substance is an individual thing.

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But if the common predicate be hypostatized as an individual thing, Socrates will be several beings: himself, and Man, and Animal—that is, if each predicate denotes one particular thing.

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These then are the consequences if the principles are universal. If on the other hand they are not universal but like particulars, they will not be knowable; for the knowledge of everything is universal. Hence there will have to be other universally predicated principles prior to the first principles, if there is to be any knowledge of them.For the answer to this problem see Aristot. Met. 7.13-15, Aristot. Met. 13.10.

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There is a science which studies Being qua Being, and the properties inherent in it in virtue of its own nature. This science is not the same as any of the so-called particular sciences, for none of the others contemplates Being generally qua Being; they divide off some portion of it and study the attribute of this portion, as do for example the mathematical sciences.

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But since it is for the first principles and the most ultimate causes that we are searching, clearly they must belong to something in virtue of its own nature. Hence if these principles were investigated by those also who investigated the elements of existing things, the elements must be elements of Being not incidentally, but qua Being. Therefore it is of Being qua Being that we too must grasp the first causes.

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The term being is used in various senses, but with reference to one central idea and one definite characteristic, and not as merely a common epithet. Thus as the term healthy always relates to health (either as preserving it or as producing it or as indicating it or as receptive of it),

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and as medical relates to the art of medicine (either as possessing it or as naturally adapted for it or as being a function of medicine)—and we shall find other terms used similarly to these—

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so being is used in various senses, but always with reference to one principle. For some things are said to be because they are substances; others because they are modifications of substance; others because they are a process towards substance, or destructions or privations or qualities of substance, or productive or generative of substance or of terms relating to substance, or negations of certain of these terms or of substance. (Hence we even say that not-being is not-being.)

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And so, just as there is one science of all healthy things, so it is true of everything else. For it is not only in the case of terms which express one common notion that the investigation belongs to one science, but also in the case of terms which relate to one particular characteristic; for the latter too, in a sense, express one common notion. Clearly then the study of things which are, qua being, also belongs to one science.

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Now in every case knowledge is principally concerned with that which is primary, i.e. that upon which all other things depend, and from which they get their names. If, then, substance is this primary thing, it is of substances that the philosopher must grasp the first principles and causes.

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Now of every single class of things, as there is one perception, so there is one science: e.g., grammar, which is one science, studies all articulate sounds.

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Hence the study of all the species of Being qua Being belongs to a science which is generically one, and the study of the several species of Being belongs to the specific parts of that science.

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Now if Being and Unity are the same, i.e. a single nature, in the sense that they are associated as principle and cause are, and not as being denoted by the same definition (although it makes no difference but rather helps our argument if we understand them in the same sense),

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since one man and man and existent man and man are the same thing, i.e. the duplication in the statement he is a man and an existent man gives no fresh meaning (clearly the concepts of humanity and existence are not dissociated in respect of either coming to be or ceasing to be), and similarly in the case of the term one, so that obviously the additional term in these phrases has the same significance, and Unity is nothing distinct from Being;

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and further if the substance of each thing is one in no accidental sense, and similarly is of its very nature something which is—then there are just as many species of Being as of Unity. And to study the essence of these species (I mean, e.g., the study of Same and Other and all the other similar concepts—

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roughly speaking all the contraries are reducible to this first principle; but we may consider that they have been sufficiently studied in the Selection of ContrariesIt is uncertain to what treatise Aristotle refers; in any case it is not extant.) is the province of a science which is generically one.

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And there are just as many divisions of philosophy as there are kinds of substance; so that there must be among them a First Philosophy and one which follows upon it.

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For Being and Unity at once entail genera, and so the sciences will correspond to these genera. The term philosopher is like the term mathematician in its uses; for mathematics too has divisions—there is a primary and a secondary science, and others successively, in the realm of mathematics.

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Now since it is the province of one science to study opposites, and the opposite of unity is plurality, and it is the province of one science to study the negation and privation of Unity, because in both cases we are studying Unity, to which the negation (or privation) refers, stated either in the simple form that Unity is not present, or in the form that it is not present in a particular class; in the latter case Unity is modified by the differentia, apart from the content of the negation (for the negation of Unity is its absence); but in privation there is a substrate of which the privation is predicated.—

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The opposite of Unity, then, is Plurality; and so the opposites of the above-mentioned concepts—Otherness, Dissimilarity, Inequality and everything else which is derived from these or from Plurality or Unity— fall under the cognizance of the aforesaid science. And one of them is Oppositeness; for this is a form of Difference, and Difference is a form of Otherness.

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Hence since the term one is used in various senses, so too will these terms be used; yet it pertains to one science to take cognizance of them all. For terms fall under different sciences, not if they are used in various senses, but if their definitions are neither identical nor referable to a common notion.

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And since everything is referred to that which is primary, e.g. all things which are called one are referred to the primary One, we must admit that this is also true of Identity and Otherness and the Contraries. Thus we must first distinguish all the senses in which each term is used, and then attribute them to the primary in the case of each predicate, and see how they are related to it; for some will derive their name from possessing and others from producing it, and others for similar reasons.

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Thus clearly it pertains to one science to give an account both of these concepts and of substance (this was one of the questions raised in the DifficultiesSee Aristot. Met. 3.1.8-10, Aristot. Met. 3.2.18, 19.), and it is the function of the philosopher to be able to study all subjects.

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If this is not so, who is it who in will investigate whether Socrates and Socrates seated are the same thing; or whether one thing has one contrary, or what the contrary is, or how many meanings it has?Cf. Aristot. Met. 10.4. and similarly with all other such questions.

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Thus since these are the essential modifications of Unity qua Unity and of Being qua Being, and not qua numbers or lines or fire, clearly it a pertains to that sciencei.e., Philosophy or Metaphysics. to discover both the essence and the attributes of these concepts.

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And those who investigate them err, not in being unphilosophical, but because the substance, of which they have no real knowledge, is prior. For just as number qua number has its peculiar modifications, e.g. oddness and evenness, commensurability and equality, excess and defect, and these things are inherent in numbers both considered independently and in relation to other numbers; and as similarly other peculiar modifications are inherent in the solid and the immovable and the moving and the weightless and that which has weight; so Being qua Being has certain peculiar modifications, and it is about these that it is the philosopher’s function to discover the truth. And here is evidence of this fact.

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Dialecticians and sophists wear the same appearance as the philosopher, for sophistry is Wisdom in appearance only, and dialecticians discuss all subjects, and Being is a subject common to them all; but clearly they discuss these concepts because they appertain to philosophy.

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For sophistry and dialectic are concerned with the same class of subjects as philosophy, but philosophy differs from the former in the nature of its capability and from the latter in its outlook on life. Dialectic treats as an exercise what philosophy tries to understand, and sophistry seems to be philosophy; but is not.

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Further, the second column of contraries is privative, and everything is reducible to Being and Not being, and Unity and Plurality; e.g. Rest falls under Unity and Motion under Plurality. And nearly everyone agrees that substance and existing things are composed of contraries; at any rate all speak of the first principles as contraries—

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some as Odd and Even,The Pythagoreans. some as Hot and Cold,Perhaps Parmenides. some as Limit and Unlimited,The Platonists. some as Love and Strife.Empedocles. And it is apparent that all other things also are reducible to Unity and Plurality (we may assume this reduction); and the principles adduced by other thinkers fall entirely under these as genera.

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It is clear, then, from these considerations also, that it pertains to a single science to study Being qua Being; for all things are either contraries or derived from contraries, and the first principles of the contraries are Unity and Plurality. And these belong to one science, whether they have reference to one common notion or not. Probably the truth is that they have not; but nevertheless even if the term one is used in various senses, the others will be related to the primary sense (and similarly with the contraries)—

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even if Being or Unity is not a universal and the same in all cases, or is not separable from particulars (as it presumably is not; the unity is in some cases one of reference and in others one of succession). For this very reason it is not the function of the geometrician to inquire what is Contrariety or Completeness or Being or Unity or Identity or Otherness, but to proceed from the assumption of them.

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Clearly, then, it pertains to one science to study Being qua Being, and the attributes inherent in it qua Being; and the same science investigates, besides the concepts mentioned above, Priority and Posteriority, Genus and Species, Whole and Part, and all other such concepts.

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We must pronounce whether it pertains to the same science to study both the so-called axioms in mathematics and substance, or to different sciences. It is obvious that the investigation of these axioms too pertains to one science, namely the science of the philosopher; for they apply to all existing things, and not to a particular class separate and distinct from the rest. Moreover all thinkers employ them—because they are axioms of Being qua Being, and every genus possesses Being—

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but employ them only in so far as their purposes require; i.e., so far as the genus extends about which they are carrying out their proofs. Hence since these axioms apply to all things qua Being (for this is what is common to them), it is the function of him who studies Being qua Being to investigate them as well.

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For this reason no one who is pursuing a particular inquiry—neither a geometrician nor an arithmetician—attempts to state whether they are true or false; but some of the physicists did so, quite naturally; for they alone professed to investigate nature as a whole, and Being.

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But inasmuch as there is a more ultimate type of thinker than the natural philosopher (for nature is only a genus of Being), the investigation of these axioms too will belong to the universal thinker who studies the primary reality. Natural philosophy is a kind of Wisdom, but not the primary kind.

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As for the attempts of some of those who discuss how the truth should be received, they are due to lack of training in logic; for they should understand these things before they approach their task, and not investigate while they are still learning.

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Clearly then it is the function of the philosopher, i.e. the student of the whole of reality in its essential nature, to investigate also the principles of syllogistic reasoning. And it is proper for him who best understands each class of subject to be able to state the most certain principles of that subject; so that he who understands the modes of Being qua Being should be able to state the most certain principles of all things.

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Now this person is the philosopher, and the most certain principle of all is that about which one cannot be mistaken; for such a principle must be both the most familiar (for it is about the unfamiliar that errors are always made), and not based on hypothesis.

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For the principle which the student of any form of Being must grasp is no hypothesis; and that which a man must know if he knows anything he must bring with him to his task.

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Clearly, then, it is a principle of this kind that is the most certain of all principles. Let us next state what this principle is.

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It is impossible for the same attribute at once to belong and not to belong to the same thing and in the same relation; and we must add any further qualifications that may be necessary to meet logical objections. This is the most certain of all principles, since it possesses the required definition;

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for it is impossible for anyone to suppose that the same thing is and is not, as some imagine that Heraclitus saysFor examples of Heraclitus’s paradoxes cf. Heraclitus Fr. 36, 57, 59 (Bywater); and for their meaning see Burnet, E.G.P. 80.—for what a man says does not necessarily represent what he believes.

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And if it is impossible for contrary attributes to belong at the same time to the same subject (the usual qualifications must be added to this premiss also), and an opinion which contradicts another is contrary to it, then clearly it is impossible for the same man to suppose at the same time that the same thing is and is not; for the man who made this error would entertain two contrary opinions at the same time.

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Hence all men who are demonstrating anything refer back to this as an ultimate belief; for it is by nature the starting-point of all the other axioms as well.

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There are some, however, as we have said, who both state themselves that the same thing can be and not be, and say that it is possible to hold this view. Many even of the physicists adopt this theory. But we have just assumed that it is impossible at once to be and not to be, and by this means we have proved that this is the most certain of all principles.

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Some, indeed, demand to have the law proved, but this is because they lack educationsc., in logic.; for it shows lack of education not to know of what we should require proof, and of what we should not. For it is quite impossible that everything should have a proof; the process would go on to infinity, so that even so there would be no proof.Every proof is based upon some hypothesis, to prove which another hypothesis must be assumed, and so on ad infinitum.

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If on the other hand there are some things of which no proof need be sought, they cannot say what principle they think to be more self-evident. Even in the case of this law, however, we can demonstrate the impossibility by refutation, if only our opponent makes some statement. If he makes none, it is absurd to seek for an argument against one who has no arguments of his own about anything, in so far as he has none; for such a person, in so far as he is such, is really no better than a vegetable.

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And I say that proof by refutation differs from simple proof in that he who attempts to prove might seem to beg the fundamental question, whereas if the discussion is provoked thus by someone else, refutation and not proof will result.

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The starting-point for all such discussions is not the claim that he should state that something is or is not so (because this might be supposed to be a begging of the question), but that he should say something significant both to himself and to another (this is essential if any argument is to follow; for otherwise such a person cannot reason either with himself or with another);

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and if this is granted, demonstration will be possible, for there will be something already defined. But the person responsible is not he who demonstrates but he who acquiesces; for though he disowns reason he acquiesces to reason. Moreover, he who makes such an admission as this has admitted the truth of something apart from demonstration [so that not everything will be so and not so].

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Thus in the first place it is obvious that this at any rate is true: that the term to be or not to be has a definite meaning; so that not everything can be so and not so. Again, if man has one meaning, let this be two-footed animal.

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By has one meaning I mean this: if X means man, then if anything is a man, its humanity will consist in being X. And it makes no difference even if it be said that man has several meanings, provided that they are limited in number; for one could assign a different name to each formula.

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For instance, it might be said that man has not one meaning but several, one of which has the formula two-footed animal, and there might be many other formulae as well, if they were limited in number; for a particular name could be assigned to each for formula.

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If on the other hand it be said that man has an infinite number of meanings, obviously there can be no discourse; for not to have one meaning is to have no meaning, and if words have no meaning there is an end of discourse with others, and even, strictly speaking, with oneself; because it is impossible to think of anything if we do not think of one thing; and even if this were possible, one name might be assigned to that of which we think.

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Now let this name, as we said at the beginning, have a meaning; and let it have one meaning. Now it is impossible that being man should have the same meaning as not being man, that is, if man is not merely predicable of one subject but has one meaning

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(for we do not identify having one meaning with being predicable of one subject, since in this case cultured and white and man would have one meaning, and so all things would be one; for they would all have the same meaning). And it will be impossible for the same thing to be and not to be, except by equivocation, as e.g. one whom we call man others might call not-man;

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but the problem is whether the same thing can at once be and not be man, not in name , but in fact . If man and not-man have not different meanings, clearly not being a man will mean nothing different from being a man; and so being a man will be not being a man; they will be one.

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For to be one means, as in the case of garment and coat, that the formula is one. And if being man and being not-man are to be one, they will have the same meaning; but it has been proved above that they have different meanings. If then anything can be truly said to be man, it must be two-footed animal; for this is what man was intended to mean.

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And if this is necessarily so, it is impossible that at the same time the same thing should not be two-footed animal. For to be necessarily so means this: that it is impossible not to be so. Thus it cannot be true to say at the same time that the same thing is and is not man.

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And the same argument holds also in the case of not being man; because being man and being not-man have different meanings if being white and being man have different meanings (for the opposition is much stronger in the former case so as to produce different meanings).

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And if we are told that white too means one and the same thing,i.e. the same as man. we shall say again just what we said before,Aristot. Met. 4.4.12. that in that case all things, and not merely the opposites, will be one. But if this is impossible, what we have stated follows; that is, if our opponent answers our question; but if when asked the simple question he includes in his answer the negations, he is not answering our question.

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There is nothing to prevent the same thing from being man and white and a multitude of other things; but nevertheless when asked whether it is true to say that X is man, or not, one should return an answer that means one thing, and not add that X is white and large. It is indeed impossible to enumerate all the infinity of accidents; and so let him enumerate either all or none.

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Similarly therefore, even if the same thing is ten thousand times man and not-man, one should not include in one’s answer to the question whether it is man that it is at the same time also not-man, unless one is also bound to include in one’s answer all the other accidental things that the subject is or is not. And if one does this, he is not arguing properly.

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In general those who talk like this do away with substance and essence,

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for they are compelled to assert that all things are accidents, and that there is no such thing as being essentially man or animal. For if there is to be such a thing as being essentially man, this will not be being not-man nor not-being man (and yet these are negations of it); for it was intended to have one meaning, i.e. the substance of something.

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But to denote a substance means that the essence is that and nothing else; and if for it being essentially man is the same as either being essentially not-man or essentially not-being man, the essence will be something else.

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Thus they are compelled to say that nothing can have such a definition as this, but that all things are accidental; for this is the distinction between substance and accident: white is an accident of man, because although he is white, he is not white in essence.

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And since the accidental always implies a predication about some subject, if all statements are accidental, there will be nothing primary about which they are made; so the predication must proceed to infinity. But this is impossible, for not even more than two accidents can be combined in predication. An accident cannot be an accident of an accident unless both are accidents of the same thing.

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I mean, e.g., that white is cultured and cultured white merely because both are accidents of a man. But it is not in this sense—that both terms are accidents of something else—that Socrates is cultured. Therefore since some accidents are predicated in the latter and some in the former sense, such as are predicated in the way that white is of Socrates cannot be an infinite series in the upper direction; e.g. there cannot be another accident of white Socrates, for the sum of these predications does not make a single statement.

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Nor can white have a further accident, such as cultured; for the former is no more an accident of the latter than vice versa; and besides we have distinguished that although some predicates are accidental in this sense, others are accidental in the sense that cultured is to Socrates; and whereas in the former case the accident is an accident of an accident, it is not so in the latter; and thus not all predications will be of accidents.

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Therefore even so there will be something which denotes substance. And if this is so, we have proved that contradictory statements cannot be predicated at the same time.

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Again, if all contradictory predications of the same subject at the same time are true, clearly all things will be one.

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For if it is equally possible either to affirm or deny anything of anything, the same thing will be a trireme and a wall and a man; which is what necessarily follows for those who hold the theory of Protagoras.i.e., that all appearances and opinions are true. For if anyone thinks that a man is not a trireme, he is clearly not a trireme; and so he also is a trireme if the contradictory statement is true.

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And the result is the dictum of Anaxagoras, all things mixed together Fr. 1 (Diels). ; so that nothing truly exists. It seems, then, that they are speaking of the Indeterminate; and while they think that they are speaking of what exists, they are really speaking of what does not; for the Indeterminate is that which exists potentially but not actually.

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But indeed they must admit the affirmation or negation of any predicate of any subject, for it is absurd that in the case of each term its own negation should be true, and the negation of some other term which is not true of it should not be true. I mean, e.g., that if it is true to say that a man is not a man, it is obviously also true to say that he is or is not a trireme.

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Then if the affirmation is true, so must the negation be true; but if the affirmation is not true the negation will be even truer than the negation of the original term itself. Therefore if the latter negation is true, the negation of trireme will also be true; and if this is true, the affirmation will be true too.

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And not only does this follow for those who hold this theory, but also that it is not necessary either to affirm or to deny a statement.

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For if it is true that X is both man and not-man, clearly he will be neither man nor not-man; for to the two statements there correspond two negations, and if the former is taken as a single statement compounded out of two, the latter is also a single statement and opposite to it.

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Again, either this applies to all terms, and the same thing is both white and not-white, and existent and non-existent, and similarly with all other assertions and negations; or it does not apply to all, but only to some and not to others.

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And if it does not apply to all, the exceptions will be admittedi.e., it will be admitted that in certain cases where an attribute is true of a subject, the negation is not true; and therefore some propositions are indisputable.; but if it does apply to all, again either (a) the negation will be true wherever the affirmation is true, and the affirmation will be true wherever the negation is true, or (d) the negation will be true wherever the assertion is true, but the assertion will not always be true where the negation is true.

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And in the latter case there will be something which definitely is not, and this will be a certain belief; and if that it is not is certain and knowable, the opposite assertion will be still more knowable. But if what is denied can be equally truly asserted, it must be either true or false to state the predicates separately and say, e.g., that a thing is white, and again that it is not-white.

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And if it is not-true to state them separately, our opponent does not say what he professes to say, and nothing exists; and how can that which does not exist speak or walk?If our opponent holds that you can only say A is B and not B, (1) he contradicts every statement that he makes; (2) he must say that what exists does not exist. Therefore nothing exists, and so he himself does not exist; but how can he speak or walk if he does not exist? And again all things will be one, as we said before,Aristot. Met. 4.4.27. and the same thing will be man and God and trireme and the negations of these terms.

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For if it is equally possible to assert or deny anything of anything, one thing will not differ from another; for if anything does differ, it will be true and unique. And similarly even if it is possible to make a true statement while separating the predicates, what we have stated follows. Moreover it follows that all statements would be true and all false; and that our opponent himself admits that what he says is false. Besides, it is obvious that discussion with him is pointless, because he makes no real statement.

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For he says neither yes nor no, but yes and no; and again he denies both of these and says neither yes nor no; otherwise there would be already some definite statement.

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Again, if when the assertion is true the negation is false, and when the latter is true the affirmation is false, it will be impossible to assert and deny with truth the same thing at the same time.

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But perhaps it will be said that this is the point at issue.

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Again, is the man wrong who supposes that a thing is so or not so, and he who supposes both right? If he is right, what is the meaning of saying that such is the nature of reality?If everything is both so and not so, nothing has any definite nature. And if he is not right, but is more right than the holder of the first view, reality will at once have a definite nature, and this will be true, and not at the same time not-true.

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And if all men are equally right and wrong, an exponent of this view can neither speak nor mean anything, since at the same time he says both yes and no. And if he forms no judgement, but thinks and thinks not indifferently, what difference will there be between him and the vegetables?

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Hence it is quite evident that no one, either of those who profess this theory or of any other school, is really in this position.

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Otherwise, why does a man walk to Megara and not stay at home, when he thinks he ought to make the journey? Why does he not walk early one morning into a well or ravine, if he comes to it, instead of clearly guarding against doing so, thus showing that he does not think that it is equally good and not good to fall in? Obviously then he judges that the one course is better and the other worse.

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And if this is so, he must judge that one thing is man and another not man, and that one thing is sweet and another not sweet. For when, thinking that it is desirable to drink water and see a man, he goes to look for them, he does not look for and judge all things indifferently; and yet he should, if the same thing were equally man and not-man.

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But as we have said, there is no one who does not evidently avoid some things and not others. Hence, as it seems, all men form unqualified judgements, if not about all things, at least about what is better or worse.

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And if they do this by guesswork and without knowledge, they should be all the more eager for truth; just as a sick man should be more eager for health than a healthy man; for indeed the man who guesses, as contrasted with him who knows, is not in a healthy relation to the truth.

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Again, however much things may be so and not so, yet differences of degree are inherent in the nature of things. For we should not say that 2 and 3 are equally even; nor are he who thinks that 4 is 5, and he who thinks it is 1000, equally wrong: hence if they are not equally wrong, the one is clearly less wrong, and so more right.

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If then that which has more the nature of something is nearer to that something, there will be some truth to which the more true is nearer. And even if there is not, still there is now something more certain and true, and we shall be freed from the undiluted doctrine which precludes any mental determination.

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From the same view proceeds the theory of Protagoras, and both alike must be either true or false. For if all opinions and appearances are true, everything must be at once true and false; for many people form judgements which are opposite to those of others, and imagine that those who do not think the same as themselves are wrong: hence the same thing must both be and not be.

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And if this is so, all opinions must be true; for those who are wrong and those who are right think contrarily to each other. So if reality is of this nature, everyone will be right.

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Clearly then both these theories proceed from the same mental outlook. But the method of approach is not the same for all cases; for some require persuasion and others compulsion.

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The ignorance of those who have formed this judgement through perplexity is easily remedied, because we are dealing not with the theory but with their mental outlook; but those who hold the theory for its own sake can only be cured by refuting the theory as expressed in their own speech and words.

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This view comes to those who are perplexed from their observation of sensible things. (1.) The belief that contradictions and contraries can be true at the same time comes to them from seeing the contraries generated from the same thing.

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Then if what is not cannot be generated, the thing must have existed before as both contraries equally—just as Anaxagoras saysCf. Aristot. Met. 4.4.28. that everything is mixed in everything; and also Democritus, for he too saysCf. Aristot. Met. 1.4.9. that Void and Plenum are present equally in any part, and yet the latter is , and the former is not.

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To those, then, who base their judgement on these considerations, we shall say that although in one sense their theory is correct, in another they are mistaken. For being has two meanings, so that there is a sense in which something can be generated from not-being, and a sense in which it cannot; and a sense in which the same thing can at once be and not be; but not in the same respect. For the same thing can be contraries at the same time potentially, but not actually.

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And further, we shall request them to conceive another kind also of substance of existing things, in which there is absolutely no motion or destruction or generation. And (2.) similarly the theory that there is truth in appearances has come to some people from an observation of sensible things.

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They think that the truth should not be judged by the number or fewness of its upholders; and they say that the same thing seems sweet to some who taste it, and bitter to others; so that if all men were diseased or all insane, except two or three who were healthy or sane, the latter would seem to be diseased or insane, and not the others.

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And further they say that many of the animals as well get from the same things impressions which are contrary to ours, and that the individual himself does not always think the same in matters of sense-perception. Thus it is uncertain which of these impressions are true or false; for one kind is no more true than another, but equally so. And hence Democritus saysCf. Ritter and Preller, 204. that either there is no truth or we cannot discover it.

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And in general it is because they suppose that thought is sense-perception, and sense-perception physical alteration, that they say that the impression given through sense-perception is necessarily true; for it is on these grounds that both Empedocles and Democritus and practically all the rest have become obsessed by such opinions as these.

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For Empedocles says that those who change their bodily condition change their thought:

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For according to that which is present to them doth thought increase in men.Empedocles Fr. 106.

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And in another passage he says:

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And as they change into a different nature, so it ever comes to them to think differently.Empedocles Fr. 108.

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And Parmenides too declares in the same way:

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For as each at any time hath the temperament of his many-jointed limbs, so thought comes to men. For for each and every man the substance of his limbs is that very thing which thinks; for thought is that which preponderates.Empedocles Fr. 16; quoted also (in a slightly different form; see critical notes) by Theophrastus, De Sensu 3.

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There is also recorded a saying of Anaxagoras to some of his disciples, that things would be for them as they judged them to be.

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And they say that in Homer too clearly held this view, because he made Hector,The only passage in our text of Homer to which this reference could apply isHom. Il. 23.698; but there the subject is Euryalus, not Hector. when he was stunned by the blow, lie with thoughts deranged—thus implying that even those who are out of their minds still think, although not the same thoughts. Clearly then, if both are kinds of thought, reality also will be both so and not so.

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It is along this path that the consequences are most difficult; for if those who have the clearest vision of such truth as is possible (and these are they who seek and love it most) hold such opinions and make these pronouncements about the truth, surely those who are trying to be philosophers may well despair; for the pursuit of truth will be chasing birds in the air. Cf. Leutsch and Schneidewin, Paroemiographi Graeci, 2.677.

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But the reason why these men hold this view is that although they studied the truth about reality, they supposed that reality is confined to sensible things, in which the nature of the Indeterminate, i.e. of Being in the sense which we have explained,Aristot. Met. 4.4.28. is abundantly present. (Thus their statements, though plausible, are not true;

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this form of the criticism is more suitable than that which EpicharmusFl. early 5th century; held views partly Pythagorean, partly Heraclitean. applied to Xenophanes.) And further, observing that all this indeterminate substance is in motion, and that no true predication can be made of that which changes, they supposed that it is impossible to make any true statement about that which is in all ways and entirely changeable.

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For it was from this supposition that there blossomed forth the most extreme view of those which we have mentioned, that of the professed followers of Heraclitus, and such as Cratylus held, who ended by thinking that one need not say anything, and only moved his finger; and who criticized Heraclitus for saying that one cannot enter the same river twice,Heraclitus Fr. 41 (Bywater). for he himself held that it cannot be done even once.

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But we shall reply to this theory also that although that which is changeable supplies them, when it changes, with some real ground for supposing that it is not, yet there is something debatable in this; for that which is shedding any quality retains something of that which is being shed, and something of that which is coming to be must already exist.

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And in general if a thing is ceasing to be, there will be something there which is ; and if a thing is coming to be, that from which it comes and by which it is generated must be ; and this cannot go on to infinity. But let us leave this line of argument and remark that quantitative and qualitative change are not the same.

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Let it be granted that there is nothing permanent in respect of quantity; but it is by the form that we recognize everything. And again those who hold the theory that we are attacking deserve censure in that they have maintained about the whole material universe what they have observed in the case of a mere minority of sensible things.

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For it is only the realm of sense around us which continues subject to destruction and generation, but this is a practically negligible part of the whole; so that it would have been fairer for them to acquit the former on the ground of the latter than to condemn the latter on account of the former.

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Further, we shall obviously say to these thinkers too the same as we said some time agoAristot. Met. 4.5.7.; for we must prove to them and convince them that there is a kind of nature that is not moved

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(and yet those who claim that things can at once be and not be are logically compelled to admit rather that all things are at rest than that they are in motion; for there is nothing for them to change into, since everything exists in everything). And as concerning reality, that not every appearance is real, we shall say, first, that indeed the perception, at least of the proper object of a sense, is not false, but the impression we get of it is not the same as the perception.

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And then we may fairly express surprise if our opponents raise the question whether magnitudes and colors are really such as they appear at a distance or close at hand, as they appear to the healthy or to the diseased; and whether heavy things are as they appear to the weak or to the strong; and whether truth is as it appears to the waking or to the sleeping.

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For clearly they do not really believe the latter alternative—at any rate no one, if in the night he thinks that he is at Athens whereas he is really in Africa, starts off to the Odeum.A concert-hall (used also for other purposes) built by Pericles. It lay to the south-east of the Acropolis. And again concerning the future (as indeed Plato saysPlat. Theaet. 171e, 178cff..) the opinion of the doctor and that of the layman are presumably not equally reliable, e.g. as to whether a man will get well or not.

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And again in the case of the senses themselves, our perception of a foreign object and of an object proper to a given sense, or of a kindred object and of an actual object of that sense itself, is not equally reliableAn object of taste is foreign to the sense of sight; a thing may look sweet without tasting sweet. Similarly although the senses of taste and smell (and therefore their objects) are kindred (Aristot. De Sensu 440b 29), in judging tastes the sense of taste is the more reliable.; but in the case of colors sight, and not taste, is authoritative, and in the case of flavor taste, and not sight. But not one of the senses ever asserts at the same time of the same object that it is so and not so.

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Nor even at another time does it make a conflicting statement about the quality, but only about that to which the quality belongs. I mean, e.g., that the same wine may seem, as the result of its own change or of that of one’s body, at one time sweet and at another not; but sweetness, such as it is when it exists, has never yet changed, and there is no mistake about it, and that which is to be sweet is necessarily of such a nature.

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Yet all these theories destroy the possibility of anything’s existing by necessity, inasmuch as they destroy the existence of its essence; for the necessary cannot be in one way and in another; and so if anything exists of necessity, it cannot be both so and not so.

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And in general, if only the sensible exists, without animate things there would be nothing; for there would be no sense-faculty.

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That there would be neither sensible qualities nor sensations is probably trueCf. Aristot. De Anima 425b 25-426b 8.(for these depend upon an effect produced in the percipient), but that the substrates which cause the sensation should not exist even apart from the sensation is impossible.

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For sensation is not of itself, but there is something else too besides the sensation, which must be prior to the sensation; because that which moves is by nature prior to that which is moved, and this is no less true if the terms are correlative.

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But there are some, both of those who really hold these convictions and of those who merely profess these views, who raise a difficulty; they inquire who is to judge of the healthy man, and in general who is to judge rightly in each particular case. But such questions are like wondering whether we are at any given moment asleep or awake;

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and all problems of this kind amount to the same thing. These people demand a reason for everything. They want a starting-point, and want to grasp it by demonstration; while it is obvious from their actions that they have no conviction. But their case is just what we have stated beforeAristot. Met. 4.4.2.; for they require a reason for things which have no reason, since the starting-point of a demonstration is not a matter of demonstration.

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The first class, then, may be readily convinced of this, because it is not hard to grasp. But those who look only for cogency in argument look for an impossibility, for they claim the right to contradict themselves, and lose no time in doing so.

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Yet if not everything is relative, but some things are self-existent, not every appearance will be true; for an appearance is an appearance to someone. And so he who says that all appearances are true makes everything relative.

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Hence those who demand something cogent in argument, and at the same time claim to make out a case, must guard themselves by saying that the appearance is true; not in itself, but for him to whom it appears, and at, the time when it appears, and in the way and manner in which it appears. And if they make out a case without this qualification, as a result they will soon contradict themselves;

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for it is possible in the case of the same man for a thing to appear honey to the sight, but not to the taste, and for things to appear different to the sight of each of his two eyes, if their sight is unequal. For to those who assert (for the reasons previously stated Aristot. Met. 4.5.7-17. ) that appearances are true, and that all things are therefore equally false and true, because they do not appear the same to all, nor always the same to the same person, but often have contrary appearances at the same time

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(since if one crosses the fingers touch says that an object is two, while sight says that it is only oneCf. Aristot. Problemata 958b 14, 959a 5, 965a 36.), we shall say but not to the same sense or to the same part of it in the same way and at the same time; so that with this qualification the appearance will be true. But perhaps it is for this reason that those who argue not from a sense of difficulty but for argument’s sake are compelled to say that the appearance is not true in itself, but true to the percipient;

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and, as we have said before, are compelled also to make everything relative and dependent upon opinion and sensation, so that nothing has happened or will happen unless someone has first formed an opinion about it; otherwise clearly all things would not be relative to opinion.

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Further, if a thing is one, it is relative to one thing or to something determinate. And if the same thing is both a half and an equal, yet the equal is not relative to the double.

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If to the thinking subject man and the object of thought are the same, man will be not the thinking subject but the object of thought; and if each thing is to be regarded as relative to the thinking subject, the thinking subject will be relative to an infinity of specifically different things.

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That the most certain of all beliefs is that opposite statements are not both true at the same time, and what follows for those who maintain that they are true, and why these thinkers maintain this, may be regarded as adequately stated. And since the contradiction of a statement cannot be true at the same time of the same thing, it is obvious that contraries cannot apply at the same time to the same thing.

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For in each pair of contraries one is a privation no less than it is a contrary—a privation of substance. And privation is the negation of a predicate to some defined genus. Therefore if it is impossible at the same time to affirm and deny a thing truly, it is also impossible for contraries to apply to a thing at the same time; either both must apply in a modified sense, or one in a modified sense and the other absolutely.

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Nor indeed can there be any intermediate between contrary statements, but of one thing we must either assert or deny one thing, whatever it may be. This will be plain if we first define truth and falsehood. To say that what is is not, or that what is not is, is false; but to say that what is is, and what is not is not, is true; and therefore also he who says that a thing is or is not will say either what is true or what is false.

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But neither what is nor what is not is said not to be or to be. Further, an intermediate between contraries will be intermediate either as grey is between black and white, or as neither man nor horse is between man and horse. If in the latter sense, it cannot change (for change is from not-good to good, or from good to not-good);

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but in fact it is clearly always changing; for change can only be into the opposite and the intermediate. And if it is a true intermediate, in this case too there would be a kind of change into white not from not-white; but in fact this is not seen.It is not qua grey (i.e. intermediate between white and black) that grey changes to white, but qua not-white (i.e. containing a certain proportion of black). Further, the understanding either affirms or denies every object of understanding or thought (as is clear from the definitionAristot. Met. 4.7.1.)

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whenever it is right or wrong. When, in asserting or denying, it combines the predicates in one way, it is right; when in the other, it is wrong.

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Again, unless it is maintained merely for argument’s sake, the intermediate must exist beside all contrary terms; so that one will say what is neither true nor false. And it will exist beside what is and what is not; so that there will be a form of change beside generation and destruction.

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Again, there will also be an intermediate in all classes in which the negation of a term implies the contrary assertion; e.g., among numbers there will be a number which is neither odd nor not-odd. But this is impossible, as is clear from the definition.What definition Aristotle had in mind we cannot tell; but it must have stated that every number is either even or odd.

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Again, there will be an infinite progression, and existing things will be not only half as many again, but even more.

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For again it will be possible to deny the intermediate in reference both to its assertion and to its negation, and the result will be somethingIf besides A and not-A there is an intermediate B, besides B and not-B there will be an intermediate C which is neither B nor not-B; and so on.; for its essence is something distinct.

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Again, when a man is asked whether a thing is white and says no, he has denied nothing except that it is <white>, and its not-being <white> is a negation.

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Now this view has occurred to certain people in just the same way as other paradoxes have also occurred; for when they cannot find a way out from eristic arguments, they submit to the argument and admit that the conclusion is true. Some, then, hold the theory for this kind of reason, and others because they require an explanation for everything. In dealing with all such persons the starting-point is from definition;

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and definition results from the necessity of their meaning something; because the formula, which their term implies, will be a definition.Cf. Aristot. Met. 4.4.5, 6. The doctrine of Heraclitus, which says that everything is and is not,Cf. Aristot. Met. 4.3.10. seems to make all things true; and that of AnaxagorasCf. Aristot. Met. 4.4.28. seems to imply an intermediate in contradiction, so that all things are false; for when things are mixed, the mixture is neither good nor not-good; and so no statement is true.

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It is obvious from this analysis that the one-sided and sweeping statements which some people make cannot be substantially true—some maintaining that nothing is true (for they say that there is no reason why the same rule should not apply to everything as applies to the commensurability of the diagonal of a squareA stock example of impossibility and falsity; see Index.), and some that everything is true.

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These theories are almost the same as that of Heraclitus. For the theory which says that all things are true and all false also makes each of these statements separately; so that if they are impossible in combination they are also impossible individually. And again obviously there are contrary statements, which cannot be true at the same time. Nor can they all be false, although from what we have said, this might seem more possible.

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But in opposing all such theories we must demand, as was said in our discussion above,Aristot. Met. 4.4.5. not that something should be or not be, but some significant statement; and so we must argue from a definition, having first grasped what falsehood or truth means. And if to assert what is true is nothing else than to deny what is false, everything cannot be false; for one part of the contradiction must be true.

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Further, if everything must be either asserted or denied, both parts cannot be false; for one and only one part of the contradiction is false. Indeed, the consequence follows which is notorious in the case of all such theories, that they destroy themselves;

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for he who says that everything is true makes the opposite theory true too, and therefore his own untrue (for the opposite theory says that his is not true); and he who says that everything is false makes himself a liar.

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And if they make exceptions, the one that the opposite theory alone is not true, and the other that his own theory alone is not false, it follows none the less that they postulate an infinite number of true and false statements. For the statement that the true statement is true is also true; and this will go on to infinity.

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Nor, as is obvious, are those right who say that all things are at rest; nor those who say that all things are in motion. For if all things are at rest, the same things will always be true and false, whereas this state of affairs is obviously subject to change; for the speaker himself once did not exist, and again he will not exist. And if all things are in motion, nothing will be true, so everything will be false; but this has been proved to be impossible.

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Again, it must be that which is that changes, for change is from something into something. And further, neither is it true that all things are at rest or in motion sometimes, but nothing continuously; for there is something The sphere of the fixed stars; cf. Aristot. Met. 12.6, 12.7.1, 12.8.18. which always moves that which is moved, and the prime mover is itself unmoved.Cf. Aristot. Met. 12.7.

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Beginningἀρχή means starting-point, principle, rule or ruler. means: (a) That part of a thing from which one may first move; eg., a line or a journey has one beginning here , and another at the opposite extremity. (b) The point from which each thing may best come into being; e.g., a course of study should sometimes be begun not from what is primary or from the starting-point of the subject, but from the point from which it is easiest to learn. (c) That thing as a result of whose presence something first comes into being; e.g., as the keel is the beginning of a ship, and the foundation that of a house, and as in the case of animals some thinkers suppose the heartThis was Aristotle’s own view,Aristot. De Gen. An. 738b 16. to be the beginning, others the brain,So Plato held,Plat. Tim. 44 d. and others something similar, whatever it may be. (d) That from which, although not present in it, a thing first comes into being, and that from which motion and change naturally first begin, as the child comes from the father and mother, and fighting from abuse. (e) That in accordance with whose deliberate choice that which is moved is moved, and that which is changed is changed; such as magistracies, authorities, monarchies and despotisms.

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(f) Arts are also called beginnings,As directing principles. especially the architectonic arts. (g) Again, beginning means the point from which a thing is first comprehensible, this too is called the beginning of the thing; e.g. the hypotheses of demonstrations. (Cause can have a similar number of different senses, for all causes are beginnings. )

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It is a common property, then, of all beginnings to be the first thing from which something either exists or comes into being or becomes known; and some beginnings are originally inherent in things, while others are not. Hence nature is a beginning, and so is element and understanding and choice and essence and final cause—for in many cases the Good and the Beautiful are the beginning both of knowledge and of motion.

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Cause means: (a) in one sense, that as the result of whose presence something comes into being—e.g. the bronze of a statue and the silver of a cup, and the classessc. of material—metal, wood, etc. which contain these; (b) in another sense, the form or pattern; that is, the essential formula and the classes which contain it—e.g. the ratio 2:1 and number in general is the cause of the octave—and the parts of the formula.

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(c) The source of the first beginning of change or rest; e.g. the man who plans is a cause, and the father is the cause of the child, and in general that which produces is the cause of that which is produced, and that which changes of that which is changed. (d) The same as end; i.e. the final cause; e.g., as the end of walking is health.

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For why does a man walk? To be healthy, we say, and by saying this we consider that we have supplied the cause. (e) All those means towards the end which arise at the instigation of something else, as, e.g. fat-reducing, purging, drugs and instruments are causes of health; for they all have the end as their object, although they differ from each other as being some instruments, others actions.

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These are roughly all the meanings of cause, but since causes are spoken of with various meanings, it follows that there are several causes (and that not in an accidental sense) of the same thing. E.g., both statuary and bronze are causes of the statue; not in different connections, but qua statue. However, they are not causes in the same way, but the one as material and the other as the source of motion. And things are causes of each other; as e.g. labor of vigor, and vigor of labor—but not in the same way; the one as an end , and the other as source of motion .

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And again the same thing is sometimes the cause of contrary results; because that which by its presence is the cause of so-and-so we sometimes accuse of being, by its absence, the cause of the contrary—as, e.g., we say that the absence of the pilot is the cause of a capsize, whereas his presence was the cause of safety.

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And both, presence and privation, are moving causes.

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Now there are four senses which are most obvious under which all the causes just described may be classed.

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The components of syllables; the material of manufactured articles; fire, earth and all such bodies; the parts of a whole; and the premisses of a syllogistic conclusion; are causes in the material sense. Of these some are causes as substrate: e.g. the parts; and others as essence : the whole, and the composition, and the form.

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The seed and the physician and the contriver and in general that which produces, all these are the source of change or stationariness. The remainder represent the end and good of the others; for the final cause tends to be the greatest good and end of the rest.

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Let it be assumed that it makes no difference whether we call it good or apparent good. In kind , then, there are these four classes of cause.

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The modes of cause are numerically many, although these too are fewer when summarized.

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For causes are spoken of in many senses, and even of those which are of the same kind, some are causes in a prior and some in a posterior sense; e.g., the physician and the expert are both causes of health; and the ratio 2:1 and number are both causes of the octave; and the universals which include a given cause are causes of its particular effects.

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Again, a thing may be a cause in the sense of an accident, and the classes which contain accidents; e.g., the cause of a statue is in one sense Polyclitus and in another a sculptor, because it is an accident of the sculptor to be Polyclitus. And the universal terms which include accidents are causes; e.g., the cause of a statue is a man, or even, generally, an animal; because Polyclitus is a man, and man is an animal.

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And even of accidental causes some are remoter or more proximate than others; e.g., the cause of the statue might be said to be white man or cultured man, and not merely Polyclitus or man.

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And besides the distinction of causes as proper and accidental , some are termed causes in a potential and others in an actual sense; e.g., the cause of building is either the builder or the builder who builds.

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And the same distinctions in meaning as we have already described will apply to the effects of the causes; e.g. to this statue, or a statue, or generally an image; and to this bronze, or bronze, or generally material.Effects, just like causes (10), may be particular or general. The metal-worker produces (a) the bronze for a particular statue by the sculptor, (b) bronze for a statue, (c) metal for an image. And it is the same with accidental effects. Again, the proper and accidental senses will be combined; e.g., the cause is neither Polyclitus nor a sculptor but the sculptor Polyclitus.

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However, these classes of cause are in all six in number, each used in two senses. Causes are (1.) particular, (2.) generic, (3.) accidental, (4.) generically accidental; and these may be either stated singly or (5, 6) in combinationThe cause of a statue may be said to be (1) a sculptor, (2) an artist, (3) Polyclitus, (4) a man, (5) the sculptor Polyclitus (combination of (1) and (3)), (6) an artistic man (combination of (2) and (4)).; and further they are all either actual or potential.

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And there is this difference between them, that actual and particular causes coexist or do not coexist with their effects (e.g. this man giving medical treatment with this man recovering his health, and this builder with this building in course of erection); but potential causes do not always do so; for the house and the builder do not perish together.

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Element means (a) the primary immanent thing, formally indivisible into another form, of which something is composed. E.g., the elements of a sound are the parts of which that sound is composed and into which it is ultimately divisible, and which are not further divisible into other sounds formally different from themselves. If an element be divided, the parts are formally the same as the whole: e.g., a part of water is water; but it is not so with the syllable.

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(b) Those who speak of the elements of bodies similarly mean the parts into which bodies are ultimately divisible, and which are not further divisible into other parts different in form. And whether they speak of one such element or of more than one, this is what they mean.

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(c) The term is applied with a very similar meaning to the elements of geometrical figures, and generally to the elements of demonstrations; for the primary demonstrations which are contained in a number of other demonstrations are called elements of demonstrations.Cf. Aristot. Met. 3.3.1. Such are the primary syllogisms consisting of three terms and with one middle term.

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(d) The term element is also applied metaphorically to any small unity which is useful for various purposes; and so that which is small or simple or indivisible is called an element.

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(e) Hence it comes that the most universal things are elements; because each of them, being a simple unity, is present in many things—either in all or in as many as possible. Some too think that unity and the point are first principles.

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(f) Therefore since what are called generaThis must refer to the highest genera, which have no definition because they cannot be analyzed into genus and differentia ( Ross). are universal and indivisible (because they have no formula), some people call the genera elements, and these rather than the differentia, because the genus is more universal. For where the differentia is present, the genus also follows; but the differentia is not always present where the genus is. And it is common to all cases that the element of each thing is that which is primarily inherent in each thing.

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NatureOn the meaning of φύσις cf. Burnet, E.G.P. pp. 10-12, 363-364. means: (a) in one sense, the genesis of growing things—as would be suggested by pronouncing the υ of φύσις long—and (b) in another, that immanent thingProbably the seed (Bonitz). from which a growing thing first begins to grow. (c) The source from which the primary motion in every natural object is induced in that object as such. All things are said to grow which gain increase through something else by contact and organic unity (or adhesion, as in the case of embryos).

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Organic unity differs from contact; for in the latter case there need be nothing except contact, but in both the things which form an organic unity there is some one and the same thing which produces, instead of mere contact, a unity which is organic, continuous and quantitative (but not qualitative).

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Again, nature means (d) the primary stuff, shapeless and unchangeable from its own potency, of which any natural object consists or from which it is produced; e.g., bronze is called the nature of a statue and of bronze articles, and wood that of wooden ones, and similarly in all other cases.

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For each article consists of these natures, the primary material persisting. It is in this sense that men call the elements of natural objects the nature, some calling it fire, others earth or air or water, others something else similar, others some of these, and others all of them.

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Again in another sense nature means (e) the substance of natural objects; as in the case of those who say that the nature is the primary composition of a thing, or as Empedocles says: Of nothing that exists is there nature, but only mixture and separation of what has been mixed; nature is but a name given to these by men.Empedocles Fr. 8 (Diels).

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Hence as regards those things which exist or are produced by nature, although that from which they naturally are produced or exist is already present, we say that they have not their nature yet unless they have their form and shape.

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That which comprises both of these exists by nature; e.g. animals and their parts. And nature is both the primary matter (and this in two senses: either primary in relation to the thing, or primary in general; e.g., in bronze articles the primary matter in relation to those articles is bronze, but in general it is perhaps water—that is if all things which can be melted are water) and the form or essence, i.e. the end of the process, of generation. Indeed from this sense of nature, by an extension of meaning, every essence in general is called nature, because the nature of anything is a kind of essence.

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From what has been said, then, the primary and proper sense of nature is the essence of those things which contain in themselves as such a source of motion; for the matter is called nature because it is capable of receiving the nature, and the processes of generation and growth are called nature because they are motions derived from it. And nature in this sense is the source of motion in natural objects, which is somehow inherent in them, either potentially or actually.

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Necessary means: (a) That without which, as a concomitant condition, life is impossible; e.g. respiration and food are necessary for an animal, because it cannot exist without them. (b) The conditions without which good cannot be or come to be, or without which one cannot get rid or keep free of evil—e.g., drinking medicine is necessary to escape from ill-health, and sailing to Aegina is necessary to recover one’s money.

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(c) The compulsory and compulsion; i.e. that which hinders and prevents, in opposition to impulse and purpose. For the compulsory is called necessary, and hence the necessary is disagreeable; as indeed EvenusOf Poros; sophist and poet, contemporary with Socrates. says: For every necessary thing is by nature grievous. Evenus Fr. 8 (Hiller).

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And compulsion is a kind of necessity, as Sophocles says: Compulsion makes me do this of necessity. Soph. El. 256 (the quotation is slightly inaccurate).

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And necessity is held, rightly, to be something inexorable; for it is opposed to motion which is in accordance with purpose and calculation. (d) Again, what cannot be otherwise we say is necessarily so.

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It is from this sense of necessary that all others are somehow derived; for the term compulsory is used of something which it is necessary for one to do or suffer only when it is impossible to act according to impulse, because of the compulsion: which shows that necessity is that because of which a thing cannot be otherwise; and the same is true of the concomitant conditions of living and of the good. For when in the one case good, and in the other life or existence, is impossible without certain conditions, these conditions are necessary, and the cause is a kind of necessity.

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(e) Again, demonstration is a necessary thing, because a thing cannot be otherwise if the demonstration has been absolute. And this is the result of the first premisses, when it is impossible for the assumptions upon which the syllogism depends to be otherwise.

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Thus of necessary things, some have an external cause of their necessity, and others have not, but it is through them that other things are of necessity what they are.

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Hence the necessary in the primary and proper sense is the simple , for it cannot be in more than one condition. Hence it cannot be in one state and in another; for if so it would ipso facto be in more than one condition. Therefore if there are certain things which are eternal and immutable, there is nothing in them which is compulsory or which violates their nature.

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The term one is used (1.) in an accidental, (2.) in an absolute sense. (1.) In the accidental sense it is used as in the case of CoriscusCoriscus of Scepsis was a Platonist with whom Aristotle was probably acquainted; but the name is of course chosen quite arbitrarily. and cultured and cultured Coriscus (for Coriscus and cultured and cultured Coriscus mean the same);

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and cultured and upright and cultured upright Coriscus. For all these terms refer accidentally to one thing; upright and cultured because they are accidental to one substance, and cultured and Coriscus because the one is accidental to the other.

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And similarly in one sense cultured Coriscus is one with Coriscus, because one part of the expression is accidental to the other, e.g. cultured to Coriscus; and cultured Coriscus is one with upright Coriscus,

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because one part of each expression is one accident of one and the same thing. It is the same even if the accident is applied to a genus or a general term; e.g., man and cultured man are the same, either because cultured is an accident of man, which is one substance, or because both are accidents of some individual, e.g. Coriscus.

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But they do not both belong to it in the same way; the one belongs presumably as genus in the substance, and the other as condition or affection of the substance. Thus all things which are said to be one in an accidental sense are said to be so in this way.

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(2.) Of those things which are said to be in themselves one, (a) some are said to be so in virtue of their continuity; e.g., a faggot is made continuous by its string, and pieces of wood by glue; and a continuous line, even if it is bent, is said to be one, just like each of the limbs; e.g. the leg or arm. And of these things themselves those which are naturally continuous are one in a truer sense than those which are artificially continuous.

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Continuous means that whose motion is essentially one, and cannot be otherwise; and motion is one when it is indivisible, i.e. indivisible in time . Things are essentially continuous which are one not by contact only; for if you put pieces of wood touching one another you will not say that they are one piece of wood, or body, or any other continuous thing.

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And things which are completely continuous are said to be one even if they contain a joint, and still more those things which contain no joint; e.g., the shin or the thigh is more truly one than the leg, because the motion of the leg may not be one.

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And the straight line is more truly one than the bent. We call the line which is bent and contains an angle both one and not one, because it may or may not move all at once; but the straight line always moves all at once, and no part of it which has magnitude is at rest while another moves, as in the bent line.

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(b) Another sense of one is that the substrate is uniform in kind.

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Things are uniform whose form is indistinguishable to sensation; and the substrate is either that which is primary, or that which is final in relation to the end. For wine is said to be one, and water one, as being something formally indistinguishable. And all liquids are said to be one (e.g. oil and wine), and melted things; because the ultimate substrate of all of them is the same, for all these things are water or vapor.

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(c) Things are said to be one whose genus is one and differs in its opposite differentiae. All these things too are said to be one because the genus, which is the substrate of the differentiae, is one (e.g., horse, man and dog are in a sense one, because they are all animals); and that in a way very similar to that in which the matter is one.

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Sometimes these things are said to be one in this sense, and sometimes their higher genus is said to be one and the same (if they are final species of their genus)—the genus, that is, which is above the genera of which their proximate genus is one; e.g., the isosceles and equilateral triangles are one and the same figure (because they are both triangles), but not the same triangles.

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(d) Again, things are said to be one when the definition stating the essence of one is indistinguishable from a definition explaining the other; for in itself every definition is distinguishable <into genus and differentiae>. In this way that which increases and decreases is one, because its definition is one; just as in the case of planes the definition of the form is one.

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And in general those things whose concept, which conceives the essence, is indistinguishable and cannot be separated either in time or in place or in definition, are in the truest sense one; and of these such as are substances are most truly one. For universally such things as do not admit of distinction are called one in so far as they do not admit of it; e.g., if man qua man does not admit of distinction, he is one man; and similarly if qua animal, he is one animal; and if qua magnitude, he is one magnitude.

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Most things, then, are said to be one because they produce, or possess, or are affected by, or are related to, some other one thing; but some are called one in a primary sense, and one of these is substance. It is one either in continuity or in form or in definition; for we reckon as more than one things which are not continuous, or whose form is not one, or whose definition is not one.

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Again, in one sense we call anything whatever one if it is quantitative and continuous; and in another sense we say that it is not one unless it is a whole of some kind, i.e. unless it is one in form (e.g., if we saw the parts of a shoe put together anyhow, we should not say that they were one — except in virtue of their continuity; but only if they were so put together as to be a shoe, and to possess already some one form).

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Hence the circumference of a circle is of all lines the most truly one, because it is whole and complete.

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The essence of one is to be a kind of starting point of number; for the first measure is a starting point, because that by which first we gain knowledge of a thing is the first measure of each class of objects. The one, then, is the starting-point of what is knowable in respect of each particular thing. But the unit is not the same in all classes,

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for in one it is the quarter-tone, and in another the vowel or consonant; gravity has another unit, and motion another. But in all cases the unit is indivisible, either quantitatively or formally.

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Thus that which is quantitatively and qua quantitative wholly indivisible and has no position is called a unit; and that which is wholly indivisible and has position, a point; that which is divisible in one sense, a line; in two senses, a plane; and that which is quantitatively divisible in all three senses, a body.

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And reversely that which is divisible in two senses is a plane, and in one sense a line; and that which is in no sense quantitatively divisible is a point or a unit; if it has no position, a unit, and if it has position, a point.

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Again, some things are one numerically, others formally, others generically, and others analogically; numerically, those whose matter is one; formally, those whose definition is one; generically, those which belong to the same category; and analogically, those which have the same relation as something else to some third object.

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In every case the latter types of unity are implied in the former: e.g., all things which are one numerically are also one formally, but not all which are one formally are one numerically; and all are one generically which are one formally, but such as are one generically are not all one formally, although they are one analogically; and such as are one analogically are not all one generically.

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It is obvious also that many will have the opposite meanings to one. Some things are called many because they are not continuous; others because their matter (either primary or ultimate) is formally divisible; others because the definitions of their essence are more than one.

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Being means (1.) accidental being, (2.) absolute being. (1.) E.g., we say that the upright person is cultured, and that the man is cultured, and that the cultured person is a man; very much as we say that the cultured person builds, because the builder happens to be cultured, or the cultured person a builder; for in this sense X is Y means that Y is an accident of X.

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And so it is with the examples cited above; for when we say that the man is cultured and the cultured person is a man or the white is cultured or the cultured is white, in the last two cases it is because both predicates are accidental to the same subject, and in the first case because the predicate is accidental to what is ; and we say that the cultured is a man because the cultured is accidental to a man.

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(Similarly not-white is said to be, because the subject of which not-white is an accident, is .) These, then, are the senses in which things are said to be accidentally: either because both predicates belong to the same subject, which is ; or because the predicate belongs to the subject, which is ; or because the subject to which belongs that of which it is itself predicated itself is .

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(2.) The senses of essential being are those which are indicated by the figures of predicationThe categories. For the full list of these see Aristot. Categories 1b 25-27.; for being has as many senses as there are ways of predication. Now since some predicates indicate (a) what a thing is, and others its (b) quality, (c) quantity, (d) relation, (e) activity or passivity, (f) place, (g) time, to each of these corresponds a sense of being.

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There is no difference between the man is recovering and the man recovers; or between the man is walking or cutting and the man walks or cuts; and similarly in the other cases.

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(3.) Again, to be and is mean that a thing is true, and not to be that it is false.

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Similarly too in affirmation and negation; e.g., in Socrates is cultured is means that this is true; or in Socrates is not-white that this is true; but in the diagonal is not commensurableCf. Aristot. Met. 1.2.15.is not means that the statement is false. (4.) Again, to be <or is> means that some of these statements can be made in virtue of a potentiality and others in virtue of an actuality.

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For we say that both that which sees potentially and that which sees actually is a seeing thing. And in the same way we call understanding both that which can use the understanding, and that which does ; and we call tranquil both that in which tranquillity is already present, and that which is potentially tranquil.

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Similarly too in the case of substances. For we say that Hermes is in the stone,Cf. Aristot. Met. 3.5.6. and the half of the line in the whole; and we call corn what is not yet ripe. But when a thing is potentially existent and when not, must be defined elsewhere.Aristot. Met. 9.9.

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Substance means (a) simple bodies, e.g. earth, fire, water and the like; and in general bodies, and the things, animal or divine, including their parts, which are composed of bodies. All these are called substances because they are not predicated of any substrate, but other things are predicated of them.

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(b) In another sense, whatever, being immanent in such things as are not predicated of a substrate, is the cause of their being; as, e.g., the soul is the cause of being for the animal.

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(c) All parts immanent in things which define and indicate their individuality, and whose destruction causes the destruction of the whole; as, e.g., the plane is essential to the body (as someThe Pythagoreans and Platonists. hold) and the line to the plane. And number in general is thought by someThe Pythagoreans and Platonists. to be of this nature, on the ground that if it is abolished nothing exists, and that it determines everything.

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(d) Again, the essence , whose formula is the definition, is also called the substance of each particular thing.

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Thus it follows that substance has two senses: the ultimate subject, which cannot be further predicated of something else; and whatever has an individual and separate existence. The shape and form of each particular thing is of this nature.

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The same means (a) accidentally the same. E.g., white and cultured are the same because they are accidents of the same subject; and man is the same as cultured, because one is an accident of the other; and cultured is the same as man because it is an accident of man; and cultured man is the same as each of the terms cultured and man, and vice versa; for both man and cultured are used in the same way as cultured man, and the latter in the same way as the former.

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Hence none of these predications can be made universally. For it is not true to say that every man is the same as the cultured; because universal predications are essential to things, but accidental predications are not so, but are made of individuals and with a single application. Socrates and cultured Socrates seem to be the same; but Socrates is not a class-name, and hence we do not say every Socrates as we say every man.

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Some things are said to be the same in this sense, but (b) others in an essential sense, in the same number of senses as the one is essentially one; for things whose matter is formally or numerically one, and things whose substance is one, are said to be the same. Thus sameness is clearly a kind of unity in the being, either of two or more things, or of one thing treated as more than one; as, e.g., when a thing is consistent with itself; for it is then treated as two.

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Things are called other of which either the forms or the matter or the definition of essence is more than one; and in general other is used in the opposite senses to same.

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Things are called different which, while being in a sense the same, are other not only numerically, but formally or generically or analogically; also things whose genus is not the same; and contraries; and all things which contain otherness in their essence.

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Things are called like which have the same attributes in all respects; or more of those attributes the same than different; or whose quality is one. Also that which has a majority or the more important of those attributes of something else in respect of which change is possible (i.e. the contraries) is like that thing. And unlike is used in the opposite senses to like.

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The term opposite is applied to (a) contradiction; (b) contraries; (c) relative terms; (d) privation; (e) state; (f) extremes; e.g. in the process of generation and destruction. And (g) all things which cannot be present at the same time in that which admits of them both are called opposites; either themselves or their constituents. Grey and white do not apply at the same time to the same thing, and hence their constituents are opposite.

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Contrary means: (a) attributes, generically different, which cannot apply at the same time to the same thing. (b) The most different attributes in the same genus; or (c) in the same subject; or (d) falling under the same faculty. (e) Things whose difference is greatest absolutely, or in genus, or in species.

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Other things are called contrary either because they possess attributes of this kind, or because they are receptive of them, or because they are productive of or liable to them, or actually produce or incur them, or are rejections or acquisitions or possessions or privations of such attributes.

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And since one and being have various meanings, all other terms which are used in relation to one and being must vary in meaning with them; and so same, other and contrary must so vary, and so must have a separate meaning in accordance with each category.

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Things are called other in species (a) which belong to the same genus and are not subordinate one to the other; or (b) which are in the same genus and contain a differentia; or (c) which contain a contrariety in their essence.

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(d) Contraries, too (either all of them or those which are called so in a primary sense), are other in species than one another; and (e) so are all things of which the formulae are different in the final species of the genus (e.g., man and horse are generically indivisible, but their formulae are different); and (f) attributes of the same substance which contain a difference. The same in species has the opposite meanings to these.

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Prior and posterior mean: (1.) (a) In one sense (assuming that there is in each genus some primary thing or starting-point) that which is nearer to some starting-point, determined either absolutely and naturally, or relatively, or locally, or by some agency; e.g., things are prior in space because they are nearer either to some place naturally determined, such as the middle or the extreme, or to some chance relation; and that which is further is posterior.

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(b) In another sense, prior or posterior in time . Some things are prior as being further from the present, as in the case of past events (for the Trojan is prior to the Persian war, because it is further distant from the present); and others as being nearer the present, as in the case of future events (for the Nemean are prior to the Pythian games because they are nearer to the present, regarded as a starting-point and as primary).

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(c) In another sense, in respect of motion (for that which is nearer to the prime mover is prior; e.g., the boy is prior to the man). This too is a kind of starting point in an absolute sense. (d) In respect of potency; for that which is superior in potency, or more potent, is prior. Such is that in accordance with whose will the other, or posterior, thing must follow, so that according as the former moves or does not move, the latter is or is not moved. And the will is a starting-point.

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(e) In respect of order; such are all things which are systematically arranged in relation to some one determinate object. E.g., he who is next to the leader of the chorus is prior to him who is next but one, and the seventh string is prior to the eighthThe octachord to which Aristotle refers was composed of the following notes: E (ὑπάτη ) F (παρυπάτη) G (λιχανός) A (μέση) B (παραμέση) C (τρίτη) D (παρανήτη) E (νήτη).; for in one case the leader is the starting-point, and in the other the middleStrictly speaking there was no middle string in the octachord; the name was taken over from the earlier heptachord EFGABbCD, in which there was no παραμέση. The μέση was apparently what we should call the tonic. Cf. Aristot. Met. 14.6.5; Aristot. Problemata 919b 20. string.

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In these examples prior has this sense; but (2.) in another sense that which is prior in knowledge is treated as absolutely prior; and of things which are prior in this sense the prior in formula are different from the prior in perception . Universals are prior in formula, but particulars in perception. And in formula the attribute is prior to the concrete whole: e.g. cultured to the cultured man; for the formula will not be a whole without the part.

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Yet cultured cannot exist apart from some cultured person.

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Again, (3.) attributes of prior subjects are called prior; e.g., straightness is prior to smoothness, because the former is an attribute of the line in itself, and the latter of a surface.

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Some things, then, are called prior and posterior in this sense; but others (iv.) in virtue of their nature and substance, namely all things which can exist apart from other things, whereas other things cannot exist without them. This distinction was used by Plato.Not, apparently, in his writings.(And since being has various meanings, (a) the substrate, and therefore substance, is prior; (b) potential priority is different from actual priority.

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Some things are prior potentially, and some actually; e.g., potentially the half-line is prior to the whole, or the part to the whole, or the matter to the substance; but actually it is posterior, because it is only upon dissolution that it will actually exist.)

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Indeed, in a sense all things which are called prior or posterior are so called in this connection; for some things can exist apart from others in generation (e.g. the whole without the parts), and others in destruction (e.g. the parts without the whole). And similarly with the other examples.

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PotencyOr capacity or potentiality. means: (a) the source of motion or change which is in something other than the thing changed, or in it qua other. E.g., the science of building is a potency which is not present in the thing built; but the science of medicine, which is a potency, may be present in the patient, although not qua patient.

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Thus potency means the source in general of change or motion in another thing, or in the same thing qua other; or the source of a thing’s being moved or changed by another thing, or by itself qua other (for in virtue of that principle by which the passive thing is affected in any way we call it capable of being affected; sometimes if it is affected at all, and sometimes not in respect of every affection, but only if it is changed for the better).

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(b) The power of performing this well or according to intention; because sometimes we say that those who can merely take a walk, or speak, without doing it as well as they intended, cannot speak or walk. And similarly in the case of passivity.

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(c) All states in virtue of which things are unaffected generally, or are unchangeable, or cannot readily deteriorate, are called potencies. For things are broken and worn out and bent and in general destroyed not through potency but through impotence and deficiency of some sort; and things are unaffected by such processes which are scarcely or slightly affected because they have a potency and are potent and are in a definite state.

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Since potency has all these meanings, potent (or capable) will mean (a) that which contains a source of motion or change (for even what is static is potent in a sense) which takes place in another thing, or in itself qua other. (b) That over which something else has a potency of this kind. (c) That which has the potency of changing things, either for the worse or for the better (for it seems that even that which perishes is capable of perishing; otherwise, if it had been incapable, it would not have perished. As it is, it has a kind of disposition or cause or principle which induces such an affection.

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Sometimes it seems to be such as it is because it has something, and sometimes because it is deprived of something; but if privation is in a sense a state or habit, everything will be potent through having something; and so a thing is potent in virtue of having a certain habit or principle, and also in virtue of having the privation of that habit, if it can have privation; and if privation is not in a sense habit, the term potent is equivocal).

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(d) A thing is potent if neither any other thing nor itself qua other contains a potency or principle destructive of it. (e) All these things are potent either because they merely might chance to happen or not to happen, or because they might do so well . Even in inanimate things this kind of potency is found; e.g. in instruments; for they say that one lyre can be played, and another not at all, if it has not a good tone.

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Impotence is a privation of potency—a kind of abolition of the principle which has been described—either in general or in something which would naturally possess that principle, or even at a time when it would naturally already possess it (for we should not use impotence—in respect of begetting—in the same sense of a boy, a man and a eunuch). Again, there is an impotence corresponding to each kind of potency; both to the kinetic and to the successfully kinetic.

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Some things are said to be impotent in accordance with this meaning of impotence, but others in a different sense, namely possible and impossible. Impossible means: (a) that whose contrary is necessarily true; e.g., it is impossible that the diagonal of a square should be commensurable with the sides, because such a thing is a lie, whose contrary is not only true but inevitable. Hence that it is commensurable is not only a lie but necessarily a lie.

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And the contrary of the impossible, i.e. the possible, is when the contrary is not necessarily a lie; e.g., it is possible that a man should be seated, for it is not necessarily a lie that he should not be seated. Possible, then, means in one sense, as we have said, that which is not necessarily a lie; in another, that which is true; and in another, that which may be true.

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(The power in geometryA square was called a δύναμις. Plat. Rep 587d; Plat. Tim. 31c. is so called by an extension of meaning.)

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These are the senses of potent which do not correspond to potency. Those which do correspond to it all refer to the first meaning, i.e. a source of change which exists in something other than that in which the change takes place, or in the same thing qua other.

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Other things are said to be potentsc. in a passive sense, which the English word potent cannot bear. because something else has such a potency over them; others because it does not possess it; others because it possesses it in a particular way. The term impotent is similarly used. Thus the authoritative definition of potency in the primary sense will be a principle producing change, which is in something other than that in which the change takes place, or in the same thing qua other.

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Quantity means that which is divisible into constituent parts, eachi.e., if there are only two. or every one of which is by nature some one individual thing. Thus plurality, if it is numerically calculable, is a kind of quantity; and so is magnitude, if it is measurable. Plurality means that which is potentially divisible into non-continuous parts; and magnitude that which is potentially divisible into continuous parts. Of kinds of magnitude, that which is continuous in one direction is length; in two directions, breadth; in three, depth.

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And of these, plurality, when limited, is a number; length, a line; breadth, a plane; depth, a body. Again, some things are essentially quantitative, but others only accidentally; e.g. the line is essentially, but cultured accidentally quantitative.

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And of the former class some are quantitative in virtue of their substance, e.g. the fine (because the definition which describes it is quantitative in some form); and others are attributes and conditions of a substance of this kind— e.g., much and little, long and short, broad and narrow, deep and shallow, heavy and light, etc.

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Moreover, great and small, and greater and smaller, whether used absolutely or relatively to one another, are essential attributes of quantity; by an extension of meaning, however, these terms are also applied to other things.

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Of things called quantitative in an accidental sense, one kind is so called in the sense in which we said above that cultured or white is quantitative—because the subject to which they belong is quantitative; and others in the sense that motion and time are so called—for these too are said in a sense to be quantitative and continuous, since the subjects of which they are attributes are divisible. I mean, not the thing moved, but that through or along which the motion has taken place; for it is because the latter is quantitative that the motion is quantitative, and because the motion is quantitative that the time is also.

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Quality means (a) in one sense, the differentia of essence; e.g., a man is an animal of a certain quality because he is two-footed; and so is a horse, because it is four-footed. Also a circle is a geometrical figure of a certain quality, because it has no angles; which shows that the essential differentia is quality.

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In this one sense, then, quality means differentia of essence; but (b) in another it is used as of immovable and mathematical objects, in the sense that numbers are in a way qualitative—e.g. such as are composite and are represented geometrically not by a line but by a plane or solid (these are products respectively of two and of three factors)—and in general means that which is present besides quantity in the essence. For the essence of each number is that which goes into it once; e.g. that of 6 is not what goes twice or three times, but what goes once; for 6 is once 6.

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(c) All affections of substance in motion in respect of which bodies become different when they (the affections) change—e.g. heat and cold, whiteness and blackness, heaviness and lightness, etc. (d) The term is used with reference to goodness and badness, and in general to good and bad.

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Thus there are, roughly speaking, two meanings which the term quality can bear, and of these one is more fundamental than the other. Quality in the primary sense is the differentia of the essence; and quality in numbers falls under this sense, because it is a kind of differentia of essences, but of things either not in motion or not qua in motion. Secondly, there are the affections of things in motion qua in motion, and the differentiae of motions.

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Goodness and badness fall under these affections, because they denote differentiae of the motion or functioning in respect of which things in motion act or are acted upon well or badly. For that which can function or be moved in such-and-such a way is good, and that which can function in such-and-such a way and in the contrary way is bad. Quality refers especially to good and bad in the case of living things, and of these especially in the case of such as possess choice.

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Things are called relative (a) In the sense that the double is relative to the half, and the triple to the third; and in general the many times greater to the many times smaller, and that which exceeds to the thing exceeded. (b) In the sense that the thing which heats or cuts is relative to the thing heated or cut; and in general the active to the passive. (c) In the sense that the measurable is relative to the measure, and the knowable to knowledge, and the sensible to sensation.

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(a) In the first sense they are said to be numerically relative; either simply, or in a definite relation to numbers or to 1. E.g., the double in relation to 1 is a definite number; the many times as great is in a numerical relation to 1, but not in a definite relation such as this or that;

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the relation of that which is 1.5 times something else to that something is a definite numerical relation to a number; and that which is (n+1)/n times something else is in an indefinite relation to a number, just as the many times as great is in an indefinite relation to 1.

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The relation of that which exceeds to that which is exceeded is numerically quite indefinite, for number is commensurate, and is not predicated of the incommensurate; whereas that which exceeds, in relation to that which is exceeded, is so much plus something more; and this something more is indefinite, for it is indifferently equal or not equal to the so much.

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Thus not only are all these things said to be relative in respect of number, but also the equal and like and same, though in another way: for all these terms are used in respect of one. Things are the same whose essence is one; like whose quality is one; equal whose quantity is one. Now one is the starting-point and standard of number; and so all these relations involve number, though not all in the same way.

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(b) Active and passive things are called relative in virtue of an active or passive potentiality or actualization of the potentialities; e.g., that which can heat is called relative to that which can be heated, because it can heat; and again the thing heating is called relative to the thing heated, and the thing cutting to the thing cut, because their potentialities are actualized. Numerical relations, on the other hand, are not actualized (except as has been described elsewhere)The reference is quite uncertain, but cf. Aristot. Met. 9.9.4, 5. The point is that the actualization of a numerical (or geometrical) relation does not imply an active functioning, as in the case of the potentialities just described.; they have no actualizations in respect of motion.

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Of things potentially relative, some are further relative in respect of particular times; as, e.g., that which has made or will make is relative to that which has been or will be made. It is in this way that a father is called father of a son; the one has acted, and the other has been acted upon, in a particular way. Again, some things are relative in virtue of a privation of their potentiality; such is the impossible and all similar terms, e.g. the invisible.

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Thus relative terms which involve number and potentiality are all relative because their very essence contains a reference to something else; but not because something else is related to their essence. But (c) that which is measurable or knowable or thinkable is called relative because something else is related to its essence.

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For thinkable signifies that there is a thought which thinks it; but thought is not relative to that of which it is the thought (for then the same thing would have been said twice). And similarly sight is the sight of something; not of that of which it is the sight, although this is of course true—it is relative to some color or other similar thing.

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To describe it in the other way—the sight of the object of sight—would be to say the same thing twice. Things, then, which are called relative of their own nature are so called, some in these senses, and others because the classes which contain them are of this kind. E.g., medicine is reckoned as relative because its genus, science, is thought to be a relative thing.

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Further, there are the properties in virtue of which the things which possess them are called relative; e.g., equality is relative because the equal is relative, and similarity because the similar is relative. Other things are accidentally relative; e.g., a man is relative because he happens to be double something else, and double is a relative term; or white is relative if the same thing happens to be white as well as double.

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Perfect <or complete> means: (a) That outside which it is impossible to find even a single one of its parts; e.g., the complete time of each thing is that outside which it is impossible to find any time which is a part of it. (b) That which, in respect of goodness or excellence, cannot be surpassed in its kind; e.g., a doctor and a musician are perfect when they have no deficiency in respect of the form of their peculiar excellence.

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And thus by an extension of the meaning we use the term in a bad connection, and speak of a perfect humbug and a perfect thief; since indeed we call them good— e.g. a good thief and a good humbug.

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(c) And goodness is a kind of perfection. For each thing, and every substance, is perfect when, and only when, in respect of the form of its peculiar excellence, it lacks no particle of its natural magnitude. (d) Things which have attained their end, if their end is good, are called perfect; for they are perfect in virtue of having attained the end.

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Hence, since the end is an ultimate thing, we extend the meaning of the term to bad senses, and speak of perishing perfectly or being perfectly destroyed, when the destruction or calamity falls short in no respect but reaches its extremity. Hence, by an extension of the meaning, death is called an end, because they are both ultimate things. And the ultimate object of action is also an end.

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Things, then, which are called perfect in themselves are so called in all these senses; either because in respect of excellence they have no deficiency and cannot be surpassed, and because no part of them can be found outside them; or because, in general, they are unsurpassed in each particular class, and have no part outside. All other things are so called in virtue of these, because they either produce or possess something of this kind, or conform to it, or are referred in some way or other to things which are perfect in the primary sense.

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Limit means: (a) The furthest part of each thing, and the first point outside which no part of a thing can be found, and the first point within which all parts are contained. (b) Any form of magnitude or of something possessing magnitude.

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(c) The end of each thing. (This end is that to which motion and action proceed, and not the end from which. But sometimes it is both the end from which and the end to which, i.e. the final cause.) (d) The reality or essence of each thing; for this is the limit of our knowledge of it, and if it is a limit of the knowledge, it is also a limit of the thing. Thus it is obvious that limit has not only as many senses as beginning but even more; because the beginning is a kind of limit, but not every limit is a beginning.

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That in virtue of which has various meanings. (a) The form or essence of each individual thing; e.g., that in virtue of which a man is good is goodness itself. (b) The immediate substrate in which a thing is naturally produced; as, e.g., color is produced in the surface of things. Thus that in virtue of which in the primary sense is the form , and in the secondary sense, as it were, the matter of each thing, and the immediate substrate.

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And in general that in virtue of which will exist in the same number of senses as cause. For we say indifferently in virtue of what has he come? or for what reason has he come? and in virtue of what has he inferred or inferred falsely? or what is the cause of his inference or false inference? (And further, there is the positional sense of καθ’ ὅ, in which he stands, or in which he walks; all these examples denote place or position.)

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Hence in virtue of itself must also have various meanings. It denotes (a) The essence of each particular; e.g., Callias is in virtue of himself Callias and the essence of Callias. (b) Everything contained in the definition; e.g., Callias is in virtue of himself an animal, because animal is present in the definition, since Callias is a kind of animal.

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(c) Any attribute which a thing has received directly in itself or in any of its parts; e.g., the surface is white in virtue of itself; and man lives in virtue of himself, because the soul is a part of the man, and life is directly contained in it. (d) That which has no other cause. Man has many causes: animal, twofooted, etc.; but nevertheless man is in virtue of himself man. (e) All things which belong to a thing alone and qua alone; and hence that which is separate is in virtue of itself. This seems to be a slightly irrelevant reference to καθ’ ἁυτό in the sense of independent; but corruption in the text has made the true reading uncertain.

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Disposition means arrangement of that which has parts, either in space or in potentiality or in form. It must be a kind of position, as indeed is clear from the word, disposition.

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Havingἕξις means not only having but habit or state. Cf. Latin, habitus. means (a) In one sense an activity, as it were, of the haver and the thing had, or as in the case of an action or motion; for when one thing makes and another is made, there is between them an act of making. In this way between the man who has a garment and the garment which is had, there is a having. Clearly, then, it is impossible to have a having in this sense; for there will be an infinite series if we can have the having of what we have.

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But (b) there is another sense of having which means a disposition, in virtue of which the thing which is disposed is disposed well or badly, and either independently or in relation to something else. E.g., health is a state, since it is a disposition of the kind described. Further, any part of such a disposition is called a state; and hence the excellence of the parts is a kind of state.

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Affection means (a) In one sense, a quality in virtue of which alteration is possible; e.g., whiteness and blackness, sweetness and bitterness, heaviness and lightness, etc. (b) The actualizations of these qualities; i.e. the alterations already realized. (c) More particularly, hurtful alterations and motions, and especially hurts which cause suffering. (d) Extreme cases of misfortune and suffering are called affections. The English equivalent for πάθος in this sense would be calamity or disaster.

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We speak of privation: (a) In one sense, if a thing does not possess an attribute which is a natural possession, even if the thing itself would not naturally possess itThis is not a proper sense of privation, as Aristotle implies by choosing an example from everyday speech.; e.g., we say that a vegetable is deprived of eyes. (b) If a thing does not possess an attribute which it or its genus would naturally possess. E.g., a blind man is not deprived of sight in the same sense that a mole is; the latter is deprived in virtue of its genus, but the former in virtue of himself.i.e., a mole is blind as being a member of a blind genus, whereas a man is blind only as an individual. Of course moles are not really blind, but we still speak as though they were.

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(c) If a thing has not an attribute which it would naturally possess, and when it would naturally possess it (for blindness is a form of privation; but a man is not blind at any age, but only if he lacks sight at the age when he would naturally possess itThe qualification refers, I suppose, to the fact that an embryo does not naturally possess sight.), and similarly if itThe subject seems to be indefinite, but no doubt Aristotle is thinking primarily of the particular example which he has just given. A man is not called blind if he does not see in the dark, or if he does not see with his ears, or if he does not see sound, or if he does not see what is behind him or too far away ( Ross). lacks an attribute in the medium and organ and relation and manner in which it would naturally possess it.

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(d) The forcible removal of anything is called privation. (e) Privation has as many senses as there are senses of negation derived from the negative affix (ἀ-). For we call a thing unequal because it does not possess equality (though it would naturally do so); and invisible either because it has no color at all or because it has only a faint one; and footless either because it has no feet at all or because it has rudimentary feet.

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Again, a negative affix may mean having something in a small degree—e.g. stoneless— that is, having it in some rudimentary manner. Again, it may mean having it not easily or not well; e.g., uncutable means not only that which cannot be cut, but that which cannot be cut easily or well. And again, it may mean not having a thing at all; for it is not the one-eyed man, but the man who lacks sight in both eyes, who is called blind. Hence not every man is good or bad, moral or immoral; there is also the intermediate state.

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To have <or possess> is used in various senses. (a) To direct in accordance with one’s own nature or impulse; whence we say that fever possesses a man, and despots possess cities, and people who wear clothes possess them. (b) We speak of anything as having in which, as receptive material, something is present. E.g., the bronze has the shape of the statue, and the body has the disease.

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(c) In the sense that the container holds the contained; for when A is contained in B, we say that A is held by B. E.g., we say that the vessel holds the liquid, and the city holds men, and the ship holds sailors, and so too that the whole holds the parts.

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(d) The same term is applied to that which prevents anything from moving or acting in accordance with its own impulse; as pillars hold <up> the weights which are imposed upon them, and as the poets make AtlasCf. Hes. Th. 517. hold up the heaven, because otherwise it would fall upon the earth (as some of the physicistse.g., Empedocles held that the heavens were kept in place by the velocity of their rotation;Aristot. De Caelo 284a 24, 295a 16 (Ritter and Preller, 170 b). maintain also).

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It is in this sense that we say that that which holds together holds what it holds together; because otherwise the latter would disperse, each part in accordance with its own impulse.

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To be in a thing is used similarly in senses corresponding to those of to have.

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To come from something means: (a) In one sense, to come from something as matter, and this in two ways: in respect either of the primary genus or of the ultimate species. E.g., in the one sense everything liquefiable comes from water, and in the other the statue comes from bronze.

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(b) To come from something as the first moving principle; e.g., from what comes fighting? From abuse; because this is the beginning of a fight. (c) To come from the combination of matter and form (as the parts come from the whole, and the verse from the Iliad , and the stones from the house); for the shape is an end, and that is a complete thing which has attained its end.

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(d) In the sense that the form is made out of the part of its definition; as, e.g., man is made out of two-footed and the syllable out of its elementIn the sense that στοιχεῖον(letter) forms part of the definition of syllable. (this is a different way from that in which the statue is made out of the bronze; for the composite entity is made out of perceptible material, but the form is also made out of the material of the form).

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These, then, are some of the meanings of from <or out of>, but (e) sometimes one of these senses only partially applies; e.g., the child comes from the father and mother, and plants from the earth, because they come from some part of those things. (f) It means after in time; e.g., we say that night comes from day, and storm from fine weather, because one comes after the other.

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And we speak thus of some of these things in view of their alternation with each other, as in the examples just mentioned, and of others in view merely of their succession in time; e.g., the voyage was made from the equinox, meaning that it was made after it; and the Thargelia are from the Dionysia, meaning after the Dionysia.The (city) Dionysia were celebrated in March; the Thargelia (a festival in honor of Apollo and Artemis) at the end of May.

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Part means: (a) That into which a quantity can be in any way divided; for that which is taken from a quantity qua quantity is always called a part of that quantity—e.g., we call 2 part (in a sense) of 3. (b) In another sense the term is only applied to those parts in sense (a) which measure the whole; hence in one sense we call 2 part of 3, and in another not.

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Again, (c) those divisions into which the form, apart from quantity, can be divided, are also called parts of the form. Hence species are called parts of their genus. (d) That into which the whole (either the form or that which contains the form) is divided, or of which it is composed. E.g., of a bronze sphere or cube not only is the bronze

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(i.e. the material which contains the form) a part, but also the angle. (e) The elements in the definition of each thing are also called parts of the whole. Hence the genus is even called a part of the species, whereas in another sense the species is part of the genus.

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Whole means: (a) That from which no part is lacking of those things as composed of which it is called a natural whole. (b) That which so contains its contents that they form a unity; and this in two ways, either in the sense that each of them is a unity, or in the sense that the unity is composed of them.

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For (i) the universal, or term generally applied as being some whole thing, is universal in the sense that it contains many particulars; because it is predicated of each of them, and each and all of them (e.g. man, horse, god) are one; because they are all living things. And (2) that which is continuous and limited is a whole when it is a unity composed of several parts (especially if the parts are only potentially present in it; but otherwise even if they are present actually).

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And of these things themselves, those which are so naturally are more truly wholes than those which are so artificially; just as we said of the one, because wholeness is a kind of oneness. Again, since a quantity has a beginning, middle and end, those to which position makes no difference we describe as all, and those to which position makes a difference we describe as whole, and those to which both descriptions can be applied, as both all and whole.

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These are all things whose nature remains the same in transposition, but whose shape does not; e.g. wax or a coat. They are described as both whole and all; for they have both characteristics. Water, however, and all liquids, and number, are described as all; we do not speak of a whole number or whole water except by an extension of meaning. Things are described as all in the plural qua differentiated which are described as all in the singular qua one; all this number, all these units.

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We do not describe any chance quantity as mutilated; it must have parts, and must be a whole. The number 2 is not mutilated if one of its 1’s is taken away—because the part lost by mutilation is never equal to the remainder—nor in general is any number mutilated; because the essence must persist. If a cup is mutilated, it must still be a cup; but the number is no longer the same.

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Moreover, not even all things which have dissimilar parts are mutilated; for a number has in a sense dissimilar as well as similar parts—e.g. 2, 3. But in general of things whose position makes no difference, e.g. water or fire, none is mutilated;— to be mutilated, things must be such as have their position according to their essence.

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Further, they must be continuous; for a musical scale is composed of dissimilar parts, and has position; but it does not become mutilated. Moreover, even things which are wholes are not mutilated by the removal of any of their parts; the parts removed must be neither proper to their essence nor in any chance location. E.g., a cup is not mutilated if a hole is made in it, but only if the handle or some projection is broken;

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and a man is not mutilated if he loses flesh or his spleen, but if he loses some extremity; and not every extremity, but only such as cannot grow again when completely removed. Hence bald people are not mutilated.

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The term genus <or race> is used: (a) When there is a continuous generation of things of the same type; e.g., as long as the human race exists means as long as the generation of human beings is continuous. (b) Of anything from which things derive their being as the prime mover of them into being. Thus some are called Hellenes by race, and others Ionians, because some have Hellen and others Ion as their first ancestor.

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(Races are called after the male ancestor rather than after the material.Aristotle regards the mother as providing the material, and the father the formal element of the child. Cf. Aristot. Met. 1.6.8, Aristot. Met. 8.4.5. Some derive their race from the female as well; e.g. the descendants of PyrrhaWife of Deucalion, the Greek Noah.. ) (c) In the sense that the plane is the genus of plane figures, and the solid of solids (for each one of the figures is either a particular plane or a particular solid); i.e., that which underlies the differentiae.

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(d) In the sense that in formulae the first component, which is stated as part of the essence, is the genus, and the qualities are said to be its differentiae. The term genus, then, is used in all these senses—(a) in respect of continuous generation of the same type; (b) in respect of the first mover of the same type as the things which it moves; (c) in the sense of material. For that to which the differentia or quality belongs is the substrate, which we call material.

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Things are called generically different whose immediate substrates are different and cannot be resolved one into the other or both into the same thing. E.g., form and matter are generically different, and all things which belong to different categories of being; for some of the things of which being is predicated denote the essence, others a quality, and others the various other things which have already been distinguished. For these also cannot be resolved either into each other or into any one thing.

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False means: (i) false as a thing ; (a) because it is not or cannot be substantiated; such are the statements that the diagonal of a square is commensurable, or that you are sitting. Of these one is false always, and the other sometimes; it is in these senses that these things are not facts.

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(b) Such things as really exist, but whose nature it is to seem either such as they are not, or like things which are unreal; e.g. chiaroscuro and dreams. For these are really something, but not that of which they create the impression. Things, then, are called false in these senses: either because they themselves are unreal, or because the impression derived from them is that of something unreal.

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(2.) A false statement is the statement of what is not, in so far as the statement is false. Hence every definition is untrue of anything other than that of which it is true; e.g., the definition of a circle is untrue of a triangle. Now in one sense there is only one definition of each thing, namely that of its essence; but in another sense there are many definitions,Here Aristotle is using the word λόγος not in the strict sense of definition but in the looser sense of a statement about something. since the thing itself, and the thing itself qualified (e.g. Socrates and cultured Socrates) are in a sense the same.

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But the false definition is not strictly a definition of anything. Hence it was foolish of AntisthenesThe Cynic; contemporary and renegade disciple of Socrates. He taught that definition, and even predication, are strictly speaking impossible. A simple entity can only be named; a complex entity can only be defined by naming its simple constituents. Cf. Aristot. Met. 8.3.7, 8; Plat. Theaet. 201d-202c, Plat. Soph. 251b, c. to insist that nothing can be described except by its proper definition: one predicate for one subject; from which it followed that contradiction is impossible, and falsehoodCf. Plat. Euthyd. 283e-284c, 286c, d. nearly so. But it is possible to describe everything not only by its own definition but by that of something else; quite falsely, and yet also in a sense truly—e.g., 8 may be described as double by the definition of 2.

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Such are the meanings of false in these cases. (3.) A false man is one who readily and deliberately makes such statements, for the sake of doing so and for no other reason; and one who induces such statements in others—just as we call things false which induce a false impression. Hence the proof in the HippiasPlat. Hipp. Min 365-375. that the same man is false and true is misleading;

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for it assumes (a) that the false man is he who is able to deceive, i.e. the man who knows and is intelligent; (b) that the man who is willingly bad is better. This false assumption is due to the induction; for when he says that the man who limps willingly is better than he who does so unwillingly, he means by limping pretending to limp. For if he is willingly lame, he is presumably worse in this case just as he is in the case of moral character.

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Accident <or attribute> means that which applies to something and is truly stated, but neither necessarily nor usually; as if, for example, while digging a hole for a plant one found a treasure. Then the finding of treasure is an accident to the man who is digging the hole; for the one thing is not a necessary consequence or sequel of the other, nor does one usually find treasure while planting.

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And a cultured man might be white; but since this does not happen necessarily or usually, we call it an accident. Thus since there are attributes and subjects, and some attributes apply to their subjects only at a certain place and time, any attribute which applies to a subject, but not because it was a particular subject or time or place, will be an accident.

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Nor is there any definite cause for an accident, but only a chance, i.e. indefinite, cause. It was by accident that X went to Aegina if he arrived there, not because he intended to go there but because he was carried out of his course by a storm, or captured by pirates.

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The accident has happened or exists, but in virtue not of itself but of something else; for it was the storm which was the cause of his coming to a place for which he was not sailing—i.e. Aegina.

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Accident has also another sense,i.e. property. namely, whatever belongs to each thing in virtue of itself, but is not in its essence; e.g. as having the sum of its angles equal to two right angles belongs to the triangle. Accidents of this kind may be eternal, but none of the former kind can be. There is an account of this elsewhere.The reference is probably to the Aristot. Analytica Posteriora 75a 18, 39-41.

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It is the principles and causes of the things which are that we are seeking; and clearly of the things which are qua being. There is a cause of health and physical fitness; and mathematics has principles and elements and causes; and in general every intellectual science or science which involves intellect deals with causes and principles, more or less exactly or simply considered.

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But all these sciences single out some existent thing or class, and concern themselves with that; not with Being unqualified, nor qua Being, nor do they give any account of the essence; but starting from it, some making it clear to perception, and others assuming it as a hypothesis, they demonstrate, more or less cogently, the essential attributes of the class with which they are dealing.

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Hence obviously there is no demonstration of substance or essence from this method of approach, but some other means of exhibiting it. And similarly they say nothing as to whether the class of objects with which they are concerned exists or not; because the demonstration of its essence and that of its existence belong to the same intellectual process.

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And since physical science also happens to deal with a genus of Being (for it deals with the sort of substance which contains in itself the principle of motion and rest), obviously it is neither a practical nor a productive science.

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For in the case of things produced the principle of motion (either mind or art or some kind of potency) is in the producer; and in the case of things done the will is the agent—for the thing done and the thing willed are the same. Thus if every intellectual activity is either practical or productive or speculative, physics will be a speculative science; but speculative about that kind of Being which can be moved, and about formulated substance for the most part only qua inseparable from matter.

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But we must not fail to observe how the essence and the formula exist, since without this our inquiry is ineffectual.

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Now of things defined, i.e. of essences, some apply in the sense that snub does, and some in the sense that concave does. The difference is that snub is a combination of form with matter; because the snub is a concave nose , whereas concavity is independent of sensible matter.

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Now if all physical terms are used in the same sense as snub—e.g. nose, eye, face, flesh, bone, and in general animal; leaf, root, bark, and in general vegetable (for not one of these has a definition without motion; the definition invariably includes matter)—it is clear how we should look for and define the essence in physical things, and why it is the province of the physicist to study even some aspects of the soul, so far as it is not independent of matter.

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It is obvious, then, from these considerations, that physics is a form of speculative science. And mathematics is also speculative; but it is not clear at present whether its objects are immutable and separable from matter; it is clear, however, that some branches of mathematics study their objects qua immutable and qua separable from matter. Obviously it is the province of a speculative science to discover whether a thing is eternal and immutable and separable from matter;

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not, however, of physics (since physics deals with mutable objects) nor of mathematics, but of a science prior to both. For physics deals with things which exist separately but are not immutable; and some branches of mathematics deal with things which are immutable, but presumably not separable, but present in matter; but the primary science treats of things which are both separable and immutable.

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Now all causes must be eternal, but these especially; since they are the causes of what is visible of things divine. Hence there will be three speculative philosophies: mathematics, physics, and theology— since it is obvious that if the divine is present anywhere, it is present in this kind of entity; and also the most honorable science must deal with the most honorable class of subject.

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The speculative sciences, then, are to be preferred to the other sciences, and theology to the other speculative sciences. One might indeed raise the question whether the primary philosophy is universal or deals with some one genus or entity; because even the mathematical sciences differ in this respect—geometry and astronomy deal with a particular kind of entity, whereas universal mathematics applies to all kinds alike.

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Then if there is not some other substance besides those which are naturally composed, physics will be the primary science; but if there is a substance which is immutable, the science which studies this will be prior to physics, and will be primary philosophy, and universal in this sense, that it is primary. And it will be the province of this science to study Being qua Being; what it is, and what the attributes are which belong to it qua Being.

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But since the simple term being is used in various senses, of which we saw that one was accidental , and another true (not-being being used in the sense of false); and since besides these there are the categories, e.g. the what, quality, quantity, place, time, and any other similar meanings; and further besides all these the potential and actual : since the term being has various senses, it must first be said of what is accidentally, that there can be no speculation about it.

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This is shown by the fact that no science, whether practical, productive or speculative, concerns itself with it. The man who produces a house does not produce all the attributes which are accidental to the house in its construction; for they are infinite in number. There is no reason why the house so produced should not be agreeable to some, injurious to others, and beneficial to others, and different perhaps from every other existing thing; but the act of building is productive of none of these results.

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In the same way the geometrician does not study the accidental attributes of his figures, nor whether a triangle is different from a triangle the sum of whose angles is equal to two right angles. And this accords with what we should reasonably expect, because accident is only, as it were, a sort of name. Hence in a way PlatoCf. Plat. Soph. 254a. was not far wrong in making sophistry deal with what is nonexistent;

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because the sophists discuss the accident more, perhaps, than any other people—whether cultured and grammatical,i.e. able to read and write. The sophistic argument is given by Alexander as follows: A is grammatical; therefore grammatical A=A. A is cultured; therefore cultured A=A. Therefore grammatical=cultured, and he who is grammatical must be cultured. But B, though grammatical, is not cultured. Therefore the grammatical is not the same as the cultured. and cultured Coriscus and Coriscus,If Coriscus is the same as cultured Coriscus, he is the same as cultured cultured Coriscus, and soad infinitum. Cf. Soph. Elench. 173a 34. are the same or different; and whether everything that is, but has not always been, has come into being, so that if a man who is cultured has become grammatical, he has also, being grammatical, become culturedIf A, being cultured, has become grammatical, then being cultured he is grammatical. Then being grammatical he is cultured. But he has not always, being grammatical, been cultured. So if that which is but has not always been must have come to be, then being grammatical he has become cultured; i.e., he must have been both grammatical before he was cultured and cultured before he was grammatical; which is absurd ( Ross).; and all other such discussions. Indeed it seems that the accidental is something closely akin to the nonexistent.

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This is clear too from such considerations as the following: of things which are in other senses there is generation and destruction, but of things which are accidentally there is not.i.e., the process of becoming or change takes place in the subject—the man , who is accidentally cultured, becomes grammatical, and when the process is complete the cultured is accidentally grammatical; but it does not become so. Nevertheless we must state further, so far as it is possible, with regard to the accidental, what its nature is and through what cause it exists. At the same time it will doubtless also appear why there is no science of it.

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Since, then, there are among existing things some which are invariable and of necessity (not necessity in the sense of compulsion,Cf. Aristot. Met. 5.5.2. but that by which we mean that it cannot be otherwise Aristot. Met. 5.5.3 ), and some which are not necessarily so, nor always, but usually: this is the principle and this the cause of the accidental. For whatever is neither always nor usually so, we call an accident.

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E.g., if in the dog-daysThe period from July 3 to August 11, during which the dog-star Sirius rises and sets with the sun. we have storm and cold, we call it an accident; but not if we have stifling and intense heat, because the latter always or usually comes at this time, but not the former. It is accidental for a man to be white (since this is neither always nor usually so), but it is not accidental for him to be an animal.

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It is by accident that a builder restores to health, because it is not a builder but a doctor who naturally does this; but the builder happened accidentally to be a doctor. A confectioner, aiming at producing enjoyment, may produce something health-giving; but not in virtue of his confectioner’s art. Hence, we say, it was accidental; and he produces it in a sense, but not in an unqualified sense.

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For there are potencies which produce other things, but there is no art or determinate potency of accidents, since the cause of things which exist or come to be by accident is also accidental.

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Hence, since not everything is or comes to be of necessity and always, but most things happen usually, the accidental must exist. E.g., the white man is neither always nor usually cultured; but since this sometimes happens, it must be regarded as accidental. Otherwise, everything must be regarded as of necessity.

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Therefore the cause of the accidental is the matter, which admits of variation from the usual.

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We must take this as our starting-point: Is everything either always or usually? This is surely impossible. Then besides these alternatives there is something else: the fortuitous and accidental. But again, are things usually so, but nothing always , or are there things which are eternal? These questions must be inquired into laterCf. Aristot. Met. 12.6-8.; but it is clear that there is no science of the accidental—because all scientific knowledge is of that which is always or usually so. How else indeed can one learn it or teach it to another? For a fact must be defined by being so always or usually; e.g., honey-water is usually beneficial in case of fever.

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But science will not be able to state the exception to the rule: when it is not beneficial—e.g. at the new moon; because that which happens at the new moon also happens either always or usually; but the accidental is contrary to this. We have now explained the nature and cause of the accidental, and that there is no science of it.

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It is obvious that there are principles and causes which are generable and destructible apart from the actual processes of generation and destructionOn the analogy of accidental events; see 2. 5.; for if this is not true, everything will be of necessity: that is, if there must necessarily be some cause, other than accidental, of that which is generated and destroyed. Will A be, or not? Yes, if B happens; otherwise not. And B will happen if C does.

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It is clear that in this way, as time is continually subtracted from a limited period, we shall come to the present. Accordingly So-and-so will die by disease or violence if he goes out; and this if he gets thirsty; and this if something else happens; and thus we shall come to what is the case now, or to something which has already happened. E.g. if he is thirsty; this will happen if he is eating pungent food, and this is either the case or not.

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Thus of necessity he will either die or not die. And similarly if one jumps over to the past, the principle is the same; for this—I mean that which has just happened—is already present in something. Everything, then, which is to be, will be of necessity; e.g., he who is alive must die—for some stage of the process has been reached already; e.g., the contraries are present in the same body—but whether by disease or violence is not yet determined; it depends upon whether so-and-so happens.

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Clearly, then, the series goes back to some starting-point, which does not go back to something else. This, therefore, will be the starting-point of the fortuitous, and nothing else is the cause of its generation. But to what sort of starting-point and cause this process of tracing back leads, whether to a material or final or moving cause, is a question for careful consideration.

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So much, then, for the accidental sense of being; we have defined it sufficiently. As for being qua truth, and not-being qua falsity, since they depend upon combination and separation, and taken together are concerned with the arrangement of the parts of a contradiction (since the true has affirmation when the subject and predicate are combined, and negation where they are divided; but the false has the contrary arrangement.

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How it happens that we combine or separate in thought is another question. By combining or separating in thought I mean thinking them not as a succession but as a unitysc., or not as a unity but as a succession (this is separating in thought).); for falsity and truth are not in things —the good, for example, being true, and the bad false—but in thought ; and with regard to simple concepts and essences there is no truth or falsity even in thought;

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—what points we must study in connection with being and not-being in this sense, we must consider later. But since the combination and separation exists in thought and not in things, and this sense of being is different from the proper senses (since thought attaches or detaches essence or quality or quantity or some other category), we may dismiss the accidental and real sensesi.e., the senses in which the verb to be is used to express an accidental or a true relation. of being.

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For the cause of the one is indeterminate and of the other an affection of thought; and both are connected with the remaining genus of being, and do not indicate any objective reality. Let us therefore dismiss them, and consider the causes and principles of Being itself qua Being. [We have made it clear in our distinction of the number of senses in which each term is used that being has several senses.]This sentence is almost certainly a later and clumsy addition to show the connection with the following book.

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The term being has several senses, which we have classified in our discussionAristot. Met. 5.7. of the number of senses in which terms are used. It denotes first the what of a thing, i.e. the individuality; and then the quality or quantity or any other such category. Now of all these senses which being has, the primary sense is clearly the what, which denotes the substance

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(because when we describe the quality of a particular thing we say that it is good or bad, and not five feet high or a man; but when we describe what it is, we say not that it is white or hot or five feet high, but that it is a man or a god), and all other things are said to be because they are either quantities or qualities or affections or some other such thing.

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Hence one might raise the question whether the terms to walk and to be well and to sit signify each of these things as being, or not; and similarly in the case of any other such terms; for not one of them by nature has an independent existence or can be separated from its substance. Rather, if anything it is the thing which walks or sits or is well that is existent.

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The reason why these things are more truly existent is because their subject is something definite; i.e. the substance and the individual, which is clearly implied in a designation of this kind, since apart from it we cannot speak of the good or sitting. Clearly then it is by reason of the substance that each of the things referred to exists.

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Hence that which is primarily, not in a qualified sense but absolutely, will be substance.

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Now primary has several meanings; but nevertheless substance is primary in all senses, both in definition and in knowledge and in time. For none of the other categories can exist separately, but substance alone;

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and it is primary also in definition, because in the formula of each thing the formula of substance must be inherent; and we assume that we know each particular thing most truly when we know what man or fire is— rather than its quality or quantity or position; because we know each of these points too when we know what the quantity or quality is.

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Indeed, the question which was raised long ago, is still and always will be, and which always baffles us—What is Being?—is in other words What is substance? Some say that it is oneThe Milesians and Eleatics.; others, more than one; some, finiteThe Pythagoreans and Empedocles.; others, infinite.Anaxagoras and the Atomists. And so for us too our chief and primary and practically our only concern is to investigate the nature of being in the sense of substance.

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Substance is thought to be present most obviously in bodies. Hence we call animals and plants and their parts substances, and also natural bodies, such as fire, water, earth, etc., and all things which are parts of these or composed of these, either of parts or them or of their totality; e.g. the visible universe and its parts, the stars and moon and sun.

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We must consider whether (a) these are the only substances, or (b) these and some others, or (c) some of these, or (d) some of these and some others, or (e) none of these, but certain others. SomeThe Pythagoreans. hold that the bounds of body—i.e. the surface, line, point and unit—are substances, and in a truer sense than body or the solid.

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Again, someThe pre-Socratics. believe that there is nothing of this kind besides sensible things, while others believe in eternal entities more numerous and more real than sensible things. Thus Plato posited the Forms and the objects of mathematics as two kinds of substance, and as a third the substance of sensible bodies;

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and SpeusippusPlato’s nephew and successor as the head of the Academy. assumed still more kinds of substances, starting with the One, and positing principles for each kind: one for numbers, another for magnitudes, and then another for the soul. In this way he multiplies the kinds of substance. SomeThe followers of Xenocrates, successor to Speusippus. again hold that the Forms and numbers have the same nature, and that other things—lines and planes—are dependent upon them; and soon back to the substance of the visible universe and sensible things.

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We must consider, then, with regard to these matters, which of the views expressed is right and which wrong; and what things are substances; and whether there are any substances besides the sensible substances, or not; and how sensible substances exist; and whether there is any separable substance (and if so, why and how) or no substance besides the sensible ones. We must first give a rough sketch of what substance is.

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The term substance is used, if not in more, at least in four principal cases; for both the essence and the universal and the genus are held to be the substance of the particular, and fourthly the substrate. The substrate is that of which the rest are predicated, while it is not itself predicated of anything else. Hence we must first determine its nature, for the primary substrate is considered to be in the truest sense substance.

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Now in one sense we call the matter the substrate; in another, the shape ; and in a third, the combination of the two. By matter I mean, for instance, bronze; by shape, the arrangement of the form; and by the combination of the two, the concrete thing: the statue. Thus if the form is prior to the matter and more truly existent, by the same argument it will also be prior to the combination.

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We have now stated in outline the nature of substance—that it is not that which is predicated of a subject, but that of which the other things are predicated. But we must not merely define it so, for it is not enough. Not only is the statement itself obscure, but also it makes matter substance; for if matter is not substance, it is beyond our power to say what else is.

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For when everything else is removed, clearly nothing but matter remains; because all the other things are affections, products and potencies of bodies, and length, breadth and depth are kinds of quantity, and not substances. For quantity is not a substance; rather the substance is that to which these affections primarily belong.

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But when we take away length and breadth and depth we can see no thing remaining, unless it be the something bounded by them; so that on this view matter must appear to be the only substance. By matter I mean that which in itself is neither a particular thing nor a quantity nor designated by any of the categories which define Being.

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For there is something of which each of these is predicated, whose being is different from that of each one of the categories; because all other things are predicated of substance, but this is predicated of matter. Thus the ultimate substrate is in itself neither a particular thing nor a quantity nor anything else. Nor indeed is it the negations of these; for the negations too will only apply to it accidentally.

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If we hold this view, it follows that matter is substance. But this is impossible; for it is accepted that separability and individuality belong especially to substance. Hence it would seem that the form and the combination of form and matter are more truly substance than matter is.

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The substance, then, which consists of both—I mean of matter and form—may be dismissed, since it is posterior and obvious. Matter too is in a sense evident. We must consider the third type, for this is the most perplexing.

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Now it is agreed that some sensible things are substances, and so we should begin our inquiry in connection with these.

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It is convenient to advance to the more intelligiblesc. by nature. All learning proceeds by induction from that which is intelligible to us (i.e., the complex facts and objects of our experience, which are bound up with sensation and therefore less intelligible in themselves), to that which is intelligible in itself (i.e., the simple universal principles of scientific knowledge).; for learning is always acquired in this way, by advancing through what is less intelligible by nature to what is more so. And just as in actions it is our task to start from the good of the individual and make absolute good good for the individual,Cf. Aristot. Ethics 1129b 5. so it is our task to start from what is more intelligible to oneself and make what is by nature intelligible intelligible to oneself.

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Now that which is intelligible and primary to individuals is often but slightly intelligible, and contains but little reality; but nevertheless, starting from that which is imperfectly intelligible but intelligible to oneself, we must try to understand the absolutely intelligible; advancing, as we have said, by means of these very things which are intelligible to us.

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Since we distinguished at the beginningAristot. Met. 7.3.1. the number of ways in which substance is defined, and since one of these appeared to be essence, we must investigate this.

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First, let us make certain linguistic statements about it.

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The essence of each thing is that which it is said to be per se. To be you is not to be cultured, because you are not of your own nature cultured. Your essence, then, is that which you are said to be

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of your own nature. But not even all of this is the essence; for the essence is not that which is said to be per se in the sense that whiteness is said to belong to a surface,Cf. Aristot. Met. 5.18.3, 4. because being a surface is not being white.

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Nor is the essence the combination of both, being a white surface. Why? Because the word itself is repeated. Hence the formula of the essence of each thing is that which defines the term but does not contain it. Thus if being a white surface is the same as being a smooth surface, white and smooth are one and the same.The statement that to be a white surface is the same as to be a smooth surface tells us nothing fresh about surface; it simply identifies white with smooth. Aristotle has in mind Democritus’s theory of color (that it is an impression conveyed to our eyes from the superficial texture of the object; Theophrastus, De Sensu 73-75); cf.Aristot. De Sensu 442b 11, Aristot. De Gen. et Corr. 316a 1.

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But since in the other categories too there are compounds with substance (because there is a substrate for each category, e.g. quality, quantity, time, place and motion), we must inquire whether there is a formula of the essence of each one of them; whether these compounds, e.g. white man, also have an essence.

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Let the compound be denoted by X.Literally cloak, but the word is chosen quite arbitrarily. Cf. Aristot. Met. 8.6.4. What is the essence of X?

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But this is not even a per se expression. We reply that there are two ways in which a definition can be not per se true of its subject: (a) by an addition, and (b) by an omission.

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In one case the definition is not per se true because the term which is being defined is combined with something else; as if, e.g., in defining whiteness one were to state the definition of a white man. In the other, because something else (which is not in the definition) is combined with the subject; as if, e.g., X were to denote white man, and X were defined as white. White man is white, but its essence is not to be white. But is to be X an essence at all?

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Surely not. The essence is an individual type; but when a subject has something distinct from it predicated of it, it is not an individual type. E.g., white man is not an individual type; that is, assuming that individuality belongs only to substances. Hence essence belongs to all things the account of which is a definition.

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We have a definition, not if the name and the account signify the same (for then all accounts would be definitions; because any account can have a name, so that even the Iliad will be a definition), but if the account is of something primary. Such are all statements which do not involve the predication of one thing of another.

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Hence essence will belong to nothing except species of a genus, but to these only; for in these the predicate is not considered to be related to the subject by participation or affection, nor as an accident. But of everything else as well, if it has a name, there will be a formula of what it means—that X belongs to Y; or instead of a simple formula one more exact—but no definition, nor essence.

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Or perhaps definition, like the what, has more than one sense. For the what in one sense means the substance and the individual, and in another each one of the categories: quantity, quality, etc.

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Just as is applies to everything, although not in the same way, but primarily to one thing and secondarily to others; so what it is applies in an unqualified sense to substance, and to other things in a qualified sense. For we might ask also what quality is, so that quality also is a what it is; not however without qualification, but just as in the case of not-being some say by a verbal quibble that not-being is—not in an unqualified sense, but is not-being—so too with quality.

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Now although we must also consider how we should express ourselves in each particular case, it is still more important to consider what the facts are. Hence now, since the language which we are using is clear, similarly essence also will belong primarily and simply to substance, and secondarily to other things as well; just as the what it is is not essence simply, but the essence of a quality or quantity.

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For it must be either by equivocation that we say that these things are , or by adding and subtracting qualifications, as we say that the unknowable is knownsc. to be unknowable.; since the truth is that we use the terms neither equivocally nor in the same sense, but just as we use the term medical in relation to one and the same thing; but not of one and the same thing, nor yet equivocally. The term medical is applied to a body and a function and an instrument, neither equivocally nor in one sense, but in relation to one thing.Cf. Aristot. Met. 4.2.2.

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However, in whichever way one chooses to speak of these things, it matters nothing; but this point is clear: that the primary and unqualified definition, and the essence, belong to substances. It is true that they belong equally to other things too, but not primarily . For if we assume this, it does not necessarily follow that there is a definition of anything which means the same as any formula; it must mean the same as a particular kind of formula, i.e. the formula of one thing—

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one not by continuity like the Iliad, or things which are arbitrarily combined, but in one of the proper senses of one. And one has the same variety of senses as being. Being means sometimes the individual thing, sometimes the quantity, sometimes the quality. Hence even white man will have a formula and definition; but in a different sense from the definition of whiteness and substance.

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The question arises: If one denies that a formula involving an added determinant is a definition, how can there be a definition of terms which are not simple but coupled? Because they can only be explained by adding a determinant.

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I mean, e.g., there is nose and concavity and snubness, the term compounded of the two, because the one is present in the other. Neither concavity nor snubness is an accidental, but a per se affection of the nose.Snubness is a per se affection of the nose, because it applies only to the nose and cannot be explained apart from it, but the same can hardly be said of concavity. Aristotle himself uses the word (κοιλότης) elsewhere in other connections. Nor are they attributes in the sense that white is of Callias or a man, because Callias is white and is by accident a man; but in the sense that male is an attribute of animal, and equality of quantity, and all other attributes which we say belong per se.

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That is, all things which involve the formula or name of the subject of the affection, and cannot be explained apart from it. Thus white can be explained apart from man, but not female apart from animal. Thus either these terms have no essence or definition, or else they have it in a different sense, as we have said.

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But there is also another difficulty about them. If snub nose is the same as concave nose, snub will be the same as concave. But if not, since it is impossible to speak of snub apart from the thing of which it is a per se affection (because snub means a concavity in the nose), either it is impossible to call the nose snub, or it will be a tautology, concave-nose nose because snub nose will equal concave-nose nose.

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Hence it is absurd that such terms as these should have an essence. Otherwise there will be an infinite regression; for in snub-nose nose there will be yet another nose. Clearly, then, there is definition of substance alone. If there were definition of the other categories also, it would have to involve an added determinant, as in the case of the qualitative; and of the odd, for this cannot be defined apart from number; nor can female apart from animal.

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By involving an added determinant I mean descriptions which involve a tautology, as in the above examples. Now if this is true, there will be no definition of compound expressions either; e.g., odd number. We fail to realize this because our terms are not used accurately. If on the other hand there are definitions of these too, either they are defined in a different way, or, as we have said, definition and essence must be used in more than one sense;

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thus in one sense there will be no definition of anything, and nothing will have an essence, except substances; and in another those other things will have a definition and essence. It is obvious, then, that the definition is the formula of the essence, and that the essence belongs either only to substances, or especially and primarily and simply.

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We must inquire whether the essence is the same as the particular thing, or different. This is useful for our inquiry about substance; because a particular thing is considered to be nothing other than its own substance, and the essence is called the substance of the thing.

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In accidental predications, indeed, the thing itself would seem to be different from its essence; e.g., white man is different from essence of white man. If it were the same, essence of man and essence of white man would be the same. For man and white man are the same, they say, and therefore essence of white man is the same as essence of man.

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But perhaps it is not necessarily true that the essence of accidental combinations is the same as that of the simple terms; because the extremes of the syllogism are not identical with the middle term in the same way.The argument consists of two syllogisms: White=essence of white man. Man=white man. Therefore man=essence of white man. But essence of man=man. Therefore essence of man=essence of white man. The conclusion is faulty because whereas the first identity is assumed to be absolute, the second is accidental. Perhaps it might be thought to follow that the accidental extremes are identical; e.g. essence of white and essence of cultured; but this is not admitted.Aristotle seems to mean that both essence of white man and essence of cultured man might be proved by the former syllogism to be identical in the same way with the middle term man, in which case it would seem that essence of white and essence of cultured are the same. There is, however, the same fallacy as before.

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But in per se expressions, is the thing necessarily the same as its essence, e.g., if there are substances which have no other substances or entities prior to them, such as some hold the Ideas to be?

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For if the Ideal Good is to be different from the essence of good, and the Ideal Animal and Being from the essence of animal and being, there will be other substances and entities and Ideas besides the ones which they describe; and prior to them, if essence is substance. And if they are separate from each other, there will be no knowledge of the Ideas, and the essences will not exist

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(by being separate I mean if neither the essence of good is present in the Ideal Good, nor being good in the essence of good); for it is when we know the essence of it that we have knowledge of a thing. And it is the same with other essences as with the essence of good; so that if the essence of good is not good, neither will the essence of being be, nor the essence of one be one.

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Either all essences exist alike, or none of them; and so if not even the essence of being is, neither will any other essence exist. Again that to which essentially good does not apply cannot be good. Hence the good must be one with the essence of good, the beautiful with the essence of beauty, and so with all terms which are not dependent upon something else, but self-subsistent and primary.The example of the Ideas as per se terms is used by Aristotle to show incidentally the fallacy of the Ideal theory: there can be no self-subsistent entity apart from the essence.

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For it is enough if this is so, even if they are not Forms; or perhaps rather even if they are. (At the same time it is clear also that if the Ideas are such as some hold, the substrate will not be substance; for the Ideas must be substances, but not involving a substrate, because if they did involve one they would exist in virtue of its participation in them.)This criticism is irrelevant to the point under discussion. It simply points out that the Ideal theory conflicts with received opinion (cf. Aristot. Met. 7.3.1).

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That each individual thing is one and the same with its essence, and not merely accidentally so, is apparent, not only from the foregoing considerations, but because to have knowledge of the individual is to have knowledge of its essence; so that by setting out examples it is evident that both must be identical.

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But as for the accidental term, e.g. cultured or white, since it has two meanings, it is not true to say that the term itself is the same as its essence; for both the accidental term and that of which it is an accident are white, so that in one sense the essence and the term itself are the same, and in another they are not, because the essence is not the same as the man or the white man, but it is the same as the affection.

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The absurdity <of separating a thing from its essence> will be apparent also if one supplies a name for each essence; for then there will be another essence besides the original one, e.g. the essence of horse will have a further essence. Yet why should not some things be identified with their essence from the outset,i.e. to avoid the infinite series implied in the last sentence. if essence is substance? Indeed not only are the thing and its essence one, but their formula is the same, as is clear from what we have just stated; for it is not by accident that the essence of one, and the one, are one.

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Moreover, if they are different, there will be an infinite series; for the essence of one and the one will both exist; so that in that case too the same principle will apply.i.e. since there is a distinct term essence of one besides one, there will be a third distinct term essence of essence of one; and so on as in the case of horse above. Clearly, then, in the case of primary and self-subsistent terms, the individual thing and its essence are one and the same.

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It is obvious that the sophistical objections to this thesis are met in the same way as the question whether Socrates is the same as the essence of Socrates; for there is no difference either in the grounds for asking the question or in the means of meeting it successfully. We have now explained in what sense the essence is, and in what sense it is not, the same as the individual thing.

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Of things which are generated, some are generated naturally, others artificially, and others spontaneously; but everything which is generated is generated by something and from something and becomes something. When I say becomes something I mean in any of the categories; it may come to be either a particular thing or of some quantity or quality or in some place.

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Natural generation is the generation of things whose generation is by nature.

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That from which they are generated is what we call matter; that by which, is something which exists naturally; and that which they become is a man or a plant or something else of this kind, which we call substance in the highest degree. All things which are generated naturally or artificially have matter; for it is possible for each one of them both to be and not to be, and this possibility is the matter in each individual thing.

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And in general both that from which and that in accordance with which they are generated, is nature; for the thing generated, e.g. plant or animal, has a nature. And that by which they are generated is the so-called formal nature, which has the same form as the thing generated (although it is in something else); for man begets man.

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Such is the generation of things which are naturally generated; the other kinds of generation are called productions. All productions proceed from either art or potency or thought.

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Some of them are also generated spontaneously and by chance in much the same way as things which are naturally generated; for sometimes even in the sphere of nature the same things are generated both from seed and without it.e.g. fish (Aristot. Hist. An. 569a 11) and insects (Aristot. Hist. An. 539a 24). We shall consider cases of this kind later.In Aristot. Met. 7.9. Things are generated artificially whose form is contained in the soul (by form I mean the essence of each thing, and its primary substance);

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for even contraries have in a sense the same form.The logical connection is: It is sufficient to say that the form of objects which are artificially produced is contained in the soul; for although artificial production can produce contrary effects, the form of the positive effect is the absence of the form of the negative effect, so that in a sense they have the same form. For the substance of the privation is the opposite substance; e.g., health is the substance of disease; for disease is the absence of health, and health is the formula and knowledge in the soul. Now the healthy subject is produced as the result of this reasoning: since health is so-and-so, if the subject is to be healthy, it must have such-and-such a quality, e.g. homogeneity; and if so, it must have heat.

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And the physician continues reasoning until he arrives at what he himself finally can do; then the process from this point onwards, i.e. the process towards health, is called production. Therefore it follows in a sense that health comes from health and a house from a house; that which has matter from that which has not (for the art of medicine or of building is the form of health or the house). By substance without matter I mean the essence.

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In generations and motions part of the process is called cogitation, and part production—that which proceeds from the starting-point and the form is cogitation, and that which proceeds from the conclusion of the cogitation is production. Each of the other intermediate measures is carried out in the same way. I mean, e.g., that if A is to be healthy, his physical condition will have to be made uniform. What, then, does being made uniform entail? So-and-so; and this will be achieved if he is made hot. What does this entail? So-and-so; now this is potentially present, and the thing is now in his power.

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The thing which produces, and from which the process of recovering health begins, is the form in the soul, if the process is artificial; if spontaneous, it is whatever is the starting-point of the production for the artificial producer; as in medical treatment the starting-point is, perhaps, the heating of the patient; and this the doctor produces by friction. Heat in the body, then, is either a part of health, or is followed (directly or through several intermediaries) by something similar which is a part of health. This is the ultimate thing, namely that produces, and in this sense is a part of, health—or of the house

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(in the form of stones)There is no real analogy between the casual relationship of heat to health and of stones to a house. The former is both material and efficient; the latter only material. Cf. Aristot. Met. 7.9.1. or of other things. Therefore, as we say, generation would be impossible if nothing were already existent. It is clear, then, that some part must necessarily pre-exist; because the matter is a part, since it is matter which pre-exists in the product and becomes something. But then is matter part of the formula? Well, we define bronze circles in both ways; we describe the matter as bronze, and the form as such-and-such a shape; and this shape is the proximate genus in which the circle is placed.

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The bronze circle, then, has its matter in its formula. Now as for that from which, as matter, things are generated, some things when they are generated are called not so-and-so, but made of so-and-so; e.g., a statue is not called stone, but made of stone. But the man who becomes healthy is not called after that from which he becomes healthy. This is because the generation proceeds from the privation and the substrate, which we call matter (e.g., both the man and the invalid become healthy),

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but it is more properly said to proceed from the privation; e.g., a man becomes healthy from being an invalid rather than from being a man. Hence a healthy person is not called an invalid, but a man, and a healthy man. But where the privation is obscure and has no name—e.g. in bronze the privation of any given shape, or in bricks and wood the privation of the shape of a house—the generation is considered to proceed from these materials, as in the former case from the invalid.

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Hence just as in the former case the subject is not called that from which it is generated, so in this case the statue is not called wood, but is called by a verbal change not wood, but wooden; not bronze, but made of bronze; not stone, but made of stone; and the house is called not bricks, but made of bricks. For if we consider the matter carefully, we should not even say without qualification that a statue is generated from wood, or a house from bricks; because that from which a thing is generated should not persist, but be changed. This, then, is why we speak in this way.

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Now since that which is generated is generated by something (by which I mean the starting-point of the process of generation), and from something (by which let us understand not the privation but the matter; for we have already distinguished the meanings of these), and becomes something (i.e. a sphere or circle or whatever else it may be); just as the craftsman does not produce the substrate, i.e. the bronze, so neither does he produce the sphere; except accidentally, inasmuch as the bronze sphere is a sphere, and he makes the former.

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For to make an individual thing is to make it out of the substrate in the fullest sense. I mean that to make the bronze round is not to make the round or the sphere, but something else; i.e. to produce this form in another medium. For if we make the form, we must make it out of something else; for this has been assumed. E.g., we make a bronze sphere; we do this in the sense that from A, i.e. bronze, we make B, i.e. a sphere.

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If, then, we make the spherical form itself, clearly we shall have to make it in the same way; and the processes of generation will continue to infinity.

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It is therefore obvious that the form (or whatever we should call the shape in the sensible thing) is not generated—generation does not apply to it— nor is the essence generated; for this is that which is induced in something else either by art or by nature or by potency.

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But we do cause a bronze sphere to be, for we produce it from bronze and a sphere; we induce the form into this particular matter, and the result is a bronze sphere. But if the essence of sphere in general is generated, something must be generated from something; for that which is generated will always have to be divisible, and be partly one thing and partly another; I mean partly matter and partly form.

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If then a sphere is the figure whose circumference is everywhere equidistant from the center, part of this will be the medium in which that which we produce will be contained, and part will be in that medium; and the whole will be the thing generated, as in the case of the bronze sphere. It is obvious, then, from what we have said, that the thing in the sense of form or essence is not generated, whereas the concrete whole which is called after it is generated; and that in everything that is generated matter is present, and one part is matter and the other form.

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Is there then some sphere besides the particular spheres, or some house besides the bricks? Surely no individual thing would ever have been generated if form had existed thus independently.If forms are self-subsistent substances, individual substances cannot be generated from them; for the individual contains the form, but one substance cannot contain another actually existing substance (Aristot. Met. 7.8.8). Form, however, is not a substance but a characteristic. Form means of such a kind; it is not a definite individual, but we produce or generate from the individual something of such a kind; and when it is generated it is an individual of such a kind.

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The whole individual, Callias or Socrates, corresponds to this bronze sphere, but man and animal correspond to bronze sphere in general.

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Obviously therefore the cause which consists of the Forms (in the sense in which some speak of them, assuming that there are certain entities besides particulars), in respect at least of generation and destruction, is useless; nor, for this reason at any rate, should they be regarded as self-subsistent substances.

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Indeed in some cases it is even obvious that that which generates is of the same kind as that which is generated—not however identical with it, nor numerically one with it, but formally one—e.g. in natural productions (for man begets man), unless something happens contrary to nature, as when a horse sires a mule. And even these cases are similar; for that which would be common to both horse and ass, the genus immediately above them, has no name; but it would probably be both, just as the mule is both.Normally the sire communicates his form to the offspring. In the case of a mule, the material element contributed by the dam, which is an ass, limits the effect of the formal element contributed bu the sire, which is a horse; but even so the form of the sire is generically the same as that of the offspring.

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Thus obviously there is no need to set up a form as a pattern (for we should have looked for Forms in these cases especially, since living things are in a special sense substances); the thing which generates is sufficient to produce, and to be the cause of the form in the matter. The completed whole, such-and-such a form induced in this flesh and these bones, is Callias or Socrates. And it is different from that which generated it, because the matter is different but identical in form, because the form is indivisible.

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The question might be raised why some things are generated both artificially and spontaneously—e.g. health—and others not; e.g. a house. The reason is that in some cases the matter—which is the starting-point of the process in the production and generation of artificial things, and in which some part of the result is already existent—is such that it can initiate its own motion, and in other cases it is not; and of the former kind some can initiate motion in a particular way, and some cannot. For many things can move themselves, but not in a particular way, e.g. so as to dance.

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It is impossible, then, for any things whose matter is of this kind (e.g. stones) to be moved in this particular way except by something else; but in that particular way it is possible. And it is so with fire.Stones can fall by themselves, but cannot by themselves build a house; fire can rise by itself, but cannot boil a kettle. For this reason some things cannot exist apart from the possessor of the art, and others can; because the motion can be initiated by those things which do not indeed possess the art, but can themselves be moved either by other things which do not possess the art, or by the motion from the part of the product which pre-exists in them.e.g., health can be produced as the result of the activity set up by heat in the body.

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It is clear also from what we have said that in a sense all artificial things are generated either from something which bears the same name (as is the case with natural objects) or from a part of themselves which bears the same name as themselves (e.g. a house from a house, inasmuch as it is generated by mind; for the art is the form), or from something which contains some part; that is if the generation is not accidental; for the direct and independent cause of the production is a part of the product.

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Heat in the motion produces heat in the body; and either this is health or a part of health, or a part of health or health accompanies it. And this is why heat is said to produce health, because it produces that of which health is a concomitant and consequence. Therefore as essence is the starting-point of everything in syllogisms (because syllogisms start from the what of a thing), so too generation proceeds from it.

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And it is the same with natural formations as it is with the products of art. For the seed produces just as do those things which function by art. It contains the form potentially, and that from which the seed comes has in some sense the same name as the product (for we must not expect that all should have the same name in the sense that man is produced by man—since woman is also produced by man); unless the product is a freak. This is why a mule is not produced by a mule.

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Those natural objects which are produced, like artificial objects, spontaneously, are those whose matter can also initiate for itself that motion which the seed initiates. Those whose matter cannot do this cannot be generated otherwise than by their proper parents.

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It is not only with reference to substance that our argument shows that the form is not generated; the same argument is common in its application to all the primary divisions, i.e. quantity, quality and the other categories.

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For just as the bronze sphere is generated, but not the sphere nor the bronze; and as in the case of bronze, if it is generated the form and matter are not (because they must always pre-exist), so it is too with the what and the quality and quantity and the other categories similarly; for it is not the quality that is generated, but the wood of that quality; nor is it the size, but the wood or animal of that size.

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But a peculiarity of substance may be gathered from this: that some other substance must pre-exist in actuality which produces it; e.g. an animal, if an animal is being generated; but a quality or quantity need not pre-exist otherwise than potentially.

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Since a definition is a formula, and every formula has parts; and since the formula is related to the thing in the same way as the part of the formula to the part of the thing, the questionThe questions discussed in chs. 10-12 arise out of the consideration of essence as definition. now arises: Must the formula of the parts be contained in the formula of the whole, or not? It seems clear that it is so in some cases, but not in others.

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The formula of the circle does not include that of the segments, but the formula of the syllable includes that of the letters. And yet the circle is divisible into its segments in just the same way as the syllable into its letters.

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Again, if the parts are prior to the whole, and the acute angle is part of the right angle, and the finger part of the animal, the acute angle will be prior to the right angle, and the finger to the man.

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But it is considered that the latter are prior; for in the formula the parts are explained from them; and the wholes are prior also in virtue of their ability to exist independently. The truth probably is that part has several meanings, one of which is that which measures in respect of quantity. However, let us dismiss this question and consider of what, in the sense of parts, substance consists.

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If then matter, form, and the combination of the two are distinct, and if both matter and form and their combination are substance, there is one sense in which even matter may be called part of a thing; and another in which it is not, but the only parts are those elements of which the formula of the form consists. E.g., flesh is not a part of concavity, because flesh is the matter in which concavity is induced; but it is a part of snubness. And bronze is part of the statue as a concrete whole, but not of the statue in the sense of form.

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We may speak of the form (or the thing as having a form) as an individual thing, but we may never so speak of that which is material by itself. This is why the formula of the circle does not contain that of the segments, whereas the formula of the syllable does contain that of the letters; for the letters are parts of the formula of the form; they are not matter; but the segments are parts in the sense of matter in which the form is induced. They approximate, however, more closely to the form than does the bronze when roundness is engendered in bronze.

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But there is a sense in which not even all the letters will be contained in the formula of the syllable; e.g. particular letters on waxi.e. written on a waxed tablet. or sounds in the air; for these too are part of the syllable in the sense that they are its sensible matter.

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For even if the line is divided and resolved into its halves, or if the man is resolved into bones and muscles and flesh, it does not follow that they are composed of these as parts of their essence, but as their matter; and these are parts of the concrete whole, but not of the form, or that to which the formula refers. Hence they are not in the formulae.

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Accordingly in some cases the formula will include the formula of such parts as the above, but in others it need not necessarily contain their formula, unless it is the formula of the concrete object. It is for this reason that some things are composed of parts in the sense of principles into which they can be resolved, while others are not.

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All things which are concrete combinations of form and matter (e.g. the snub or the bronze circle) can be resolved into form and matter, and the matter is a part of them; but such as are not concrete combinations with matter, but are without matter—whose formulae refer to the form only—cannot be resolved; either not at all, or at least not in this way.

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Thus these material components are principles and parts of the concrete objects, but they are neither parts nor principles of the form. For this reason the clay statue can be resolved into clay, and the sphere into bronze, and Callias into flesh and bones, and the circle too into segments, because it is something which is combined with matter. For we use the same name for the absolute circle and for the particular circle, since there is no special name for the particular circles.

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We have now stated the truth; nevertheless let us recapitulate and state it more clearly. All constituents which are parts of the formula, and into which the formula can be divided, are prior to their wholes—either all or some of them. But the formula of the right angle is not divisible into the formula of an acute angle, but vice versa; since in defining the acute angle we use the right angle, because the acute angle is less than a right angle.

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It is the same with the circle and the semicircle; for the semicircle is defined by means of the circle. And the finger is defined by means of the whole body; for a finger is a particular kind of part of a man. Thus such parts as are material, and into which the whole is resolved as into matter, are posterior to the whole; but such as are parts in the sense of parts of the formula and of the essence as expressed in the formula, are prior; either all or some of them.

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And since the soul of animals (which is the substance of the living creature) is their substance in accordance with the formula, and the form and essence of that particular kind of body (at least each part, if it is to be properly defined, will not be defined apart from its function; and this will not belong to it apart from perceptionWhich implies soul.); therefore the parts of the soul are prior, either all or some of them, to the concrete animal; and similarly in other individual cases.

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But the body and its parts are posterior to this substance, and it is not the substance, but the concrete whole, which is resolved into these parts as into matter. Therefore in one sense these parts are prior to the concrete whole, and in another not; for they cannot exist in separation. A finger cannot in every state be a part of a living animal; for the dead finger has only the name in common with the living one.

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Some parts are contemporary with the whole: such as are indispensable and in which the formula and the essence are primarily present; e.g. the heart or perhaps the brain,Cf. Aristot. Met. 5.1.1. for it does not matter which of them is of this nature. But man and horse and terms which are applied in this way to individuals, but universally, are not substance, but a kind of concrete whole composed of this particular formula and this particular matter regarded as universal. But individually Socrates is already composed of ultimate matter; and similarly in all other cases.

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A part, then, may be part of the form (by form I mean essence), or of the concrete whole composed of form and matter, or of the matter itself. But only the parts of the form are parts of the formula, and the formula refers to the universal; for circle is the same as essence of circle, and soul the same as essence of soul.

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But when we come to the concrete thing, e.g. this circle—which is a particular individual, either sensible or intelligible (by intelligible circles I mean those of mathematics,i.e., something very similar to the Platonic intermediates. Cf. Introduction. and by sensible those which are of bronze or wood)—of these individuals there is no definition;

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we apprehend them by intelligence or perception; and when they have passed from the sphere of actuality it is uncertain whether they exist or not, but they are always spoken of and apprehended by the universal formula. But the matter is in itself unknowable. Some matter is sensible and some intelligible; sensible, such as bronze and wood and all movable matter; intelligible, that which is present in sensible things not qua sensible, e.g. the objects of mathematics.See Aristot. Met. 13.2, 3.

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We have now discussed the case of the whole and part, and of prior and posterior. But we must answer the question, when we are asked which is prior—the right angle and circle and animal, or that into which they are resolved and of which they are composed, i.e. their parts—by saying that neither is absolutely prior.

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For if the soul also is the animal or living thing, or the soul of the individual is the individual, and being a circle is the circle, and being a right angle or the essence of the right angle is the right angle, then we must admit that the whole in one sense is posterior to the part in one sense: e.g. to the parts in the formula and the parts of a particular right angle

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(since both the material right angle of bronze and the right angle included by individual lines are posterior to their parts), but the immaterial angle is posterior to the parts in the formula, but prior to the parts in the individual. We must not give an unqualified answer. And if the soul is not the animal but something else, even so we must say that some wholes are prior and some are not, as has been stated.

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The question naturally presents itself, what sort of parts belong to the form and what sort belong not to it but to the concrete object. Yet if this is not plain it is impossible to define the particular; because the definition refers to the universal and the form. Therefore if it is not clear what kind of parts are material and what kind are not, the formula of the thing will not be clear either.

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In the case of things which can be seen to be induced in specifically different materials, as, e.g., a circle is in bronze and stone and wood, it seems clear that these things, the bronze and the stone, are in no sense part of the essential substance of the circle, because it is separable from them.

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As for things which are not visibly separable, there is no reason why the same should not apply to them; e.g., if all the circles that had ever been seen were bronze; for the bronze would be none the less no part of the form, but it is difficult to separate it in thought.

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For example, the form of man is always manifested in flesh and bones and elements of this kind; then are these actually parts of the form and formula, or are they not so, but matter, though since the form is not induced in other materials, we cannot separate it?

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Now since this seems to be possible, but it is not clear when, some thinkersThe Pythagoreans. are doubtful even in the case of the circle and the triangle, considering that it is not proper to define them by lines and continuous space, but that all these are to the circle or triangle as flesh or bone is to man, and bronze or stone to the statue; and they reduce everything to numbers, and say that the formula of line is the formula of 2.

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And of the exponents of the Forms, some make 2 the Ideal line, and some the form of the lineThe distinction seems to be that given in Aristot. Met. 8.3.1. Some held that the line, considered absolutely, is simply twoness; others that it is twoness in length. ; for they say that in some cases the form and that of which it is the form, e.g. 2 and the form of 2, are the same; but in the case of line this is no longer so.

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It follows, then, that there is one form of many things whose form is clearly different (a consequence which confronted the Pythagoreans tooCf. Aristot. Met. 1.5.17.), and that it is possible to make one supreme Form of everything, and not to regard the rest as forms. In this way, however, all things would be one.

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Now we have stated that the question of definitions involves some difficulty, and have shown why this is so. Hence to reduce everything in this way and to dispose of the matter is going too far; for some things are presumably a particular form in particular matter, or particular things in a particular state.

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And the analogy in the case of the living thing which the younger SocratesA disciple of the great Socrates; one of the speakers in the PoliticusPlat. Stat. and referred to in Plat. Theaet. 147c, Plat. Soph. 218b. used to state is not a good one; for it leads one away from the truth, and makes one suppose that it is possible for a man to exist without his parts, as a circle does without the bronze. But the case is not similar; for the animal is sensible and cannot be defined without motion, and hence not unless its parts are in some definite condition;

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for it is not the hand in any condition that is a part of a man, but only when it can perform its function, and so has life in it. Without life in it it is not a part.

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And with respect to mathematical objects, why are the formulae of the parts not parts of the formulae of the whole; e.g., why are the formulae of the semicircles not parts of the formula of the circle? for they are not sensible.

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Probably this makes no difference; because there will be matter even of some things which are not sensible. Indeed there will be matter in some sense in everything which is not essence or form considered independently, but a particular thing. Thus the semicircles will be parts not of the universal circle but of the particular circles, as we said beforeAristot. Met. 7.10.17.—for some matter is sensible, and some intelligible.

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It is clear also that the soul is the primary substance, and the body matter; and man or animal is the combination of both taken universally. And Socrates or Coriscus has a double sense, that is if the soul too can be called Socrates (for by Socrates some mean the soul and some the concrete person); but if Socrates means simply this soul and this body, the individual is composed similarly to the universal.

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Whether there is some other material component of these substances besides their matter, and whether we should look for some further substance in them, such as numbers or something of that kind, must be considered later.In Books 13 and 14. It is with a view to this that we are trying to determine the nature of sensible substances, since in a sense the study of sensible substances belongs to physics or secondary philosophy; for the physicist must know not only about the matter, but also about the substance according to the formula; this is even more essential.

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And in the case of definitions, in what sense the elements in the formula are parts of the definition, and why the definition is one formula (for the thing is clearly one, but in virtue of what is it one, seeing that it has parts?); this must be considered later.Aristot. Met. 8.6.

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We have stated, then, in a general account which covers all cases, what essence is, and how it is independent; and why the formula of the essence of some things contains the parts of the thing defined, while that of others does not; and we have shown that the material parts of a thing cannot be present in the formula of the substance (since they are not even parts of the substance in that sense, but of the concrete substance; and of this in one sense there is a formula, and in another sense there is not.

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There is no formula involving the matter, for this is indeterminate; but there is a formula in accordance with the primary substance, e.g., in the case of a man, the formula of the soul; because the substance is the indwelling form, of which and of the matter the so called concrete substance is composed. E.g., concavity is such a form, since from this and nose is derived snub nose and snubness—for nose will be present twice over in these expressions);

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but in the concrete substance, e.g. snub nose or Callias, matter will be present too.Chapters. 10-11; and cf. Aristot. Met. 7.4. We have stated also that the essence and the individual are in some cases the same, as in the case of the primary substances; e.g. crookedness and essence of crookedness, if this is primary.

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By primary I mean that which does not imply the presence of something in something else as a material substrate. But such things as are material or are compounded with matter are not the same as their essence; not even if they are accidentally one, e.g. Socrates and cultured; for these are only accidentally the same.

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Now let us first deal with definition, in so far as it has not been dealt with in the Analytics; for the problem stated thereAristot. An. Post. 92a 29. has a bearing upon our discussion of substance. The problem I mean is this: what constitutes the unity of the thing of which we say that the formula is a definition? E.g., in the case of man, two-footed animal; for let us take this as the formula of man.

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Why, then, is this a unity and not a plurality, animal and two-footed? For in the case of man and white we have a plurality when the latter does not refer to the former, but a unity when it does refer to it, and the subject, man, has an attribute; for then they become a unity and we have the white man.

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But in the case before us one term does not partake of the other; the genus is not considered to partake of its differentiae, for then the same thing would be partaking simultaneously of contraries, since the differentiae by which the genus is distinguished are contrary. And even if it does partake of them, the same argument applies, since the differentiae are many; e.g. terrestrial, two-footed, wingless.

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Why is it that these are a unity and not a plurality? Not because they are present in one genus, for in that case all the differentiae of the genus will form a unity. But all the elements in the definition must form a unity, because the definition is a kind of formula which is one and defines substance, so that it must be a formula of one particular thing; because the substance denotes one thing and an individual, as we say.

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We must firstThe other type of definition, that which states the constituent parts of a thing, is not discussed here. examine definitions which are reached by the process of division.

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For there is nothing else in the definition but the primary genus and the differentiae; the other genera consist of the primary genus together with the differentiae which are taken with it. E.g., the primary genus is animal; the next below it, two-footed animal; and again, two-footed wingless animal; and similarly also if the expression contains more terms still.

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In general it does not matter whether it contains many or few terms, nor, therefore, whether it contains few or two. Of the two one is differentia and the other genus; e.g., in two-footed animal animal is genus, and the other term differentia.

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If, then, the genus absolutely does not exist apart from the species which it includes, or if it exists, but only as matter (for speech is genus and matter, and the differentiae make the species, i.e. the letters, out of it), obviously the definition is the formula composed of the differentiae.

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But further we must also divide by the differentia of the differentia. E.g., having feet is a differentia of animal; then in turn we must discover the differentia of animal having feet qua having feet. Accordingly we should not say that of that which has feet one kind is winged and another wingless, (that is if we are to speak correctly; if we say this it will be through incapability), but only that one kind is cloven-footed and another not; because these are differentiae of foot, since cloven-footedness is a kind of footedness.

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And thus we tend always to progress until we come to the species which contain no differentiae. At this point there will be just as many species of foot as there are differentiae, and the kinds of animals having feet will be equal in number to the differentiae. Then, if this is so, obviously the ultimate differentia will be the substance and definition of the thing, since we need not state the same things more than once in definitions, because this is superfluous.

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However, it does happen; for when we say footed two-footed animal we have simply said animal having feet, having two feet. And if we divide this by its proper division, we shall be stating the same thing several times, as many times as there are differentiae.

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If, then, we keep on taking a differentia of a differentia, one of them, the last, will be the form and the substance. But if we proceed with reference to accidental qualities—e.g. if we divide that which has feet into white and black—there will be as many differentiae as there are divisions. It is therefore obvious that the definition is the formula derived from the differentiae, and strictly speaking from the last of them.

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This will be clear if we change the order of such definitions, e.g. that of man, saying two-footed footed animal; for footed is superfluous when we have already said two-footed. But there is no question of order in the substance; for how are we to think of one part as posterior and the other prior?

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With regard, then, to definitions by division, let this suffice as a preliminary statement of their nature.

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Since the subject of our inquiry is substance, let us return to it. Just as the substrate and the essence and the combination of these are called substance, so too is the universal. With two of these we have already dealt, i.e. with the essenceChs. 4-5.,10-12. and the substrateCh. 3.; of the latter we have said that it underlies in two senses—either being an individual thing (as the animal underlies its attributes), or as matter underlies the actuality.

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The universal also is thought by someThe Platonists. to be in the truest sense a cause and a principle. Let us therefore proceed to discuss this question too; for it seems impossible that any universal term can be substance.

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First, the substance of an individual is the substance which is peculiar to it and belongs to nothing else; whereas the universal is common; for by universal we mean that which by nature appertains to several things.

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Of what particular, then, will the universal be the substance? Either of all or of none. But it cannot be the substance of all; while, if it is to be the substance of one, the rest also will be that one; because things whose substance is one have also one essence and are themselves one.

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Again, substance means that which is not predicated of a subject, whereas the universal is always predicated of some subject.

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But perhaps although the universal cannot be substance in the sense that essence is, it can be present in the essence, as animal can be present in man and horse.

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Then clearly there is in some sense a formula of the universal. It makes no difference even if there is not a formula of everything that is in the substance; for the universal will be none the less the substance of something; e.g., man will be the substance of the man in whom it is present. Thus the same thing will happen againi.e., the argument in ch. 3 will apply to this case also.; e.g. animal will be the substance of that in which it is present as peculiar to it.

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Again, it is impossible and absurd that the individual or substance, if it is composed of anything, should be composed not of substances nor of the individual, but of a quality; for then non-substance or quality will be prior to substance or the individual. Which is impossible; for neither in formula nor in time nor in generation can the affections of substance be prior to the substance, since then they would be separable.

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Again, a substance will be present in Socrates, who is a substance; so that it will be the substance of two things. And in general it follows that if man and all terms used in this way are substance, none of the elements in the formula is the substance of anything, nor can it exist apart from the species or in anything else; I mean, e.g., that neither animal nor any other element of the formula can exist apart from the particular species.

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If we look at the question from this standpoint it is obvious that no universal attribute is substance; and it is also clear from the fact that none of the common predicates means so-and-so, but such and-such. Otherwise amongst many other awkward consequences we have the third man. See note on Aristot. Met. 1.9.3.

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Again, it is clear in this way too. Substance can not consist of substances actually present in it; for that which is actually two can never be actually one, whereas if it is potentially two it can be one. E.g., the double consists of two halves—that is, potentially; for the actualization separates the halves.

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Thus if substance is one, it cannot consist of substances present in it even in this sense, as Democritus rightly observes; he says that it is impossible for two to come from one, or one from two, because he identifies substance with the atoms.Cf. Aristot. De Caelo 303a 6, Aristot. De Gen. et Corr. 325a 35.

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Clearly then the same will also hold good in the case of number (assuming that number is a composition of units, as it is said to be by some); because either 2 is not 1, or there is not actually a unit in it.

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The consequence involves a difficulty; for if no substance can consist of universals, because they mean of such a kind, and not a particular thing; and if no substance can be actually composed of substances, every substance will be incomposite, and so there will be no formula of any substance.

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But in point of fact it is universally held, and has been previously stated,Aristot. Met. 7.5.5-7. that substance is the only or chief subject of definition; but on this showing there is no definition even of substance. Then there can be no definition of anything; or rather in a sense there can, and in a sense cannot. What this means will be clearer from what follows later.Aristot. Met. 7.15, Aristot. Met. 8.6.

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From these same considerations it is clear also what consequence follows for those who maintain that the Forms are substances and separable, and who at the same time make the species consist of the genus and the differentiae. If there are Forms, and if animal is present in the man and the horse, it is either numerically one and the same with them, or not.

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(In formula they are clearly one; for in each case the speaker will enunciate the same formula.) If, then, there is in some sense an Absolute Man, who is an individual and exists separately, then the constituents, e.g. animal and two-footed, must have an individual meaning and be separable and substances. Hence there must be an Absolute Animal too.

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(i) Then if the animal which is in the horse and the man is one and the same, as you are one and the same with yourself, how can the one which in things that exist separately be one, and why should not this animal also be separated from itself? Again, if it is to partake of two-footed and of many-footed, an impossibility follows; for contrary attributes will belong to it although it is one and individual.

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But if it does not, in what sense is it that one calls an animal two-footed or terrestrial? Perhaps the terms are combined and in contact or mixed. But all these expressions are absurd.

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(2) But there is a different animal in each species. Then there will be practically an infinity of things of which animal is the substance, since it is not in an accidental sense that man is derived from animal.

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Again, the Absolute Animal will be a plurality. For (a) the animal in each species will be the substance of that species, since the species is called after it and no other thing. Otherwise man would be derived from that other thing, which would be the genus of man. (b) Further, all the constituents of man will be Ideas. Then, since nothing can be the Idea of one thing and the substance of another (for this is impossible),

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each and every animal in the various species will be the Absolute Animal.

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Further, from what will these Forms be derived, and how can they be derived from the Absolute Animal? Or how can the animal, whose very essence is animal, exist apart from the Absolute Animal? And further, in the case of sensible things both these and still more absurd consequences follow. If, then, these consequences are impossible, clearly there are not Forms of sensible things in the sense in which some hold that there are.

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Since substance is of two kinds, the concrete thing and the formula (I mean that one kind of substance is the formula in combination with the matter, and the other is the formula in its full sense), substances in the former sense admit of destruction, for they also admit of generation. But the formula does not admit of destruction in the sense that it is ever being destroyed, since neither does it so admit of generation (for the essence of house is not generated, but only the essence of this house); formulae are , and are not, independently of generation and destruction; for it has been shownCf. Aristot. Met. 7.8.3. that no one either generates or creates them.

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For this reason also there is no definition or demonstration of particular sensible substances, because they contain matter whose nature is such that it can both exist and not exist. Hence all the individual instances of them are perishable.

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If, then, the demonstration and definition of necessary truths requires scientific knowledge, and if, just as knowledge cannot be sometimes knowledge and sometimes ignorance (it is opinion that is of this nature), so too demonstration and definition cannot vary (it is opinion that is concerned with that which can be otherwise than it is)— then clearly there can be neither definition nor demonstration of individual sensible substances.

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For (a) things which perish are obscure to those who have knowledge of them when they are removed from the sphere of their perception, and (b) even though their formulae are preserved in the soul, there will no longer be either definition or demonstration of them. Therefore in cases relating to definition, when we are trying to define any individual, we must not fail to realize that our definition may always be upset; because it is impossible to define these things.

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Nor, indeed, can any Idea be defined; for the Idea is an individual, as they say, and separable; and the formula must consist of words, and the man who is defining must not coin a word, because it would not be comprehensible. But the words which are in use are common to all the things which they denote; and so they must necessarily apply to something else as well. E.g., if a man were to define you, he would say that you are an animal which is lean or white or has some other attribute, which will apply to something else as well.

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And if it should be said that there is no reason why all the attributes separately should not belong to several things, and yet in combination belong to this alone, we must reply, (1.) that they also belong to both the elements; e.g., two-footed animal belongs both to animal and to two-footed (and in the case of eternal elements this is even necessarily so; since they are prior to the compound, and parts of it.

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Indeed they are also separable, if the term man is separable—for either neither can be separable, or both are so. If neither, the genus will not exist apart from the species, or if it is so to exist, so will the differentia); (2.) that animal and two-footed are prior in being to two-footed animal, and that which is prior to something else is not destroyed together with it.

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Again, if the Ideas are composed of Ideas (for constituents are less composite than that which they compose), still the elements of which the Idea is composed (e.g. animal and two-footed) will have to be predicated of many particulars. Otherwise, how can they be known? For there would be an Idea which cannot be predicated of more than one thing. But this is not considered possible; every Idea is thought to admit of participation.

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Thus, as we have said,The statement has only been implied in the preceding arguments. the impossibility of defining individuals is hard to realize when we are dealing with eternal entities, especially in the case of such as are unique, e.g. the sun and moon. For people go wrong not only by including in the definition attributes on whose removal it will still be sun—e.g., that which goes round the earth, or night-hidden (for they suppose that if it stops or becomes visiblesc. in the night. it will no longer be sun; but it is absurd that this should be so, since the sun denotes a definite substance)—they also mention attributes which may apply to something else; e.g., if another thing with those attributes comes into being, clearly it will be a sun. The formula, then, is general; but the sun was supposed to be an individual, like Cleon or Socrates.

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Why does not one of the exponents of the Ideas produce a definition of them? If they were to try, it would become obvious that what we have just said is true.

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It is obvious that even of those things which are thought to be substances the majority are potentialities; both the parts of living things (for none of them has a separate substantial existence; and when they are separated, although they still exist, they exist as matter), and earth, fire and air; for none of these is one thing —they are a mere aggregate before they are digested and some one thing is generated from them.

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It might be supposed very reasonably that the parts of living things and the corresponding parts of their vital principle are both, i.e. exist both actually and potentially, because they contain principles of motion derived from something in their joints; and hence some animalse.g. wasps, bees, tortoises (P. Nat. 467a 18, 468a 25). live even when they are divided. Nevertheless it is only potentially that all of them will exist when they are one and continuous by nature and not by force or concretion; for this sort of thing is malformation.i.e., it is only when they do not properly constitute a unity that parts can be said to exist actually.

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And since unity has the same variety of senses as being, and the substance of Unity is one, and things whose substance is numerically one are numerically one, evidently neither Unity nor Being can be the substance of things, just as neither being an element or principle can be the substance; but we ask what the principle is so that we may refer to something more intelligible.i.e., a thing is a principle in relation to something else which it explains; therefore a principle is less substantial than unity or being, which belong to a thing in itself.

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Now of these concepts Being and Unity are more nearly substance than are principle, element and cause; but not even the former are quite substance, since nothing else that is common is substance; for substance belongs to nothing except itself and that which contains it and of which it is the substance.

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Again, Unity cannot exist in many places at the same time, but that which is common is present in many things at the same time. Hence it is clear that no universal exists in separation apart from its particulars. The exponents of the Forms are partly right in their account when they make the Forms separate; that is, if the Forms are substances, but they are also partly wrong, since by Form they mean the one-over-many. i.e. universal; cf. Aristot. Met. 1.9.1.

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The reason for this is that they cannot explain what are the imperishable substances of this kind which exist besides particular sensible substances; so they make them the same in kind as perishable things (for these we know); i.e., they make Ideal Man and Ideal Horse, adding the word Ideal to the names of sensible things.

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However, I presume that even if we had never seen the stars, none the less there would be eternal substances besides those which we knew; and so in the present case even if we cannot apprehend what they are, still there must be eternal substances of some kind.

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It is clear, then, both that no universal term is substance and that no substance is composed of substances.

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As for what and what sort of thing we mean by substance, let us explain this by making, as it were, another fresh start. Perhaps in this way we shall also obtain some light upon that kind of substance which exists in separation from sensible substances. Since, then, substance is a kind of principle and cause, we had better pursue our inquiry from this point.

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Now when we ask why a thing is, it is always in the sense why does A belong to B?

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To ask why the cultured man is a cultured man is to ask either, as we have said, why the man is cultured, or something else. Now to ask why a thing is itself is no question; because when we ask the reason of a thing the fact must first be evident; e.g., that the moon suffers eclipse;

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and because it is itself is the one explanation and reason which applies to all questions such as why is man man? or why is the cultured person cultured? (unless one were to say that each thing is indivisible from itself, and that this is what being one really means); but this, besides being a general answer, is a summary one.The argument is: The question Why is the cultured man a cultured man? if it does not mean Why is the man cultured? can only mean Why is a thing itself? But when we ask a question the fact must be obvious; and since it is obvious that a thing is itself, because it is itself (or because each thing is indivisible from itself) is the one and only complete answer to all questions of this type. Since this answer (in either form) is clearly unsatisfactory, the question which it answers cannot be a proper question. We may, however, ask why a man is an animal of such-and-such a kind.

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It is clear, then, that we are not asking why he who is a man is a man; therefore we are asking why A, which is predicated of B, belongs to B. (The fact that A does belong to B must be evident, for if this is not so, the question is pointless.) E.g., Why does it thunder? means why is a noise produced in the clouds? for the true form of the question is one thing predicated in this way of another.

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Or again, why are these things, e.g. bricks and stones, a house? Clearly then we are inquiring for the cause (i.e., to speak abstractly, the essence); which is in the case of some things, e.g. house or bed, the end , and in others the prime mover—for this also is a cause. We look for the latter kind of cause in the case of generation and destruction, but for the former also in the case of existence.

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What we are now looking for is most obscure when one term is not predicated of another; e.g. when we inquire what man is; because the expression is a simple one not analyzed into subject and attributes. We must make the question articulate before we ask it; otherwise we get something which shares the nature of a pointless and of a definite question.

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Now since we must know that the fact actually exists, it is surely clear that the question is why is the matter so-and-so? e.g. why are these materials a house? Because the essence of house is present in them. And this matter, or the body containing this particular form, is man. Thus what we are seeking is the cause (i.e. the form) in virtue of which the matter is a definite thing; and this is the substance of the thing.

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Clearly then in the case of simple entitiesPure forms which contain no matter; in their case the method just described obviously will not apply. They can only be apprehended intuitively (cf. Aristot. Met. 9.10.). inquiry and explanation are impossible; in such cases there is a different mode of inquiry.

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Now since that which is composed of something in such a way that the whole is a unity; not as an aggregate is a unity, but as a syllable isThis sentence is not finished; the parenthesis which follows lasts until the end of the chapter.—the syllable is not the letters, nor is BA the same as B and A; nor is flesh fire and earth; because after dissolution the compounds, e.g. flesh or the syllable, no longer exist; but the letters exist, and so do fire and earth.

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Therefore the syllable is some particular thing; not merely the letters, vowel and consonant, but something else besides. And flesh is not merely fire and earth, or hot and cold, but something else besides.

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Since then this something else must be either an element or composed of elements, (a) if it is an element, the same argument applies again; for flesh will be composed of this and fire and earth, and again of another element, so that there will be an infinite regression. And (b) if it is composed of elements, clearly it is composed not of one (otherwise it will itself be that element) but of several; so that we shall use the same argument in this case as about the flesh or the syllable.

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It would seem, however, that this something else is something that is not an element, but is the cause that this matter is flesh and that matter a syllable, and similarly in other cases.

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And this is the substance of each thing, for it is the primary cause of its existence. And since, although some things are not substances, all substances are constituted in accordance with and by nature, substance would seem to be this nature, which is not an element but a principle.i.e. the formal cause. Cf. Aristot. Met. 5.4.4-6. An element is that which is present as matter in a thing, and into which the thing is divided; e.g., A and B are the elements of the syllable.

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We must now draw our conclusions from what has been said, and after summing up the result, bring our inquiry to a close. We have saidCf. Aristot. Met. 7.1. that the objects of our inquiry are the causes and principles and elements of substances. Now some substances are agreed upon by all; but about others certain thinkers have stated individual theories.

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Those about which there is agreement are natural substances: e.g. fire, earth, water, air and all the other simple bodies; next, plants and their parts, and animals and the parts of animals; and finally the sensible universe and its parts; and certain thinkers individually include as substances the Forms and the objects of mathematics.Cf. Aristot. Met. 7.2.

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And arguments show that there are yet other substances: the essence and the substrate.Cf. Aristot. Met. 7.3-4. Again, from another point of view, the genus is more nearly substance than the species, and the universal than the particularsCf. Aristot. Met. 7.13.; and there is a close connection between the universal and genus and the Ideas, for they are thought to be substance on the same grounds.Cf. Aristot. Met. 7.14.

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And since the essence is substance, and definition is the formula of the essence, we have therefore systematically examined definition and essential predication.Cf. Aristot. Met. 7.4-6, 12, 15. And since the definition is a formula, and the formula has parts, we have been compelled to investigate parts, and to discover what things are parts of the substance, and what are not; and whether the parts of the substance are also parts of the definition.Cf. Aristot. Met. 7.10, 11. Further, then, neither the universal nor the genus is substance.Cf. Aristot. Met. 7.13, 16.

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As for the Ideas and the objects of mathematics (for some say that these exist apart from sensible substances) we must consider them later.Books 13 and 14. But now let us proceed to discuss those substances which are generally accepted as such.

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Now these are the sensible substances, and all sensible substances contain matter.

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And the substrate is substance; in one sense matter (by matter I mean that which is not actually, but is potentially, an individual thing); and in another the formula and the specific shape (which is an individual thing and is theoretically separable); and thirdly there is the combination of the two, which alone admits of generation and destruction,Cf. Aristot. Met. 7.8. and is separable in an unqualified sense—for of substances in the sense of formula some are separableIn point of fact the only form which is absolutely separable is Mind or Reason. Cf. Aristot. Met. 12.7, 9. and some are not.

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That matter is also substance is evident; for in all opposite processes of change there is something that underlies those processes; e.g., if the change is of place , that which is now in one place and subsequently in another; and if the change is of magnitude , that which is now of such-and-such a size, and subsequently smaller or greater; and if the change is of quality , that which is now healthy and subsequently diseased.

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Similarly, if the change is in respect of being , there is something which is now in course of generation, and subsequently in course of destruction, and which is the underlying substrate, now as this individual thing, and subsequently as deprived of its individuality. In this last process of change the others are involved, but in either one or twoi.e., locomotion does not involve substantial change; alteration may or may not involve it (in Aristot. Met. 9.8.17 we find that it does not); increase or decrease does involve it. of the others it is not involved; for it does not necessarily follow that if a thing contains matter that admits of change of place, it also contains matter that is generable and destructible.e.g., the heavenly bodies, though imperishable, can move in space (Aristot. Met. 8.4.7, Aristot. Met. 12.2.4). The difference between absolute and qualified generation has been explained in the Physics.Aristot. Phys. 225a 12-20; cf. Aristot. De Gen. et Corr. 317a 17-31.

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Since substance in the sense of substrate or matter is admittedly substance, and this is potential substance, it remains to explain the nature of the actual substance of sensible things. Now DemocritusCf. Aristot. Met. 1.4.11. apparently assumes three differences in substance; for he says that the underlying body is one and the same in material, but differs in figure, i.e. shape; or inclination, i.e. position; or intercontact, i.e. arrangement.

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But evidently there are many differences; e.g. some things are defined by the way in which their materials are combined, as, for example, things which are unified by mixture, as honey-water; or by ligature, as a faggot; or by glue, as a book; or by clamping, as a chest; or by more than one of these methods. Other things are defined by their position, e.g. threshold and lintel (for these differ in being situated in a particular way); and others by place <or direction>, e.g. the winds; others by time, e.g. dinner and breakfast; and others by the attributes peculiar to sensible things, e.g. hardness and softness, density and rarity, dryness and humidity. Some are distinguished by some of these differences, and others by all of them; and in general some by excess and some by defect.

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Hence it is clear that is has the same number of senses; for a thing is a threshold because it is situated in a particular way, and to be a threshold means to be situated in this particular way, and to be ice means to be condensed in this particular way. Some things have their being defined in all these ways: by being partly mixed, partly blended, partly bound, partly condensed, and partly subjected to all the other different processes; as, for example, a hand or a foot.

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We must therefore comprehend the various kinds of differences—for these will be principles of being—i.e. the differences in degree, or in density and rarity, and in other such modifications, for they are all instances of excess and defect.

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And if anything differs in shape or in smoothness or roughness, all these are differences in straightness and curvature. For some things mixture will constitute being, and the opposite state not-being.

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From this it is evident that if substance is the cause of the existence of each thing, we must look among these differences for the cause of the being of each thing.

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No one of them, nor the combination of any two of them, is substance, but nevertheless each one of them contains something analogous to substance. And just as in the case of substances that which is predicated of the matter is the actuality itself, so in the other kinds of definition it is the nearest approximation to actuality. E.g., if we have to define a threshold, we shall call it a piece of wood or stone placed in such-and-such a way; and we should define a house as bricks and timber arranged in such-and-such a way;

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or again in some cases there is the final cause as well. And if we are defining ice, we shall describe it as water congealed or condensed in such-and-such a way; and a harmony is such-and-such a combination of high and low; and similarly in the other cases.

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From this it is evident that the actuality or formula is different in the case of different matter; for in some cases it is a combination, in others a mixture, and in others some other of the modes which we have described.

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Hence in defining the nature of a house, those who describe it as stones, bricks and wood, describe the potential house, since these things are its matter; those who describe it as a receptacle for containing goods and bodies, or something else to the same effect, describe its actuality; but those who combine these two definitions describe the third kind of substance, that which is composed of matter and form.

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For it would seem that the formula which involves the differentiae is that of the form and the actuality, while that which involves the constituent parts is rather that of the matter. The same is true of the kind of definitions which ArchytasA celebrated Pythagorean, contemporary with Plato. used to accept; for they are definitions of the combined matter and form. E.g., what is windlessness? Stillness in a large extent of air; for the air is the matter, and the stillness is the actuality and substance.

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What is a calm? Levelness of sea. The sea is the material substrate, and the levelness is the actuality or form.

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From the foregoing account it is clear what sensible substance is, and in what sense it exists; either as matter, or as form and actuality, or thirdly as the combination of the two.

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We must not fail to realize that sometimes it is doubtful whether a name denotes the composite substance or the actuality and the form—e.g. whether house denotes the composite thing, a covering made of bricks and stones arranged in such-and-such a way, or the actuality and form, a covering; and whether line means duality in length or dualityCf. Aristot. Met. 7.11.6.; and whether animal means a soul in a body or a soul; for the soul is the substance and actuality of some body.

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The term animal would be applicable to both cases; not as being defined by one formula, but as relating to one concept. These distinctions are of importance from another point of view, but unimportant for the investigation of sensible substance; because the essence belongs to the form and the actualization.

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Soul and essence of soul are the same, but man and essence of man are not, unless the soul is also to be called man; and although this is so in one sense, it is not so in another.

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It appears, then, upon inquiry into the matter,Cf. Plat. Theaet. 204aff. that a syllable is not derived from the phonetic elements plus combination, nor is a house bricks plus combination. And this is true; for the combination or mixture is not derived from the things of which it is a combination or mixture,

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nor, similarly, is any other of the differences. E.g., if the threshold is defined by its position, the position is not derived from the threshold, but rather vice versa. Nor, indeed, is man animal plus two-footed; there must be something which exists besides these, if they are matter; but it is neither an element nor derived from an element, but the substance; and those who offer the definition given above are omitting this and describing the matter.

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If, then, this something else is the cause of a man’s being, and this is his substance, they will not be stating his actual substance.

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Now the substance must be either eternal or perishable without ever being in process of perishing, and generated without ever being in process of generation. It has been clearly demonstrated elsewhereCf. Aristot. Met. 7.8. that no one generates or creates the form; it is the individual thing that is created, and the compound that is generated.

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But whether the substances of perishable things are separable or not is not yet at all clearCf. Aristot. Met. 8.1.6. n..; only it is clear that this is impossible in some cases, i.e. in the case of all things which cannot exist apart from the particular instances; e.g. house or implement.Cf. Aristot. Met. 7.8.6. Probably, then, neither these things themselves, nor anything else which is not naturally composed, are substances; for their nature is the only substance which one can assume in the case of perishable things.

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Hence the difficulty which perplexed the followers of AntisthenesCf. Aristot. Met. 5.29.4. and others similarly unlearned has a certain application; I mean the difficulty that it is impossible to define what a thing is (for the definition, they say, is a lengthy formula), but it is possible actually to teach others what a thing is like; e.g., we cannot say what silver is, but we can say that it is like tin.

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Hence there can be definition and formula of one kind of substance, i.e. the composite, whether it is sensible or intelligible; but not of its primary constituents, since the defining formula denotes something predicated of something, and this must be partly of the nature of matter and partly of the nature of form.

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It is also obvious that, if numbers are in any sense substances, they are such in this sense, and not, as someAristotle is referring to the Pythagoreans and Platonists, but seems as usual to misrepresent their views. His object in this section is to show that the relation of number to substance is only one of analogy. Cf. Aristot. Met. 13.6, 7, and see Introduction. describe them, aggregates of units. For (a) the definition is a kind of number, since it is divisible, and divisible into indivisible parts (for formulae are not infinite); and number is of this nature.

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And (b) just as when any element which composes the number is subtracted or added, it is no longer the same number but a different one, however small the subtraction or addition is; so neither the definition nor the essence will continue to exist if something is subtracted from or added to it. And (c) a number must be something in virtue of which it is a unity (whereas our opponents cannot say what makes it one); that is, if it is a unity.

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For either it is not a unity but a kind of aggregate, or if it is a unity, we must explain what makes a unity out of a plurality. And the definition is a unity; but similarly they cannot explain the definition either. This is a natural consequence, for the same reason applies to both, and substance is a unity in the way which we have explained, and not as some thinkers say: e.g. because it is a kind of unit or point; but each substance is a kind of actuality and nature.

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Also (d) just as a number does not admit of variation in degree, so neither does substance in the sense of form; if any substance does admit of this, it is substance in combination with matter.In Aristot. Categories 3b 33-4a 9 Aristotle does not allow this exception.

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Let this suffice as a detailed account of the generation and destruction of so-called substances, in what sense they are possible and in what sense they are not; and of the reference of things to number.

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As regards material substance, we must not fail to realize that even if all things are derived from the same primary cause, or from the same things as primary causesi.e. from prime matter or the four elements.; i.e. even if all things that are generated have the same matter for their first principle, nevertheless each thing has some matter peculiar to it; e.g., the sweet or the viscous is the proximate matter of mucus, and the bitter or some such thing is that of bile— although probably mucus and bile are derived from the same ultimate matter.

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The result is that there is more than one matter of the same thing, when one thing is the matter of the other; e.g., mucus is derived from the viscous; and from the sweet, if the viscous is derived from the sweet; and from bile, by the analysis of bile into its ultimate matter. For there are two senses in which X comes from Y; either because X will be found further on than Y in the process of development, or because X is produced when Y is analyzed into its original constituents.

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And different things can be generated by the moving cause when the matter is one and the same, e.g. a chest and a bed from wood. But some different things must necessarily have different matter; e.g., a saw cannot be generated from wood, nor does this lie in the power of the moving cause, for it cannot make a saw of wool or wood.

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If, then, it is possible to make the same thing from different matter, clearly the art, i.e. the moving principle, is the same; for if both the matter and the mover are different, so too is the product.

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So whenever we inquire what the cause is, since there are causes in several senses, we must state all the possible causes.

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E.g., what is the material cause of a man? The menses. What is the moving cause? The semen. What is the formal cause? The essence. What is the final cause? The end. (But perhaps both the latter are the same.) We must, however, state the most proximate causes. What is the matter? Not fire or earth, but the matter proper to man.

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Thus as regards generable natural substances we must proceed in this manner, if we are to proceed correctly; that is, if the causes are these and of this number, and it is necessary to know the causes. But in the case of substances which though natural are eternal the principle is different. For presumably some of them have no matter; or no matter of this kind, but only such as is spatially mobile.Cf. Aristot. Met. 8.1.8 n.

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Moreover, things which exist by nature but are not substances have no matter; their substrate is their substance. E.g., what is the cause of an eclipse; what is its matter? It has none; it is the moon which is affected. What is the moving cause which destroys the light? The earth. There is probably no final cause. The formal cause is the formula; but this is obscure unless it includes the efficient cause.

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E.g., what is an eclipse? A privation of light; and if we add caused by the earth’s intervention, this is the definition which includes the <efficient> cause. In the case of sleep it is not clear what it is that is proximately affected. Is it the animal? Yes; but in respect of what, and of what proximately? The heart, or some other part. Again, by what is it affected? Again, what is the affection which affects that part, and not the whole animal? A particular kind of immobility? Yes; but in virtue of what affection of the proximate subject is it this?

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Since some things both are and are not, without being liable to generation and destructionCf. Aristot. Met. 6.3.1, Aristot. Met. 7.8.3.—e.g. points,Cf. Aristot. Met. 3.5.8, 9. if they exist at all; and in general the forms and shapes of things (because white does not come to be, but the wood becomes white, since everything which comes into being comes from something and becomes something)—not all the contrariesi.e., we must distinguish contraries in the sense of contrary qualities from contraries in the sense of things characterized by contrary qualities. can be generated from each other. White is not generated from black in the same way as a white man is generated from a black man; nor does everything contain matter, but only such things as admit of generation and transformation into each other.

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And such things as, without undergoing a process of change, both are and are not, have no matter.

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There is a difficulty in the question how the matter of the individual is related to the contraries. E.g., if the body is potentially healthy, and the contrary of health is disease, is the body potentially both healthy and diseased? And is water potentially wine and vinegar? Probably in the one case it is the matter in respect of the positive state and form, and in the other case in respect of privation and degeneration which is contrary to its proper nature.

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There is also a difficulty as to why wine is not the matter of vinegar, nor potentially vinegar (though vinegar comes from it), and why the living man is not potentially dead. In point of fact they are not; their degeneration is accidental, and the actual matter of the living body becomes by degeneration the potentiality and matter of the dead body, and water the matter of vinegar; for the one becomes the other just as day becomes night.

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All things which change reciprocally in this way must return into the matter; e.g., if a living thing is generated from a dead one, it must first become the matter, and then a living thing; and vinegar must first become water, and then wine.

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With regard to the difficulty which we have describedAristot. Met. 7.12, Aristot. Met. 8.3.10, 11. in connection with definitions and numbers, what is the cause of the unification? In all things which have a plurality of parts, and which are not a total aggregate but a whole of some sort distinct from the parts, there is some cause ; inasmuch as even in bodies sometimes contact is the cause of their unity, and sometimes viscosity or some other such quality.

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But a definition is one account, not by connection, like the Iliad , but because it is a definition of one thing.

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What is it, then, that makes man one thing, and why does it make him one thing and not many, e.g. animal and two-footed, especially if, as some say, there is an Idea of animal and an Idea of two-footed?

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Why are not these Ideas man, and why should not man exist by participation, not in any man, but in two Ideas, those of animal and two-footed? And in general man will be not one, but two things—animal and two-footed. Evidently if we proceed in this way, as it is usual to define and explain, it will be impossible to answer and solve the difficulty.

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But if, as we maintain, man is part matter and part form—the matter being potentially, and the form actually man—, the point which we are investigating will no longer seem to be a difficulty. For this difficulty is just the same as we should have if the definition of XLiterally cloak; cf. Aristot. Met. 7.4.7 n. were round bronze; for this name would give a clue to the formula, so that the question becomes what is the cause of the unification of round and bronze?

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The difficulty is no longer apparent, because the one is matter and the other form. What then is it (apart from the active cause) which causes that which exists potentially to exist actually in things which admit of generation? There is no other cause of the potential sphere’s being an actual sphere; this was the essence of each.i.e., it was the essence of the potential sphere to become the actual sphere, and of the actual sphere to be generated from the potential sphere.

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Some matter is intelligible and some sensible, and part of the formula is always matter and part actuality; e.g., the circle is a plane figure.Even formulae contain matter in a sense (intelligible matter); i.e. the generic element in the species. Plane figure is the generic element of circle. But such thingThe highest genera, or categories. as have no matter, neither intelligible nor sensible, are ipso facto each one of them essentially something one; just as they are essentially something existent: an individual substance, a quality, or a quantity. Hence neither existent nor one is present in their definitions. And their essence is ipso facto something one, just as it is something existent.

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Hence also there is no other cause of the unity of any of these things, or of their existence; for each one of them is one and existent not because it is contained in the genus being or unity, nor because these genera exist separately apart from their particulars, but ipso facto.

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It is because of this difficulty that some thinkersThe Platonists. speak of participation, and raise the question of what is the cause of participation, and what participation means; and others speak of communion; e.g., LycophronA sophist, disciple of Gorgias. says that knowledge is a communion of the soul with knowing; and others call life a combination or connection of soul with body.

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The same argument, however, applies in every case; for being healthy will be the communion or connection or combination of soul and health; and being a bronze triangle a combination of bronze and triangle; and being white a combination of surface and whiteness. The reason for this is that people look for a unifying formula, and a difference, between potentiality and actuality.

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But, as we have said,Cf. sects. 4, 5. the proximate matter and the shape are one and the same; the one existing potentially, and the other actually. Therefore to ask the cause of their unity is like asking the cause of unity in general; for each individual thing is one, and the potential and the actual are in a sense one. Thus there is no cause other than whatever initiates the development from potentiality to actuality. And such things as have no matter are all, without qualification, essential unities.

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We have now dealt with Being in the primary sense, to which all the other categories of being are related; i.e. substance. For it is from the concept of substance that all the other modes of being take their meaning; both quantity and quality and all other such terms; for they will all involve the concept of substance, as we stated it in the beginning of our discussion.Aristot. Met. 7.1.

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And since the senses of being are analyzableCf. Aristot. Met. 6.2.1. not only into substance or quality or quantity, but also in accordance with potentiality and actuality and function, let us also gain a clear understanding about potentiality and actuality; and first about potentiality in the sense which is most proper to the word, but not most useful for our present purpose— for potentiality and actuality extend beyond the sphere of terms which only refer to motion.

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When we have discussed this sense of potentiality we will, in the course of our definitions of actuality,Chs. 6-10. explain the others also.

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We have made it plain elsewhereAristot. Met. 5.12. that potentiality and can have several senses.

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All senses which are merely equivocal may be dismissed; for some are used by analogy, as in geometry,Cf. Aristot. Met. 5.12.11. and we call things possible or impossible because they are or are not in some particular way. But the potentialities which conform to the same type are all principles, and derive their meaning from one primary sense of potency, which is the source of change in some other thing, or in the same thing qua other.

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One kind of potentiality is the power of being affected; the principle in the patient itself which initiates a passive change in it by the action of some other thing, or of itself qua other. Another is a positive state of impassivity in respect of deterioration or destruction by something else or by itself qua something else; i.e. by a transformatory principle—for all these definitions contain the formula of the primary sense of potentiality.

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Again, all these potentialities are so called either because they merely act or are acted upon in a particular way, or because they do so well . Hence in their formulae also the formulae of potentiality in the senses previously described are present in some degree.

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Clearly, then, in one sense the potentiality for acting and being acted upon is one (for a thing is capable both because it itself possesses the power of being acted upon, and also because something else has the power of being acted upon by it);

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and in another sense it is not; for it is partly in the patient (for it is because it contains a certain principle, and because even the matter is a kind of principle, that the patient is acted upon; i.e., one thing is acted upon by another: oily stuff is inflammable, and stuff which yields in a certain way is breakable, and similarly in other cases)—

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and partly in the agent; e.g. heat and the art of building: the former in that which produces heat, and the latter in that which builds. Hence in so far as it is a natural unity, nothing is acted upon by itself; because it is one, and not a separate thing.

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Incapacity and the incapable is the privation contrary to capacity in this sense; so that every capacity has a contrary incapacity for producing the same result in respect of the same subject.

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Privation has several sensesCf. Aristot. Met. 5.22.—it is applied (1.) to anything which does not possess a certain attribute; (2.) to that which would naturally possess it, but does not; either (a) in general, or (b) when it would naturally possess it; and either (1) in a particular way, e.g. entirely, or (2) in any way at all. And in some cases if things which would naturally possess some attribute lack it as the result of constraint, we say that they are deprived.

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Since some of these principles are inherent in inanimate things, and others in animate things and in the soul and in the rational part of the soul, it is clear that some of the potencies also will be irrational and some rational. Hence all arts, i.e. the productive sciences, are potencies; because they are principles of change in another thing, or in the artist himself qua other.

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Every rational potency admits equally of contrary results, but irrational potencies admit of one result only. E.g., heat can only produce heat, but medical science can produce disease and health. The reason of this is that science is a rational account, and the same account explains both the thing and its privation, though not in the same way; and in one sense it applies to both, and in another sense rather to the actual fact.

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Therefore such sciences must treat of contraries—essentially of the one, and non-essentially of the other; for the rational account also applies essentially to the one, but to the other in a kind of accidental way, since it is by negation and removal that it throws light on the contrary. For the contrary is the primary privation,Cf. Aristot. Met. 10.4.7. and this is the removal of that to which it is contrary.Literally of the other, i.e. the positive term.

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And since contrary attributes cannot be induced in the same subject, and science is a potency which depends upon the possession of a rational formula, and the soul contains a principle of motion, it follows that whereas the salutary can only produce health, and the calefactory only heat, and the frigorific only cold, the scientific man can produce both contrary results.

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For the rational account includes both, though not in the same way; and it is in the soul, which contains a principle of motion, and will therefore, by means of the same principle, set both processes in motion, by linking them with the same rational account. Hence things which have a rational potency produce results contrary to those of things whose potency is irrationalThe meaning of this awkward sentence is clearly shown in the latter part of 4.; for the results of the former are included under one principle, the rational account.

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It is evident also that whereas the power of merely producing (or suffering) a given effect is implied in the power of producing that effect well , the contrary is not always true; for that which produces an effect well must also produce it, but that which merely produces a given effect does not necessarily produce it well.

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There are some, e.g. the Megaric school,Founded by Euclides of Megara, an enthusiastic admirer of Socrates. The Megarics adopted the Eleatic system and developed it along dialectical lines. who say that a thing only has potency when it functions, and that when it is not functioning it has no potency. E.g., they say that a man who is not building cannot build, but only the man who is building, and at the moment when he is building; and similarly in the other cases.

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It is not difficult to see the absurd consequences of this theory. Obviously a man will not be a builder unless he is building, because to be a builder is to be capable of building; and the same will be true of the other arts.

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If, therefore, it is impossible to possess these arts without learning them at some time and having grasped them, and impossible not to possess them without having lost them at some time (through forgetfulness or some affection or the lapse of time; not, of course, through the destruction of the object of the art,i.e. the form of house. because it exists always), when the artist ceases to practice his art, he will not possess it;

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and if he immediately starts building again, how will he have re-acquired the art?

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The same is true of inanimate things. Neither the cold nor the hot nor the sweet nor in general any sensible thing will exist unless we are perceiving it (and so the result will be that they are affirming Protagoras’ theoryCf. IV. v., vi.). Indeed, nothing will have the faculty of sensation unless it is perceiving, i.e. actually employing the faculty.

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If, then, that is blind which has not sight, though it would naturally have it, and when it would naturally have it, and while it still exists, the same people will be blind many times a day; and deaf too.

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Further, if that which is deprived of its potency is incapable, that which is not happening will be incapable of happening; and he who says that that which is incapable of happening is or will be, will be in error, for this is what incapable meant.i.e., we have just said that that which is incapable is deprived of its potency—in this case, of its potency for happening.

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Thus these theories do away with both motion and generation; for that which is standing will always stand, and that which is sitting will always sit; because if it is sitting it will not get up, since it is impossible that anything which is incapable of getting up should get up.

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Since, then, we cannot maintain this, obviously potentiality and actuality are different. But these theories make potentiality and actuality identical; hence it is no small thing that they are trying to abolish.

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Thus it is possible that a thing may be capable of being and yet not be, and capable of not being and yet be; and similarly in the other categories that which is capable of walking may not walk, and that which is capable of not walking may walk.

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A thing is capable of doing something if there is nothing impossible in its having the actuality of that of which it is said to have the potentiality. I mean, e.g., that if a thing is capable of sitting and is not prevented from sitting, there is nothing impossible in its actually sitting; and similarly if it is capable of being moved or moving or standing or making to stand or being or becoming or not being or not becoming.

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The term actuality, with its implication of complete reality, has been extended from motions, to which it properly belongs, to other things; for it is agreed that actuality is properly motion.

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Hence people do not invest non-existent things with motion, although they do invest them with certain other predicates. E.g., they say that non-existent things are conceivable and desirable, but not that they are in motion. This is because, although these things do not exist actually, they will exist actually; for some non-existent things exist potentially; yet they do not exist, because they do not exist in complete reality.

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Now if, as we have said, that is possible which does not involve an impossibility, obviously it cannot be true to say that so-and-so is possible, but will not be, this view entirely loses sight of the instances of impossibility.If it is true to say that a thing which is possible will not be, anything may be possible, and nothing impossible. I mean, suppose that someone—i.e. the sort of man who does not take the impossible into account—were to say that it is possible to measure the diagonal of a square, but that it will not be measured, because there is nothing to prevent a thing which is capable of being or coming to be from neither being nor being likely ever to be.

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But from our premisses this necessarily follows: that if we are to assume that which is not, but is possible, to be or to have come to be, nothing impossible must be involved. But in this case something impossible will take place; for the measuring of the diagonal is impossible.

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The false is of course not the same as the impossible; for although it is false that you are now standing, it is not impossible.

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At the same time it is also clear that if B must be real if A is, then if it is possible for A to be real, it must also be possible for B to be real; for even if B is not necessarily possible, there is nothing to prevent its being possible. Let A, then, be possible. Then when A was possible, if A was assumed to be real, nothing impossible was involved; but B was necessarily real too. But ex hypothesi B was impossible. Let B be impossible.

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Then if B is impossible, A must also be impossible. But A was by definition possible. Therefore so is B.

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If, therefore, A is possible, B will also be possible; that is if their relation was such that if A is real, B must be real.

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Then if, A and B being thus related, B is not possible on this condition, A and B will not be related as we assumed; and if when A is possible B is necessarily possible, then if A is real B must be real too. For to say that B must be possible if A is possible means that if A is real at the time when and in the way in which it was assumed that it was possible for it to be real, then B must be real at that time and in that way.

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Since all potencies are either innate, like the senses, or acquired by practice, like flute-playing, or by study, as in the arts, some—such as are acquired by practice or a rational formula—we can only possess when we have first exercised themCf. Aristot. Met. 9.8.6, 7.; in the case of others which are not of this kind and which imply passivity, this is not necessary.

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Since anything which is possible is something possible at some time and in some way, and with any other qualifications which are necessarily included in the definition; and since some things can set up processes rationally and have rational potencies, while others are irrational and have irrational potencies; and since the former class can only belong to a living thing, whereas the latter can belong both to living and to inanimate things: it follows that as for potencies of the latter kind, when the agent and the patient meet in accordance with the potency in question, the one must act and the other be acted upon; but in the former kind of potency this is not necessary, for whereas each single potency of the latter kind is productive of a single effect, those of the former kind are productive of contrary effects,Cf. Aristot. Met. 9.2.4, 5. so that one potency will produce at the same time contrary effects.sc., if every potency must act automatically whenever agent and patient meet.

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But this is impossible. Therefore there must be some other deciding factor, by which I mean desire or conscious choice. For whichever of two things an animal desires decisively it will do, when it is in circumstances appropriate to the potency and meets with that which admits of being acted upon. Therefore everything which is rationally capable, when it desires something of which it has the capability, and in the circumstances in which it has the capability, must do that thing.

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Now it has the capability when that which admits of being acted upon is present and is in a certain state; otherwise it will not be able to act. (To add the qualification if nothing external prevents it is no longer necessary; because the agent has the capability in so far as it is a capability of acting; and this is not in all, but in certain circumstances, in which external hindrances will be excluded; for they are precluded by some of the positive qualifications in the definition.)

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Hence even if it wishes or desires to do two things or contrary things simultaneously, it will not do them, for it has not the capability to do them under these conditions, nor has it the capability of doing things simultaneously, since it will only do the things to which the capability applies and under the appropriate conditions.

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Since we have now dealt with the kind of potency which is related to motion, let us now discuss actuality; what it is, and what its qualities are. For as we continue our analysis it will also become clear with regard to the potential that we apply the name not only to that whose nature it is to move or be moved by something else, either without qualification or in some definite way, but also in other senses; and it is on this account that in the course of our inquiry we have discussed these as well.

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Actuality means the presence of the thing, not in the sense which we mean by potentially. We say that a thing is present potentially as Hermes is present in the wood, or the half-line in the whole, because it can be separated from it; and as we call even a man who is not studying a scholar if he is capable of studying. That which is present in the opposite sense to this is present actually.

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What we mean can be plainly seen in the particular cases by induction; we need not seek a definition for every term, but must comprehend the analogy: that as that which is actually building is to that which is capable of building, so is that which is awake to that which is asleep; and that which is seeing to that which has the eyes shut, but has the power of sight; and that which is differentiated out of matter to the matter; and the finished article to the raw material.

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Let actuality be defined by one member of this antithesis, and the potential by the other.

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But things are not all said to exist actually in the same sense, but only by analogy—as A is in B or to B, so is C in or to D; for the relation is either that of motion to potentiality, or that of substance to some particular matter.

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Infinity and void and other concepts of this kind are said to be potentially or actually in a different sense from the majority of existing things, e.g. that which sees, or walks, or is seen.

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For in these latter cases the predication may sometimes be truly made without qualification, since that which is seen is so called sometimes because it is seen and sometimes because it is capable of being seen; but the Infinite does not exist potentially in the sense that it will ever exist separately in actuality; it is separable only in knowledge. For the fact that the process of division never ceases makes this actuality exist potentially, but not separately.For Aristotle’s views about infinity and void see Aristot. Physics 3.4-8, 4.6-9 respectively.

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Since no action which has a limit is an end, but only a means to the end, as, e.g., the process of thinning; and since the parts of the body themselves, when one is thinning them, are in motion in the sense that they are not already that which it is the object of the motion to make them, this process is not an action, or at least not a complete one, since it is not an end; it is the process which includes the end that is an action.

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E.g., at the same time we see and have seen, understand and have understood, think and have thought; but we cannot at the same time learn and have learnt, or become healthy and be healthy. We are living well and have lived well, we are happy and have been happy, at the same time; otherwise the process would have had to cease at some time, like the thinning-process; but it has not ceased at the present moment; we both are living and have lived.

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Now of these processes we should call the one type motions, and the other actualizations.

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Every motion is incomplete—the processes of thinning, learning, walking, building—these are motions, and incomplete at that. For it is not the same thing which at the same time is walking and has walked, or is building and has built, or is becoming and has become, or is being moved and has been moved, but two different things; and that which is causing motion is different from that which has caused motion.

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But the same thing at the same time is seeing and has seen, is thinking and has thought. The latter kind of process, then, is what I mean by actualization, and the former what I mean by motion.

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What the actual is, then, and what it is like, may be regarded as demonstrated from these and similar considerations.

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We must, however, distinguish when a particular thing exists potentially, and when it does not; for it does not so exist at any and every time. E.g., is earth potentially a man? No, but rather when it has already become semen,This is inconsistent with Aristotle’s doctrine that the semen is the formal element in reproduction. Cf. Aristot. Met. 8.4.5, Aristot. Met. 6.9.5. and perhaps not even then; just as not everything can be healed by medicine, or even by chance, but there is some definite kind of thing which is capable of it, and this is that which is potentially healthy.

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The definition of that which as a result of thought comes, from existing potentially, to exist actually, is that, when it has been willed, if no external influence hinders it, it comes to pass; and the condition in the case of the patient, i.e. in the person who is being healed, is that nothing in him should hinder the process. Similarly a house exists potentially if there is nothing in X, the matter, to prevent it from becoming a house, i.e., if there is nothing which must be added or removed or changed; then X is potentially a house;

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and similarly in all other cases where the generative principle is external. And in all cases where the generative principle is contained in the thing itself, one thing is potentially another when, if nothing external hinders, it will of itself become the other. E.g., the semen is not yet potentially a man; for it must further undergo a change in some other medium.This is inconsistent with Aristotle’s doctrine that the semen is the formal element in reproduction. Cf. Aristot. Met. 8.4.5, Aristot. Met. 9.6.5. But when, by its own generative principle, it has already come to have the necessary attributes, in this state it is now potentially a man, whereas in the former state it has need of another principle;

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just as earth is not yet potentially a statue, because it must undergo a change before it becomes bronze.

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It seems that what we are describing is not a particular thing, but a definite material; e.g., a box is not wood, but wooden material,Cf. Aristot. Met. 7.7.10-12. and wood is not earth, but earthen material; and earth also is an illustration of our point if it is similarly not some other thing, but a definite material—it is always the latter term in this series which is, in the fullest sense, potentially something else.

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E.g., a box is not earth, nor earthen, but wooden; for it is this that is potentially a box, and this is the matter of the box—that is, wooden material in general is the matter of box in general, whereas the matter of a particular box is a particular piece of wood.

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If there is some primary stuff, which is not further called the material of some other thing, this is primary matter. E.g., if earth is made of air, and air is not fire, but made of fire, then fire is primary matter, not being an individual thing.

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For the subject or substrate is distinguishable into two kinds by either being or not being an individual thing. Take for example as the subject of the attributes man, or body or soul, and as an attribute cultured or white. Now the subject, when culture is induced in it, is called not culture but cultured, and the man is called not whiteness but white; nor is he called ambulation or motion, but walking or moving; just as we said that things are of a definite material.

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Thus where subject has this sense, the ultimate substrate is substance; but where it has not this sense, and the predicate is a form or individuality, the ultimate substrate is matter or material substance. It is quite proper that both matter and attributes should be described by a derivative predicate, since they are both indefinite.

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Thus it has now been stated when a thing should be said to exist potentially, and when it should not.

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Now since we have distinguishedAristot. Met. 5.11. the several senses of priority, it is obvious that actuality is prior to potentiality. By potentiality I mean not that which we have defined as a principle of change which is in something other than the thing changed, or in that same thing qua other, but in general any principle of motion or of rest; for nature also is in the same genus as potentiality, because it is a principle of motion, although not in some other thing, but in the thing itself qua itself.Cf. Aristot. Met. 5.4.1.

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To every potentiality of this kind actuality is prior, both in formula and in substance; in time it is sometimes prior and sometimes not.

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That actuality is prior in formula is evident; for it is because it can be actualized that the potential, in the primary sense, is potential, I mean, e.g., that the potentially constructive is that which can construct, the potentially seeing that which can see, and the potentially visible that which can be seen.

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The same principle holds in all other cases too, so that the formula and knowledge of the actual must precede the knowledge of the potential.

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In time it is prior in this sense: the actual is prior to the potential with which it is formally identical, but not to that with which it is identical numerically.

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What I mean is this: that the matter and the seed and the thing which is capable of seeing, which are potentially a man and corn and seeing, but are not yet so actually, are prior in time to the individual man and corn and seeing subject which already exist in actuality.

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But prior in time to these potential entities are other actual entities from which the former are generated; for the actually existent is always generated from the potentially existent by something which is actually existent—e.g., man by man, cultured by cultured—there is always some prime mover; and that which initiates motion exists already in actuality.

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We have saidAristot. Met. 7.7, 8. in our discussion of substance that everything which is generated is generated from something and by something; and by something formally identical with itself.

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Hence it seems impossible that a man can be a builder if he has never built, or a harpist if he has never played a harp; because he who learns to play the harp learns by playing it, and similarly in all other cases.

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This was the origin of the sophists’ quibble that a man who does not know a given science will be doing that which is the object of that science, because the learner does not know the science. But since something of that which is being generated is already generated, and something of that which is being moved as a whole is already moved (this is demonstrated in our discussion on MotionAristot. Physics, 6.6.), presumably the learner too must possess something of the science.

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At any rate from this argument it is clear that actuality is prior to potentiality in this sense too, i.e. in respect of generation and time.

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But it is also prior in substantiality; (a) because things which are posterior in generation are prior in form and substantiality; e.g., adult is prior to child, and man to semen, because the one already possesses the form, but the other does not;

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and (b) because everything which is generated moves towards a principle, i.e. its end . For the object of a thing is its principle; and generation has as its object the end . And the actuality is the end, and it is for the sake of this that the potentiality is acquired; for animals do not see in order that they may have sight, but have sight in order that they may see.

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Similarly men possess the art of building in order that they may build, and the power of speculation that they may speculate; they do not speculate in order that they may have the power of speculation—except those who are learning by practice; and they do not really speculate, but only in a limited sense, or about a subject about which they have no desire to speculate.

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Further, matter exists potentially, because it may attain to the form; but when it exists actually, it is then in the form. The same applies in all other cases, including those where the end is motion.

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Hence, just as teachers think that they have achieved their end when they have exhibited their pupil performing, so it is with nature. For if this is not so, it will be another case of Pauson’s HermesProbably a trick picture of some kind. So Pauson is said to have painted a picture of a horse galloping which when inverted showed the horse rolling on its back. Cf. Aelian, Var. Hist. 14.15; Lucian, Demosth. Enc. 24; Plut. Moralia, 396e; Pfuhl, Malerei und Zeichnung der Griechen, 763.; it will be impossible to say whether the knowledge is in the pupil or outside him, as in the case of the Hermes. For the activity is the end, and the actuality is the activity; hence the term actuality is derived from activity, and tends to have the meaning of complete reality.

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Now whereas in some cases the ultimate thing is the use of the faculty, as, e.g., in the case of sight seeing is the ultimate thing, and sight produces nothing else besides this; but in other cases something is produced, e.g. the art of building produces not only the act of building but a house; nevertheless in the one case the use of the faculty is the end, and in the other it is more truly the end than is the potentiality. For the act of building resides in the thing built; i.e., it comes to be and exists simultaneously with the house.

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Thus in all cases where the result is something other than the exercise of the faculty, the actuality resides in the thing produced; e.g. the act of building in the thing built, the act of weaving in the thing woven, and so on; and in general the motion resides in the thing moved. But where there is no other result besides the actualization, the actualization resides in the subject; e.g. seeing in the seer, and speculation in the speculator, and life in the soul

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(and hence also happiness, since happiness is a particular kind of life). Evidently, therefore, substance or form is actuality. Thus it is obvious by this argument that actuality is prior in substantiality to potentiality; and that in point of time, as we have said, one actuality presupposes another right back to that of the prime mover in each case.

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It is also prior in a deeper sense; because that which is eternal is prior in substantiality to that which is perishable, and nothing eternal is potential. The argument is as follows. Every potentiality is at the same time a potentiality for the opposite.Cf. 19. For whereas that which is incapable of happening cannot happen to anything, everything which is capable may fail to be actualized.

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Therefore that which is capable of being may both be and not be. Therefore the same thing is capable both of being and of not being. But that which is capable of not being may possibly not be; and that which may possibly not be is perishable; either absolutely, or in the particular sense in which it is said that it may possibly not be; that is, in respect either of place or of quantity or of quality. Absolutely means in respect of substance.

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Hence nothing which is absolutely imperishable is absolutely potential (although there is no reason why it should not be potential in some particular respect; e.g. of quality or place); therefore all imperishable things are actual. Nor can anything which is of necessity be potential; and yet these things are primary, for if they did not exist, nothing would exist. Nor can motion be potential, if there is any eternal motion. Nor, if there is anything eternally in motion, is it potentially in motion (except in respect of some starting-point or destination), and there is no reason why the matter of such a thing should not exist.

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Hence the sun and stars and the whole visible heaven are always active, and there is no fear that they will ever stop—a fear which the writerse.g. Empedocles; cf. Aristot. Met. 5.23.3 n. on physics entertain. Nor do the heavenly bodies tire in their activity; for motion does not imply for them, as it does for perishable things, the potentiality for the opposite, which makes the continuity of the motion distressing; this results when the substance is matter and potentiality, not actuality.

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Imperishable things are resembled in this respect by things which are always undergoing transformation, such as earth and fire; for the latter too are always active, since they have their motion independently and in themselves.Cf. Aristot. De Gen. et Corr. 337a 1-7. Other potentialities, according to the distinctions already made,Aristot. Met. 9.5.2. all admit of the opposite result; for that which is capable of causing motion in a certain way can also cause it not in that way; that is if it acts rationally.

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The same irrational potentialities can only produce opposite results by their presence or absence.

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Thus if there are any entities or substances such as the dialecticiansFor this description of the Platonists cf. Aristot. Met. 1.6.7. describe the Ideas to be, there must be something which has much more knowledge than absolute knowledge, and much more mobility than motion; for they will be in a truer sense actualities, whereas knowledge and motion will be their potentialities.This is a passing thrust at the Ideal theory. Absolute knowledge (the faculty of knowledge) will be a mere potentiality, and therefore substantially posterior to its actualization in particular instances. Thus it is obvious that actuality is prior both to potentiality and to every principle of change.

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That a good actuality is both better and more estimable than a good potentiality will be obvious from the following arguments. Everything of which we speak as capable is alike capable of contrary results; e.g., that which we call capable of being well is alike capable of being ill, and has both potentialities at once; for the same potentiality admits of health and disease, or of rest and motion, or of building and of pulling down, or of being built and of falling down.

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Thus the capacity for two contraries can belong to a thing at the same time, but the contraries cannot belong at the same time; i.e., the actualities, e.g. health and disease, cannot belong to a thing at the same time. Therefore one of them must be the good; but the potentiality may equally well be both or neither. Therefore the actuality is better.

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Also in the case of evils the end or actuality must be worse than the potentiality; for that which is capable is capable alike of both contraries.

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Clearly, then, evil does not exist apart from things ; for evil is by nature posterior to potentiality.The argument is presumably as follows (the fallacy, as pointed out by Bonitz, is indicated in parenthesis): That which has a separate substantial existence is actuality. Actuality is prior (substantially) to potentiality. Potentiality is prior to evil (in the moral scale. But since by evil Aristotle means the actualization of a potentiality for evil, potentiality is substantially posterior to evil). Therefore that which has a separate substantial existence is prior to evil; i.e., evil does not exist apart from particular instances of evil. The argument is directed against the Platonic Idea of evil (Plat. Rep. 476a); and the corollary which follows against the identification of Evil with one of the principles of the universe (Aristot. Met. 1.6.10, Aristot. Met. 12.10.6, Aristot. Met. 14.4.10, 11; cf. Plat. Laws 896e, Plat. Laws 898c). Nor is there in things which are original and eternal any evil or error, or anything which has been destroyed—for destruction is an evil.

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Geometrical constructions, too, are discovered by an actualization, because it is by dividing that we discover them. If the division were already done, they would be obvious; but as it is the division is only there potentially. Why is the sum of the interior angles of a triangle equal to two right angles? Because the angles about one point <in a straight line> are equal to two right angles. If the line parallel to the side had been already drawn, the answer would have been obvious at sight.The figure, construction and proof are as follows: ***

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Why is the angle in a semicircle always a right angle? If three lines are equal, the two forming the base, and the one set upright from the middle of the base, the answer is obvious to one who knows the former proposition.Aristotle implies a proof something after this fashion: FIGURE BAC is an angle in a semicircle. From D, the mid-point of the diameter BC, draw a perpendicular DE to meet the circumference at E. Join EB, EC.*** Thus it is evident that the potential constructions are discovered by being actualized. The reason for this is that the actualization is an act of thinking. Thus potentiality comes from actuality (and therefore it is by constructive action that we acquire knowledge). <But this is true only in the abstract>, for the individual actuality is posterior in generation to its potentiality.This whole passage (sects. 4, 5) should be compared with Aristot. Met. 9.8.3-7, where it logically belongs.

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The terms being and not-being are used not only with reference to the types of predication, and to the potentiality or actuality, or non-potentiality and non-actuality, of these types, but also (in the strictest senseThis appears to contradict Aristot. Met. 6.4.3. But it is just possible to interpret κυριώτατα(with Jaeger) as in the commonest sense. ) to denote truth and falsity. This depends, in the case of the objects, upon their being united or divided; so that he who thinks that what is divided is divided, or that what is united is united, is right; while he whose thought is contrary to the real condition of the objects is in error. Then when do what we call truth and falsity exist or not exist? We must consider what we mean by these terms.

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It is not because we are right in thinking that you are white that you are white; it is because you are white that we are right in saying so. Now if whereas some things are always united and cannot be divided, and others are always divided and cannot be united, others again admit of both contrary states, then to be is to be united, i.e. a unity; and not to be is to be not united, but a plurality.

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Therefore as regards the class of things which admit of both contrary states, the same opinion or the same statement comes to be false and true, and it is possible at one time to be right and at another wrong; but as regards things which cannot be otherwise the same opinion is not sometimes true and sometimes false, but the same opinions are always true or always false.

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But with regard to incomposite things, what is being or not-being, and truths or falsity? Such a thing is not composite, so as to be when it is united and not to be when it is divided, like the proposition that the wood is white, or the diagonal is incommensurable; nor will truth and falsity apply in the same way to these cases as to the previous ones.

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In point of fact, just as truth is not the same in these cases, so neither is being. Truth and falsity are as follows: contacti.e. direct and accurate apprehension. and assertion are truth (for assertion is not the same as affirmation), and ignorance is non-contact. I say ignorance, because it is impossible to be deceived with respect to what a thing is, except accidentallyi.e. we cannot be mistaken with regard to a simple term X. We either apprehend it or not. Mistake arises when we either predicate something wrongly of X, or analyze X wrongly.;

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and the same applies to incomposite substances, for it is impossible to be deceived about them. And they all exist actually, not potentially; otherwise they would be generated and destroyed; but as it is, Being itself is not generated (nor destroyed); if it were, it would be generated out of something. With respect, then, to all things which are essences and actual, there is no question of being mistaken, but only of thinking or not thinking them.

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Inquiry as to what they are takes the form of inquiring whether they are of such-and-such a nature or not.

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As for being in the sense of truth, and not-being in the sense of falsity, a unity is true if the terms are combined, and if they are not combined it is false. Again, if the unity exists, it exists in a particular way, and if it does not exist in that way, it does not exist at all.

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Truth means to think these objects, and there is no falsity or deception, but only ignorance—not, however, ignorance such as blindness is; for blindness is like a total absence of the power of thinking. And it is obvious that with regard to immovable things also, if one assumes that there are immovable things, there is no deception in respect of time.

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E.g., if we suppose that the triangle is immutable, we shall not suppose that it sometimes contains two right angles and sometimes does not, for this would imply that it changes; but we may suppose that one thing has a certain property and another has not; e.g., that no even number is a prime, or that some are primes and others are not. But about a single number we cannot be mistaken even in this way, for we can no longer suppose that one instance is of such a nature, and another not, but whether we are right or wrong, the fact is always the same.

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That one has several meanings has been already statedAristot. Met. 5.6. in our distinction of the various meanings of terms. But although it has a number of senses, the things which are primarily and essentially called one, and not in an accidental sense, may be summarized under four heads:

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(1.) That which is continuous, either absolutely or in particular that which is continuous by natural growth and not by contact or ligature; and of these things those are more strictly and in a prior sense one whose motion is more simple and indivisible.

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(2.) Of this kind in a still higher degree is that which is a whole and has a definite shape or form, particularly that which is such by nature and not by constraint (like things which are joined by glue or nails or by being tied together), but which contains in itself the cause of its continuity.

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A thing is of this kind if its motion is one and indivisible in respect of place and time; so that clearly if a thing has as its principle of motion the primary kind of motion (i.e. locomotion) in its primary form (i.e. circular locomotion), it is in the primary sense one spatial magnitude.This description applies to the celestial spheres.

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Some things, then, are one in this sense, qua continuous or whole; the other things which are one are those whose formula is one.

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Such are the things of which the concept is one, i.e. of which the concept is indivisible; and this is indivisible when the object is indivisible (3.) in form or (4.) in number. Now in number the individual is indivisible, and in form that which is indivisible in comprehension and knowledge; so that that which causes the unity of substances must be one in the primary sense.

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Such, then, in number are the meanings of one: the naturally continuous, the whole, the individual, and the universal. All these are one because they are indivisible; some in motion, and others in concept or formula. But we must recognize that the questions, What sort of things are called one? and What is essential unity, and what is the formula? must not be taken to be the same.

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One has these several meanings, and each thing to which some one of these senses applies will be one; but essential unity will have now one of these senses and now something else, which is still nearer to the term one, whereas they are nearer to its denotation . This is also true of element and cause, supposing that one had to explain them both by exhibiting concrete examples and by giving a definition of the term.

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There is a sense in which fire is an element (and no doubt so too is the indeterminateThe reference is undoubtedly to Anaximander. or some other similar thing, of its own nature), and there is a sense in which it is not; because to be fire and to be an element are not the same. It is as a concrete thing and as a stuff that fire is an element; but the term element denotes that it has this attribute: that something is made of it as a primary constituent.

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The same is true of cause or one and all other such terms.

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Hence to be one means to be indivisible (being essentially a particular thing, distinct and separate in place or form or thought), or to be whole and indivisible; but especially to be the first measure of each kind, and above all of quantity; for it is from this that it has been extended to the other categories.

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Measure is that by which quantity is known, and quantity qua quantity is known either by unity or by number, and all number is known by unity. Therefore all quantity qua quantity is known by unity, and that by which quantities are primarily known is absolute unity.

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Thus unity is the starting point of number qua number. Hence in other cases too measure means that by which each thing is primarily known, and the measure of each thing is a unit—in length, breadth, depth, weight and speed.

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(The terms weight and speed are common to both contraries, for each of them has a double meaning; e.g., weight applies to that which has the least amount of gravity and also to that which has excess of it, and speed to that which has the least amount of motion and also to that which has excess of it; for even the slow has some speed, and the light some weight.)

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In all these cases, then, the measure and starting-point is some indivisible unit (since even in the case of lines we treat the one-foot line as indivisible). For everywhere we require as our measure an indivisible unit; i.e., that which is simple either in quality or in quantity.

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Now where it seems impossible to take away or add, there the measure is exact. Hence the measure of number is most exact, for we posit the unit as in every way indivisible; and in all other cases we follow this example, for with the furlong or talent or in general with the greater measure an addition or subtraction would be less obvious than with a smaller one.

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Therefore the first thing from which, according to our perception, nothing can be subtracted is used by all men as their measure of wet and dry, weight and magnitude; and they think that they know the quantity only when they know it in terms of this measure. And they know motion too by simple motion and the most rapid, for this takes least time.

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Hence in astronomy a unit of this kind is the starting point and measure; for they assume that the motion of the heavens is uniform and the most rapid, and by it they judge the others. In music the measure is the quarter tone, because it is the smallest interval; and in language the letter. All these are examples of units in this sense—not in the sense that unity is something common to them all, but in the sense which we have described.

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The measure is not always numerically one, but sometimes more than one; e.g., there are two quarter tones, distinguished not by our hearing but by their theoretical ratiosi.e., the enharmonic (or quarter-tone proper) and the chromatic, which was 1/3 of a tone (Aristoxenus 1.21, 2.51). There was also the δίεσις ἡμιολία, which was 3/8 of a tone.; and the articulate sounds by which we measure speech are more than one; and the diagonal of a square is measured by two quantities,The meaning seems to be that the diameter consists of two parts, one equal to the side, and the other representing its excess over the side; the two parts being incommensurate are measured by different units (Ross). καὶ ἡ πλευρά must, I think, be a gloss. and so are all magnitudes of this kind. Thus unity is the measure of all things, because we learn of what the substance is composed by dividing it, in respect of either quantity or form.

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Hence unity is indivisible, because that which is primary in each class of things is indivisible. But not every unit is indivisible in the same sense—e.g. the foot and the arithmetical unit; but the latter is absolutely indivisible, and the former must be classed as indivisible with respect to our power of perception, as we have already stated; since presumably everything which is continuous is divisible.

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The measure is always akin to the thing measured. The measure of magnitude is magnitude, and in particular the measure of length is a length; of breadth, a breadth; of sounds, a sound; of weight, a weight; of units, a unit; for this is the view that we must take, and not that the measure of numbers is a number. The latter, indeed, would necessarily be true, if the analogy held good; but the supposition is not analogous—it is as though one were to suppose that the measure of units is units, and not a unit; for number is a plurality of units.

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We also speak of knowledge or sense perception as a measure of things for the same reason, because through them we come to know something; whereas really they are measured themselves rather than measure other things. But our experience is as though someone else measured us, and we learned our height by noticing to what extent he applied his foot-rule to us.

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Protagoras says that man is the measure of all things, meaning, as it were, the scholar or the man of perception; and these because they possess, the one knowledge, and the other perception, which we hold to be the measures of objects. Thus, while appearing to say something exceptional, he is really saying nothing.What Protagoras really meant was (apparently) that appearances are true relatively to the percipient. Cf. Aristot. Met. 4.4.27, and see Burnet, Greek Philosophy (Part I. Thales to Plato), 92.

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Obviously, then, unity in the strictest sense, if we make our definition in accordance with the meaning of the term, is a measure; particularly of quantity, and secondarily of quality. Some things will be of this kind if they are indivisible in quantity, and others if in quality. Therefore that which is one is indivisible, either absolutely or qua one.

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We must inquire, with regard to the substance and nature of unity, in which sense it exists. This is the same question which we approached in our discussion of difficultiesAristot. Met. 3.4.24-27.: what unity is, and what view we are to take of it; whether that unity itself is a kind of substance—as first the Pythagoreans, and later Plato, both maintain—or whether rather some nature underlies it, and we should give a more intelligible account of it, and more after the manner of the physicists; for of them oneEmpedocles. holds that the One is Love, anotherAnaximenes. Air, and anotherAnaximander. the Indeterminate.

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Now if no universal can be a substance (as we have stated in our discussionAristot. Met. 7.13. of substance and being), and being itself cannot be a substance in the sense of one thing existing alongside the many (since it is common to them), but only as a predicate, then clearly neither can unity be a substance; because being and unity are the most universal of all predicates.

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Therefore (a) genera are not certain entities and substances separate from other things; and (b) unity cannot be a genus, for the same reasons that being and substance cannot.Cf. Aristot. Met. 3.3.7.

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Further, the nature of unity must be the same for all categories.

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Now being and unity have the same number of meanings; so that since in the category of qualities unity is something definite, i.e. some definite entity, and similarly in the category of quantity, clearly we must also inquire in general what unity is, just as in the case of being; since it is not enough to say that its nature is simply unity or being.

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But in the sphere of colors unity is a color, e.g. white; that is if all the other colors are apparently derived from white and black, and black is a privation of white, as darkness is of light. Thus if all existing things were colors, all existing things would be a number; but of what?

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Clearly of colors. And unity would be some one color, e.g. white. Similarly if all existing things were tunes, there would be a number—of quarter-tones; but their substance would not be a number; and unity would be something whose substance is not unity but a quarter-tone. Similarly in the case of sounds, existing things would be a number of letters, and unity would be a vowel;

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and if existing things were right-lined figures, they would be a number of figures, and unity would be a triangle. And the same principle holds for all other genera. Therefore if in the categories of passivity and quality and quantity and motion there is in every category a number and a unity, and if the number is of particular things and the unity is a particular unity, and its substance is not unity, then the same must be true in the case of substances, because the same is true in all cases.

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It is obvious, then, that in every genus one is a definite entity, and that in no case is its nature merely unity; but as in the sphere of colors the One-itself which we have to seek is one color, so too in the sphere of substance the One-itself is one substance.

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And that in a sense unity means the same as being is clear (a) from the fact that it has a meaning corresponding to each of the categories, and is contained in none of them—e.g., it is contained neither in substance nor in quality, but is related to them exactly as being is; (b) from the fact that in one man nothing more is predicated than in manCf. Aristot. Met. 4.2.6-8.(just as Being too does not exist apart from some thing or quality or quantity); and (c) because to be one is to be a particular thing.

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One and Many are opposed in several ways. Unity and Plurality are opposed as being indivisible and divisible; for that which is divided or divisible is called a plurality, and that which is indivisible or undivided is called one. Then since opposition is of four kinds, and one of the present pairs of opposites is used in a privative sense, they must be contraries, and neither contradictories nor relative terms.

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Unity is described and explained by its contrary—the indivisible by the divisible—because plurality, i.e. the divisible, is more easily perceptible than the indivisible; and so in formula plurality is prior to the indivisible, on account of our powers of perception.

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To Unity belong (as we showed by tabulation in our distinction of the contrariesCf. Aristot. Met. 4.2.9.) Identity, Similarity and Equality; and to Plurality belong Otherness, Dissimilarity and Inequality.

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IdentityOr the same. Cf. Aristot. Met. 5.9. has several meanings. (a) Sometimes we speak of it in respect of number. (b) We call a thing the same if it is one both in formula and in number, e.g., you are one with yourself both in form and in matter; and again (c) if the formula of the primary substance is one, e.g., equal straight lines are the same, and equal quadrilaterals with equal angles, and there are many more examples; but in these equality means unity.

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Things are similarOr like. Cf. Aristot. Met. 5.9.5.(a) if, while not being the same absolutely or indistinguishable in respect of their concrete substance, they are identical in form; e.g the larger square is similar to the smaller, and unequal straight lines are similar. These are similar, but not absolutely the same. (b) If, having the same form, and being capable of difference in degree, they have no difference of degree.

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(c) If things have an attribute which is the same and one in form—e.g. white—in different degrees, we say that they are similar because their form is one. (d) If the respects in which they are the same are more than those in which they differ, either in general or as regards their more prominent qualities; e.g., tin is similar to silver, as being white; and gold to fire, as being yellow or flame-colored.

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Thus it is obvious that OtherCf. Aristot. Met. 5.9.4. and Unlike also have several meanings. (a) In one sense other is used in the sense opposite to the same; thus everything in relation to every other thing is either the same or other. (b) In another sense things are other unless both their matter and their formula are one; thus you are other than your neighbor. (c) The third sense is that which is found in mathematics.sc. as opposed to same in sense (a); 3 above. Therefore everything in relation to everything else is called either other or the same; that is, in the case of things of which unity and being are predicated;

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for other is not the contradictory of the same, and so it is not predicated of non-existent things (they are called not the same), but it is predicated of all things which exist; for whatever is by nature existent and one is either one or not one with something else.

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Other and same, then, are opposed in this way; but differenceCf. Aristot. Met. 5.9.4. is distinct from otherness.

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For that which is other than something need not be other in a particular respect, since everything which is existent is either other or the same. But that which is different from something is different in some particular respect, so that that in which they differ must be the same sort of thing; i.e. the same genus or species.

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For everything which is different differs either in genus or in species—in genus, such things as have not common matter and cannot be generated into or out of each other, e.g. things which belong to different categories; and in species, such things as are of the same genus (genus meaning that which is predicated of both the different things alike in respect of their substance).

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The contrariesCf. Aristot. Met. 5.10. are different, and contrariety is a kind of difference. That this is rightly premissed is made clear by induction; for the contraries are obviously all different, since they are not merely other, but some are other in genus, and others are in the same line of predication, and so are in the same genus and the same in genus. We have distinguished elsewhereAristot. Met. 5.28.4. what sort of things are the same or other in genus.

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Since things which differ can differ from one another in a greater or less degree, there is a certain maximum difference, and this I call contrariety. That it is the maximum difference is shown by induction. For whereas things which differ in genus have no means of passing into each other, and are more widely distant, and are not comparable, in the case of things which differ in species the contraries are the extremes from which generation takes place;

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and the greatest distance is that which is between the extremes, and therefore also between the contraries. But in every class the greatest thing is complete. For (a) that is greatest which cannot be exceeded, and (b) that is complete outside which nothing proper to it can be found. For complete difference implies an end, just as all other things are called complete because they imply an end.

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And there is nothing beyond the end; for in everything the end is the last thing, and forms the boundary. Thus there is nothing beyond the end, and that which is complete lacks nothing.

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From this argument, then, it is clear that contrariety is maximum difference; and since we speak of contraries in various senses, the sense of completeness will vary in accordance with the sense of contrariety which applies to the contraries.

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This being so, evidently one thing cannot have more than one contrary (since there can be nothing more extreme than the extreme, nor can there be more than two extremes of one interval); and in general this is evident, if contrariety is difference, and difference (and therefore complete difference) is between two things.

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The other definitions of contraries must also be true, for (1.) complete difference is the maximum difference; since (a) we can find nothing beyond it, whether things differ in genus or in species (for we have shown that difference in relation to things outside the genus is impossible; this is the maximum difference between them); and (b) the things which differ most in the same genus are contraries; for complete difference is the maximum difference between these.

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(2.) The things which differ most in the same receptive material are contraries; for contraries have the same matter. (3.) The most different things which come under the same faculty are contraries; for one science treats of one class of things, in which complete difference is the greatest.

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Positive state and Privation constitute primary contrariety—not every form of privation (for it has several senses), but any form which is complete. All other contraries must be so called with respect to these; some because they possess these, others because they produce them or are productive of them, and others because they are acquisitions or losses of these or other contraries.

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Now if the types of opposition are contradiction, privation, contrariety and relation, and of these the primary type is contradiction, and an intermediate is impossible in contradiction but possible between contraries, obviously contradiction is not the same as contrariety; and privation is a form of contradiction;

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for it is either that which is totally incapable of possessing some attribute,This is not a proper example of privation. Cf. Aristot. Met. 5.22. or that which would naturally possess some attribute but does not, that suffers privation—either absolutely or in some specified way. Here we already have several meanings, which we have distinguished elsewhere. Thus privation is a kind of contradiction or incapacity which is determinate or associated with the receptive material.

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This is why though there is no intermediate in contradiction there is one in some kinds of privation. For everything is either equal or not equal, but not everything is either equal or unequal; if it is, it is only so in the case of a material which admits of equality. If, then, processes of material generation start from the contraries, and proceed either from the form and the possession of the form, or from some privation of the form or shape, clearly all contrariety must be a form of privation, although presumably not all privation is contrariety.

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This is because that which suffers privation may suffer it in several senses; for it is only the extremes from which changes proceed that are contraries.

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This can also be shown by induction. Every contrariety involves privation as one of its contraries, but not always in the same way: inequality involves the privation of equality, dissimilarity that of similarity, evil that of goodness.

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And the differences are as we have stated: one case is, if a thing is merely deprived; another, if it is deprived at a certain time or in a certain part—e.g. at a certain age or in the important part—or entirely. Hence in some cases there is an intermediate (there are men who are neither good nor bad), and in others there is not—a thing must be either odd or even.

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Again, some have a determinate subject, and others have not. Thus it is evident that one of a pair of contraries always has a privative sense; but it is enough if this is true of the primary or generic contraries, e.g. unity and plurality; for the others can be reduced to them.

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Since one thing has one contrary, it might be asked in what sense unity is opposed to plurality, and the equal to the great and to the small. For if we always use the word whether in an antithesis—e.g., whether it is white or black, or whether it is white or not (but we do not ask whether it is a man or white, unless we are proceeding upon some assumption, and asking, for instance, whether it was Cleon who came or Socrates.

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This is not a necessary disjunction in any class of things, but is derived from the use in the case of opposites—for it is only opposites that cannot be true at the same time—and we have this same use here in the question which of the two came? for if both alternatives were possible, the question would be absurd; but even so the question falls into an antithesis: that of one or many—i.e., whether both came, or one)—

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if, then, the question whether is always concerned with opposites, and we can ask whether it is greater or smaller, or equal, what is the nature of the antithesis between equal and greater or smaller? It is contrary neither to one only, nor to both: for (a) it is no more contrary to the greater than to the smaller; (b) equal is contrary to unequal, and thus it will be contrary to more than one thing;

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(c) if unequal means the same as both greater and smaller at the same time, equal must still be opposed to them both: This difficulty supports the theoryHeld by the Platonists. Cf. Aristot. Met. 14.1.4, 5. that the unequal is a duality. But the result is that one thing is contrary to two; which is impossible.

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Further, it is apparent that equal is intermediate between great and small, but it is not apparent that any contrariety is intermediate, nor can it be, by definition; for it could not be complete if it were the intermediate of something, but rather it always has something intermediate between itself and the other extreme.

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It remains, then, that it is opposed either as negation or as privation. Now it cannot be so opposed to one of the two, for it is no more opposed to the great than to the small.

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Therefore it is a privative negation of both. For this reason we say whether with reference to both, and not to one of the two—e.g., whether it is greater or equal, or whether it is equal or smaller; there are always three alternatives. But it is not a necessary privation; for not everything is equal which is not greater or smaller, but only things which would naturally have these attributes.

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The equal, then, is that which is neither great nor small, but would naturally be either great or small; and it is opposed to both as a privative negation, and therefore is intermediate between them. And that which is neither good nor bad is opposed to both, but it has no name (for each of these terms has several meanings, and there is no one material which is receptive of both); that which is neither white nor black is better entitled to a name,

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although even this has no single name, but the colors of which this negation is privatively predicated are to a certain extent limited; for it must be either grey or buff or something similar.

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Therefore those persons are wrong in their criticism who imagine that all terms are used analogously, so that that which is neither a shoe nor a hand will be intermediate between shoe and hand, because that which is neither good nor bad is intermediate between good and bad—as though there must be an intermediate in all cases; but this does not necessarily follow.

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For the one is a joint negation of opposites where there is an intermediate and a natural interval; but in the other case there is no question of difference, since the joint negation applies to things which are in different genera, and therefore the substrate is not one.Cf. Aristot. Met. 10.3.8

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A similar question might be raised about one and many. For if many is absolutely opposed to one, certain impossibilities result. (1) One will be few; for many is also opposed to few.

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(2) Two will be many; since twofold is manifold, and twofold is derived from two. Therefore one will be few; for in what relation can two be many if not in relation to one, which must therefore be few? for there can be nothing less. (3) If much and little are in plurality what long and short are in length, and if whatever is much is also many,

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and many is much (unless indeed there is a difference in the case of a plastic continuumi.e., a fluid, which cannot be described as many. ), few will be a plurality. Therefore one will be a plurality, if it is few; and this necessarily follows if two is many. Presumably, however, although many in a sense means much, there is a distinction; e.g., water is called much but not many.

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To all things, however, which are divisible the term many is applicable: in one sense, if there is a plurality which involves excess either absolutely or relatively (and similarly few is a plurality involving defect); and in another in the sense of number, in which case it is opposed to one only. For we say one or many just as if we were to say one and ones, or white thing and white things, or were to compare the things measured with the measure.

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Multiples, too, are spoken of in this way; for every number is many, because it consists of ones, and because every number is measurable by one; and also as being the opposite of one, and not of few. In this sense even two is many; but as a plurality involving excess either relatively or absolutely it is not many, but the first plurality. Two is, however, absolutely few; because it is the first plurality involving defect

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(hence AnaxagorasCf. Aristot. Met. 1.3.9. was not right in leaving the subject by saying all things were together, infinite both in multitude and in smallness; instead of in smallness he should have said in fewness,sc. and then the absurdity of his view would have been apparent, for, etc. Aristotle assumes the Anaxagoras meant smallness (μικρότης) to be the opposite of multitude (πλῆθος); but he meant just what he said—that the particles of which things consist are infinitely many and infinitely small. See Bowman in Classical Review 30, 42-44. for things cannot be infinite in fewness), since fewness is constituted not by one, as some hold, but by two.

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In the sphere of numbers one is opposed to many as the measure to the measurable, i.e., as relative terms are opposed which are not of their own nature relative. We have distinguished elsewhereAristot. Met. 5.15.8, 9. that things are called relative in two senses—either as being contraries, or as knowledge is related to the knowable, A being related to B because B is described in relation to A.

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There is no reason why one should not be fewer than something, e.g. two; for if it is fewer it is not therefore few. Plurality is, as it were, a genus of number, since number is a plurality measurable by one. And in a sense one and number are opposed; not, however, as being contrary, but as we have said some relative terms to be; for it is qua measure and measurable that they are opposed.

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(Hence not everything which is one is a number—e.g., a thing which is indivisible.) But although the relation between knowledge and the knowable is said to be similar to this, it turns out not to be similar. For it would seem that knowledge is a measure, and the knowable that which is measurable by it; but it happens that whereas all knowledge is knowable, the knowable is not always knowledge, because in a way knowledge is measured by the knowable.Cf. Aristot. Met. 10.1.19.

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Plurality is contrary neither to the few (whose real contrary is the many, as an excessive plurality to an exceeded plurality) nor in all senses to one; but they are contrary in one sense (as has been said) as being the one divisible and the other indivisible; and in another as being relative (just as knowledge is relative to the knowable) if plurality is a number and one is the measure.

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Since there can be, and in some cases is, an intermediate between contraries, intermediates must be composed of contraries; for all intermediates are in the same genus as the things between which they are intermediate.

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By intermediates we mean those things into which that which changes must first change. E.g., if we change from the highest string to the lowest by the smallest gradations we shall first come to the intermediate notes; and in the case of colors if we change from white to black we shall come to red and grey before we come to black; and similarly in other cases.

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But change from one genus into another is impossible except accidentally; e.g., from color to shape. Therefore intermediates must be in the same genus as one another and as the things between which they are intermediate.

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But all intermediates are between certain opposites, for it is only from these per se that change is possible.

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Hence there can be no intermediate between things which are not opposites; for then there would be change also between things which are not opposites. Of things which are opposites, contradiction has no intermediate term (for contradiction means this: an antithesis one term of which must apply to any given thing, and which contains no intermediate term); of the remaining types of opposites some are relative, others privative, and others contrary.

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Those relative opposites which are not contrary have no intermediate. The reason for this is that they are not in the same genus— for what is intermediate between knowledge and the knowable?—but between great and small there is an intermediate. Now since intermediates are in the same genus, as has been shown, and are between contraries, they must be composed of those contraries. For the contraries must either belong to a genus or not. And if there is a genus in such a way

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that it is something prior to the contraries, then the differentiae which constitute the contrary species (for species consist of genus and differentiae) will be contraries in a prior sense.

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E.g., if white and black are contraries, and the one is a penetrativeThis is Plato’s definition. Cf. Plat. Tim. 67d, e. and the other a compressive color, these differentiae, penetrative and compressive, are prior, and so are opposed to each other in a prior sense.

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But it is the species which have contrary differentiae that are more truly contraries; the other, i.e. intermediate, species will consist of genus and differentiae. E.g., all colors which are intermediate between white and black should be described by their genus (i.e. color) and by certain differentiae.

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But these differentiae will not be the primary contraries; otherwise every thing will be either white or black. Therefore they will be different from the primary contraries. Therefore they will be intermediate between them, and the primary differentiae will be the penetrative and the compressive. Thus we must first investigate the contraries which are not contained in a genus, and discover of what their intermediates are composed.

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For things which are in the same genus must either be composed of differentiae which are not compounded with the genus, or be incomposite. Contraries are not compounded with one another, and are therefore first principles; but intermediates are either all incomposite or none of them. Now from the contraries something is generated in such a way that change will reach it before reaching the contraries themselves (for there must be something which is less in degree than one contrary and greater than the other). Therefore this also will be intermediate between the contraries.

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Hence all the other intermediates must be composite; for that which is greater in degree than one contrary and less than the other is in some sense a compound of the contraries of which it is said to be greater in degree than one and less than the other. And since there is nothing else homogeneous which is prior to the contraries, all intermediates must be composed of contraries.

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Therefore all the lower terms, both contraries and intermediates, must be composed of the primary contraries. Thus it is clear that intermediates are all in the same genus, and are between contraries, and are all composed of contraries.

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That which is other in species than something else is other in respect of something and that something must apply to both. E.g., if an animal is other in species than something else, they must both be animals. Hence things which are other in species must be in the same genus. The sort of thing I mean by genus is that in virtue of which two things are both called the same one thing; and which is not accidentally differentiated, whether regarded as matter or otherwise.

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For not only must the common quality belong to both, e.g., that they are both animals, but the very animality of each must be different; e.g., in one case it must be equinity and in the other humanity. Hence the common quality must for one be other in species than that which it is for the other. They must be, then, of their very nature, the one this kind of animal, and the other that ; e.g., the one a horse and the other a man.

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Therefore this difference must be otherness of genus (I say otherness of genus because by difference of genus I mean an otherness which makes the genus itself other); this, then, will be a form of contrariety. This is obvious by induction.Aristotle does not use induction to prove his point; indeed he does not prove it at all. For all differentiation is by opposites, and we have shownIn ch. 4. that contraries are in the same genus, because contrariety was shown to be complete difference. But difference in species is always difference from something in respect of something; therefore this is the same thing, i.e. the genus, for both.

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(Hence too all contraries which differ in species but not in genus are in the same line of predication,Or category. and are other than each other in the highest degree; for their difference is complete, and they cannot come into existence simultaneously.) Hence the difference is a form of contrariety.

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To be other in species, then, means this: to be in the same genus and involve contrariety, while being indivisible

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(and the same in species applies to all things which do not involve contrariety, while being indivisible); for it is in the course of differentiation and in the intermediate terms that contrariety appears, before we come to the indivisibles.i.e., indivisible species and individuals.

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Thus it is evident that in relation to what is called genus no species is either the same or other in species (and this is as it should be, for the matter is disclosed by negation, and the genus is the matter of that of which it is predicated as genus; not in the sense in which we speak of the genus or clan of the Heraclidae,Cf. Aristot. Met. 5.28.1. but as we speak of a genus in nature); nor yet in relation to things which are not in the same genus. From the latter it will differ in genus, but in species from things which are in the same genus. For the difference of things which differ in species must be a contrariety; and this belongs only to things which are in the same genus.

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The question might be raised as to why woman does not differ in species from man, seeing that female is contrary to male, and difference is contrariety; and why a female and a male animal are not other in species, although this difference belongs to animal per se, and not as whiteness or blackness does; male and female belong to it qua animal.

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This problem is practically the same as why does one kind of contrariety (e.g. footed and winged) make things other in species, while another (e.g. whiteness and blackness) does not? The answer may be that in the one case the attributes are peculiar to the genus, and in the other they are less so; and since one element is formula and the other matter, contrarieties in the formula produce difference in species, but contrarieties in the concrete whole do not.

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Hence the whiteness or blackness of a man does not produce this, nor is there any specific difference between a white man and a black man; not even if one term is assigned to each. For we are now regarding man as matter, and matter does not produce difference; and for this reason, too, individual men are not species of man, although the flesh and bones of which this and that man consist are different. The concrete whole is other, but not other in species, because there is no contrariety in the formula, and this is the ultimate indivisible species.

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But Callias is definition and matter. Then so too is white man, because it is the individual, Callias, who is white. Hence man is only white accidentally. Again, a bronze circle and a wooden one do not differ in species; and a bronze triangle and a wooden circle differ in species not because of their matter, but because there is contrariety in their formulae.

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But does not matter, when it is other in a particular way, make things other in species? Probably there is a sense in which it does. Otherwise why is this particular horse other in species than this particular man, although the definitions involve matter? Surely it is because there is contrariety in the definition, for so there also is in white man and black horse; and it is a contrariety in species, but not because one is white and the other black; for even if they had both been white, they would still be other in species.

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Male and female are attributes peculiar to the animal, but not in virtue of its substance; they ar material or physical. Hence the same semen may, as the result of some modification, become either female or male.

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We have now stated what to be other in species means, and why some things differ in species and others do not.

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Since contraries are other in form,It appears that in this chapter (apart from 5, which may be a later addition) the terms εἶδος and γένος are used in a non-technical sense. Cf. Ross on Aristot. Met. 1058b 28. and the perishable and imperishable are contraries (for privation is a definite incapacity), the perishable must be other in kind than the imperishable. But so far we have spoken only of the universal terms; and so it might appear to be unnecessary that anything perishable and imperishable should be other in form, just as in the case of white and black.

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For the same thing may be both at the same time, if it is a universal (e.g, man may be both white and black); and it may still be both if it is a particular, for the same person may be white and black, although not at the same time. Yet white is contrary to black. But although some contraries

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(e.g. those which we have just mentioned, and many others) can belong to certain things accidentally, others cannot; and this applies to the perishable and the imperishable. Nothing is accidentally perishable; for that which is accidental may not be applicable; but perishability is an attribute which applies necessarily when it is applicable at all. Otherwise one and the same thing will be imperishable as well as perishable, if it is possible for perishability not to apply to it.

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Thus perishability must be either the substance or in the substance of every perishable thing. The same argument also applies to the imperishable; for both perishability and imperishability are attributes which are necessarily applicable. Hence the characteristics in respect of which and in direct consequence of which one thing is perishable and another imperishable are opposed; and therefore they must be other in kind.

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Thus it is obvious that there cannot be Forms such as some thinkers maintain; for then there would be both a perishable and an imperishable man. i.e., the individual man is perishable and the Idea of man imperishable; and these must be other in kind (γένει non-technical). But the Platonists hold that the Idea is the same in species as the particular. This is impossible if it is other in genus (γένει technical). Yet the Forms are said to be the same in species as the particulars, and not merely to share a common predicate with them; but things which are other in genus differ more widely than things which are other in species.

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That wisdom is a science of first principles is clear from our Introductory remarks,Aristot. Met. 1.3-10. in which we of raised objections to the statements of other thinkers about the first principles. It might be asked, however, whether we should regard Wisdom as one science or as more than one.Cf. Aristot. Met. 3.1.5, Aristot. Met. 3.2.1-10. If as one, it may be objected that the objects of one science are always contraries; but the first principles are not contraries. And if it is not one, what sort of sciences are we to suppose them to be?

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Again, is it the province of one science, or of more than one, to study the principles of demonstration?Cf. Aristot. Met. 3.1.5, , Aristot. Met. 3.2.10-15, where the problem takes a slightly different form. If of one, why of it rather than of any other? And if of more than one, of what sort are we to suppose them to be?

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Again, are we to suppose that Wisdom deals with all substances or not?Cf. Aristot. Met. 3.1.6, Aristot. Met. 3.2.15-17. If not with all, it is hard to lay down with what kind it does deal; while if there is one science of them all, it is not clear how the same science can deal with more than one subject.

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Again, is this science concerned only with substances, or with attributes as well?Cf. Aristot. Met. 3.1.8-10, Aristot. Met. 3.2.18-19. For if it is a demonstration of attributes, it is not concerned with substances; and if there is a separate science of each, what is each of these sciences, and which of them is Wisdom? qua demonstrative, the science of attributes appears to be Wisdom; but qua concerned with that which is primary, the science of substances.

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Nor must we suppose that the science which we are seeking is concerned with the causes described in the Physics.Aristot. Physics 2.3. It is not concerned with the final cause; for this is the Good, and this belongs to the sphere of action and to things which are in motion; and it is this which first causes motion (for the end is of this nature); but there is no Prime Mover in the sphere of immovable things.

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And in general it is a difficult question whether the science which we are now seeking is concerned with sensible substances, or not with sensible substances, but with some other kind.Cf. Aristot. Met. 3.1.7, Aristot. Met.3.2.20-30. If with another kind, it must be concerned either with the Forms or with mathematical objects. Now clearly the Forms do not exist. (But nevertheless, even if we posit them, it is a difficult question as to why the same rule does not apply to the other things of which there are Forms as applies to the objects of mathematics.

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I mean that they posit the objects of mathematics as intermediate between the Forms and sensible things, as a third class besides the Forms and the things of our world; but there is no third manThis phrase has no technical sense here; cf. Aristot. Met. 1.9.4. or horse besides the Ideal one and the particulars. If on the other hand it is not as they make out, what sort of objects are we to suppose to be the concern of the mathematician? Not surely the things of our world; for none of these is of the kind which the mathematical sciences investigate.)

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Nor indeed is the science which we are now seeking concerned with the objects of mathematics; for none of them can exist separately. But it does not deal with sensible substances either; for they are perishable.

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In general the question might be raised, to what science it pertains to discuss the problems concerned with the matteri.e., intelligible matter (cf. Aristot. Met. 7.10.18). This problem is not raised in Book 3. of mathematical objects.

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It is not the province of physics, because the whole business of the physicist is with things which contain in themselves a principle of motion and rest; nor yet of the science which inquires into demonstration and

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scientific knowledge, for it is simply this sort of thing which forms the subject of its inquiry. It remains, therefore, that it is the science which we have set ourselves to find that treats of these subjects.

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One might consider the question whether we should regard the science which we are now seeking as dealing with the principles which by some are called elements.Cf. Aristot. Met. 3.1.10, Aristot. Met. 3.3. But everyone assumes that these are present in composite things; and it would seem rather that the science which we are seeking must be concerned with universals, since every formula and every science is of universals and not of ultimate species; so that in this case it must deal with the primary genera.

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These would be Being and Unity; for these, if any, might best be supposed to embrace all existing things, and to be most of the nature of first principles, because they are by nature primary; for if they are destroyed, everything else is destroyed with them, since everything exists and is one.

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But inasmuch as, if Being and Unity are to be regarded as genera, they must be predicable of their differentiae, whereas no genus is predicable of any of its differentiae, from this point of view it would seem that they should be regarded neither as genera nor as principles.

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Further, since the more simple is more nearly a principle than the less simple, and the ultimate subdivisions of the genus are more simple than the genera (because they are indivisible), and the genera are divided into a number of different species, it would seem that species are more nearly a principle than genera.

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On the other hand, inasmuch as species are destroyed together with their genera, it seems more likely that the genera are principles; because that which involves the destruction of something else is a principle. These and other similar points are those which cause us perplexity.

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Again, ought we to assume the existence of something else besides particular things, or are they the objects of the science which we are seeking?Cf. Aristot. Met. 3.1.11, Aristot. Met. 3.4.1-8. It is true that they are infinite in number; but then the things which exist besides particulars are genera or species, and neither of these is the object of the science which we are now seeking. We have explained Aristot. Met. 11.1.11-13 why this is impossible.

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Indeed, in general it is a difficult question whether we should suppose that there is some substance which exists separately besides sensible substances (i.e. the substances of our world), or that the latter constitute reality, and that it is with them that Wisdom is concerned. It seems that we are looking for some other kind of substance, and that this is the object of our undertaking: I mean, to see whether there is anything which exists separately and independently, and does not appertain to any sensible thing.

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But again, if there is another kind of substance besides sensible substances, to what kind of sensible things are we to suppose that it corresponds? Why should we suppose that it corresponds to men or horses rather than to other animals, or even to inanimate objects in general? And yet to manufacture a set of eternal substances equal in number to those which are sensible and perishable would seem to fall outside the bounds of plausibility.

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Yet if the principle which we are now seeking does not exist in separation from bodies, what can we suppose it to be if not matter? Yes, but matter does not exist actually, but only potentially. It might seem rather that a more appropriate principle would be form or shape; but this is perishableForms which are induced in matter are perishable, although not subject to the process of destruction; they are at one time and are not at another (cf. Aristot. Met. 7.15.1). The only pure form (i.e., the only form which is independent of matter in any and every sense) is the prime mover (Aristot. Met. 12.7).; and so in general there is no eternal substance which exists separately and independently.

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But this is absurd, because it seems natural that there should be a substance and principle of this kind, and it is sought for as existing by nearly all the most enlightened thinkers. For how can there be any order in the universe if there is not something eternal and separate and permanent?

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Again, if there is a substance and principle of such a nature as that which we are now seeking, and if it is one for all things, i.e. the same for both eternal and perishable things, it is a difficult question as to why, when the principle is the same, some of the things which come under that principle are eternal, and others not; for this is paradoxical.Cf. Aristot. Met. 3.1.12, Aristot. Met. 3.4.11-23.

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But if there is one principle of perishable things, and another of eternal things, if the principle of perishable things is also eternal, we shall still have the same difficulty; because if the principle is eternal, why are not the things which come under that principle eternal? And if it is perishable, it must have another principle behind it, and that principle must have another behind it; and the process will go on to infinity.

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On the other hand, if we posit the principles which seem most unchangeable, Being and Unity,Cf. Aristot. Met. 3.1.13, Aristot. Met. 3.4.24-34.(a) unless each of them denotes a particular thing and a substance, how can they be separate and independent? but the eternal and primary principles for which we are looking are of this nature.

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(b) If, however, each of them denotes a particular thing and a substance, then all existing things are substances; for Being is predicated of everything, and Unity also of some things.

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But that all things are substances is false. (c) As for those who maintain that Unity is the first principle and a substance, and who generate number from Unity and matter as their first product, and assert that it is a substance, how can their theory be true? How are we to conceive of 2 and each of the other numbers thus composed, as one? On this point they give no explanation; nor is it easy to give one.

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But if we posit lines or the things derived from them (I mean surfaces in the primary sensei.e., intelligible surfaces, etc.) as principles,Cf. Aristot. Met. 3.1.15, Aristot. Met. 3.5. these at least are not separately existing substances, but sections and divisions, the former of surfaces and the latter of bodies (and points are sections and divisions of lines); and further they are limits of these same things. All these things are integral parts of something else, and not one of them exists separately.

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Further, how are we to suppose that there is a substance of unity or a point? for in the case of every substancesc. which is liable to generation or destruction. there is a process of

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generation, but in the case of the point there is not; for the point is a division.

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It is a perplexing fact also that whereas every science treats of universals and types, substance is not a universal thing, but rather a particular and separable thing; so that if there is a science that deals with first principles, how can we suppose that substance is a first principle?Cf. Aristot. Met. 3.1.14, Aristot. Met. 3.6.7-9.

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Again, is there anything besides the concrete whole (I mean the matter and the form in combination) or not?This section belongs to the problem discussed in 1-5 above. If not, all things in the nature of matter are perishable; but if there is something, it must be the form or shape. It is hard to determine in what cases this is possible and in what it is not; for in some cases, e.g. that of a house, the form clearly does not exist in separation.

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Again, are the first principles formally or numerically the same?Cf. Aristot. Met. 3.1.12, Aristot. Met. 3.4.8-10. If they are numerically one, all things will be the same.

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Since the science of the philosopher is concerned with Being qua Being universally,This chapter corresponds to Aristot. Met. 4.1, 2, with which it should be compared. and not with some part of it, and since the term Being has several meanings and is not used only in one sense, if it is merely equivocal and has no common significance it cannot fall under one science (for there is no one class in things of this kind); but if it has a common significance it must fall under one science.

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Now it would seem that it is used in the sense which we have described, like medical and healthy, for we use each of these terms in several senses; and each is used in this way because it has a reference, one to the science of medicine, and another to health, and another to something else; but each refers always to the same concept. A diagnosis and a scalpel are both called medical, because the one proceeds from medical science and the other is useful to it.

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The same is true of healthy; one thing is so called because it is indicative, and another because it is productive, of health; and the same applies to all other cases. Now it is in this same way that everything which exists is said to be ; each thing is said to be because it is a modification or permanent or temporary state or motion or some other such affection of Being qua Being.

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And since everything that is can be referred to some one common concept, each of the contrarieties too can be referred to the primary differentiae and contrarieties of Being—whether the primary differentiae of Being are plurality and unity, or similarity and dissimilarity, or something else; for we may take them as already discussed.Cf. Aristot. Met. 4.2.9 n.

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It makes no difference whether that which is is referred to Being or Unity; for even if they are not the same but different, they are in any case convertible, since that which is one also in a sense is , and that which is is one.

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Now since the study of contraries pertains to one and the same science, and each contrary is so called in virtue of privation (although indeed one might wonder in what sense they can be called contraries in virtue of privation when they admit of a middle term—e.g. unjust and just), in all such cases we must regard the privation as being not of the whole definition but of the ultimate species. E.g., if the just man is one who is obedient to the laws in virtue of some volitional state, the unjust man will not be entirely deprived of the whole definition, but will be one who is in some respect deficient in obedience to the laws; and it is in this respect that the privation of justice will apply to him (and the same holds good in all other cases).

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And just as the mathematician makes a study of abstractions (for in his investigations he first abstracts everything that is sensible, such as weight and lightness, hardness and its contrary, and also heat and cold and all other sensible contrarieties, leaving only quantity and continuity—sometimes in one, sometimes in two and sometimes in three dimensions—and their affections qua quantitative and continuous, and does not study them with respect to any other thing; and in some cases investigates the relative positions of things and the properties of these, and in others their commensurability or incommensurability, and in others their ratios; yet nevertheless we hold that there is one and the same science of all these things, viz. geometry), so it is the same with regard to Being.

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For the study of its attributes in so far as it is Being, and of its contrarietiesi.e., identity, otherness, etc. qua Being, belongs to no other science than Philosophy; for to physics one would assign the study of things not qua Being but qua participating in motion, while dialectics and sophistry deal with the attributes of existing things, but not of things qua Being, nor do they treat of Being itself in so far as it is Being.

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Therefore it remains that the philosopher is the man who studies the things which we have described, in so far as they are Being. And since everything that is , although the term has several meanings, is so described in virtue of some one common concept, and the same is true of the contraries (since they can be referred to the primary contrarieties and differences of Being), and since things of this kind can fall under one science, the difficulty which we stated at the beginningAristot. Met. 11.1.1. may be regarded as solvedAlso the problem stated in ch. i. 3.—I mean the problem as to how there can be one science of several things which are different in genus.

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Since even the mathematician uses the common axioms only in a particular application, it will be the province of Primary Philosophy to study the principles of these as well.This chapter corresponds to Aristot. Met. 4.3.1-6, and answers the problem stated in Aristot. Met. 11.1.2.

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That when equals are taken from equals the remainders are equal is an axiom common to all quantities; but mathematics isolates a particular part of its proper subject matter and studies it separately; e.g. lines or angles or numbers or some other kind of quantity, but not qua Being, but only in so far as each of them is continuous in one, two or three dimensions. But philosophy does not investigate particular things in so far as each of them has some definite attribute, but studies that which is , in so far as each particular thing is .

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The same applies to the science of physics as to mathematics, for physics studies the attributes and first principles of things qua in motion, and not qua Being; but Primary Science, as we have said, deals with these things only in so far as the subjects which underlie them are existent, and not in respect of anything else. Hence we should regard both physics and mathematics as subdivisions of Wisdom.

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There is a principle in existing things about which we cannot make a mistakeThis chapter corresponds to Aristot. Met. 4.3.7-4.31.; of which, on the contrary, we must always realize the truth—viz. that the same thing cannot at one and the same time be and not be, nor admit of any other similar pair of opposites. Of such axioms although there is a proof ad hominem, there is no absolute proof;

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because there is no principle more convincing than the axiom itself on which to base an argument, whereas there must be such a principle if there is to be absolute proof.

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But he who wants to convince an opponent who makes opposite statements that he is wrong must obtain from him an admission which shall be identical with the proposition that the same thing cannot at one and the same time be and not be, but shall seem not to be identical with it. This is the only method of proof which can be used against one who maintains that opposite statements can be truly made about the same subject.

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Now those who intend to join in discussion must understand one another to some extent; for without this how can there be any common discussion between them? Therefore each of the terms which they use must be intelligible and signify something; not several things, but one only; or if it signifies more than one thing, it must be made clear to which of these the term is applied.

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Now he who says that A is and is not denies what he asserts, and therefore denies that the term signifies what it does signify. But this is impossible. Therefore if to be so-and-so has a definite meaning, the opposite statement about the same subject cannot be true.

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Again, if the term has a definite significance and this is truly stated, it must of necessity be so.sect. 6=Aristot. Met. 4.4.14-16. But that which of necessity is can never not be. Hence opposite statements about the same subject cannot be true.

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Again, if the assertion is no more true than the negation, it will be no more true to say A is man than to say A is not man. With this section cf. Aristot. Met. 4.4.26-30.

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But it would also be admitted that it is more or at least not less true to say that a man is not a horse than to say that he is not a man; and therefore, since it was assumed that opposite statements are equally true, it will be true to say that the same person is also a horse. It follows therefore, that the same person is a man and a horse, or any other animal.

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Thus, although there is no absolute proof of these axioms, there is an ad hominem proof where one’s opponent makes these assumptions.sect. 8=Aristot. Met. 4.3.10. Perhaps even Heraclitus himself, if he had been questioned on these lines, would have been compelled to admit that opposite statements can never be true of the same subjects; as it is, he adopted this theory through ignorance of what his doctrine implied.

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In general,sect. 9-11=Aristot. Met. 4.4.31. if what he says is true, not even this statement itself (I mean that the same thing can at one and the same time be and not be) will be true;

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because just as, when they are separated, the affirmation is no more true than the negation, so in the same way, if the complex statement is taken as a single affirmation, the negation will be just as true as the whole statement regarded as an affirmation.

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And further, if nothing can be truly affirmed, then this very statement—that there is no such thing as a true affirmation—will be false. But if there is such a thing, the contentions of those who raise objections of this kind and utterly destroy rational discourse may be considered to be refuted.Cf. Aristot. Met. 4.8.4, 5.

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Very similar to the views which we have just mentioned is the dictum of ProtagorasThis chapter forms a summary of Aristot. Met. 4.5-8. sect. 1-3=Aristot. Met. 4.5.1-5.; for he said that man is the measure of all things, by which he meant simply that each individual’s impressions are positively true.

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But if this is so, it follows that the same thing is and is not, and is bad and good, and that all the other implications of opposite statements are true; because often a given thing seems beautiful to one set of people and ugly to another, and that which seems to each individual is the measure.

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This difficulty will be solved if we consider the origin of the assumption. It seems probable that it arose in some cases from the doctrine of the natural philosophers, and in others from the fact that everyone does not form the same opinion about the same things, but to some a given thing seems sweet and to others the contrary.

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For that nothing comes from what is not, but everything from what is, is a doctrine common to nearly all natural philosophers.With sect. 4, 5 cf. Aristot. Met. 4.5.6. Since, then, a thing does not become white which was before completely white and in no respect not-white, that which becomes white must come from what was not-white. Hence according to this theory there would be generation from what is not, unless the same thing were originally white and not-white.

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However, it is not hard to solve this difficulty. We have explained in the PhysicsAristot. Physics 1.7-9. in what sense things which are generated are generated from what is not, and in what sense from what is.

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But to attach equal importance to the opinions and impressions of opposing parties is foolish, because clearly one side or the other must be wrong.sect. 5-7=Aristot. Met. 4.5.23-27.

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This is evident from what happens in the sphere of sensation; for the same thing never seems to some people sweet and to others to the contrary unless one of the parties has the organ of sense which distinguishes the said flavors injured or impaired. Such being the case, the one party should be taken as the measure, and the other not.

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And I hold the same in the case of good and bad, and of beautiful and ugly, and of all other such qualities. For to maintain this viewi.e., that the same thing has contrary qualities. is just the same as to maintain that what appears to us when we press the finger below the eye and make a thing seem two instead of one must be two because it appears to be so, and then afterwards that it must be one; because if we do not interfere with our sight that which is one appears to be one.

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And in general it is absurd to form our opinion of the truth from the appearances of things in this world of ours which are subject to change and never remain in the same statesect. 8, 9 (first half)=Aristot. Met. 4.5.21, 22.; for it is by reference to those things which are always the same state and undergo no change that we should prosecute our search for truth.

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Of this kind are the heavenly bodies; for these do not appear to be now of one nature and subsequently of another, but are manifestly always the same and have no change of any kind.

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Again, if there is motion there is also something which is moved; and everything is moved from something and into something. Therefore that which is moved must be in that from which it is to be moved, and must also not be in it; and must be moved into so-and-so and must also come to be in it; but the contradictory statements cannot be true at the same time, as our opponents allege.

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And if the things of our world are in a state of continuous flux and motion in respect of quantity, and we assume this although it is not true, why should they not be constant in respect of quality?Cf. Aristot. Met. 4.5.20, 21. It appears that not the least reason why our opponents predicate opposite statements of the same thing is that they start with the assumption that quantity is not constant in the case of bodies; hence they say that the same thing is and is not six feet long.

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But essence depends upon quality, and this is of a determinate, whereas quantity is of an indeterminate nature.

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Again, when the doctor orders them to adopt some article of diet, why do they adopt it?Cf. Aristot. Met. 4.4.39-42. For on their view it is no more true that a thing is bread than that it is not; and therefore it would make no difference whether they ate it or not. But as it is, they adopt a particular food as though they knew the truth about it and it were the food prescribed;

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yet they ought not to do so if there were no fixed and permanent nature in sensible things and everything were always in a state of motion and flux.

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Again, if we are always changing and never remain the same, is it any wonder that to us, as to the diseased, things never appear the same?With this section cf. Aristot. Met. 4.5.7-14.

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For to the diseased, since they are not in the same physical condition as when they were well, sensible qualities do not appear to be the same; although this does not mean that the sensible things themselves partake of any change, but that they cause different, and not the same, sensations in the diseased. Doubtless the same must be true if the change which we have referred to takes place in us.

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If, however, we do not change but remain always the same, there must be something permanent.

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As for those who raise the aforesaid difficulties on dialectical grounds,With this section cf. Aristot. Met. 4.5.3, 4, Aristot. Met. 4.6.1-3. it is not easy to find a solution which will convince them unless they grant some assumption for which they no longer require an explanation; for every argument and proof is possible only in this way. If they grant no assumption, they destroy discussion and reasoning in general.

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Thus there is no arguing with people of this kind; but in the case of those who are perplexed by the traditional difficulties it is easy to meet and refute the causes of their perplexity. This is evident from what has been already said.

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Thus from these considerations it is obvious that opposite statements cannot be true of the same thing at one time; nor can contrary statements, since every contrariety involves privation. This is clear if we reduce the formulae of contraries to their first principles.Cf. Aristot. Met. 4.6.10, 11.

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Similarly no middle term can be predicated of one and the same thing of which one of the contraries is predicated.Cf. Aristot. Met. 4.7 where, however, the point which is proved is that there can be no intermediate between contradictories.

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If, when the subject is white, we say that it is neither white nor black, we shall be in error; for it follows that it is and is not white, because the first of the two terms in the complex statement will be true of the subject, and this is the contradictory of white.

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Thus we cannot be right in holding the views either of HeraclitusCf. Aristot. Met. 11.5.8 or of Anaxagoras.Cf. Aristot. Met. 4.7.8-8.5

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If we could, it would follow that contraries are predicable of the same subject; for when heAnaxagoras. What he really meant was that even the sweetest things contain some bitter particles. Cf. Anaxagoras Fr. 11 (Diels); Burnet, E.G.P. 129. says that in everything there is a part of everything, he means that nothing is sweet any more than it is bitter, and similarly with any of the other pairs of contraries; that is, if everything is present in everything not merely potentially but actually and in differentiation.

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Similarly all statements cannot be false, nor all true. Among many other difficulties which might be adduced as involved by this supposition there is the objection that if all statements were false, not even this proposition itself would be true; while if they were all true it would not be false to say that they are all false.

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Every science inquires for certain principles and causes with respect to every knowable thing which comes within its scopeThis chapter corresponds to Aristot. Met. 6.1; cf. also Aristot. Met. 4.3.1-6 and ch. 4 above. It also answers the problem stated in ch. 1.2.; e.g., the sciences of medicine and physical culture do this, and so does each of the other productive and mathematical sciences. Each one of these marks out for itself some class of objects, and concerns itself with this as with something existent and real, but not qua real; it is another science distinct from these which does this.

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Each of the said sciences arrives in some way at the essence in a particular class of things, and then tries to prove the rest more or less exactly. Some arrive at the essence through sense-perception, and some by hypothesis; hence it is obvious from such a process of induction that there is no demonstration of the reality or essence.

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Now since there is a science of nature, clearly it must be different from both practical and productive science. In a productive science the source of motion is in the producer and not in the thing produced, and is either an art or some other kind of potency; and similarly in a practical science the motion is not in the thing acted upon but rather in the agent.

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But the science of the natural philosopher is concerned with things which contain in themselves a source of motion. From this it is clear that natural science must be neither practical nor productive, but speculative; since it must fall under one of these classes.

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And since every science must have some knowledge of the essence and must use it as a starting-point, we must be careful to observe how the natural philosopher should define, and how he should regard the formula of essence—whether in the same way as the term snub, or rather as the term concave.

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For of these the formula of snub is stated in conjunction with the matter of the object, whereas that of concave is stated apart from the matter; since snubness is only found in the nose, which is therefore included in the formula, for the snub is a concave nose . Thus it is obvious that the formula of flesh and eye and the other parts of the body must always be stated in conjunction with their matter.

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Since there is a science of Being qua Being and separately existent, we must inquire whether this should be regarded as identical with natural science or rather as a distinct branch of knowledge. Physics deals with things which contain a source of motion in themselves, and mathematics is speculative and is a science which deals with permanent things, but not with things which can exist separately.

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Hence there is a science distinct from both of these, which deals with that which exists separately and is immovable; that is, if there really is a substance of this kind—I mean separately existent and immovable—as we shall endeavor to prove.Aristot. Met. 12.6, 7. And if there is an entity of this kind in the world of reality, here surely must be the Divine, and this must be the first and most fundamental principle.

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Evidently, then, there are three kinds of speculative science: physics, mathematics, and theology. The highest class of science is the speculative, and of the speculative sciences themselves the highest is the last named, because it deals with the most important side of reality; and each science is reckoned higher or lower in accordance with the object of its study.

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The question might be raised as to whether the science of Being qua Being should be regarded as universal or not.

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Each of the mathematical sciences deals with some one class of things which is determinate, but universal mathematics is common to all alike. If, then, natural substances are the first of existing things, physics will be the first of the sciences; but if there is some other nature and substance which exists separately and is immovable, then the science which treats of it must be different from and prior to physics, and universal because of its priority.

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Since the term Being in its unqualified sense is used with several meanings, of which one is accidental Being, we must first consider Being in this sense.Sections 1-9 of this chapter correspond to Aristot. Met. 6.2-4. Clearly none of the traditional sciences concerns itself with the accidental; the science of building does not consider what will happen to the occupants of the house, e.g. whether they will find it unpleasant or the contrary to live in; nor does the science of weaving or of shoemaking or of confectionery.

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Each of these sciences considers only what is proper to it, i.e. its particular end. As for the question whether the cultured is also the lettered, or the quibbleThis is a different form of the quibble in Aristot. Met. 6.2.4. Here the fallacy obviously consists in the wrong application of the word ἅμα(at once or at the same time). that the man who is cultured, when he has become lettered, will be both at once although he was not before; but that which is but was not always so must have come to be; therefore he must have become at the same time cultured and lettered

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—none of the recognized sciences considers this, except sophistry. This is the only science which concerns itself with the accidental, and hence Plato was not far wrong in sayingPlat. Sop. 254a. that the sophist spends his time in the study of unreality. But that it is not even possible for there to be a science of the accidental will be apparent if we try to see what the accidental really is.

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Of some things we say that they are so always and of necessity (necessity having the sense not of compulsion, but that which we use in logical demonstrationCf. Aristot. Met. 6.2.6.), and of others that they are so usually, but of others that they are so neither usually nor always and of necessity, but fortuitously. E.g., there might be a frost at midsummer, although this comes about neither always and of necessity nor usually; but it might happen sometimes.

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The accidental, then, is that which comes about, but not always nor of necessity nor usually. Thus we have now stated what the accidental is; and it is obvious why there can be no science of such a thing, because every science has as its object that which is so always or usually, and the accidental falls under neither of these descriptions.

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Clearly there can be no causes and principles of the accidental such as there are of that which is per se; otherwise everything would be of necessity. For if A is when B is, and B is when C is, and C is not fortuitously but of necessity, then that of which C was the cause will also be of necessity, and so on down to the last causatum , as it is called.

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(But this was assumed to be accidental.) Therefore everything will be of necessity, and the element of chance, i.e. the possibility of a thing’s either happening or not, is entirely banished from the world of events. Even if we suppose the cause not to exist already but to be coming to be, the result will be the same; for everything will come to be of necessity.

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The eclipse tomorrow will come about if A does, and A will if B does, and B if C does; and in this way if we keep on subtracting time from the finite time between now and to-morrow, we shall at some point arrive at the present existing condition. Therefore since this exists, everything subsequent to it will happen of necessity, and so everything happens of necessity.

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As for what is in the sense of what is true or what is accidental , the former depends upon a combination in thought, and is an affection of thought (hence we do not look for the principles of Being in this sense, but only for those of objective and separable Being) the latter is not necessary but indeterminate (I mean the accidental); and of such a thing the causes are indefinite and cannot be reduced to a system.

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Teleology is found in events which come about in the course of nature or as a result of thought.This section is taken from Aristot. Physics 2.5, 6. It is chance <or luck> when one of these comes about by accident; for a thing may be a cause, just as it may exist, either per se or accidentally. Chance is an accidental cause of normally purposive teleological events.

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Hence chance and thought have the same sphere of action, for there is no purpose without thought. Causes from which chance results may come about are indeterminate; hence chance is inscrutable to human calculation, and is a cause only accidentally, but in the strictest sense is a cause of nothing.

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It is good or bad luck when the result is good or bad, and good or bad fortune when the result is on a large scale.

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Since nothing accidental is prior to that which is per se, neither are accidental causes prior. Therefore if chance or spontaneity is the cause of the universe, mind and nature are prior causes.The argument is stated more fully and clearly in Aristot. Physics 2.6ff.. Chance produces indirectly the effects produced directly by mind; and spontaneity is similarly related to nature. But the indirect cause presupposes the direct. The argument is directed against the Atomists. Cf. Aristot. Phys. 196a 24, Simplicius 327.24, Cicero De Nat. Deor. 1.66 (nulla cogente natura, sed concursu quodam fortuito).

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A thing may exist only actually or potentially, or actually and potentially; it may be a substance or a quantity or one of the other categories. There is no motionThe discussion of motion in this chapter consists of extracts from Aristot. Physics 3.1-3. apart from things, for change is always in accordance with the categories of Beingi.e., change is substantial (generation and destruction); quantitative (increase and decrease); qualitative (alteration); spatial (locomotion). Cf. Aristot. Met. 11.12.1, 2.; and there is nothing which is common to these and in no one category. Each category belongs to all its members in two ways—e.g. substance, for this is sometimes the form of the thing and sometimes its privation;

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and as regards quality there is white and black; and as regards quantity, complete and incomplete; and as regards spatial motion there is up and down or light and heavy—so that there are as many forms of motion and change as there are of Being.This is inaccurate; see previous note.

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Now since every kind of thing is divided into the potential and the real, I call the actualization of the potential as such,What Aristotle means by this is explained more clearly in the following sections, which may be summarized thus. The material substrate, e.g. bricks, etc., which is potentially a house, may be regarded (a) as potential material; in this sense it is actualized as bricks before building begins; (b) as potentially a house; in this sense when it is actualized it is no longer buildable but built, i.e., it is no longer potential; (c) as potentially buildable into a house. In this sense its actualization is conterminous with the process of building, and is incomplete (sect.11), and should not be described as ἐντελέχεια or complete reality. But Aristotle often uses this term as synonymous with the vaguer ἐνέργεια. motion.

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That this is a true statement will be clear from what follows. When the buildable in the sense in which we call it such exists actually, it is being built; and this is the process of building. The same is true of the processes of learning, healing, walking, jumping, ageing, maturing. Motion results when the complete reality itself exists, and neither sooner nor later.

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The complete reality, then, of that which exists potentially, when it is completely real and actual, not qua itself but qua movable, is motion. By qua I mean this. The bronze is potentially a statue; but nevertheless the complete reality of the bronze qua bronze is not motion. To be bronze is not the same as to be a particular potentiality; since if it were absolutely the same by definition the complete reality of the bronze would be a kind of motion; but it is not the same.

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(This is obvious in the case of contraries; for the potentiality for health and the potentiality for illness are not the same—for if they were, health and illness would be the same too—but the substrate which becomes healthy or ill, whether it is moisture or blood, is one and the same.) And since it is not the same, just as color and visible are not the same, it is the complete reality of the potential qua potential that is motion.

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It is evident that it is this, and that motion results when the complete reality itself exists, and neither sooner nor later. For everything may sometimes be actual, and sometimes not; e.g. the buildable qua buildable; and the actualization of the buildable qua buildable is the act of building.

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For the actualization is either this—the act of building—or a house. But when the house exists, it will no longer be buildable; the buildable is that which is being built. Hence the actualization must be the act of building, and the act of building is a kind of motion. The same argument applies to the other kinds of motion.

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That this account is correct is clear from what the other authorities say about motion, and from the fact that it is not easy to define it otherwise. For one thing, it could not be placed in any other class; this is clear from the fact that some peoplePythagoreans and Platonists. Cf. Aristot. Met. 1.5.6, Plat. Soph. 256d. identify it with otherness and inequality and not-being, none of which is necessarily moved;

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moreover change is no more into these or out of them than into or out of their opposites.The criticism implied is: If motion is identified with otherness, inequality, etc., then these concepts must be either (a) subjects of motion, which is absurd, or (b) termini of motion, in which case the same must be true of their contraries, since motion is between contraries. The reason for placing motion in this class is that it is considered to be indeterminate, and the principles in one of the columns of contraries are indeterminate, being privative; for none of them is a determinate thing or quality or any of the other categories.

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The reason for considering motion to be indeterminate is that it cannot be associated either with the potentiality or with the actuality of things; for neither that which is potentially nor that which is actually of a certain size is necessarily moved.

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And motion is considered to be a kind of actualization, but incompleteCf. note on sect. 2 (end) above, and Aristot. Met. 9.6.7-10.; the reason of this is that the potential, of which it is the actualization, is incomplete.

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Thus it is difficult to comprehend what motion is; for we must associate it either with privation or with potentiality or with absolute actuality; and apparently none of these is possible.

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There remains, then, the account which we have given; that it is an actuality, and an actuality of the kind which we have described, which is hard to visualize but capable of existing.

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That motion is in the movable is evident; for it is the complete realization of the movable by that which is capable of causing motion, and the actualization of that which is capable of causing motion is identical with that of the movable.

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For it must be a complete realization of them both; since a thing is capable of moving because it has the potentiality, but it moves only when it is active; but it is upon the movable that it is capable of acting. Thus the actuality of both alike is one; just as there is the same interval from one to two as from two to one, and the hill up and the hill down are one, although their being is not one; the case of the mover and the thing moved is similar.

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This chapter consists of extracts from Aristot. Physics 3.4, 5, 7.The infinite is either (a) that which cannot be traversed because it is not its nature to be traversed (just as sound is by nature invisible); or (b) that which admits of an endless traverse; or (c) scarcely admits of traverse; or (d) which, though it would naturally admit of traverse or limit, does not do so. Further, it may be infinite in respect of addition or of subtraction or of both.

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That the infinite should be a separate independent entity,The Pythagorean and Platonic view. and yet imperceptible, is impossible.

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For if it is neither magnitude nor plurality, but infinity itself is the essence of it, and not merely an accident, it must be indivisible; because that which is divisible is either magnitude or plurality. And if it is indivisible it cannot be infinite, except in the same way as sound is invisible. But this is not what people mean by infinite; and it is not the infinite in this sense that we are investigating, but the infinite in the sense of the untraversable.

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Again, how can the infinite exist independently unless number and magnitude, of which infinity is an attribute, also exist independently?Aristotle has argued that they do not in Aristot. Met. 1.9.16-25. And further, if the infinite is accidental, it cannot, qua infinite, be an element of things; just as the invisible is not an element of speech, although sound is invisible. It is clear also that the infinite cannot exist actually.

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Otherwise any part of it which we might take would be infinite; for infinity and the infinite are the same, if the infinite is substance and is not predicated of a subject. Therefore it is either indivisible, or if it is partible, the parts into which it is divisible are infinite. But the same thing cannot be many infinites; for just as a part of air is air, so a part of the infinite will be infinite, if the infinite is a substance and principle.

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Therefore it is impartible and indivisible. But this is impossible of the actually infinite, because it must be some quantity. Therefore infinity is an accidental attribute. But if so, as we have said, it cannot be it that is a principle, but that of which it is an accident: airAccording to Anaximenes; cf. Theophrastus, Phys. Opin. Fr. 2 (Ritter and Preller 26). or the even. According to the Pythagoreans. Cf. Aristot. Met. 1.5.5. n

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The foregoing inquiry is general; but what follows will show that the infinite does not exist in sensible things.

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If the definition of a body is that which is bounded by surfaces, then no body, whether sensible or intelligible, can be infinite nor can there be any separate and infinite number, since number or that which involves number is numerable. This is clearly shown by the following concrete argument. The infinite can neither be composite nor simple. For (a) it cannot be a composite body if the elements are limited in numberThis is proved in Aristot. Physics 1.6.;

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for the contraries must be equal, and no one of them must be infinite; for if the potency of one of the two corporeal elements is in any way inferior, the finite element will be destroyed by the infinite. And every element cannot be infinite, because body is that which has extension in all directions, and the infinite is that which is extended without limit; so that if the infinite is corporeal it will be infinite in all directions.sc. and so no other body can exist beside it.

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Nor (b) can the infinite be any simple body; neither, as someAnaximander. It seems, however, that by ἄπειρον he meant indeterminate or undifferentiated, although he no doubt regarded this principle as infinite as well. Cf. notes on Aristot. Met. 1.7.3, Aristot. Met. 12.2.3. hold, something which is apart from the elements and from which they suppose the elements to be generated (for there is no such body apart from the elements; everything can be resolved into that of which it consists, but we do not see things resolved into anything apart from the simple bodies), nor fire nor any other element.

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Apart from the question of how any of them could be infinite, the All, even if it is finite, cannot be or become any one of the elements, as Heraclitus saysCf. Hereclitus Fr. 20-22 (Bywater). all things at certain times become fire. The same argument applies as to the One which the physicists posit besides the elements; for all change proceeds from the contrary, e.g. from hot to cold.The argument seems to be: Since all change is from contrary to contrary, and it is impossible that either (a) one of the elements should be contrary to the rest, or (b) one material principle should be contrary to all four elements, it follows that no one element, and similarly that no one material principle apart from the elements, can be the ultimate material principle of the universe.

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Again, a sensible body is in some region, and the region of the whole and of the part (e.g. of the earth) is the same.i.e., the region of the universe which is proper to a given element is proper also to any part of that element. The proper region of earth is the center, of fire the circumference of the universe. Cf. Aristot. De Caelo 1.2. Therefore if the infinite body is homogeneous, it will be immovable or will always be in motionRoss is evidently right in taking this to refer to the rest or motion of the parts. An infinite body cannot move as a whole, because there is no space outside it.; but this is impossible, for why should there be rest or motion below rather than above or in any other region? E.g., if there were a clod, in what region would it move or be at rest?

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The region proper to the body which is homogeneous with the clod is infinite. Then will the clod occupy the whole of that region? How can it? Then what of its rest or motion? It will either rest everywhere—in which case it cannot move—or move everywhere; in which case it cannot rest.If earth is an infinite body, its region must be infinite. But the infinite has no center (cf. sect. 13). Therefore a clod, which cannot occupy the whole region proper to earth, will have no region proper to itself to which it can move or in which it can rest. And if the whole is not alike throughout, the regions proper to its parts are unlike also; and (a) the body of the whole is not one, except in virtue of contact; (b) the parts will be either finite or infinite in kind.

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Finite they cannot be, for then those of one kind would be infinitesc. in quantity. If the universe is infinite in quantity, and the elements are limited in kind, some of the elements (or at least one) must be infinite in quantity. But this is impossible, just as it is impossible that all the elements should be infinite in quantity. Cf. sect. 7 above and those of another would not (if the whole is infinite); e.g., fire or water would be infinite. But such a condition would involve the destruction of the contraries. But if the parts are infinitesc. in kind or number. and simple, the regions proper to them are infinite and the elements will be infinite. And since this is impossible,Cf. sect. 6 n. the regions are finiteCf. sect. 14 n. and the whole must be finite.

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In general, there cannot be an infinite body and a place for bodies if every body which is sensible has either weight or lightness; for it will have to move either towards the center or upwards, and the infinite—either the whole or the half—cannot do either; for how can you divide it? How can the infinite be part up and part down, or part extreme and part center?

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Further, every sensible body is in some place, and of place there are six kinds,i.e., above and below, before and behind, right and left (Aristot. Phys. 205b 31). but these cannot exist in an infinite body. In general, if an infinite place is impossible, so is an infinite body; because that which is in a place is somewhere, and this means either up or down or one of the other kinds of place, and each of these is a limit.

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The infinite is not the same in the sense that it is one nature whether it applies to magnitude or to motion or to time; the posterior is derived from the prior sense, e.g. motion is called infinite in virtue of the magnitude involved when a thing is moved or changed or increased, and time is so called on account of motion.Cf. Aristot. Met. 5.13.5.

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That which changes either changes accidentally, as when the cultured walks; or is said to change in general because something in it changes, as in the case of things which change in their parts; the body becomes healthy because the eye does.

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But there is something which is moved directly per se, i.e. the essentially movable. The same applies to that which moves, for it moves sometimes accidentally, sometimes partially, and sometimes per se. There is something that moves directly, and something that is moved; and also a time in which, and something from which, and something into which it is moved. But the forms and modifications and place into which moving things are moved are immovable; e.g. knowledge and warmth. It is not warmth that is motion, but the process of warming.

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Non-accidental change is not found in all things, but only between contraries and intermediates and contradictories. We can convince ourselves of this by means of induction. That which changes changes either from positive into positive, or from negative into negative, or from positive into negative, or from negative into positive.

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By positive I mean that which is denoted by an affirmation. Thus there must be three forms of change; for that which is from negative into negative is not change, because they are neither contraries nor contradictories, since they entail no opposition. The change from the negative into its contradictory positive is generation—absolute change absolute generation, and qualified change qualified generation; and the change from the positive to the negative is destruction—absolute change absolute destruction, and qualified change qualified destruction.The change from positive to positive is omitted here (but cf. sect. 7). Aristotle no doubt intended to use it as an example of non-substantial change, e.g. from poor man to rich man; but since this can be regarded as change from poor man to not-poor man, or not-rich man to rich man, he includes it as a qualified type of substantial change.

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Now if what is not has several meanings, and neither that which implies a combination or separation of terms,i.e., falsity. Cf. Aristot. Met. 9.10.1. nor that which relates to potentiality and is opposed to unqualified Being, admits of motion (not-white or not-good, however, admits of motion accidentally, because not-white may be a man; but that which is not so-and-so in an absolute sense does not admit of it at all), then what is not cannot be moved. If this is so, generation cannot be motion; for it is what is not that is generated.

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For even if the generation is in the highest degree accidental, still it is true to say that not-being is predicable of that which is generated absolutely. And the argument applies similarly to rest. Thus not only do these difficult conclusions follow, but also that everything which is moved is in a place, whereas what is not is not in a place; for then it would be somewhere. Nor is destruction motion; for the contrary of motion is motion or rest, but the contrary of destruction is generation.

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And since every motion is a kind of change, and the three kinds of change are those which we have described,sect. 3. and of these those which relate to generation and destruction are not motions, and these are the changes between contradictories, the change from positive to positive must alone be motion. The subjects are either contraries or intermediates (for privative terms may also be regarded as contraries) and are denoted by a positive term—e.g. naked or toothless or black.

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Now since the categories are distinguished as substance, quality, place, activity or passivity, relation and quantity,Aristotle generally distinguishes eight categories (originally ten, but he seems to have abandoned κεῖσθαιposition and ἔχεινstate at an early date); here he omits time as being relative to motion (it is that by which motion can be numerically estimated; cf. Aristot. Met. 12.6.2, Aristot. Phys. 219b 1) and therefore neither the subject nor the terminus of motion. Cf. Ross ad loc. there must be three kinds of motion, in respect of quality, quantity and place. There is no motionThere is, however, change in respect of substance (generation and destruction), but this is between contradictories and is not motion in the strict sense. Cf. Aristot. Met. 11.11.6, and sect. 4 below. The distinction between motion and change is not always maintained. in respect of substance, because substance has no contrary; nor of the relative, because it is possible that when one of two related things changes the relation to it of the other thing, even though the thing itself does not change, may become untrue; therefore the motion of these related things is accidental.

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Nor is there motion of the agent or patient, or of the mover and the thing moved, because there is no motion of motion nor no generation of generation, nor in general is there change of change. There are two ways in which there might be motion of motion: (1) Motion might be the subject of motion, as, e.g., a man is moved because he changes from white to black; in this way motion might be heated or cooled or might change its place or increase.

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But this is impossible, because the change is not a subject. Or (2) some other subject might change from change to some other form of existence, as, e.g., a man changes from sickness to health. But this is also impossible except accidentally.

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Every motion is a change from one thing into something else; and the same is true of generation and destruction, except that these are changes into opposites in one sense,sc. contradictories. while the other, i.e. motion, is a change into opposites in another sense.sc. contraries. Hence a thing changes at the same time from health to sickness, and from this change itself into another.

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Now clearly if it has fallen ill it will be already changed (for it cannot remain at rest) into that other change, whatever it may be; and further this cannot be, in any given case, any chance change; and it also must be from something into something else. Therefore it will be the opposite change, viz. becoming healthy. But this is so accidentally; just as there is change from recollecting to forgetting because the subject changes, now in the direction of knowledge and now in that of ignorance.

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Further, we shall have an infinite series if there is to be change of change and becoming of becoming, because if the latter of two becomings comes to be from the former, the former must come to be too. E.g., if simple becoming was once coming to be, that which comes to be something was also once coming to be. Therefore that which simply comes to be was not yet, but there was already something coming to be coming to be something.

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But this too was at one time coming to be, and therefore it was not at that time coming to be something. But in infinite series there is no first term, and therefore in this series the first term cannot exist, nor can any subsequent term. Therefore nothing can be either generated or moved or changed.

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Further, the same thing which admits of motion admits also of the contrary motion and of rest, and that which admits of generation admits also of destruction.

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Therefore that which comes to be, when it has come to be coming to be, is then in course of perishingsc. which is absurd.; for it does not perish as soon as it is coming to be coming to be, nor afterwards, because that which is perishing must exist .That which comes to be must cease to be, and it can cease to be only when it exists. Therefore if that which comes to be comes to be coming to be, it must cease to be when it is coming to be; before this it does not exist, but is only coming to be coming to be, and after this it is not that which comes to be but that which has come to be.

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Further, there must be some matter underlying that which is coming to be or changing. What then will it be? What is it that becomes motion or generation in the same way as it is body or soul that undergoes change? And moreover what is that which is the terminus of the motion? For that which we are considering must be a motion or generation of A from B into C.

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How then can these conditions be fulfilled? There can be no learning of learning, and therefore there can be no generation of generation.

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Since there is no motion of substance or of the relative or of activity and passivity, it remains that there is motion in respect of quality, quantity and place; for each of these admits of contrariety. By quality I mean not that which is in the substance (for indeed even the differentia is a quality), but the passive quality in virtue of which a thing is said to be acted upon or to be immune from being acted upon.Cf. Aristot. Met. 5.14.

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The immovable is either that which is wholly incapable of being moved, or that which is scarcely moved in the course of a long time or is slow in starting, or that which would naturally be moved but cannot be moved at the time when and from the place whence and in the way in which it would naturally be moved. This last is the only kind of immovable thing which I recognize as being at rest; for rest is contrary to motion, and so must be a privation of that which admits of motion.

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Things are together in place which are in the primary sensei.e., when they occupy one place to the exclusion of anything else. Cf. Aristot. Phys. 209a 33-b 1. in one place, and separate which are in different places. Contrary in place is that which is at a maximum distance in a straight line.I have transferred this sentence from the end of the section, where it is placed in the text, on the ground that it fits more naturally here. I suspect that it, like the displaced portion of sect. 13, was originally a marginal note which was later inserted in the body of the text, but in the wrong position. Things are said to be in contact whose extremes are together in place. An intermediate is that at which a changing thing which changes continuously in accordance with its nature naturally arrives before it arrives at the extreme into which it is changing. Since all change takes place between opposites, and these are either contraries or contradictories, and contradictories have no middle term, clearly it is to the sphere of contraries that the intermediate belongs.I have followed Prantl’s suggestion in transferring this sentence from the end of sect. 13.

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Successive is that which comes after the beginning (the order being determined by position or form or in some other way) and has nothing of the same class between itself and that which it succeeds; e.g. lines in the case of a line, and units in that of a unit, and a house in the case of a house (but there is nothing to prevent something else from coming between). For that which is successive is a thing which is successive and posterior to some other thing. 1 is not successive to 2, nor is the new mooni.e., the first day of the month. to the second day of the month.

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Contiguous is that which is successive and in contact. The continuous is a species of the contiguous.

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I call two things continuous when their respective boundaries, by which they are kept together in contact, become one and the same; hence clearly the continuous belongs to the sphere of things whose nature it is to become one by contiguity.

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Clearly successive is the most ultimate term; for the successive need not be in contact, but contact implies succession; and if there is continuity there is contact, but if there is contact there is not necessarily continuity;

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and where there is no contact there is no coalescence. Therefore a point is not the same as a unit; for points admit of contact, whereas units do not, but only of succession; and between points there is something intermediate, but between units there is not.

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Our inquiry is concerned with substance; for it is the principles and causes of substances that we are investigating. Indeed if the universe is to be regarded as a whole, substance is its first part; and if it is to be regarded as a succession,Cf. Aristot. Met. 12.10.14, Aristot. Met. 14.3.9. even so substance is first, then quality, then quantity. Moreover, the latter hardly exist at all in the full sense, but are merely qualifications and affections of Being. Otherwise not-white and not-straight would also exist; at any rate we say that they too are, e.g., it is not white.

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Further, none of the other categories is separately existent. Even the ancients in effect testify to this, for it was of substance that they sought the principles and elements and causes. Present-day thinkersPlatonists. tend to regard universals as substance, because genera are universal, and they hold that these are more truly principles and substances because they approach the question theoretically; but the ancients identified substance with particular things, e.g. fire and earth, and not with body in general.

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Now there are three kinds of substance. One is sensible (and may be either eternali.e., the celestial bodies. or perishable; the latter, e.g. plants and animals, is universally recognized); of this we must apprehend the elements, whether they are one or many.

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Another is immutable , which certain thinkers hold to exist separately; some dividing it into two classes, others combining the Forms and the objects of mathematics into a single class, and others recognizing only the objects of mathematics as of this nature.These three views were held respectively by Plato, Xenocrates and Speusippus. Cf. Aristot. Met. 7.2.3, 4; Aristot. Met. 13.1.4, and see Introduction. The first two kinds of substance come within the scope of physics, since they involve motion; the last belongs to some other science, if there is no principle common to all three.

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Sensible substance is liable to change. Now if change proceeds from opposites or intermediates—not however from all opposites (for speech is not white), but only from the contraryCf. Aristot. Met. 10.7.—then there must be something underlying which changes into the opposite contrary; for the contrariesi.e., contrary qualities. Cf. Aristot. Met. 8.5.1. do not change.

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Further, something persists, whereas the contrary does not persist. Therefore besides the contraries there is some third thing, the matter . Now if change is of four kinds, in respect either of substance or of quality or of quantity or of place, and if change of substance is generation or destruction in the simple sense, and change of quantity is increase or decrease, and change of affection is alteration, and change of place is locomotion, then changes must be in each case into the corresponding contrary state.

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It must be the matter, then, which admits of both contraries, that changes. And since that which is is twofold, everything changes from that which is potentially to that which is actually; e.g. from potentially white to actually white. The same applies to increase and decrease. Hence not only may there be generation accidentally from that which is not, but also everything is generated from that which is, but is potentially and is not actually.

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And this is the one of Anaxagoras; for his all things were together,Anaxagoras Fr. 1 (Diels). and the mixture of Empedocles and Anaximander and the doctrine of Democritus would be better expressed as all things were together potentially, but not actually. In this passage I follow Ross’s punctuation and interpretation, which seem to me to be certainly right. Anaxagoras’s undifferentiated infinity of homoeomerous particles (although contrasted with the unifying principle of Mind, cf. Aristot. Met. 1.8.14) can be regarded as in a sense a unity. Again, μῖγμα(as Ross points out) in its Aristotelian sense of complete fusion is a fair description of Anaximander’s indeterminate. The general meaning of the passage is that in each of the systems referred to the material principle in its elemental state should have been described as existing only potentially.

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Hence these thinkers must have had some conception of matter. All things which change have matter, but different things have different kinds; and of eternal things such as are not generable but are movable by locomotion have matter; matter, however, which admits not of generation, but of motion from one place to another.Cf. Aristot. Met. 12.1.3, Aristot. Met. 8.1.7, 8.

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One might raise the question from what sort of not-being generation takes place; for not-being has three senses.(1) the negation of a category, (2) falsity, (3) unrealized potentiality. Cf. Aristot. Met. 14.2.10. If a thing exists through a potentiality, nevertheless it is not through a potentiality for any chance thing; different things are derived from different things.

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Nor is it satisfactory to say that all things were together, for they differ in their matter, since otherwise why did they become an infinity and not one? For Mind is one; so that if matter is also one, only that could have come to be in actuality whose matter existed potentially. The causes and principles, then, are three; two being the pair of contraries, of which one is the formula or form and the other the privation, and the third being the matter.This classification is found in Aristot. Physics 1.6, 7, but is foreign to the main treatise of the Metaphysics. See Introduction.

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We must next observeSee Introduction. that neither matter nor form (I mean in the proximate sense) is generated. All change is of some subject by some agent into some object. The agent is the immediate mover; the subject is the matter; and the object is the form. Thus the process will go on to infinity if not only the bronze comes to be round, but also roundness or bronze comes to be; there must, then, be some stopping-point.

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We must next observe that every substance is generated from something which has the same name (substances including not only natural but all other products). Things are generated either by art or by nature or by chance or spontaneously. Art is a generative principle in something else; nature is a generative principle in the subject itselfIn natural reproduction the generative principle is obviously in the parent. But the offspring is in a sense a part of the parent, and so Aristotle identifies the two.(for man begets man); the other causes are privations of these.Cf. Aristot. Met. 11.8.12 n.

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There are three kinds of substance: (1.) matter, which exists individually in virtue of being apparentAristotle is contrasting proximate with primary matter. Fire, the primary matter of a man, is a simple undifferentiated element which cannot be perceived as such, and has no individuality. The head, and the other parts of the body, considered merely as in contact and not as forming an organic unity, are the proximate matter of a man; they are perceptible and individual. Flesh (in general) represents the matter in an intermediate stage.(for everything which is characterized by contact and so not by coalescence is matter and substrate; e.g. fire, flesh and head; these are all matter, and the last is the matter of a substance in the strictest sense); (2.) the naturei.e., form.(existing individually)—i.e. a kind of positive state which is the terminus of motion; and (3.) the particular combination of these, e.g. Socrates or Callias. In some cases the individuality does not exist apart from the composite substance (e.g., the form of a house does not exist separately, except as the art of building;

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nor are these forms liable to generation and destruction; there is a distinct sense in which house and health and every artificial product, considered in the abstract, do or do not existi.e., in the mind of the architect or doctor.); if it does so at all, it does so in the case of natural objects. Hence Plato was not far wrong in sayingSee Introduction. that there are as many Forms as there are kinds of natural objects; that is if there are Forms distinct from the things of our world.

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Moving causes are causes in the sense of pre-existent things, but formal causes coexist with their effects. For it is when the man becomes healthy that health exists, and the shape of the bronze sphere comes into being simultaneously with the bronze sphere.

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Whether any form remains also afterwards is another question. In some cases there is nothing to prevent this, e.g. the soul may be of this nature (not all of it, but the intelligent part; for presumably all of it cannot be). Clearly then there is no need on these grounds for the Ideas to exist; for man begets man, the individual begetting the particular person. And the same is true of the arts, for the art of medicine is the formula of health.

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In one sense the causes and principles are different for different things; but in another, if one speaks generally and analogically, they are the same for all. For the question might be raised whether the principles and elements of substances and of relations are the same or different; and similarly with respect to each of the other categories. But it is absurd that they should be the same for all; for then relations and substance would have the same constituents.

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What then can their common constituent be? For there is nothing common to and yet distinct from substance and the other predicable categories, yet the element is prior to that of which it is an element. Moreover substance is not an element of relations, nor is any of the latter an element of substance. Further, how can all the categories have the same elements?

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For no element can be the same as that which is composed of elements; e.g., neither B nor A can be the same as BA (nor indeed can any of the intelligibles,Unity and Being are called intelligibles as being the most universal predicates and as contrasted with particulars, which are sensible. e.g. Unity or Being, be an element; for these apply in every case, even to composite things); hence no element can be either substance or relation. But it must be one or the other. Therefore the categories have not all the same elements.

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The truth is that, as we say, in one sense all things have the same elements and in another they have not. E.g., the elements of sensible bodies are, let us say, (1) as form, the hot, and in another sense the cold, which is the corresponding privation; as matter, that which directly and of its own nature is potentially hot or cold. And not only these are substances, but so are (2) the compoundsThis apparently refers to the elements; fire and air are hot matter, water and earth cold matter. of which they are principles, and (3) any unity which is generated from hot and cold, e.g. flesh or bone; for the product of hot and cold must be distinct from them.

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These things, then, have the same elements and principles, although specifically different things have specifically different elements; we cannot, however, say that all things have the same elements in this sense, but only by analogy: i.e., one might say that there are three principles, form, privation and matter.

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But each of these is different in respect of each class of things, e.g., in the case of color they are white, black, surface; or again there is light, darkness and air, of which day and night are composed. And since not only things which are inherent in an object are its causes, but also certain external things, e.g. the moving cause, clearly principle and element are not the same; but both are causes. Principles are divided into these two kinds, and that which moves a thing or brings it to rest is a kind of principle and substance.

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Thus analogically there are three elements and four causes or principles; but they are different in different cases, and the proximate moving cause is different in different cases. Health, disease, body; and the moving cause is the art of medicine. Form, a particular kind of disorder, bricks; and the moving cause is the art of building.

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And since in the sphere of natural objects the moving cause of man is man, while in the sphere of objects of thought the moving cause is the form or its contrary, in one sense there are three causes and in another four. For in a sense the art of medicine is health, and the art of building is the form of a house, and man begets man; but besides these there is that which as first of all things moves all things.For the first time the ultimate efficient cause is distinguished from the proximate. Aristotle is leading up to the description of the Prime Mover which occupies the latter half of the book.

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Now since some things can exist in separation and others cannot, it is the former that are substances. And therefore all things have the same causes, because without substance there can be no affections and motions. Next we shall seeSee Introduction. that these causes are probably soul and body, or mind, appetite and body.Aristotle is thinking of animals and human beings, which are substances in the truest sense. Again, there is another sense in which by analogy the principles are the same viz. actuality and potentiality; but these are different for different things, and apply to them in different ways.

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For in some cases the same thing exists now actually and now potentially; e.g. wine or flesh or man (actuality and potentiality also fall under the causes as already described; for the form exists actually if it is separable, and so does the compound of form and matter, and the privation, e.g. darkness or disease; and the matter exists potentially, for it is this which has the potentiality of becoming bothi.e., of acquiring either of the contrary qualities distinguished by the form and the privation;

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but the distinction in virtue of actuality and potentiality applies in a different sense to cases where the matter of cause and effect is not the same, in some of which the form is not the same but different. E.g., the cause of a man is (i) his elements: fire and earth as matter, and the particular form; (2) some external formal cause, viz. his father; and besides these (3) the sun and the ecliptic,The sun, moving in the ecliptic, approaches nearer to the earth in summer, causing generation, and recedes farther from the earth in winter, causing destruction. Cf. Aristot. Met. 12.6.10 n., Aristot. De Gen. et Corr. 336a 32. which are neither matter nor form nor privation nor identical in form with him, but cause motion.

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Further, we must observe that some causes can be stated universally, but others cannot.

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The proximate principles of all things are the proximate actual individual and another individual which exists potentially.i.e., the proximate efficient cause and proximate matter. Therefore the proximate principles are not universal. For it is the particular that is the principle of particulars; man in general is the principle of man in general, but there is no such person as man, whereas Peleus is the principle of Achilles and your father of you, and this particular B of this particular BA; but B in general is the principle of BA regarded absolutely.

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Again, even if the causes of substances are universal, still, as has been said,Aristot. Met. 12.4.6. different things, i.e. things which are not in the same genus, as colors, sounds, substances and quantity, have different causes and elements, except in an analogical sense; and the causes of things which are in the same species are different, not in species, but because the causes of individuals are different: your matter and form and moving cause being different from mine, although in their universal formula they are the same.

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As for the question what are the principles or elements of substances and relations and qualities, whether they are the same or different, it is evident that when the terms principle and element are used with several meanings they are the same for everything; but when the meanings are distinguished, they are not the same but different; except that in a certain sense they are the same for all. In a certain sense they are the same or analogous, because (a) everything has matter, form, privation and a moving cause; (b) the causes of substances may be regarded as the causes of all things, since if substances are destroyed everything is destroyed; and further (c) that which is first in complete realityi.e., the prime mover. is the cause of all things.

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In another sense, however, proximate causes are different; there are as many proximate causes as there are contraries which are predicated neither as genera nor with a variety of meaningsi.e., individual forms and privations of individual things.; and further the particular material causes are different. Thus we have stated what the principles of sensible things are, and how many they are, and in what sense they are the same and in what sense different.

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Since we have seenAristot. Met. 12.1.3, 4. that there are three kinds of substance, two of which are natural and one immutable, we must now discuss the last named and show that there must be some substance which is eternal and immutable. Substances are the primary reality, and if they are all perishable, everything is perishable. But motion cannot be either generated or destroyed, for it always existedCf. Aristot. Physics 8.1-3; nor can time, because there can be no priority or posteriority if there is no time.The argument seems to be: If we assume that time was generated, it follows that before that there was no time; but the very term before implies time. The same applies to the destruction of time.

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Hence as time is continuous, so too is motion; for time is either identical with motion or an affection of it.Cf. Aristot. Met. 11.12.1 n. But there is no continuous motion except that which is spatial, of spatial motion only that which is circular.These statements are proved inAristot. Physics 8.8, 9.

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But even if we are to suppose that there is something which is kinetic and productive although it does not actually move or produce, there will not necessarily be motion; for that which has a potentiality may not actualize it.

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Thus it will not help matters if we posit eternal substances, as do the exponents of the Forms, unless there is in them some principle which can cause change.As there is not, according to Aristotle; cf. Aristot. Met. 1.7.4. And even this is not enough, nor is it enough if there is another substance besides the Forms; for unless it actually functions there will not be motion.

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And it will still not be enough even if it does function, if its essence is potentiality; for there will not be eternal motion, since that which exists potentially may not exist. Therefore there must be a principle of this kind whose essence is actuality. Furthermore these substancesAristotle is now thinking not only of the prime mover (God or Mind) but also of the movers of the celestial spheres. Cf. Aristot. Met. 12.8.14. must be immaterial; for they must be eternal if anything is. Therefore they are actuality.

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There is a difficulty, however; for it seems that everything which actually functions has a potentiality, whereas not everything which has a potentiality actually functions; so that potentiality is prior. But if this is so, there need be no reality; for everything may be capable of existing, but not yet existent.

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Yet if we accept the statements of the cosmologists who generate everything from Night,Cf. Hes. WD 17, Hes. Th. 116ff. or the doctrine of the physicists that all things were together,Cf. Aristot. Met. 12.2.3. we have the same impossibility; for how can there be motion if there is no actual cause? Wood will not move itself—carpentry must act upon it; nor will the menses or the earth move themselves—the seeds must act upon the earth, and the semen on the menses.

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Hence some, e.g. LeucippusCf. Aristot. Met. 1.4.12, Aristot. De Caelo 300b 8, and see Burnet, E.G.P. 178. and Plato,Cf. Plat. Tim. 30a, and sect. 8 below. posit an eternal actuality, for they say that there is always motion; but why there is, and what it is, they do not say; nor, if it moves in this or that particular way, what the cause is. For nothing is moved at haphazard, but in every case there must be some reason present; as in point of fact things are moved in one way by nature, and in another by force or mind or some other agent. And further, what kind of motion is primary? For this is an extremely important point.

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Again, Plato at least cannot even explain what it is that he sometimes thinks to be the source of motion, i.e., that which moves itself; for according to him the soul is posterior to motion and coeval with the sensible universe.Aristotle refers to Plato’s rather inconsistent account in Plat. Tim. 30-34. Now to suppose that potentiality is prior to actuality is in one sense right and in another wrong; we have explainedThe reference is probably to 5 above, but cf. Aristot. Met. 9.8. the distinction.

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But that actuality is prior is testified by Anaxagoras (since mind is actuality), and by Empedocles with his theory of Love and Strife, and by those who hold that motion is eternal, e.g. Leucippus.

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Therefore Chaos or Night did not endure for an unlimited time, but the same things have always existed, either passing through a cycle or in accordance with some other principle—that is, if actuality is prior to potentiality.

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Now if there is a regular cycle, there must be somethingThe sphere of the fixed stars, Aristot. Met. 12.8.9; cf. Aristot. De Gen. et Corr. 336a 23ff. which remains always active in the same way; but if there is to be generation and destruction, there must be something elseThe sun, which has its own yearly orbit in the ecliptic, and a daily rotation round the earth, which is explained most economically with reference to the rotation of the sphere of the fixed stars. Cf. Aristot. Met. 12.5.3 n., Aristot. De Gen. et Corr. 336a 23ff. which is always active in two different ways. Therefore this must be active in one way independently, and in the other in virtue of something else, i.e. either of some third active principle or of the first.

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It must, then, be in virtue of the first; for this is in turn the cause both of the third and of the second. Therefore the first is preferable, since it was the cause of perpetual regular motion, and something else was the cause of variety; and obviously both together make up the cause of perpetual variety. Now this is just what actually characterizes motions; therefore why need we seek any further principles?

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Since (a) this is a possible explanation, and (b) if it is not true, we shall have to regard everything as coming from Night Aristot. Met. 12.6.6 and all things together and not-being,Aristot. Met. 12.2.2, 3. these difficulties may be considered to be solved. There is something which is eternally moved with an unceasing motion, and that circular motion. This is evident not merely in theory, but in fact. Therefore the ultimate heaven must be eternal. Then there is also something which moves it.

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And since that which is moved while it moves is intermediate, there is something which moves without being moved; something eternal which is both substance and actuality.

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Now it moves in the following manner. The object of desire and the object of thought move without being moved. The primary objects of desire and thought are the same. For it is the apparent good that is the object of appetite, and the real good that is the object of the rational will.This shows that desire in general (of which appetite and will are the irrational and rational aspects) has as its object the good. Desire is the result of opinion rather than opinion that of desire; it is the act of thinking that is the starting-point.

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Now thought is moved by the intelligible, and one of the series of contrariesAristotle himself recognizes two series, lists or columns of contraries, similar to those of the Pythagoreans (Aristot. Met. 1.5.6). One, the positive, contains being, unity, substance, etc.; the other is negative and contains not-being, plurality, non-substance, etc. The negative terms are intelligible only in reference to the positive. Cf. Aristot. Met. 4.2.21. is essentially intelligible. In this series substance stands first, and of substance that which is simple and exists actually. (The one and the simple are not the same; for one signifies a measure,Cf Aristot. Met. 5.6.17. whereas simple means that the subject itself is in a certain state.)

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But the Good, and that which is in itself desirable, are also in the same series; and that which is first in a class is always best or analogous to the best.

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That the final cause may apply to immovable things is shown by the distinction of its meanings. For the final cause is not only the good for something, but also the good which is the end of some action. In the latter sense it applies to immovable things, although in the former it does not; and it causes motion as being an object of love, whereas all other things cause motion because they are themselves in motion.

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Now if a thing is moved, it can be otherwise than it is. Therefore if the actuality of the heaven is primary locomotion, then in so far as the heaven is moved, in this respect at least it is possible for it to be otherwise; i.e. in respect of place, even if not of substantiality. But since there is something—X—which moves while being itself unmoved, existing actually, X cannot be otherwise in any respect.

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For the primary kind of change is locomotion,Proved in Aristot. Physics 8.7. and of locomotion circular locomotion Aristot. Physics 8.9 ; and this is the motion which X induces. Thus X is necessarily existent; and qua necessary it is good, and is in this sense a first principle.The argument is: X (the prime mover), since it imparts the primary motion, cannot be liable to motion (or change) of any kind. Therefore it exists of necessity, and must be good (cf. Aristot. Met. 5.5.6); and it is qua good, i.e., the object of desire, that X is a first principle. For the necessary has all these meanings: that which is by constraint because it is contrary to impulse; and that without which excellence is impossible; and that which cannot be otherwise, but is absolutely necessary.Cf. Aristot. Met. 5.5

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Such, then, is the first principle upon which depend the sensible universe and the world of nature.

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And its life is like the best which we temporarily enjoy. It must be in that state always (which for us is impossible), since its actuality is also pleasure.For the relation of pleasure to actuality or activity see Aristot. Nic. Eth. 10.4.(And for this reason waking, sensation and thinking are most pleasant, and hopes and memories are pleasant because of them.) Now thinking in itself is concerned with that which is in itself best, and thinking in the highest sense with that which is in the highest sense best.Since the prime mover is pure actuality, and has or rather is the highest form of life, Aristotle identifies it with the highest activity—pure thinking.

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And thought thinks itself through participation in the object of thought; for it becomes an object of thought by the act of apprehension and thinking, so that thought and the object of thought are the same, because that which is receptive of the object of thought, i.e. essence, is thought. And it actually functions when it possesses this object.In actualization the subject and object of thought (like those of perception, Aristot. De Anima 3.2.) are identical. Hence it is actuality rather than potentiality that is held to be the divine possession of rational thought, and its active contemplation is that which is most pleasant and best.

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If, then, the happiness which God always enjoys is as great as that which we enjoy sometimes, it is marvellous; and if it is greater, this is still more marvellous. Nevertheless it is so. Moreover, life belongs to God. For the actuality of thought is life, and God is that actuality; and the essential actuality of God is life most good and eternal. We hold, then, that God is a living being, eternal, most good; and therefore life and a continuous eternal existence belong to God; for that is what God is.

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Those who suppose, as do the Pythagoreans and Speusippus,The view is referred to again in Aristot. Met. 12.10.6, Aristot. Met. 14.4.2, 3, Aristot. Met. 14.5.1. that perfect beauty and goodness do

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not exist in the beginning (on the ground that whereas the first beginnings of plants and animals are causes, it is in the products of these that beauty and perfection are found) are mistaken in their views.

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For seed comes from prior creatures which are perfect, and that which is first is not the seed but the perfect creature. E.g., one might say that prior to the seed is the man—not he who is produced from the seed, but another man from whom the seed comes.Cf. Aristot. Met. 9.8.4, 5.

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Thus it is evident from the foregoing account that there is some substance which is eternal and immovable and separate from sensible things; and it has also been shown that this substance can have no magnitude, but is impartible and indivisible (for it causes motion for infinite time, and nothing finite has an infinite potentialityCf.Aristot. Physics 266a24-b6.; and therefore since every magnitude is either finite or infinite, it cannot have finite magnitude,

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and it cannot have infinite magnitude because there is no such thing at all); and moreover that it is impassive and unalterable; for all the other kinds of motion are posterior to spatial motion. Thus it is clear why this substance has these attributes.

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We must not disregard the question whether we should hold that there is one substance of this kind or more than one, and if more than one, how many; we must review the pronouncements of other thinkers and show that with regard to the number of the substances they have said nothing that can be clearly stated.

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The theory of the Ideas contains no peculiar treatment of the question; for the exponents of the theory call the Ideas numbers, and speak of the numbers now as though they were unlimited and now as though they were limited by the number 10Cf. Aristot. Met. 13.8.17, 20. This was a Pythagorean survival, cf. Vol. I. Introduction. xvi.; but as for why there should be just so many numbers, there is no explanation given with demonstrative accuracy.

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We, however, must discuss the question on the basis of the assumptions and distinctions which we have already made.

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The first principle and primary reality is immovable, both essentially and accidentally, but it excites the primary form of motion, which is one and eternal.

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Now since that which is moved must be moved by something, and the prime mover must be essentially immovable, and eternal motion must be excited by something eternal, and one motion by some one thing; and since we can see that besides the simple spatial motion of the universei.e., the (apparent) diurnal revolution of the heavens.(which we hold to be excited by the primary immovable substance) there are other spatial motions—those of the planets—which are eternal (because a body which moves in a circle is eternal and is never at rest—this has been proved in our physical treatisesAristot. Physics 8.8, 9, Aristot. De Caelo 1.2, 2.3-8.); then each of these spatial motions must also be excited by a substance which is essentially immovable and eternal.

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For the nature of the heavenly bodies is eternal, being a kind of substance; and that which moves is eternal and prior to the moved; and that which is prior to a substance must be a substance. It is therefore clear that there must be an equal number of substances, in nature eternal, essentially immovable, and without magnitude; for the reason already stated.Aristot. Met. 12.7.12, 13.

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Thus it is clear that the movers are substances, and that one of them is first and another second and so on in the same order as the spatial motions of the heavenly bodies.

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As regards the number of these motions, we have now reached a question which must be investigated by the aid of that branch of mathematical science which is most akin to philosophy, i.e. astronomy; for this has as its object a substance which is sensible but eternal, whereas the other mathematical sciences, e.g. arithmetic and geometry, do not deal with any substance. That there are more spatial motions than there are bodies which move in space is obvious to those who have even a moderate grasp of the subject, since each of the non-fixed stars has more than one spatial motion.

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As to how many these spatial motions actually are we shall now, to give some idea of the subject, quote what some of the mathematicians say, in order that there may be some definite number for the mind to grasp; but for the rest we must partly investigate for ourselves and partly learn from other investigators, and if those who apply themselves to these matters come to some conclusion which clashes with what we have just stated, we must appreciate both views, but follow the more accurate.

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EudoxusOf Cnidus (circa 408 -355 B.C.). He was a pupil of Plato, and a distinguished mathematician. held that the motion of the sun and moon involves in either case three spheres,For a full discussion of the theories of Eudoxus and Callipus see Dreyer, Planetary Systems 87-114; Heath,Aristarchus of <placeName key="perseus,Samos City">Samos</placeName>190-224. of which the outermost is that of the fixed stars,Not identical with that of the fixed stars, but having the same motion. the second revolves in the circle which bisects the zodiac,i.e., revolves with its equator in the ecliptic. and the third revolves in a circle which is inclined across the breadth of the zodiaci.e., has the plane of its equator inclined to the plane of the ecliptic. This sphere carries the sun (or moon) fixed to a point in its equator.; but the circle in which the moon moves is inclined at a greater angle than that in which the sun moves.

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And he held that the motion of the planets involved in each case four spheres; and that of these the first and second are the sameNot the same, but having the same motion. as before (for the sphere of the fixed stars is that which carries round all the other spheres, and the sphere next in order, which has its motion in the circle which bisects the zodiac, is common to all the planets); the third sphere of all the planets has its poles in the circle which bisects the zodiac; and the fourth sphere moves in the circle inclined to the equator of the third. In the case of the third sphere, while the other planets have their own peculiar poles, those of Venus and Mercury are the same.

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Callippusof Cyzicus (fl. 380 B.C.). Simplicius says (Simplicius 493.5-8) that he corrected and elaborated Eudoxus’s theory with Aristotle’s help while on a visit to him at Athens. assumed the same arrangement of the spheres as did Eudoxus (that is, with respect to the order of their intervals), but as regards their number, whereas he assigned to Jupiter and Saturn the same number of spheres as Eudoxus, he considered that two further spheres should be added both for the sun and for the moon, if the phenomena are to be accounted for, and one for each of the other planets.

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But if all the spheres in combination are to account for the phenomena, there must be for each of the other planets other spheres, one less in number than those already mentioned, which counteract these and restore to the same position the first sphere of the star which in each case is next in order below.Aristotle is trying to establish a mechanical relation between the spheres, which Eudoxus and Callipus did not attempt to do. In this way only can the combination of forces produce the motion of the planets.

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Therefore since the forces by which the planets themselves are moved are 8 for Jupiter and Saturn, and 25 for the others, and since of these the only ones which do not need to be counteracted are those by which the lowest planetThe moon. is moved, the counteracting spheres for the first two planets will be 6, and those of the remaining four will be 16; and the total number of spheres, both those which move the planets and those which counteract these, will be 55.

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If we do not invest the moon and the sun with the additional motions which we have mentioned,In sect. 11. there will be 47 (?)Either Aristotle has made a slip in his calculations, or we should read ἐννέα(Sosigenes) for ἑπτά; this would give 49, which appears to be the correct total. For alternative explanations of an error in calculation see Ross ad loc. spheres in all.

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This, then, may be taken to be the number of the spheres; and thus it is reasonable to suppose that there are as many immovable substances and principles,i.e., the movers of the spheres.—the statement of logical necessity may be left to more competent thinkers.

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If there can be no spatial motion which is not conducive to the motion of a star, and if moreover every entity and every substance which is impassive and has in itself attained to the highest good should be regarded as an end, then there can be no other entity besides these,See previous note. and the number of the substances must be as we have said. For if there are other substances, they must move something, since they are the end of spatial motion.

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But there can be no other spatial motions besides those already mentioned. This is a reasonable inference from a general consideration of spatial motion. For if everything which moves exists for the sake of that which is moved, and every motion for the sake of something which is moved, no motion can exist for the sake of itself or of some other motion, but all motions must exist for the sake of the stars.

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For if we are to suppose that one motion is for the sake of another, the latter too must be for the sake of something else; and since the series cannot be infinite, the end of every motion must be one of the divine bodies which are moved through the heavens.

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It is evident that there is only one heaven.This paragraph seems to belong to an earlier period of Aristotle’s thought. At any rate the argument that plurality involves matter is inconsistent with the view that there are 55 immaterial movers. For if there is to be a plurality of heavens (as there is of men), the principle of each must be one in kind but many in number.

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But all things which are many in number have matter (for one and the same definition applies to many individuals, e.g. that of man; but Socrates is oneThe definition or form is one and universal; it is the combination of form with matter that constitutes an individual. Thus a plurality of individuals is caused by the combination of the same form with different matter.), but the primary essence has no matter, because it is complete reality. Therefore the prime mover, which is immovable, is one both in formula and in number; and therefore so also is that which is eternally and continuously in motion. Therefore there is only one heaven.

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A tradition has been handed down by the ancient thinkers of very early times, and bequeathed to posterity in the form of a myth, to the effect that these heavenly bodies are gods,This statement is not literally true. The planets do not seem to have been associated with the gods of popular mythology until the fourth century B.C. (see Burnet, E.G.P. p. 23 n.). But Aristotle’s general meaning seems to be that the gods were identified with the primary natural forces; and this is substantially true. and that the Divine pervades the whole of nature.

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The rest of their tradition has been added later in a mythological form to influence the vulgar and as a constitutional and utilitarian expedientCf. Aristot. Met. 2.3.1.; they say that these gods are human in shape or are like certain other animals,e.g. the Egyptian deities. Zoomorphism in Greek religion is a doubtful quantity. and make other statements consequent upon and similar to those which we have mentioned.

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Now if we separate these statements and accept only the first, that they supposed the primary substances to be gods, we must regard it as an inspired saying and reflect that whereas every art and philosophy has probably been repeatedly developed to the utmost and has perished again, these beliefs of theirs have been preserved as a relic of former knowledge. To this extent only, then, are the views of our forefathers and of the earliest thinkers intelligible to us.

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The subject of Mind involves certain difficulties. Mind is held to be of all phenomena the most supernatural; but the question of how we must regard it if it is to be of this nature involves certain difficulties. If Mind thinks nothing, where is its dignity? It is in just the same state as a man who is asleep. If it thinks, but something else determines its thinking, then since that which is its essence is not thinking but potentiality,i.e., if its thinking is determined by something else, Mind is only a potentiality, and not (as described in Aristot. Met. 12.7.1-9) the highest actuality. it cannot be the best reality; because it derives its excellence from the act of thinking.

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Again, whether its essence is thought or thinking, what does it think? It must think either itself or something else; and if something else, then it must think either the same thing always, or different things at different times. Then does it make any difference, or not, whether it thinks that which is good or thinks at random?

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Surely it would be absurd for it to think about some subjects. Clearly, then, it thinks that which is most divine and estimable, and does not change; for the change would be for the worse, and anything of this kind would immediately imply some sort of motion. Therefore if Mind is not thinking but a potentiality, (a) it is reasonable to suppose that the continuity of its thinking is laboriousCf. Aristot. Met. 9.8.18.; (b) clearly there must be something else which is more excellent than Mind; i.e. the object of thought;

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for both thought and the act of thinking will belong even to the thinker of the worst thoughts.If Mind is a potentiality, since a potentiality is of contraries, Mind may think that which is worst. Therefore if this is to be avoided (as it is, since it is better not to see some things than to see them), thinking cannot be the supreme good. Therefore Mind thinks itself, if it is that which is best; and its thinking is a thinking of thinking.

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Yet it seems that knowledge and perception and opinion and understanding are always of something else, and only incidentally of themselves.

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And further, if to think is not the same as to be thought, in respect of which does goodness belong to thought? for the act of thinking and the object of thought have not the same essence. The answer is that in some cases the knowledge is the object. In the productive sciences, if we disregard the matter, the substance, i.e. the essence, is the object; but in the speculative sciences the formula or the act of thinking is the object. Therefore since thought and the object of thought are not different in the case of things which contain no matter, they will be the same, and the act of thinking will be one with the object of thought.

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There still remains the question whether the object of thought is composite; for if so, thought would change in passing from one part of the whole to another. The answer is that everything which contains no matter is indivisible. Just as the human mind, or rather the mind of composite beings,i.e., beings composed of matter as well as form. Such beings are contrasted with the divine Mind, which is pure form. is in a certain space of timeThe meaning of this sentence is shown by the definition of Happiness in Aristot. Nic. Eth. 1098a 16-20. It takes the human mind a lifetime of the highest intellectual activity of which it is capable to attain to happiness; but the divine Mind is always happy. Cf. Aristot. Met. 12.7.9.(for it does not possess the good at this or at that moment, but in the course of a certain whole period it attains to the supreme good, which is other than itself), so is absolute self-thought throughout all eternity.

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We must also consider in which sense the nature of the universe contains the good or the supreme good; whether as something separate and independent, or as the orderly arrangement of its parts.

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Probably in both senses, as an army does; for the efficiency of an army consists partly in the order and partly in the general; but chiefly in the latter, because he does not depend upon the order, but the order depends upon him. All things, both fishes and birds and plants, are ordered together in some way, but not in the same way; and the system is not such that there is no relation between one thing and another; there is a definite connection.

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Everything is ordered together to one end; but the arrangement is like that in a household, where the free persons have the least liberty to act at random, and have all or most of their actions preordained for them, whereas the slaves and animals have little common responsibility and act for the most part at random; for the nature of each class is a principle such as we have described.The free persons correspond to the heavenly bodies, whose movements are fixed by necessity; the servile class to human beings. Each class acts in accordance with its nature, a principle which produces obedience to duty in the higher creatures, caprice in the lower ( Ross).

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I mean, for example, that everything must at least come to dissolution; and similarly there are other respects in which everything contributes to the good of the whole.

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We must not fail to observe how many impossibilities and absurdities are involved by other theories, and what views the more enlightened thinkers hold, and what views entail the fewest difficulties.

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All thinkers maintain that all things come from contraries; but they are wrong both in saying all thingsBecause there is an eternal substance, which is not derived from contraries (Aristot. Met. 12.6.1). and in saying that they come from contraries,Things are derived from a substrate as well (Aristot. Met. 12.2.1). nor do they explain how things in which the contraries really are present come from the contraries; for the contraries cannot act upon each other. For us, however, this problem is satisfactorily solved by the fact that there is a third factor. Other thinkers make one of the two contraries matter; e.g., this is done by thoseSee on Aristot. Met. 14.1.4. who make the Unequal matter for the Equal, or the Many matter for the One.

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But this also is disposed of in the same way; for the one matter of two contraries is contrary to nothing. Further, on their view everything except Unity itself will partake of evil; for the BadThe Bad was identified with the unequal; cf. Aristot. Met. 1.6.10. is itself one of the elements. The other schoolSee Aristot. Met. 12.7.10 does not even regard the Good and the Bad as principles; yet the Good is in the truest sense a principle in all things. The former school is right in holding that the Good is a principle, but they do not explain how it is a principle— whether as an end or as a moving cause or as form.

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Empedocles theory is also absurd, for he identifies the Good with Love.Cf. Aristot. Met. 1.4.3. This is a principle both as causing motion (since it combines) and as matter (since it is part of the mixture).Empedocles Fr. 17 (Diels), 18-20. Now even if it so happens that the same thing is a principle both as matter and as causing motion, still the essence of the two principles is not the same. In which respect, then, is Love a principle? And it is also absurd that Strife should be imperishable; strife is the very essence of evil.Cf. Aristot. Met. 9.9.3.

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Anaxagoras makes the Good a principle as causing motion; for Mind moves things, but moves them for some end, and therefore there must be some other GoodMotion presupposes a final cause, which was not what Anaxagoras meant by Mind. Cf. Aristot. Met. 1.7.5.—unless it is as we say; for on our view the art of medicine is in a sense health.Aristotle identifies the efficient cause, in a sense, with the final cause. Cf. Aristot. Met. 7.9.3. It is absurd also not to provide a contrary for the Good, i.e. for Mind.In Aristot. Met. 1.6.10 Aristotle describes Anaxagoras as a recognizing contrary principles of good and evil. Moreover, on Aristotle’s own showing, evil cannot be a principle (Aristot. Met. 9.9.3). But all those who recognize the contraries fail to make use of the contraries, unless we systematize their theories.

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And none of them explains why some things are perishable and others imperishable; for they make all existing things come from the same first principles.Cf. Aristot. Met. 3.4.11-20. Again, someCf. Aristot. Met. 12.2.2, 3. make existing things come from not-being, while others,The Eleatics. Cf. Aristot. Met. 1.5.10-13. to avoid this necessity, make all things one. Again, no one explains why there must always be generation, and what the cause of generation is.

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Moreover, those who posit two principles must admit another superior principle,i.e., an efficient cause. and so must the exponents of the Forms; for what made or makes particulars participate in the Forms? And on all other views it follows necessarily that there must be something which is contrary to Wisdom or supreme knowledge, but on ours it does not. For there is no contrary to that which is primary,

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since all contraries involve matter, and that which has matter exists potentially; and the ignorance which is contrary to Wisdom would tend towards the contrary of the object of Wisdom; but that which is primary has no contrary.

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Further, if there is to be nothing else besides sensible things, there will be no first principle, no order, no generation, and no celestial motions, but every principle will be based upon another,If there is nothing but what is sensible or potential, there can be no prime mover (which is actuality) to excite motion in the universe, and no teleology in causation. For the cosmologists on causation see Aristot. Met. 3.3.11-13. as in the accounts of all the cosmologists and physicists.

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And if the Forms or numbers are to exist, they will be causes of nothing; or if not of nothing, at least not of motion.

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Further, how can extension, i.e. a continuum, be produced from that which is unextended? Number cannot, either as a moving or as a formal cause, produce a continuum. Moreover, no contrary can be essentially productive and kinetic, for then it would be possible for it not to exist;

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and further, the act of production would in any case be posterior to the potentiality. Therefore the world of reality is not eternal. But there are real objects which are eternal. Therefore one of these premisses must be rejected. We have described how this may be done.By assuming an eternal actual mover (Aristot. Met. 12.6.4).

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Further, in virtue of what the numbers, or soul and body, or in general the form and the object, are one, no one attempts to explain; nor is it possible to do so except on our theory, that it is the moving cause that makes them one.Cf.Aristot. Met. 8.6.

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As for thoseSpeusippus and his followers; cf. Aristot. Met. 7.2.4, Aristot. Met. 14.3.8. who maintain that mathematical number is the primary reality, and so go on generating one substance after another and finding different principles for each one, they make the substance of the universe incoherent (for one substance in no way affects another by its existence or non-existence) and give us a great many governing principles. But the world must not be governed badly:

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The rule of many is not good; let one be the ruler.Hom. Il.2.204.

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We have already explained what the substance of sensible things is, dealing in our treatise on physicsThe reference is presumably to Aristot. Physics 1. with the material substrate, and subsequently with substance as actuality.In Books 7-9.

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Now since we are inquiring whether there is or is not some immutable and eternal substance besides sensible substances, and if there is, what it is, we must first examine the statements of other thinkers, so that if they have been mistaken in any respect, we may not be liable to the same mistakes; and if there is any view which is common to them and us, we may not feel any private self-irritation on this score. For we must be content if we state some points better than they have done, and others no worse.

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There are two views on this subject. Some say that mathematical objects, i.e. numbers and lines, are substances; and others again that the Ideas are substances.

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Now since someThis was the orthodox Platonist view; cf. Aristot. Met. 1.6.4. recognize these as two classes— the Ideas and the mathematical numbers—and othersXenocrates and his followers. regard both as having one nature, and yet othersThe Pythagoreans and Speusippus. hold that only the mathematical substances are substances, we must first consider the mathematical objects, without imputing to them any other characteristic—e.g. by asking whether they are really Ideas or not, or whether they are principles and substances of existing things or not—and merely inquire whether as mathematical objects they exist or not, and if they do, in what sense; then after this we must separately consider the Ideas themselves, simply and in so far as the accepted procedure requires; for most of the arguments have been made familiar already by the criticisms of other thinkers.

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And further, the greater part of our discussion must bear directly upon this second question—viz. when we are considering whether the substances and first principles of existing things are numbers and Ideas; for after we have dealt with the Ideas there remains this third question.

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Now if the objects of mathematics exist, they must be either in sensible things, as some hold; or separate from them (there are some also who hold this view); or if they are neither the one nor the other, either they do not exist at all, or they exist in some other way. Thus the point which we shall have to discuss is concerned not with their existence, but with the mode of their existence.

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That the objects of mathematics cannot be in sensible things, and that moreover the theory that they are is a fabrication, has been observed already in our discussion of difficultiesCf. Aristot. Met. 3.2.23-30. —the reasons being (a) that two solids cannot occupy the same space, and (b) that on this same theory all other potentialities and characteristics would exist in sensible things, and none of them would exist separately. This, then, has been already stated;

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but in addition to this it is clearly impossible on this theory for any body to be divided. For it must be divided in a plane, and the plane in a line, and the line at a point; and therefore if the point is indivisible, so is the line, and so on.

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For what difference does it make whether entities of this kind are sensible objects, or while not being the objects themselves, are yet present in them? the consequence will be the same, for either they must be divided when the sensible objects are divided, or else not even the sensible objects can be divided.

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Nor again can entities of this kind exist separately.

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For if besides sensible solids there are to be other solids which are separate from them and prior to sensible solids, clearly besides sensible planes there must be other separate planes, and so too with points and lines; for the same argument applies. And if these exist, again besides the planes, lines and points of the mathematical solid, there must be others which are separate;

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for the incomposite is prior to the composite, and if prior to sensible bodies there are other non-sensible bodies, then by the same argument the planes which exist independently must be prior to those which are present in the immovable solids. Therefore there will be planes and lines distinct from those which coexist with the separately-existent solids; for the latter coexist with the mathematical solids, but the former are prior to the mathematical solids.

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Again, in these planes there will be lines, and by the same argument there must be other lines prior to these; and prior to the points which are in the prior lines there must be other points, although there will be no other points prior to these.

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Now the accumulation becomes absurd; because whereas we get only one class of solids besides sensible solids, we get three classes of planes besides sensible planes—those which exist separately from sensible planes, those which exist in the mathematical solids, and those which exist separately from those in the mathematical solids—four classes of lines, and five of points;

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with which of these, then, will the mathematical sciences deal? Not, surely, with the planes, lines and points in the immovable solid; for knowledge is always concerned with that which is prior. And the same argument applies to numbers; for there will be other units besides each class of points, and besides each class of existing things, first the sensible and then the intelligible; so that there will be an infinite number of kinds of mathematical numbers.

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Again, there are the problems which we enumerated in our discussion of difficultiesAristot. Met. 3.2.23-27.: how can they be solved? For the objects of astronomy will similarly be distinct from sensible things, and so will those of geometry; but how can a heaven and its parts (or anything else which has motion) exist apart from the sensible heaven? And similarly the objects of optics and of harmonics will be distinct, for there will be sound and sight apart from the sensible and particular objects.

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Hence clearly the other senses and objects of sense will exist separately; for why should one class of objects do so rather than another? And if this is so, animals too will exist separately, inasmuch as the senses will.

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Again, there are certain general mathematical theorems which are not restricted to these substances.

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Here, then, we shall have yet another kind of substance intermediate between and distinct from the Ideas and the intermediates, which is neither number nor points nor spatial magnitude nor time. And if this is impossible, clearly it is also impossible that the aforesaid substances should exist separately from sensible objects.

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In general, consequences result which are contrary both to the truth and to received opinion if we thus posit the objects of mathematics as definite separately-existent entities. For if they exist in this way, they must be prior to sensible spatial magnitudes, whereas in truth they must be posterior to them; for the incomplete spatial magnitude is in point of generation prior, but in point of substantiality posterior, as the inanimate is to the animate.

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Again, in virtue of what can we possibly regard mathematical magnitudes as one? Things in this world of ours may be reasonably supposed to be one in virtue of soul or part of the soul, or some other influence; apart from this they are a plurality and are disintegrated. But inasmuch as the former are divisible and quantitative, what is the cause of their unity and cohesion?

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Again, the ways in which the objects of mathematics are generated prove our point;

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for they are generated first in the dimension of length, then in that of breadth, and finally in that of depth, whereupon the process is complete. Thus if that which is posterior in generationi.e., in the natural order of development. Thus generation (γένεσις) is used in two different senses in this argument, which therefore becomes invalid (Bonitz). is prior in substantiality, body will be prior to plane and line, and in this sense it will also be more truly complete and whole, because it can become animate; whereas how could a line or plane be animate? The supposition is beyond our powers of apprehension.

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Further, body is a kind of substance, since it already in some sense possesses completeness; but in what sense are lines substances? Neither as being a kind of form or shape, as perhaps the soul is, nor as being matter, like the body; for it does not appear that anything can be composed either of lines or of planes or of points,

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whereas if they were a kind of material substance it would be apparent that things can be so composed. Let it be granted that they are prior in formula; yet not everything which is prior in formula is also prior in substantiality. Things are prior in substantiality which when separated have a superior power of existence; things are prior in formula from whose formulae the formulae of other things are compounded. And these characteristics are not indissociable.

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For if attributes, such as moving or white, do not exist apart from their substances, white will be prior in formula to white man, but not in substantiality; for it cannot exist in separation, but always exists conjointly with the concrete whole—by which I mean white man.

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Thus it is obvious that neither is the result of abstraction prior, nor the result of adding a determinant posterior—for the expression white man is the result of adding a determinant to white.

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Thus we have sufficiently shown (a) that the objects of mathematics are not more substantial than corporeal objects; (b) that they are not prior in point of existence to sensible things, but only in formula; and (c) that they cannot in any way exist in separation.

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And since we have seensect. 1-3 above. that they cannot exist in sensible things, it is clear that either they do not exist at all, or they exist only in a certain way, and therefore not absolutely; for exist has several senses.

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The general propositions in mathematics are not concerned with objects which exist separately apart from magnitudes and numbers; they are concerned with magnitudes and numbers, but not with them as possessing magnitude or being divisible. It is clearly possible that in the same way propositions and logical proofs may apply to sensible magnitudes; not qua sensible, but qua having certain characteristics.

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For just as there can be many propositions about things merely qua movable, without any reference to the essential nature of each one or to their attributes, and it does not necessarily follow from this either that there is something movable which exists in separation from sensible things or that there is a distinct movable nature in sensible things; so too there will be propositions and sciences which apply to movable things, not qua movable but qua corporeal only; and again qua planes only and qua lines only, and qua divisible, and qua indivisible but having position, and qua indivisible only.

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Therefore since it is true to say in a general sense not only that things which are separable but that things which are inseparable exist, e.g., that movable things exist, it is also true to say in a general sense that mathematical objects exist, and in such a form as mathematicians describe them.

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And just as it is true to say generally of the other sciences that they deal with a particular subject—not with that which is accidental to it (e.g. not with white if the healthy is white, and the subject of the science is the healthy), but with that which is the subject of the particular science; with the healthy if it treats of things qua healthy, and with man if qua man—so this is also true of geometry. If the things of which it treats are accidentally sensible although it does not treat of them qua sensible, it does not follow that the mathematical sciences treat of sensible things—nor, on the other hand, that they treat of other things which exist independently apart from these.

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Many attributes are essential properties of things as possessing a particular characteristic; e.g., there are attributes peculiar to an animal qua female or qua male, although there is no such thing as female or male in separation from animals. Hence there are also attributes which are peculiar to things merely qua lines or planes.

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And in proportion as the things which we are considering are prior in formula and simpler, they admit of greater exactness; for simplicity implies exactness. Hence we find greater exactness where there is no magnitude, and the greatest exactness where there is no motion; or if motion is involved, where it is primary, because this is the simplest kind; and the simplest kind of primary motion is uniform motion.Aristot. Met. 12.7.6.

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The same principle applies to both harmonics and optics, for neither of these sciences studies objects qua sight or qua sound, but qua lines and numbersOptics studies lines and harmonics numbers because these sciences are subordinate to geometry and arithmetic (Aristot. An. Post. 75b 15).; yet the latter are affections peculiar to the former. The same is also true of mechanics.

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Thus if we regard objects independently of their attributes and investigate any aspect of them as so regarded, we shall not be guilty of any error on this account, any more than when we draw a diagram on the ground and say that a line is a foot long when it is not; because the error is not in the premisses.Cf. Aristot. Met. 14.2.9, 10. The best way to conduct an investigation in every case is to take that which does not exist in separation and consider it separately; which is just what the arithmetician or the geometrician does.

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For man, qua man, is one indivisible thing; and the arithmetician assumes man to be one indivisible thing, and then considers whether there is any attribute of man qua indivisible. And the geometrician considers man neither qua man nor qua indivisible, but qua something solid. For clearly the attributes which would have belonged to man even if man were somehow not indivisible can belong to man irrespectively of his humanity or indivisibility.

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Hence for this reason the geometricians are right in what they maintain, and treat of what really exists; i.e., the objects of geometry really exist. For things can exist in two ways, either in complete reality or as matter.i.e., potentially.

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And since goodness is distinct from beauty (for it is always in actions that goodness is present, whereas beauty is also in immovable things), theyCf. Aristot. Met. 3.2.4. are in error who assert that the mathematical sciences tell us nothing about beauty or goodness;

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for they describe and manifest these qualities in the highest degree, since it does not follow, because they manifest the effects and principles of beauty and goodness without naming them, that they do not treat of these qualities. The main species of beauty are orderly arrangement, proportion, and definiteness; and these are especially manifested by the mathematical sciences.

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And inasmuch as it is evident that these (I mean, e.g., orderly arrangement and definiteness) are causes of many things, obviously they must also to some extent treat of the cause in this sense, i.e. the cause in the sense of the Beautiful. But we shall deal with this subject more explicitly elsewhere.There is no obvious fulfilment of this promise.

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As regards the objects of mathematics, then, the foregoing account may be taken as sufficient to show that they exist, and in what sense they exist, and in what sense they are prior and in what they are not. But as regards the Ideas we must first consider the actual theory in relation to the Idea, without connecting it in any way with the nature of numbers, but approaching it in the form in which it was originally propounded by the first exponentsIt seems quite obvious that Aristotle intends this vague phrase to refer to Plato. Cf. Aristot. Met. 1.6.1-3, with which the following sections 2-5 should be compared. On the whole subject see Introduction. of the Ideas.

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The theory of Forms occurred to those who enunciated it because they were convinced as to the true nature of reality by the doctrine of Heraclitus, that all sensible things are always in a state of flux; so that if there is to be any knowledge or thought about anything, there must be certain other entities, besides sensible ones, which persist. For there can be no knowledge of that which is in flux.

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Now Socrates devoted his attention to the moral virtues, and was the first to seek a general definition of these (for of the Physicists Democritus gained only a superficial grasp of the subjectCf. Aristot. Phys. 194a 20, Aristot. De Part. Anim. 642a 24. and defined, after a fashion, the hot and the cold; while the PythagoreansCf. Aristot. Met. 1.5.2, 16. at an earlier date had arrived at definitions of some few things—whose formulae they connected with numbers—e.g., what opportunity is, or justice or marriage); and he naturally inquired into the essence of things;

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for he was trying to reason logically, and the starting-point of all logical reasoning is the essence. At that time there was as yet no such proficiency in Dialectic that men could study contraries independently of the essence, and consider whether both contraries come under the same science.

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There are two innovationsThis is perhaps too strong a word. What Aristotle means is that Socrates was the first thinker who attached importance to general definitions and systematically used arguments from analogy in order to arrive at them. The Greeks as a whole were only too readily impressed by analogy; Socrates merely developed an already prevalent tendency. For an example of his method see the reference at Aristot. Met. 5.29.5 n. which, may fairly be ascribed to Socrates: inductive reasoning and general definition. Both of these are associated with the starting-point of scientific knowledge.

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But whereas Socrates regarded neither universals nor definitions as existing in separation, the Idealists gave them a separate existence, and to these universals and definitions of existing things they gave the name of Ideas.Cf. Introduction.

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Hence on their view it followed by virtually the same argument that there are Ideas of all terms which are predicated universallyWith sect. 6-13 cf. Aristot. Met. 1.9.1-8, which are almost verbally the same. See Introduction.; and the result was very nearly the same as if a man who wishes to count a number of things were to suppose that he could not do so when they are few, and yet were to try to count them when he has added to them. For it is hardly an exaggeration to say that there are more Forms than there are particular sensible things (in seeking for whose causes these thinkers were led on from particulars to Ideas); because corresponding to each thing there is a synonymous entity, apart from the substances (and in the case of non-substantial things there is a One over the Many) both in our everyday world and in the realm of eternal entities.

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Again, not one of the ways in which it is attempted to prove that the Forms exist demonstrates their point; from some of them no necessary conclusion follows, and from others it follows that there are Form of things of which they hold that there are no Forms.

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For according to the arguments from the sciences, there will be Forms of all things of which there are sciences; and according to the One-over-Many argument, of negations too; and according to the argument that we have some conception of what has perished there will be Forms of perishable things, because we have a mental picture of these things. Further, of the most exact arguments some establish Ideas of relations, of which the Idealists deny that there is a separate genus, and others state the Third Man.

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And in general the arguments for the Forms do away with things which are more important to the exponents of the Forms than the existence of the Ideas; for they imply that it is not the Dyad that is primary, but Number; and that the relative is prior to number, and therefore to the absolute; and all the other conclusions in respect of which certain persons by following up the views held about the Forms have gone against the principles of the theory.

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Again, according to the assumption by which they hold that the Ideas exist, there will be Forms not only of substances but of many other things (since the concept is one not only in the case of substances but in the case of non-substantial things as well; and there can be sciences not only of substances but also of other things; and there are a thousand other similar consequences);

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but it follows necessarily from the views generally held about them that if the Forms are participated in, there can only be Ideas of substances, because they are not participated in accidentally; things can only participate in a Form in so far as it is not predicated of a subject.

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I mean, e.g., that if a thing participates in absolute doubleness, it participates also in something eternal, but only accidentally; because it is an accident of doubleness to be eternal. Thus the Ideas will be substance. But the same terms denote substance in the sensible as in the Ideal world; otherwise what meaning will there be in saying that something exists besides the particulars, i.e. the unity comprising their multiplicity?

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If the form of the Ideas and of the things which participate in them is the same, they will have something in common (for why should duality mean one and the same thing in the case of perishable 2’s and the 2’s which are many but eternal, and not in the case of absolute duality and a particular 2?). But if the form is not the same, they will simply be homonyms; just as though one were to call both Callias and a piece of wood man, without remarking any property common to them.

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sect. 14, 15 have no counterpart in Book 1.And if we profess that in all other respects the common definitions apply to the Forms, e.g. that plane figure and the other parts of the definition apply to the Ideal circle, only that we must also state of what the Form is a Form, we must beware lest this is a quite meaningless statement.The suggestion is that the definition of an Ideal circle is the same as that of a particular circle, except that it must have added to it the statement of what particular the Idea is an Idea.

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For to what element of the definition must the addition be made? to center, or plane or all of them? For all the elements in the essence of an Idea are Ideas; e.g. animal and two-footed. sc. in the definition or essence of Ideal man. Further, it is obvious that being an Idea, just like plane, must be a definite characteristic which belongs as genus to all its species.i.e., being an idea will be a characteristic common to all ideas, and so must be itself an Idea.

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This chapter corresponds almost verbally to Aristot. Met. 1.9.9-15. Cf. note on Aristot. Met. 13.4.6.Above all we might examine the question what on earth the Ideas contribute to sensible things, whether eternal or subject to generation and decay; for they are not the cause of any motion or change in them.

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Moreover they are no help towards the knowledge of other things (for they are not the substance of particulars, otherwise they would be in particulars) or to their existence (since they are not present in the things which participate in them. If they were, they might perhaps seem to be causes, in the sense in which the admixture of white causes a thing to be white.

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But this theory, which was stated first by Anaxagoras and later by Eudoxus in his discussion of difficulties, and by others also, is very readily refuted; for it is easy to adduce plenty of impossibilities against such a view). Again, other things are not in any accepted sense derived from the Forms.

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To say that the Forms are patterns, and that other things participate in them, is to use empty phrases and poetical metaphors; for what is it that fashions things on the model of the Ideas? Besides, anything may both be and come to be without being imitated from something else; thus a man may become like Socrates whether Socrates exists or not,

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and even if Socrates were eternal, clearly the case would be the same. Also there will be several patterns (and therefore Forms) of the same thing; e.g., animal and two-footed will be patterns of man, and so too will the Idea of man.

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Further, the Forms will be patterns not only of sensible things but of Ideas; e.g. the genus will be the pattern of its species; hence the same thing will be pattern and copy. Further, it would seem impossible for the substance and that of which it is the substance to exist in separation; then how can the Ideas, if they are the substances of things, exist in separation from them?

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In thePhaedoPlat. Phaedo 100d. this statement is made: that the Forms are causes both of being and of generation. Yet assuming that the Forms exist, still there is no generation unless there is something to impart motion; and many other things are generated (e.g. house and ring) of which the Idealists say that there are no Forms.

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Thus it is clearly possible that those things of which they say that there are Ideas may also exist and be generated through the same kind of causes as those of the things which we have just mentioned, and not because of the Forms. Indeed, as regards the Ideas, we can collect against them plenty of evidence similar to that which we have now considered; not only by the foregoing methods, but by means of more abstract and exact reasoning.

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Now that we have dealt with the problems concerning the Ideas, we had better re-investigate the problems connected with numbers that follow from the theory that numbers are separate substances and primary causes of existing things. Now if number is a kind of entity, and has nothing else as its substance, but only number itself, as some maintain; then either (a) there must be some one part of number which is primary, and some other part next in succession, and so on, each part being specifically differentThis statement bears two meanings, which Aristotle confuses: (i) There must be more than one number-series, each series being different in kind from every other series; (2) All numbers are different in kind, and inaddible. Confusion (or textual inaccuracy) is further suggested by the fact that Aristotle offers no alternative statement of the nature of number in general, such as we should expect from his language. In any case the classification is arbitrary and incomplete.—

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and this applies directly to units, and any given unit is inaddible to any other given unit; or (b) theyThe units. are all directly successive, and any units can be added to any other units, as is held of mathematical number; for in mathematical number no one unit differs in any way from another.

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Or (c) some units must be addible and others not. E.g., 2 is first after 1, and then 3, and so on with the other numbers; and the units in each number are addible, e.g. the units in the firsti.e., Ideal or natural.2 are addible to one another, and those in the first 3 to one another, and so on in the case of the other numbers; but the units in the Ideal 2 are inaddible to those in the Ideal 3;

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and similarly in the case of the other successive numbers. Hence whereas mathematical number is counted thus: after 1, 2 (which consists of another 1 added to the former) and 3 (which consists of another 1 added to these two) and the other numbers in the same way, Ideal number is counted like this: after 1, a distinct 2 not including the original 1; and a 3 not including the 2, and the rest of the numbers similarly.

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Or (d) one kind of number must be such as we first described, and another or such as the mathematicians maintain, and that which we have last described must be a third kind.

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Again, these numbers must exist either in separation from things, or not in separation, but in sensible things (not, however, in the way which we first considered,In Aristot. Met. 13.2.1-3. but in the sense that sensible things are composed of numbers which are present in themThe Pythagorean number-atomist view; See Introduction.)—either some of them and not others, or all of them.i.e., either all numbers are material elements of things, or some are and others are not.

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These are of necessity the only ways in which the numbers can exist. Now of those who say that unity is the beginning and substance and element of all things, and that number is derived from it and something else, almost everyone has described number in one of these ways (except that no one has maintained that all units are inaddibleCf. sect. 2.);

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and this is natural enough, because there can be no other way apart from those which we have mentioned. Some hold that both kinds of number exist, that which involves priority and posteriority being identical with the Ideas, and mathematical number being distinct from Ideas and sensible things, and both kinds being separable from sensible thingsCf. Aristot. Met. 1.6.4.; others hold that mathematical number alone exists,Cf. Aristot. Met. 12.10.14. being the primary reality and separate from sensible things.

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The Pythagoreans also believe in one kind of number—the mathematical; only they maintain that it is not separate, but that sensible substances are composed of it. For they construct the whole universe of numbers, but not of numbers consisting of abstract units; they suppose the units to be extended—but as for how the first extended unit was formed they appear to be at a loss.Cf. Aristot. Met. 13.8.9, 10, Aristot. Met. 14.3.15, Aristot. Met. 14.5.7, and see Introduction.

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Another thinker holds that primary or Ideal number alone exists; and someCf. 10ff., Aristot. Met. 13.1.4. identify this with mathematical number.

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The same applies in the case of lines, planes and solids.

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SomePlato. distinguish mathematical objects from those which come after the Ideasi.e., the (semi-)Ideal lines, planes, etc. Cf. Aristot. Met. 1.9.30.; and of those who treat the subject in a different manner someSpeusippus; cf. sect. 7 above. speak of the mathematical objects and in a mathematical way—viz. those who do not regard the Ideas as numbers, nor indeed hold that the Ideas exist—and othersXenocrates. For his belief in indivisible lines see Ritter and Preller 362. Aristotle ascribes the doctrine to Plato in Aristot. Met. 1.9.25. speak of the mathematical objects, but not in a mathematical way; for they deny that every spatial magnitude is divisible into extended magnitudes, or that any two given units make 2.

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But all who hold that Unity is an element and principle of existing things regard numbers as consisting of abstract units, except the Pythagoreans; and they regard number as having spatial magnitude, as has been previously stated.sect. 8.

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It is clear from the foregoing account (1.) in how many ways it is possible to speak of numbers, and that all the ways have been described. They are all impossible, but doubtless somesc. the view of Xenocrates (cf. Aristot. Met. 13.8.8). are more so than others.

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First, then, we must inquire whether the limits are addible or inaddible; and if inaddible, in which of the two ways which we have distinguished.Aristot. Met. 13.6.2, 3. For it is possible either (a) that any one unit is inaddible to any other, or (b) that the units in the Ideal 2 are inaddible to those in the Ideal 3, and thus that the units in each Ideal number are inaddible to those in the other Ideal numbers.

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Now if all units are addible and do not differ in kind, we get one type of number only, the mathematical, and the Ideas cannot be the numbers thus produced;

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for how can we regard the Idea of Man or Animal, or any other Form, as a number? There is one Idea of each kind of thing: e.g. one of Humanity and another one of Animality; but the numbers which are similar and do not differ in kind are infinitely many, so that this is no more the Idea of Man than any other 3 is. But if the Ideas are not numbers, they cannot exist at all;

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for from what principles can the Ideas be derived? Number is derived from Unity and the indeterminate dyad, and the principles and elements are said to be the principles and elements of number, and the Ideas cannot be placed either as prior or as posterior to numbers.Since the only principles which Plato recognizes are Unity and the Dyad, which are numerical (Aristotle insists on regarding them as a kind of 1 and 2), and therefore clearly principles of number; and the Ideas can only be derived from these principles if they (the Ideas) are (a) numbers (which has been proved impossible) or (b) prior or posterior to numbers (i.e., causes or effects of numbers, which they cannot be if they are composed of a different kind of units); then the Ideas are not derived from any principle at all, and therefore do not exist.

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But if the units are inaddible in the sense that any one unit is inaddible to any other, the number so composed can be neither mathematical number (since mathematical number consists of units which do not differ, and the facts demonstrated of it fit in with this character) nor Ideal number. For on this view 2 will not be the first number generated from Unity and the indeterminate dyad, and then the other numbers in succession, as theyThe Platonists. say 2, 3, because the units in the primary 2 are generated at the same time,This was the orthodox Platonist view of the generation of ideal numbers; or at least Aristotle is intending to describe the orthodox view. Plato should not have regarded the Ideal numbers as composed of units at all, and there is no real reason to suppose that he did (see Introduction). But Aristotle infers from the fact that the Ideal 2 is the first number generated (and then the other Ideal numbers in the natural order) that the units of the Ideal 2 are generated simultaneously, and then goes on to show that this is incompatible with the theory of inaddible units. whether, as the originator of the theory held, from unequalsi.e., the Great-and-Small, which Aristotle wrongly understands as two unequal things. It is practically certain that Plato used the term (as he did that of Indeterminate Dyad) to describe indeterminate quantity. See Introduction.(coming into being when these were equalized), or otherwise—

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since if we regard the one unit as prior to the other,This is a necessary implication of the theory of inaddible units (cf. Aristot. Met. 13.6.1, 2). it will be prior also to the 2 which is composed of them; because whenever one thing is prior and another posterior, their compound will be prior to the latter and posterior to the former.So the order of generation will be: (i) Unity (ungenerated); (2) first unit in 2; (3) second unit in 2; and the Ideal 2 will come between (2) and (3).

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Further, since the Ideal 1 is first, and then comes a particular 1 which is first of the other 1’s but second after the Ideal 1, and then a third 1 which is next

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after the second but third after the first 1, it follows that the units will be prior to the numbers after which they are called; e.g., there will be a third unit in 2 before 3 exists, and a fourth and fifth in 3 before these numbers exist.This is a corollary to the previous argument, and depends upon an identification of ones (including the Ideal One or Unity) with units.

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It is true that nobody has represented the units of numbers as inaddible in this way; but according to the principles held by these thinkers even this view is quite reasonable, although in actual fact it is untenable.

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For assuming that there is a first unit or first 1,i.e., the Ideal One. it is reasonable that the units should be prior and posterior; and similarly in the case of 2’s, if there is a first 2. For it is reasonable and indeed necessary that after the first there should be a second; and if a second, a third; and so on with the rest in sequence.

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But the two statements, that there is after 1 a first and a second unit, and that there is a first 2, are incompatible. These thinkers, however, recognize a first unit and first 1, but not a second and third; and they recognize a first 2, but not a second and third.

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It is also evident that if all units are inaddible, there cannot be an Ideal 2 and 3, and similarly with the other numbers;

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for whether the units are indistinguishable or each is different in kind from every other, numbers must be produced by addition; e.g. 2 by adding 1 to another 1, and 3 by adding another 1 to the 2, and 4 similarly.This is of course not true of the natural numbers.

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This being so, numbers cannot be generated as these thinkers try to generate them, from Unity and the dyad; because 2 becomes a part of 3,i.e., 3 is produced by adding 1 to 2. and 3 of 4, and the same applies to the following numbers.

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But according to them 4 was generated from the first 2 and the indeterminate dyad, thus consisting of two 2’s apart from the Ideal 2.Cf. sect. 18. Otherwise 4 will consist of the Ideal 2 and another 2 added to it, and the Ideal 2 will consist of the Ideal 1 and another 1; and if this is so the other element cannot be the indeterminate dyad, because it produces one unit and not a definite 2.The general argument is: Numbers are produced by addition; but this is incompatible with the belief in the Indeterminate Dyad as a generative principle, because, being duplicative, it cannot produce single units.

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Again, how can there be other 3’s and 2’s besides the Ideal numbers 3 and 2, and in what way can they be composed of prior and posterior units? All these theories are absurd and fictitious, and there can be no primary 2 and Ideal 3. Yet there must be, if we are to regard Unity and the indeterminate dyad as elements.i.e., if numbers are not generated by addition, there must be Ideal (or natural) numbers.

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But if the consequences are impossible, the principles cannot be of this nature.

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If, then, any one unit differs in kind from any other, these and other similar consequences necessarily follow. If, on the other hand, while the units in different numbers are different, those which are in the same number are alone indistinguishable from one another, even so the consequences which follow are no less difficult.

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For example, in the Ideal number 10 there are ten units, and 10 is composed both of these and of two 5’s. Now since the Ideal 10 is not a chance number,I think Ross’s interpretation of this passage must be right. The Ideal 10 is a unique number, and the numbers contained in it must be ideal and unique; therefore the two 5’s must be specifically different, and so must their units—which contradicts the view under discussion. and is not composed of chance 5’s, any more than of chance units, the units in this number 10 must be different;

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for if they are not different, the 5’s of which the 10 is composed will not be different; but since these are different, the units must be different too. Now if the units are different, will there or will there not be other 5’s in this 10, and not only the two? If there are not, the thing is absurdi.e., it is only reasonable to suppose that other 5’s might be made up out of different combinations of the units.; whereas if there are, what sort of 10 will be composed of them? for there is no other 10 in 10 besides the 10 itself:

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Again, it must also be true that 4 is not composed of chance 2’s. For according to them the indeterminate dyad, receiving the determinate dyad, made two dyads; for it was capable of duplicating that which it received.Cf. Introduction.

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Again, how is it possible that 2 can be a definite entity existing besides the two units, and 3 besides the three units? Either by participation of the one in the other, as white man exists besides white and man, because it partakes of these concepts; or when the one is a differentia of the other, as man exists besides animal and two-footed.

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Again, some things are one by contact, others by mixture, and others by position; but none of these alternatives can possibly apply to the units of which 2 and 3 consist. Just as two men do not constitute any one thing distinct from both of them, so it must be with the units.

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The fact that the units are indivisible will make no difference; because points are indivisible also, but nevertheless a pair of points is not anything distinct from the two single points.

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Moreover we must not fail to realize this: that on this theory it follows that 2’s are prior and posterior, and the other numbers similarly.

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Let it be granted that the 2’s in 4 are contemporaneous; yet they are prior to those in 8, and just as the <determinate> 2 produced the 2’s in 4, soIn each case the other factor is the indeterminate dyad (cf. sect. 18). they produced the 4’s in 8. Hence if the original 2 is an Idea, these 2’s will also be Ideas of a sort.

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And the same argument applies to the units, because the units in the original 2 produce the four units in 4; and so all the units become Ideas, and an Idea will be composed of Ideas. Hence clearly those things also of which these things are Ideas will be composite; e.g., one might say that animals are composed of animals, if there are Ideas of animals.

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In general, to regard units as different in any way whatsoever is absurd and fictitious (by fictitious I mean dragged in to support a hypothesis). For we can see that one unit differs from another neither in quantity nor in quality; and a number must be either equal or unequal—this applies to all numbers, but especially to numbers consisting of abstract units.

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Thus if a number is neither more nor less, it is equal; and things which are equal and entirely without difference we assume, in the sphere of number, to be identical. Otherwise even the 2’s in the Ideal 10 will be different, although they are equal; for if anyone maintains that they are not different, what reason will he be able to allege?

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Again, if every unit plus another unit makes 2, a unit from the Ideal 2 plus one from the Ideal 3 will make 2—a 2 composed of different unitsWhich conflicts with the view under discussion.; will this be prior or posterior to 3? It rather seems that it must be prior, because one of the units is contemporaneous with 3, and the other with 2.The implication seems to be, as Ross says, that the Platonists will refuse to admit that there is a number between 2 and 3.

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We assume that in general 1 and 1, whether the things are equal or unequal, make 2; e.g. good and bad, or man and horse; but the supporters of this theory say that not even two units make 2.

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If the number of the Ideal 3 is not greater than that of the Ideal 2, it is strange; and if it is greater, then clearly there is a number in it equal to the 2, so that this number is not different from the Ideal 2.

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But this is impossible, if there is a first and second number.i.e., if numbers are specifically different. Cf. Aristot. Met. 13.6.1. Nor will the Ideas be numbers. For on this particular point they are right who claim that the units must be different if there are to be Ideas, as has been already stated.sect. 2-4 above. For the form is unique; but if the units are undifferentiated, the 2’s and 3’s will be undifferentiated.

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Hence they have to say that when we count like this, l, 2, we do not add to the already existing number; for if we do, (a) number will not be generated from the indeterminate dyad, and (b) a number cannot be an Idea; because one Idea will pre-exist in another, and all the Forms will be parts of one Form.i.e., the biggest number.

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Thus in relation to their hypothesis they are right, but absolutely they are wrong, for their view is very destructive, inasmuch as they will say that this point presents a difficulty: whether, when we count and say 1, 2, 3, we count by addition or by enumerating distinct portions.This is Apelt’s interpretation of κατὰ μερίδας. For this sense of the word he quotes Plut. Mor. 644c. The meaning then is: If you count by addition, you regard number as exhibited only in concrete instances; if you treat each number as a distinct portion (i.e. generated separately), you admit another kind of number besides the mathematical. Aristotle says that number can be regarded in both ways. But we do both; and therefore it is ridiculous to refer this point to so great a difference in essence.

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First of all it would be well to define the differentia of a number; and of a unit, if it has a differentia. Now units must differ either in quantity or in quality; and clearly neither of these alternatives can be true. But units may differ, as number does, in quantity. But if units also differed in quantity, number would differ from number, although equal in number of units.

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Again, are the first units greater or smaller, and do the later units increase in size, or the opposite? All these suggestions are absurd. Nor can units differ in quality; for no modification can ever be applicable to them, because these thinkers hold that even in numbers quality is a later attribute than quantity.Numbers have quality as being prime or composite, plane or solid (i.e., products of two or three factors); but these qualities are clearly incidental to quantity. Cf. Aristot. Met. 5.14.2.

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Further, the units cannot derive quality either from unity or from the dyad; because unity has no quality, and the dyad produces quantity, because its nature causes things to be many. If, then, the units differ in some other way, they should most certainly state this at the outset, and explain, if possible, with regard to the differentia of the unit, why it must exist; or failing this, what differentia they mean.

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Clearly, then, if the Ideas are numbers, the units cannot all be addible, nor can they all be inaddible in either sense. Nor again is the theory sound which certain other thinkersCf. Aristot. Met. 13.1.4. hold concerning numbers.

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These are they who do not believe in Ideas, either absolutely or as being a kind of numbers, but believe that the objects of mathematics exist, and that the numbers are the first of existing things, and that their principle is Unity itself. For it is absurd that if, as they say, there is a 1 which is first of the 1’s,i.e., Speusippus recognized unity or the One as a formal principle, but admitted no other ideal numbers. Aristotle argues that this is inconsistent. there should not be a 2 first of the 2’s, nor a 3 of the 3’s; for the same principle applies to all cases.

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Now if this is the truth with regard to number, and we posit only mathematical number as existing, Unity is not a principle. For the Unity which is of this nature must differ from the other units; and if so, then there must be some 2 which is first of the 2’s; and similarly with the other numbers in succession.

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But if Unity is a principle, then the truth about numbers must rather be as Plato used to maintain; there must be a first 2 and first 3, and the numbers cannot be addible to each other. But then again, if we assume this, many impossibilities result, as has been already stated.Aristot. Met. 13.7.1-8.3. Moreover, the truth must lie one way or the other; so that if neither view is sound, number cannot have a separate abstract existence.

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From these considerations it is also clear that the third alternativeCf. Aristot. Met. 13.6.7.—that Ideal number and mathematical number are the same—is the worst; for two errors have to be combined to make one theory. (1.) Mathematical number cannot be of this nature, but the propounder of this view has to spin it out by making peculiar assumptions; (2.) his theory must admit all the difficulties which confront those who speak of Ideal number.

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The Pythagorean view in one way contains fewer difficulties than the view described above, but in another way it contains further difficulties peculiar to itself. By not regarding number as separable, it disposes of many of the impossibilities; but that bodies should be composed of numbers, and that these numbers should be mathematical, is impossible.See Introduction.

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For (a) it is not true to speak of indivisible magnitudesThis is proved in Aristot. De Gen. et. Corr. 315b 24-317a 17.; (b) assuming that this view is perfectly true, still units at any rate have no magnitude; and how can a magnitude be composed of indivisible parts? Moreover arithmetical number consists of abstract units. But the Pythagoreans identify number with existing things; at least they apply mathematical propositions to bodies as though they consisted of those numbers.See Introduction.

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Thus if number, if it is a self-subsistent reality, must be regarded in one of the ways described above, and if it cannot be regarded in any of these ways, clearly number has no such nature as is invented for it by those who treat it as separable.

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Again, does each unit come from the Great and the Small, when they are equalizedCf. Aristot. Met. 13.7.5 n. Aristotle is obviously referring to the two units in the Ideal 2.; or does one come from the Small and another from the Great? If the latter, each thing is not composed of all the elements, nor are the units undifferentiated; for one contains the Great, and the other the Small, which is by nature contrary to the Great.

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Again, what of the units in the Ideal 3? because there is one over. But no doubt it is for this reason that in an odd number they make the Ideal One the middle unit.Cf. DieIs, Vorsokratiker 270. 18. If on the other hand each of the units comes from both Great and Small, when they are equalized, how can the Ideal 2 be a single entity composed of the Great and Small? How will it differ from one of its units? Again, the unit is prior to the 2; because when the unit disappears the 2 disappears.

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Therefore the unit must be the Idea of an Idea, since it is prior to an Idea, and must have been generated before it. From what, then? for the indeterminate dyad, as we have seen,Aristot. Met. 13.7.18. causes duality.

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Again, number must be either infinite or finite (for they make number separable, so that one of these alternatives must be true).The point seems to be that if number is self-subsistent it must be actually finite or infinite. Aristotle himself holds that number is infinite only potentially; i.e., however high you can count, you can always count higher.

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Now it is obvious that it cannot be infinite, because infinite number is neither odd nor even, and numbers are always generated either from odd or from even number. By one process, when 1 is added to an even number, we get an odd number; by another, when 1 is multiplied by 2, we get ascending powers of 2; and by another, when powers of 2 are multiplied by odd numbers, we get the remaining even numbers.

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Again, if every Idea is an Idea of something, and the numbers are Ideas, infinite number will also be an Idea of something, either sensible or otherwise. This, however, is impossible, both logicallyi.e., as implying an actual infinite. and on their own assumption,i.e., as inconsistent with the conception of an Idea as a determining principle. since they regard the Ideas as they do.

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If, on the other hand, number is finite, what is its limit? In reply to this we must not only assert the fact, but give the reason.

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Now if number only goes up to 10, as some hold,Cf. Aristot. Met. 12.8.2. The Platonists derived this view from the Pythagoreans; see Introduction. in the first place the Forms will soon run short. For example, if 3 is the Idea of Man, what number will be the Idea of Horse? Each number up to 10 is an Idea; the Idea of Horse, then, must be one of the numbers in this series, for they are substances or Ideas.

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But the fact remains that they will run short, because the different types of animals will outnumber them. At the same time it is clear that if in this way the Ideal 3 is the Idea of Man, so will the other 3’s be also (for the 3’s in the same numbersRobin is probably right in taking this to mean that the 3 which is in the ideal 4 is like the 3 which is in the 4 which is in a higher ideal number, and so on (La Theorie platonicienne des Idees et des Nombres d’apres Aristote, p. 352). are similar), so that there will be an infinite number of men; and if each 3 is an Idea, each man will be an Idea of Man; or if not, they will still be men.

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And if the smaller number is part of the greater, when it is composed of the addible units contained in the same number, then if the Ideal 4 is the Idea of something, e.g. horse or white, then man will be part of horse, if man is 2. It is absurd also that there should be an Idea of 10 and not of 11, nor of the following numbers.

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Again, some things exist and come into being of which there are no FormsCf. Aristot. Met. 13.4.7, 8; Aristot. Met. 1.9.2, 3.; why, then, are there not Forms of these too? It follows that the Forms are not the causes of things.

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Again, it is absurd that number up to 10 should be more really existent, and a Form, than 10 itself; although the former is not generated as a unity, whereas the latter is. However, they try to make out that the series up to 10 is a complete number;

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at least they generate the derivatives, e.g. the void, proportion, the odd, etc., from within the decad. Some, such as motion, rest, good and evil, they assign to the first principles; the rest to numbers.From the Dyad were derived void (Theophrastus, Met. 312.18-313.3) and motion (cf. Aristot. Met. 1.9.29, Aristot. Met. 11.9.8). Rest would naturally be derived from unity. For good and evil see Aristot. Met. 1.6.10. Proportion alone of the derivatives here mentioned appears to be derived from number. As Syrianus says, the three types of proportion can be illustrated by numbers from within the decad—arithmetical 1. 2. 3, geometrical 1. 2. 4, harmonic 2. 3. 6.

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Hence they identify the odd with Unity; because if oddness depended on 3, how could 5 be odd?sc. because (on their theory) 3 is not contained in 5. Thus oddness had to be referred to not a number but a principle—unity.

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Again, they hold that spatial magnitudes and the like have a certain limit; e.g. the first or indivisible line, then the 2, and so on; these too extending up to 10.The indivisible line or point was connected with 1, the line with 2, the plane with 3 and the solid with 4 (Aristot. Met. 14.3.9); and 1+2+3+4=10.

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Again, if number is separable, the question might be raised whether Unity is prior, or 3 or 2.

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Now if we regard number as composite, Unity is prior; but if we regard the universal or form as prior, number is prior, because each unit is a material part of number, while number is the form of the units. And there is a sense in which the right angle is prior to the acute angle—since it is definite and is involved in the definition of the acute angle—and another sense in which the acute angle is prior, because it is a part of the other, i.e., the right angle is divided into acute angles.

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Thus regarded as matter the acute angle and element and unit are prior; but with respect to form and substance in the sense of formula, the right angle, and the whole composed of matter and form, is prior. For the concrete whole is nearer to the form or subject of the definition, although in generation it is posterior.Cf. Aristot. Met. 7.10, 11.

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In what sense, then, is the One a first principle? Because, they say, it is indivisible.

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But the universal and the part or element are also indivisible. Yes, but they are prior in a different sense; the one in formula and the other in time. In which sense, then, is the One a first principle? for, as we have just said, both the right angle seems to be prior to the acute angle, and the latter prior to the former; and each of them is one.

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Accordingly the Platonists make the One a first principle in both senses. But this is impossible; for in one sense it is the One qua form or essence, and in the other the One qua part or matter, that is primary. There is a sense in which both number and unit are one; they are so in truth potentially—that is, if a number is not an aggregate but a unity consisting of units distinct from those of other numbers, as the Platonists hold—

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but each of the twoAristotle takes the number two as an example, but the principle is of course universal. In a sense both number and unit are one; but if the number exists as an actual unity, the unit can only exist potentially. units is not one in complete reality. The cause of the error which befell the Platonists was that they were pursuing their inquiry from two points of view—that of mathematics and that of general definition—at the same time. Hence as a result of the former they conceived of the One or first principle as a point, for the unit is a point without position. (Thus they too, just like certain others,

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represented existing things as composed of that which is smallest.)Perhaps the Atomists; but cf. Aristot. Met. 1.8.3, 4. We get, then, that the unit is the material element of numbers, and at the same time is prior to the number 2; and again we get that it is posterior to 2 regarded as a whole or unity or form. On the other hand, through looking for the universal, they were led to speak of the unity predicated of a given number as a part in the formal sense also. But these two characteristics cannot belong simultaneously to the same thing.

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And if Unity itself must only be without positionIf the text is sound (and no convincing emendation has been suggested), it seems best to understand ἄθετον in a rather wider sense than the semi-technical one put forward by Ross. Without position = not localized, i.e. abstract. Unity as a principle has no concrete instance.(for it differs only in that it is a principle) and 2 is divisible whereas the unit is not, the unit will be more nearly akin to Unity itself; and if this is so, Unity itself will also be more nearly akin to the unit than to 2. Hence each of the units in 2 will be prior to 2. But this they deny; at least they make out that 2 is generated first.Cf. Aristot. Met. 13.7.5. Further, if 2 itself and 3 itself are each one thing, both together make 2. From what, then, does this 2 come?

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Since there is no contact in numbers, but units which have nothing between them—e.g. those in 2 or 3—are successive, the question might be raised whether or not they are successive to Unity itself, and whether of the numbers which succeed it 2 or one of the units in 2 is prior.

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We find similar difficulties in the case of the genera posterior to numberCf. Aristot. Met. 13.6.10.—the line, plane and solid. Some derive these from the species of the Great and Small; viz. lines from the Long and Short, planes from the Broad and Narrow, and solids from the Deep and Shallow. These are species of the Great and Small.

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As for the geometrical first principle which corresponds to the arithmetical One, different Platonists propound different views.Cf. Aristot. Met. 3.4.34, Aristot. Met. 14.3.9. In these too we can see innumerable impossibilities, fictions and contradictions of all reasonable probability. For (a) we get that the geometrical forms are unconnected with each other, unless their principles also are so associated that the Broad and Narrow is also Long and Short; and if this is so, the plane will be a line and the solid a plane.

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Moreover, how can angles and figures, etc., be explained? And (b) the same result follows as in the case of number; for these concepts are modifications of magnitude, but magnitude is not generated from them, any more than a line is generated from the Straight and Crooked, or solids from the Smooth and Rough.

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Common to all these Platonic theories is the same problem which presents itself in the case of species of a genus when we posit universals—viz. whether it is the Ideal animal that is present in the particular animal, or some other animal distinct from the Ideal animal. This question will cause no difficulty if the universal is not separable; but if, as the Platonists say, Unity and the numbers exist separately, then it is not easy to solve (if we should apply the phrase not easy to what is impossible).

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For when we think of the one in 2, or in number generally, are we thinking of an Idea or of something else?

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These thinkers, then, generate geometrical magnitudes from this sort of material principle, but othersThe reference is probably to Speusippus; Plato and Xenocrates did not believe in points (Aristot. Met. 1.9.25, Aristot. Met. 13.5.10 n). generate them from the point (they regard the point not as a unity but as similar to Unity) and another material principle which is not plurality but is similar to it; yet in the case of these principles none the less we get the same difficulties.

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For if the matter is one, line, plane and solid will be the same; because the product of the same elements must be one and the same. If on the other hand there is more than one kind of matter—one of the line, another of the plane, and another of the solid—either the kinds are associated with each other, or they are not. Thus the same result will follow in this case also; for either the plane will not contain a line, or it will be a line.

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Further, no attempt is made to explain how number can be generated from unity and plurality; but howsoever they account for this, they have to meet the same difficulties as those who generate number from unity and the indeterminate dyad. The one school generates number not from a particular plurality but from that which is universally predicated; the other from a particular plurality, but the first; for they hold that the dyad is the first plurality.Aristotle again identifies the indeterminate dyad with the number 2.

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Thus there is practically no difference between the two views; the same difficulties will be involved with regard to mixture, position, blending, generation and the other similar modes of combination.sc. of the elements of number.

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We might very well ask the further question: if each unit is one, of what it is composed; for clearly each unit is not absolute unity. It must be generated from absolute unity and either plurality or a part of plurality.

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Now we cannot hold that the unit is a plurality, because the unit is indivisible; but the view that it is derived from a part of plurality involves many further difficulties, because (a) each part must be indivisible; otherwise it will be a plurality and the unit will be divisible, and unity and plurality will not be its elements, because each unit will not be generated from pluralitysc. but from an indivisible part of plurality—which is not a plurality but a unity. and unity.

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(b) The exponent of this theory merely introduces another number; because plurality is a number of indivisible parts.i.e., to say that number is derived from plurality is to say that number is derived from number—which explains nothing.

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Again, we must inquire from the exponent of this theory whether the numbersc. which plurality has been shown to be. is infinite or finite.

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There was, it appears, a finite plurality from which, in combination with Unity, the finite units were generated; and absolute plurality is different from finite plurality. What sort of plurality is it, then, that is, in combination with unity, an element of number?

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We might ask a similar question with regard to the point, i.e. the element out of which they create spatial magnitudes.

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This is surely not the one and only point. At least we may ask from what each of the other points comes; it is not, certainly, from some interval and the Ideal point. Moreover, the parts of the interval cannot be indivisible parts, any more than the parts of the plurality of which the units are composed; because although number is composed of indivisible parts, spatial magnitudes are not.

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All these and other similar considerations make it clear that number and spatial magnitudes cannot exist separately. Further, the fact that the leading authoritiesAlexander preferred the reading πρώτους, interpreting it in this sense; and I do not see why he should not be followed. Ross objects that πρῶτος is used in the chronological sense in 16., but this is really no argument. For a much more serious (although different) inconsistency in the use of terms cf. Aristot. Met. 12.3.1. disagree about numbers indicates that it is the misrepresentation of the facts themselves that produces this confusion in their views.

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ThoseSpeusippus and his followers. who recognize only the objects of mathematics as existing besides sensible things, abandoned Ideal number and posited mathematical number because they perceived the difficulty and artificiality of the Ideal theory. Others,Xenocrates and his followers. wishing to maintain both Forms and numbers, but not seeing how, if one posits theseUnity and the indeterminate dyad; for the difficulty see Aristot. Met. 13.7.3, 4. as first principles, mathematical number can exist besides Ideal number, identified Ideal with mathematical number,—but only in theory, since actually mathematical number is done away with, because the hypotheses which they state are peculiar to them and not mathematical.Cf. Aristot. Met. 13.6.10.

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And hePlato. who first assumed that there are Ideas, and that the Ideas are numbers, and that the objects of mathematics exist, naturally separated them. Thus it happens that all are right in some respect, but not altogether right; even they themselves admit as much by not agreeing but contradicting each other. The reason of this is that their assumptions and first principles are wrong;

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and it is difficult to propound a correct theory from faulty premisses: as Epicharmus says, no sooner is it said than it is seen to be wrong. Epicharmus, Fr. 14, Diels.

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We have now examined and analyzed the questions concerning numbers to a sufficient extent; for although one who is already convinced might be still more convinced by a fuller treatment, he who is not convinced would be brought no nearer to conviction.

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As for the first principles and causes and elements, the views expressed by those who discuss only sensible substance either have been described in the PhysicsAristot. Physics 1.4-6. or have no place in our present inquiry; but the views of those who assert that there are other substances besides sensible ones call for investigation next after those which we have just discussed.

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Since, then, some thinkers hold that the Ideas and numbers are such substances, and that their elements are the elements and principles of reality, we must inquire what it is that they hold, and in what sense they hold it.

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ThoseThe Pythagoreans and Speusippus. who posit only numbers, and mathematical numbers at that, may be considered laterAristot. Met. 14.2.21, Aristot. Met. 14.3.2-8, 15, 16.; but as for those who speak of the Ideas, we can observe at the same time their way of thinking and the difficulties which befall them. For they not only treat the Ideas as universal substances, but also as separable and particular.

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(That this is impossible has been already shownAristot. Met. 3.6.7-9. by a consideration of the difficulties involved.) The reason why those who hold substances to be universal combined these two views was that they did not identify substances with sensible things. They considered that the particulars in the sensible world are in a state of flux, and that none of them persists, but that the universal exists besides them and is something distinct from them.

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This theory, as we have said in an earlier passage,Aristot. Met. 13.4, and cf. Aristot. Met. 1.6. was initiated by Socrates as a result of his definitions, but he did not separate universals from particulars; and he was right in not separating them. This is evident from the facts; for without the universal we cannot acquire knowledge, and the separation of the universal is the cause of the difficulties which we find in the Ideal theory.

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Others,The Platonists. regarding it as necessary, if there are to be any substances besides those which are sensible and transitory, that they should be separable, and having no other substances, assigned separate existence to those which are universally predicated; thus it followed that universals and particulars are practically the same kind of thing. This in itself would be one difficulty in the view which we have just described.See Introduction.

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Let us now mention a point which presents some difficulty both to those who hold the Ideal theory and to those who do not. It has been stated already, at the beginning of our treatise, among the problems.Cf. Aristot. Met. 3.4.8-10, Aristot. Met. 3.6.7-9. If we do not suppose substances to be separate, that is in the way in which particular things are said to be separate, we shall do away with substance in the sense in which we wish to maintain it; but if we suppose substances to be separable, how are we to regard their elements and principles?

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If they are particular and not universal, there will be as many real things as there are elements, and the elements will not be knowable. For let us suppose that the syllables in speech are substances, and that their letters are the elements of substances. Then there must be only one BA, and only one of each of the other syllables; that is, if they are not universal and identical in form, but each is numerically one and an individual, and not a member of a class bearing a common name.

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(Moreover, the Platonists assume that each Ideal entity is unique.) Now if this is true of the syllables, it is also true of their letters. Hence there will not be more than one A, nor more than one of any of the other letters,This is, as a matter of fact, the assumption upon which the whole argument rests; Aristotle is arguing in a circle. on the same argument by which in the case of the syllable there cannot be more than one instance of the same syllable. But if this is so, there will be no other things besides the letters, but only the letters.

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Nor again will the elements be knowable; for they will not be universal, and knowledge is of the universal. This can be seen by reference to proofs and definitions; for there is no logical conclusion that a given triangle has its angles equal to two right angles unless every triangle has its angles equal to two right angles, or that a given man is an animal unless every man is an animal.

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On the other hand, if the first principles are universal, either the substances composed of them will be universal too, or there will be a non-substance prior to substance; because the universal is not substance, and the element or first principle is universal; and the element or first principle is prior to that of which it is an element or first principle.

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All this naturally follows when they compose the Ideas of elements and assert that besides the substances which have the same form there are also Ideas each of which is a separate entity.

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But if, as in the case of the phonetic elements, there is no reason why there should not be many A’s and B’s, and no A itself or B itself apart from these many, then on this basis there may be any number of similar syllables.

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The doctrine that all knowledge is of the universal, and hence that the principles of existing things must also be universal and not separate substances, presents the greatest difficulty of all that we have discussed; there is, however, a sense in which this statement is true, although there is another in which it is not true.

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Knowledge, like the verb to know, has two senses, of which one is potential and the other actual. The potentiality being, as matter, universal and indefinite, has a universal and indefinite object; but the actuality is definite and has a definite object, because it is particular and deals with the particular.

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It is only accidentally that sight sees universal color, because the particular color which it sees is color; and the particular A which the grammarian studies is an A. For if the first principles must be universal, that which is derived from them must also be universal, as in the case of logical proofsBecause ἀπόδειξις (logical or syllogistic proof) must be in the first figure (Aristot. An. Post. 1.14), and in that figure universal premises always give a universal conclusion. (Ross.); and if this is so there will be nothing which has a separate existence; i.e. no substance. But it is clear that although in one sense knowledge is universal, in another it is not.

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With regard to this kind of substance,i.e., the Platonic Ideas or numbers, which they regarded as unchangeable substances. There is, however, no definite transition to a fresh subject at this point. The criticisms of the Ideas or numbers as substances, and of the Platonic first principles, have not been grouped systematically in Books 13 and 14. Indeed there is so little distinction in subject matter between the two books that in some Mss. 14 was made to begin at 13.9.10. (Syrianus ad loc.). See Introduction. then, let the foregoing account suffice. All thinkers make the first principles contraries; as in the realm of natural objects, so too in respect of the unchangeable substances.

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Now if nothing can be prior to the first principle of all things, that first principle cannot be first principle if it is an attribute of something else. This would be as absurd as to say that white is the first principle, not qua anything else but qua white, and yet that it is predicable of a subject, and is white because it is an attribute of something else; because the latter will be prior to it.

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Moreover, all things are generated from contraries as from a substrate, and therefore contraries must most certainly have a substrate. Therefore all contraries are predicated of a subject, and none of them exists separately. But there is no contrary to substance; not only is this apparent, but it is borne out by reasoned consideration.Cf. Aristot. Categories 3b 24-27 Thus none of the contraries is strictly a first principle; the first principle is something different.

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But the Platonists treat one of the contraries as matter, some opposing the unequal to Unity (on the ground that the former is of the nature of plurality) and others plurality.

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For according to some,Plato; cf. Aristot. Met. 13.7.5. numbers are generated from the unequal dyad of the Great and Small; and according to another,Probably Speusippus. from plurality; but in both cases they are generated by the essence of unity. For he who speaks of the unequal and Unity as elements, and describes the unequal as a dyad composed of Great and Small, speaks of the unequal, i.e. the Great and Small, as being one; and does not draw the distinction that they are one in formula but not in number.This shows clearly that by the Great-and Small Plato meant a single principle, i.e., indeterminate quantity. Aristotle admits this here because he is contrasting the Great-and Small with the One; but elsewhere he prefers to regard the Platonic material principle as a duality. See Introduction.

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Again, they state the first principles, which they call elements, badly; some say that the Great and the Small, together with Unity (making 3Cf. previous note. in all), are the elements of numbers; the two former as matter, and Unity as form. Others speak of the Many and Few, because the Great and the Small are in their nature more suited to be the principles of magnitude; and others use the more general term which covers these—the exceeding and the exceeded.

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But none of these variations makes any appreciable difference with respect to some of the consequences of the theory; they only affect the abstract difficulties, which these thinkers escape because the proofs which they themselves employ are abstract.

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There is, however, this exception: if the exceeding and the exceeded are the first principles, and not the Great and the Small, on the same principle number should be derived from the elements before 2 is derived; for as the exceeding and the exceeded is more universal than the Great and Small, so number is more universal than 2. But in point of fact they assert the one and not the other.

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Others oppose the different or other to Unity; and others contrast Plurality and Unity.

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Now if, as they maintain, existing things are derived from contraries, and if there is either no contrary to unity, or if there is to be any contrary it is plurality; and if the unequal is contrary to the equal, and the different to the same, and the other to the thing itself then those who oppose unity to plurality have the best claim to credibility—but even their theory is inadequate, because then unity will be few. For plurality is opposed to paucity, and many to few.

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That unity denotes a measureCf. Aristot. Met. 5.6.17, 18, Aristot. Met. 10.1.8, 21. is obvious. And in every case there is something else which underlies it; e.g., in the scale there is the quarter-tone; in spatial magnitude the inch or foot or some similar thing; and in rhythms the foot or syllable. Similarly in the case of gravity there is some definite weight. Unity is predicated of all things in the same way; of qualities as a quality, and of quantities as a quantity.

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(The measure is indivisible, in the former case in kind, and in the latter to our senses.) This shows that unity is not any independent substance. And this is reasonable; because unity denotes a measure of some plurality, and number denotes a measured plurality and a plurality of measures. (Hence too it stands to reason that unity is not a number; for the measure is not measures, but the measure and unity are starting-points.)

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The measure must always be something which applies to all alike; e.g., if the things are horses, the measure is a horse; if they are men, the measure is a man; and if they are man, horse and god, the measure will presumably be an animate being, and the number of them animate beings.

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If the things are man, white and walking, there will scarcely be a number of them, because they all belong to a subject which is one and the same in number; however, their number will be a number of genera, or some other such appellation.

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ThoseCf. sect. 5. who regard the unequal as a unity, and the dyad as an indeterminate compound of great and small, hold theories which are very far from being probable or possible. For these terms represent affections and attributes, rather than substrates, of numbers and magnitudes—many and few applying to number, and great and small to magnitude— just as odd and even, smooth and rough, straight and crooked, are attributes.

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Further, in addition to this error, great and small and all other such terms must be relative. And the relative is of all the categories in the least degree a definite entity or substance; it is posterior to quality and quantity. The relative is an affection of quantity, as we have said, and not its matter; since there is something else distinct which is the matter both of the relative in general and of its parts and kinds.

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There is nothing great or small, many or few, or in general relative, which is many or few, great or small, or relative to something else without having a distinct nature of its own. That the relative is in the lowest degree a substance and a real thing is shown by the fact that of it aloneCf. Aristot. Met. 11.12.1. There Aristotle refers to seven categories, but here he omits activity and passivity as being virtually identical with motion. there is neither generation nor destruction nor change in the sense that in respect of quantity there is increase and decrease, in respect of quality, alteration, in respect of place, locomotion, and in respect of substance, absolute generation and destruction.

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There is no real change in respect of the relative; for without any change in itself, one term will be now greater, now smaller or equal, as the other term undergoes quantitative change. Moreover, the matter of every thing, and therefore of substance, must be that which is potentially of that nature; but the relative is neither potentially substance nor actually.

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It is absurd, then, or rather impossible, to represent non-substance as an element of substance and prior to it; for all the other categories are posterior to substance. And further, the elements are not predicated of those things of which they are elements; yet many and few are predicated, both separately and together, of number; and long and short are predicated of the line, and the Plane is both broad and narrow.

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If, then, there is a plurality of which one term, viz. few, is always predicable, e.g. 2 (for if 2 is many, 1 will be fewCf. Aristot. Met. 10.6.1-3.), then there will be an absolute many; e.g., 10 will be many (if there is nothing more than 10Cf. Aristot. Met. 13.8.17.), or 10,000. How, then, in this light, can number be derived from Few and Many? Either both ought to be predicated of it, or neither; but according to this view only one or the other is predicated.

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But we must inquire in general whether eternal things can be composed of elements. If so, they will have matter; for everything which consists of elements is composite.

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Assuming, then, that that which consists of anything, whether it has always existed or it came into being, must come into being <if at all> out of that of which it consists; and that everything comes to be that which it comes to be out of that which is it potentially (for it could not have come to be out of that which was not potentially such, nor could it have consisted of it); and that the potential can either be actualized or not; then however everlasting number or anything else which has matter may be, it would be possible for it not to exist, just as that which is any number of years old is as capable of not existing as that which is one day old. And if this is so, that which has existed for so long a time that there is no limit to it may also not exist.

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Therefore things which contain matter cannot be eternal, that is, if that which is capable of not existing is not eternal, as we have had occasion to say elsewhere.Aristot. Met. 9.8.15-17, Aristot. De Caelo 1.12. Now if what we have just been saying—that no substance is eternal unless it is actuality—is true universally, and the elements are the matter of substance, an eternal substance can have no elements of which, as inherent in it, it consists.

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There are some who, while making the element which acts conjointly with unity the indeterminate dyad, object to the unequal, quite reasonably, on the score of the difficulties which it involves. But they are rid only of those difficultiesCf. Aristot. Met. 14.1.14-17. which necessarily attend the theory of those who make the unequal, i.e. the relative, an element; all the difficulties which are independent of this view must apply to their theories also, whether it is Ideal or mathematical number that they construct out of these elements.

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There are many causes for their resorting to these explanations, the chief being that they visualized the problem in an archaic form. They supposed that all existing things would be one, absolute Being, unless they encountered and refuted Parmenides’ dictum:

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It will ne’er be proved that things which are not, are,Parmenides Fr. 7 (Diels).

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i.e., that they must show that that which is not, is; for only so—of that which is, and of something else—could existing things be composed, if they are more than one.Cf. Plat. Soph. 237a, 241d, 256e.

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However, (i) in the first place, if being has several meanings (for sometimes it means substance, sometimes quality, sometimes quantity, and so on with the other categories), what sort of unity will all the things that are constitute, if not-being is not to be? Will it be the substances that are one, or the affections (and similarly with the other categories), or all the categories together? in which case the this and the such and the so great, and all the other categories which denote some sense of Being, will be one.

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But it is absurd, or rather impossible, that the introduction of one thing should account for the fact that what is sometimes means so-and-so, sometimes such-and-such, sometimes of such-and-such a size, sometimes in such-and-such a place.

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(2) Of what sort of not-being and Being do real things consist? Not-being, too, has several senses, inasmuch as Being has; and not-man means not so-and-so, whereas not straight means not such-and-such, and not five feet long means not of such-and-such a size. What sort of Being and not-being, then, make existing things a plurality?

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This thinker means by the not-being which together with Being makes existing things a plurality, falsity and everything of this naturePlat. Soph. 237a, 240; but Aristotle’s statement assumes too much.; and for this reason also it was saidPresumably by some Platonist. that we must assume something which is false, just as geometricians assume that a line is a foot long when it is not.

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But this cannot be so; for (a) the geometricians do not assume anything that is false (since the proposition is not part of the logical inferencei.e., the validity of a geometrical proof does not depend upon the accuracy of the figure.), and (b) existing things are not generated from or resolved into not-being in this sense. But not only has not-being in its various cases as many meanings as there are categories, but moreover the false and the potential are called not-being; and it is from the latter that generation takes place—man comes to be from that which is not man but is potentially man, and white from that which is not white but is potentially white; no matter whether one thing is generated or many.

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Clearly the point at issue is how being in the sense of the substances is many; for the things that are generated are numbers and lines and bodies. It is absurd to inquire how Being as substance is many, and not how qualities or quantities are many.

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Surely the indeterminate dyad or the Great and Small is no reason why there should be two whites or many colors or flavors or shapes; for then these too would be numbers and units. But if the Platonists had pursued this inquiry, they would have perceived the cause of plurality in substances as well; for the causeMatter, according to Aristotle; and there is matter, or something analogous to it, in every category. Cf. Aristot. Met. 12.5. is the same, or analogous.

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This deviation of theirs was the reason why in seeking the opposite of Being and unity, from which in combination with Being and unity existing things are derived, they posited the relative (i.e. the unequal), which is neither the contrary nor the negation of Being and unity, but is a single characteristic of existing things, just like substance or quality. They should have investigated this question also; how it is that relations are many, and not one.

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As it is, they inquire how it is that there are many units besides the primary unity, but not how there are many unequal things besides the Unequal. Yet they employ in their arguments and speak of Great and Small, Many and Few (of which numbers are composed), Long and Short (of which the line is composed), Broad and Narrow (of which the plane is composed), Deep and Shallow (of which solids are composed); and they mention still further kinds of relation.Cf. Aristot. Met. 14.1.6, 18, Aristot. Met. 1.9.23. Now what is the cause of plurality in these relations?

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We must, then, as I say, presuppose in the case of each thing that which is it potentially. The authorPlato. of this theory further explained what it is that is potentially a particular thing or substance, but is not per se existent—that it is the relative (he might as well have said quality); which is neither potentially unity or Being, nor a negation of unity or Being, but just a particular kind of Being.

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And it was still more necessary, as we have said,sect. 11. that, if he was inquiring how it is that things are many, he should not confine his inquiry to things in the same category, and ask how it is that substances or qualities are many, but that he should ask how it is that things in general are many; for some things are substances, some affections, and some relations.

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Now in the case of the other categories there is an additional difficulty in discovering how they are many. For it may be said that since they are not separable, it is because the substrate becomes or is many that qualities and quantities are many; yet there must be some matter for each class of entities, only it cannot be separable from substances.

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In the case of particular substances, however, it is explicable how the particular thing can be many, if we do not regard a thing both as a particular substance and as a certain characteristic.This, according to Aristotle, is how the Platonists regard the Ideas. See Introduction. The real difficulty which arises from these considerations is how substances are actually many and not one.

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Again, even if a particular thing and a quantity are not the same, it is not explained how and why existing things are many, but only how quantities are many;

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for all number denotes quantity, and the unit, if it does not mean a measure, means that which is quantitatively indivisible. If, then, quantity and substance are different, it is not explained whence or how substance is many; but if they are the same, he who holds this has to face many logical contradictions.

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One might fasten also upon the question with respect to numbers, whence we should derive the belief that they exist.

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For onePlato and his orthodox followers. who posits Ideas, numbers supply a kind of cause for existing things; that is if each of the numbers is a kind of Idea, and the Idea is, in some way or other, the cause of existence for other things; for let us grant them this assumption.

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But as for himSpeusippus. who does not hold this belief, because he can see the difficulties inherent in the Ideal theory (and so has not this reason for positing numbers), and yet posits mathematical number, what grounds have we for believing his statement that there is a number of this kind, and what good is this number to other things? He who maintains its existence does not claim that it is the cause of anything, but regards it as an independent entity; nor can we observe it to be the cause of anything; for the theorems of the arithmeticians will all apply equally well to sensible things, as we have said.Aristot. Met. 13.3.1.

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Those, then, who posit the Ideas and identify them with numbers, by their assumption (in accordance with their method of abstracting each general term from its several concrete examples) that every general term is a unity, make some attempt to explain why number exists.I have followed Ross’s text and interpretation of this sentence. For the meaning cf. Aristot. Met. 14.2.20. Since, however, their arguments are neither necessarily true nor indeed possible, there is no justification on this ground for maintaining the existence of number.

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The Pythagoreans, on the other hand, observing that many attributes of numbers apply to sensible bodies, assumed that real things are numbers; not that numbers exist separately, but that real things are composed of numbers.See Introduction. But why? Because the attributes of numbers are to be found in a musical scale, in the heavens, and in many other connections.Cf. Aristot. Met. 14.6.5.

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As for those who hold that mathematical number alone exists,Cf. Aristot. Met. 14.2.21. they cannot allege anything of this kindi.e., that things are composed of numbers. consistently with their hypotheses; what they did say was that the sciences could not have sensible things as their objects. But we maintain that they can; as we have said before. And clearly the objects of mathematics do not exist in separation; for if they did their attributes would not be present in corporeal things.

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Thus in this respect the Pythagoreans are immune from criticism; but in so far as they construct natural bodies, which have lightness and weight, out of numbers which have no weight or lightness, they appear to be treating of another universe and other bodies, not of sensible ones.See Introduction.

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But those who treat number as separable assume that it exists and is separable because the axioms will not apply to sensible objects; whereas the statements of mathematics are true and appeal to the soul.The statements of mathematics appeal so strongly to our intelligence that they must be true; therefore if they are not true of sensible things, there must be some class of objects of which they are true. The same applies to mathematical extended magnitudes.

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It is clear, then, both that the contrary theoryThe Pythagorean theory, which maintains that numbers not only are present in sensible things but actually compose them, is in itself an argument against the Speusippean view, which in separating numbers from sensible things has to face the question why sensible things exhibit numerical attributes. can make out a case for the contrary view, and that those who hold this theory must find a solution for the difficulty which was recently raisedsect. 3.—why it is that while numbers are in no way present in sensible things, their attributes are present in sensible things.

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There are someProbably Pythagoreans. Cf. Aristot. Met. 7.2.2, Aristot. Met. 3.5.3. who think that, because the point is the limit and extreme of the line, and the line of the plane, and the plane of the solid, there must be entities of this kind.

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We must, then, examine this argument also, and see whether it is not exceptionally weak. For (1.) extremes are not substances; rather all such things are merely limits. Even walking, and motion in general, has some limit; so on the view which we are criticizing this will be an individual thing, and a kind of substance. But this is absurd. And moreover (2.) even if they are substances, they will all be substances of particular sensible things, since it was to these that the argument applied. Why, then, should they be separable?

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Again, we may, if we are not unduly acquiescent, further object with regard to all number and mathematical objects that they contribute nothing to each other, the prior to the posterior. For if number does not exist, none the less spatial magnitudes will exist for those who maintain that only the objects of mathematics exist; and if the latter do not exist, the soul and sensible bodies will exist.That the criticism is directed against Speusippus is clear from Aristot. Met. 7.2.4. Cf. Aristot. Met. 12.10.14.

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But it does not appear, to judge from the observed facts, that the natural system lacks cohesion, like a poorly constructed drama. ThoseXenocrates (that the reference is not to Plato is clear from sect. 11). who posit the Ideas escape this difficulty, because they construct spatial magnitudes out of matter and a number—2 in the case of lines, and 3, presumably, in that of planes, and 4 in that of solids; or out of other numbers, for it makes no difference.

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But are we to regard these magnitudes as Ideas, or what is their mode of existence? and what contribution do they make to reality? They contribute nothing; just as the objects of mathematics contribute nothing. Moreover, no mathematical theorem applies to them, unless one chooses to interfere with the principles of mathematics and invent peculiar theoriese.g. that of indivisible lines. of one’s own. But it is not difficult to take any chance hypotheses and enlarge upon them and draw out a long string of conclusions.

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These thinkers, then, are quite wrong in thus striving to connect the objects of mathematics with the Ideas. But those who first recognized two kinds of number, the Ideal and the mathematical as well, neither have explained nor can explain in any way how mathematical number will exist and of what it will be composed; for they make it intermediate between Ideal and sensible number.

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For if it is composed of the Great and Small, it will be the same as the former, i.e. Ideal, number. But of what other Great and Small can it be composed? for Plato makes spatial magnitudes out of a Great and Small.This interpretation (Ross’s second alternative, reading τίνος for τινος) seems to be the most satisfactory. For the objection cf. Aristot. Met. 3.4.34. And if he speaks of some other component, he will be maintaining too many elements; while if some one thing is the first principle of each kind of number, unity will be something common to these several kinds.

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We must inquire how it is that unity is these many things, when at the same time number, according to him, cannot be derived otherwise than from unity and an indeterminate dyad.The argument may be summarized thus. If mathematical number cannot be derived from the Great-and-Small or a species of the Great-and-Small, either it has a different material principle (which is not economical) or its formal principle is in some sense distinct from that of the Ideal numbers. But this implies that unity is a kind of plurality, and number or plurality can only be referred to the dyad or material principle.

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All these views are irrational; they conflict both with one another and with sound logic, and it seems that in them we have a case of Simonides’ long storyThe exact reference is uncertain, but Aristotle probably means Simonides of Ceos. Cf. Simonides Fr. 189 (Bergk).; for men have recourse to the long story, such as slaves tell, when they have nothing satisfactory to say.

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The very elements too, the Great and Small, seem to protest at being dragged in; for they cannot possibly generate numbers except rising powers of 2.Assuming that the Great-and-Small, or indeterminate dyad, is duplicative (Aristot. Met. 13.7.18).

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It is absurd also, or rather it is one of the impossibilities of this theory, to introduce generation of things which are eternal.

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There is no reason to doubt whether the Pythagoreans do or do not introduce it; for they clearly state that when the One had been constituted—whether out of planes or superficies or seed or out of something that they cannot explain—immediately the nearest part of the Infinite began to be drawn in and limited by the Limit.Cf. Aristot. Physics 3.4, Aristot. Physics 4.6, and Burnet, E.G.P. sect. 53.

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However, since they are here explaining the construction of the universe and meaning to speak in terms of physics, although we may somewhat criticize their physical theories, it is only fair to exempt them from the present inquiry; for it is the first principles in unchangeable things that we are investigating, and therefore we have to consider the generation of this kind of numbers.

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TheyThe Platonists. say that there is no generation of odd numbers,This statement was probably symbolical. They described the odd numbers as ungenerated because they likened them to the One, the principle of pure form (Ross ad loc.). which clearly implies that there is generation of even ones; and some hold that the even is constructed first out of unequals—the Great and Small—when they are equalized.Cf. Aristot. Met. 13.7.5. Therefore the inequality must apply to them before they are equalized. If they had always been equalized they would not have been unequal before; for there is nothing prior to that which has always been.

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Hence evidently it is not for the sake of a logical theory that they introduce the generation of numbers

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A difficulty, and a discredit to those who make light of the difficulty, arises out of the question how the elements and first principles are related to the the Good and the Beautiful. The difficulty is this: whether any of the elements is such as we mean when weAristotle speaks as a Platonist. See Introduction. speak of the Good or the Supreme Good, or whether on the contrary these are later in generation than the elements.

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It would seem that there is an agreement between the mythologists and some present-day thinkers,The Pythagoreans and Speusippus; cf. Aristot. Met. 12.7.10. who deny that there is such an element, and say that it was only after some evolution in the natural order of things that both the Good and the Beautiful appeared. They do this to avoid a real difficulty which confronts those who hold, as some do, that unity is a first principle.

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This difficulty arises not from ascribing goodness to the first principle as an attribute, but from treating unity as a principle, and a principle in the sense of an element, and then deriving number from unity. The early poets agree with this view in so far as they assert that it was not the original forces—such as Night, Heaven, Chaos or Ocean—but Zeus who was king and ruler.

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It was, however, on the ground of the changing of the rulers of the world that the poets were led to state these theories; because those of them who compromise by not describing everything in mythological language—e.g. PherecydesOf Syros (circa 600-525 B.C.). He made Zeus one of the three primary beings (Diels,Vorsokratiker201, 202). and certain others—make the primary generator the Supreme Good; and so do the Magi,The Zoroastrian priestly caste. and some of the later philosophers such as Empedocles and Anaxagoras: the one making Love an element,Cf. Aristot. Met. 3.1.13. and the other making Mind a first principle.Cf. Aristot. Met. 1.3.16.

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And of those who hold that unchangeable substances exist, somePlato; cf. Aristot. Met. 1.6.10. identify absolute unity with absolute goodness; but they considered that the essence of goodness was primarily unity.

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This, then, is the problem: which of these two views we should hold.

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Now it is remarkable if that which is primary and eternal and supremely self-sufficient does not possess this very quality, viz. self-sufficiency and immunity, in a primary degree and as something good. Moreover, it is imperishable and self-sufficient for no other reason than because it is good. Hence it is probably true to say that the first principle is of this nature.

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But to say that this principle is unity, or if not that, that it is an element, and an element of numbers, is impossible; for this involves a serious difficulty, to avoid which some thinkersSpeusippus and his followers; cf. sect. 3. have abandoned the theory (viz. those who agree that unity is a first principle and element, but of mathematical number). For on this view all units become identical with some good, and we get a great abundance of goods.If unity is goodness, and every unit is a kind of unity, every unit must be a kind of goodness—which is absurd.

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Further, if the Forms are numbers, all Forms become identical with some good. Again, let us assume that there are Ideas of anything that we choose. If there are Ideas only of goods, the Ideas will not be substancesBecause they are Ideas not of substances but of qualities.; and if there are Ideas of substances also, all animals and plants, and all things that participate in the Ideas, will be goods.Because the Ideas are goods.

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Not only do these absurdities follow, but it also follows that the contrary element, whether it is plurality or the unequal, i.e. the Great and Small, is absolute badness. Hence one thinkerSpeusippus. avoided associating the Good with unity, on the ground that since generation proceeds from contraries, the nature of plurality would then necessarily be bad.

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OthersPlato and Xenocrates. hold that inequality is the nature of the bad. It follows, then, that all things partake of the Bad except one—absolute unity; and that numbers partake of it in a more unmitigated form than do spatial magnitudesAs being more directly derived from the first principles. Cf. Aristot. Met. 1.9.23 n.; and that the Bad is the province for the activity of the Good, and partakes of and tends towards that which is destructive of the Good; for a contrary is destructive of its contrary.

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And if, as we said,Aristot. Met. 14.1.17. the matter of each thing is that which is it potentially—e.g., the matter of actual fire is that which is potentially fire—then the Bad will be simply the potentially Good.

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Thus all these objections follow because (1.) they make every principle an element; (2.) they make contraries principles; (3.) they make unity a principle; and (4.) they make numbers the primary substances, and separable, and Forms.

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If, then, it is impossible both not to include the Good among the first principles, and to include it in this way, it is clear that the first principles are not being rightly represented, nor are the primary substances. Nor is a certain thinkerEvidently Speusippus; cf. Aristot. Met. 14.4.3. right in his assumption when he likens the principles of the universe to that of animals and plants, on the ground that the more perfect forms are always produced from those which are indeterminate and imperfect, and is led by this to assert that this is true also of the ultimate principles; so that not even unity itself is a real thing.Speusippus argued that since all things are originally imperfect, unity, which is the first principle, must be imperfect, and therefore distinct from the good. Aristotle objects that the imperfect does not really exist, and so Speusippus deprives his first principle of reality.

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He is wrong; for even in the natural world the principles from which these things are derived are perfect and complete—for it is man that begets man; the seed does not come first.Cf. Aristot. Met. 9.8.5. It is absurd also to generate space simultaneously with the mathematical solids (for space is peculiar to particular things, which is why they are separable in space, whereas the objects of mathematics have no position) and to say that they must be somewhere, and yet not explain what their spatial position is.

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Those who assert that reality is derived from elements, and that numbers are the primary realities, ought to have first distinguished the senses in which one thing is derived from another, and then explained in what way number is derived from the first principles. Is it by mixture? But (a) not everything admits of mixturee.g. to admit of mixture a thing must first have a separate existence, and the Great-and-Small, which is an affection or quality of number (Aristot. Met. 14.1.14) cannot exist separately.; (b) the result of mixture is something different; and unity will not be separable,sc. when it has once been mixed. Cf. Aristot. De Gen. et Corr. 327b 21-26. nor will it be a distinct entity, as they intend it to be.

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Is it by composition, as we hold of the syllable? But (a) this necessarily implies position; (b) in thinking of unity and plurality we shall think of them separately. This, then, is what number will be—a unit plus plurality, or unity plus the Unequal.

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And since a thing is derived from elements either as inherent or as not inherent in it, in which way is number so derived? Derivation from inherent elements is only possible for things which admit of generation.And numbers are supposed to be eternal. Cf. Aristot. Met. 14.2.1-3. Is it derived as from seed?

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But nothing can be emitted from that which is indivisible.i.e., unity, being indivisible, cannot contribute the formal principle of generation in the way that the male parent contributes it. Is it derived from a contrary which does not persist? But all things which derive their being in this way derive it also from something else which does persist. Since, therefore, one thinkerSpeusippus: Plato. Cf. Aristot. Met. 14.1.5. regards unity as contrary to plurality, and another (treating it as the Equal) as contrary to the Unequal, number must be derived as from contraries.

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Hence there is something else which persists from which, together with one contrary, number is or has been derived.The objection is directed against the Platonist treatment of the principles as contraries (cf. Aristot. Met. 14.4.12), and may be illustrated by Aristot. Met. 12.1.5-2.2. Plurality, as the contrary of unity, is privation, not matter; the Platonists should have derived numbers from unity and some other principle which is truly material.

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Further, why on earth is it that whereas all other things which are derived from contraries or have contraries perish, even if the contrary is exhausted in producing them,Because it may be regarded as still potentially present. number does not perish? Of this no explanation is given; yet whether it is inherent or not, a contrary is destructive; e.g., Strife destroys the mixture.According to Empedocles Fr. 17 (Diels). It should not, however, do this; because the mixture is not its contrary.

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Nor is it in any way defined in which sense numbers are the causes of substances and of Being; whether as bounds,The theories criticized from this point onwards to Aristot. Met. 14.6.11 are primarily Pythagorean. See Introduction. e.g. as points are the bounds of spatial magnitudes,e.g. the line by 2 points, the triangle (the simplest plane figure) by 3, the tetrahedron (the simplest solid figure) by 4. and as EurytusDisciple of Philolaus; he flourished in the early fourth century B.C. determined which number belongs to which thing—e.g. this number to man, and this to horse—by using pebbles to copy the shape of natural objects, like those who arrange numbers in the form of geometrical figures, the triangle and the square.cf. Burnet, E.G.P. sect. 47.

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Or is it because harmony is a ratio of numbers, and so too is man and everything else? But in what sense are attributes—white, and sweet, and hot—numbers?This is an objection to the view that numbers are causes as bounds. And clearly numbers are not the essence of things, nor are they causes of the form; for the ratioOr formula. is the essence, and numberIn the sense of a number of material particles. is matter.

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E.g. the essence of flesh or bone is number only in the sense that it is three parts of fire and two of earth.Cf. Empedocles Fr. 96 (Diels). And the number, whatever it is, is always a number of something; of particles of fire or earth, or of units. But the essence is the proportion of one quantity to another in the mixture; i.e. no longer a number, but a ratio of the mixture of numbers, either of corporeal particles or of any other kind. Thus number is not an efficient cause—neither number in general, nor that which consists of abstract units—nor is it the matter, nor the formula or form of things. Nor again is it a final cause.

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The question might also be raised as to what the good is which things derive from numbers because their mixture can be expressed by a number, either one which is easily calculable,i.e., a simple ratio. or an odd number.It is hard to see exactly what this means. If the terms of a ratio are rational, one of them must be odd. Alexander says a ratio like 1 : 3 is meant. Oddness was associated with goodness (cf. Aristot. Met. 1.5.6). For in point of fact honey-water is no more wholesome if it is mixed in the proportion three times threeApparently the Pythagoreans meant by this three parts of water to three of honey. Aristotle goes on to criticize this way of expressing ratios.; it would be more beneficial mixed in no particular proportion, provided that it be diluted, than mixed in an arithmetical proportion, but strong.

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Again, the ratios of mixtures are expressed by the relation of numbers, and not simply by numbers; e.g., it is 3 : 2, not 3 X 2Cf. previous note.; for in products of multiplication the units must belong to the same genus. Thus the product of 1 x 2 x 3 must be measurable by 1, and the product of 4 X 5 x 7 by 4. Therefore all products which contain the same factor must be measurable by that factor. Hence the number of fire cannot be 2 X 5 X 3 X 7 if the number of water is 2 x 3.sc. because if so, a particle of fire would simply equal 35 particles of water.

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If all things must share in number, it must follow that many things are the same; i.e., that the same number belongs both to this thing and to something else. Is number, then, a cause; i.e., is it because of number that the object exists? Or is this not conclusive? E.g., there is a certain number of the sun’s motions, and again of the moon’s,5 in each case, according to Aristotle; cf. Aristot. Met. 12.7.9, 11. and indeed of the life and maturity of every animate thing. What reason, then, is there why some of these numbers should not be squares and others cubes, some equal and others double?

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There is no reason; all things must fall within this range of numbers if, as was assumed, all things share in number, and different things may fall under the same number. Hence if certain things happened to have the same number, on the Pythagorean view they would be the same as one another, because they would have the same form of number; e.g., sun and moon would be the same.Cf. previous note.

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But why are these numbers causes? There are seven vowels,In the Greek alphabet. seven strings to the scale,In the old heptachord; cf. note on Aristot. Met. 5.11.4. seven Pleiads; most animals (though not allCf. Aristot. Hist. An. 576a 6.) lose their teeth in the seventh year; and there were seven heroes who attacked Thebes. Is it, then, because the number 7 is such as it is that there were seven heroes, or that the Pleiads consist of seven stars? Surely there were seven heroes because of the seven gates, or for some other reason, and the Pleiads are seven because we count them so; just as we count the Bear as 12, whereas others count more stars in both.

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Indeed, they assert also that Ξ, Ψ and Ζ are concords,According to Alexander ζ was connected with the fourth, ξ with the fifth, and ψ with the octave. and that because there are three concords, there are three double consonants. They ignore the fact that there might be thousands of double consonants—because there might be one symbol for ΓΡ. But if they say that each of these letters is double any of the others, whereas no other is,θ, φ , and χ are aspirated, not double, consonants. and that the reason is that there are three regionsPalate, lips, and teeth. of the mouth, and that one consonant is combined with σ in each region, it is for this reason that there are only three double consonants, and not because there are three concords—because there are really more than three; but there cannot be more than three double consonants.

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Thus these thinkers are like the ancient Homeric scholars, who see minor similarities but overlook important ones.

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Some say that there are many correspondences of this kind; e.g., the middle notesi.e., the μέση(fourth) and παραμέση(fifth), whose ratios can be expressed as 8 : 6, 9 : 6. of the octave are respectively 8 and 9, and the epic hexameter has seventeen syllables, which equals the sum of these two; and the line scans in the first half with nine syllables, and in the second with eight.i.e., a dactylic hexameter whose sixth foot is always a spondee or trochee has nine syllables in the first three feet and eight in the last three. For τὸ δεξιόν meaning the first part of a metrical system see Bassett,Journal of Classical Philology 11.458-460.

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And they point out that the interval from α to ω in the alphabet is equal to that from the lowest note of a flute to the highest, whose number is equal to that of the whole system of the universe.Alexander suggests that the number 24 may have been made up of the 12 signs of the zodiac, the 8 spheres (fixed stars, five planets, sun and moon) and 4 elements. We must realize that no one would find any difficulty either in discovering or in stating such correspondences as these in the realm of eternal things, since they occur even among perishable things.

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As for the celebrated characteristics of number, and their contraries, and in general the mathematical properties, in the sense that some describe them and make them out to be causes of the natural world, it would seem that if we examine them along these lines, they disappear; for not one of them is a cause in any of the senses which we distinguished with until respect to the first Principles.Cf. Aristot. Met. 1.3.1, Aristot. Met. 5.1, 2.

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There is a sense, however, in which these thinkers make it clear that goodness is predicable of numbers, and that the odd, the straight, the equal-by-equal,i.e., square. and the powersProbably their power of being represented as regular figures; e.g. the triangularity of 3 or 6. of certain numbers, belong to the series of the Beautiful.Cf. Aristot. Met. 1.5.6. For the seasons are connected with a certain kind of numberi.e., 4.; and the other examples which they adduce from mathematical theorems all have the same force.

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Hence they would seem to be mere coincidences, for they are accidental; but all the examples are appropriate to each other, and they are one by analogy. For there is analogy between all the categories of Being—as straight is in length, so is level in breadth, perhaps odd in number, and white in color.

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Again, it is not the Ideal numbers that are the causes of harmonic relations, etc. (for Ideal numbers, even when they are equal, differ in kind, since their units also differ in kind)Aristotle has argued (Aristot. Met. 13.6-8.) that if the Ideal numbers differ in kind, their units must differ in kind. Hence even equal numbers, being composed of different units, must be different in kind. In point of fact, since each ideal number is unique, no two of them could be equal.; so on this ground at least we need not posit Forms.

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Such, then, are the consequences of the theory, and even more might be adduced. But the mere fact that the Platonists find so much trouble with regard to the generation of Ideal numbers, and can in no way build up a system, would seem to be a proof that the objects of mathematics are not separable from sensible things, as some maintain, and that the first principles are not those which these thinkers assume.

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+ + + + + + +English +Greek + + + +EpiDoc and CTS conversion and general header review. +fixed Aristotle bibls +fixed bad bibl refs +fixed bad bibl refs +cleaned up bad place tags in a few texts and cleaned up the document format +fixed bibls for Plut. Mor. to correct work title +more reorganizing of texts module by collection +began reorganizing texts module by collection. created separate work directory in texts module to keep hopper files separate from in progress files +edited entity tags CEH +fixed bad bibls +fixed bad bibls +fixed bibl errors through book 14 - zr +fixed bibl errors through book 13 - zr +fixed bibl errors through book 12 - zr +fixed bibl errors through book 11 - zr +fixed bibl errors through book 9 - zr +fixed bibl errors through book 6 - zr +fixed bibl errors through book 4 - zr +fixed bibl errors through book 3 - zr +fixed bibl errors through book 1 - zr +added cvs log keyword +Put Bekker line 1 milestone tags at the beginning of each section so that the incoming list creator would work. Changed RREFDECL. +Tagged in conformance with Prose.e dtd. +Text was scanned at St. Olaf Spring, 1992. + + + + + + +
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All men naturally desire knowledge. An indication of this is our esteem for the senses; for apart from their use we esteem them for their own sake, and most of all the sense of sight. Not only with a view to action, but even when no action is contemplated, we prefer sight, generally speaking, to all the other senses.

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The reason of this is that of all the senses sight best helps us to know things, and reveals many distinctions.

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Now animals are by nature born with the power of sensation, and from this some acquire the faculty of memory, whereas others do not. Accordingly the former are more intelligent and capable of learning than those which cannot remember.

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Such as cannot hear sounds (as the bee, and any other similar type of creature) are intelligent, but cannot learn; those only are capable of learning which possess this sense in addition to the faculty of memory.

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Thus the other animals live by impressions and memories, and have but a small share of experience; but the human race lives also by art and reasoning.

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It is from memory that men acquire experience, because the numerous memories of the same thing eventually produce the effect of a single experience. Experience seems very similar to science and art,

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but actually it is through experience that men acquire science and art; for as Polus rightly says, experience produces art, but inexperience chance. Plat. Gorgias 448c, Plat. Gorg. 462b-c. Art is produced when from many notions of experience a single universal judgement is formed with regard to like objects.

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To have a judgement that when Callias was suffering from this or that disease this or that benefited him, and similarly with Socrates and various other individuals, is a matter of experience; but to judge that it benefits all persons of a certain type, considered as a class, who suffer from this or that disease (e.g. the phlegmatic or bilious when suffering from burning fever) is a matter of art.

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It would seem that for practical purposes experience is in no way inferior to art; indeed we see men of experience succeeding more than those who have theory without experience.

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The reason of this is a that experience is knowledge of particulars, but art of universals; and actions and the effects produced are all concerned with the particular. For it is not man that the physician cures, except incidentally, but Callias or Socrates or some other person similarly named, who is incidentally a man as well.

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So if a man has theory without experience, and knows the universal, but does not know the particular contained in it, he will often fail in his treatment; for it is the particular that must be treated.

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Nevertheless we consider that knowledge and proficiency belong to art rather than to experience, and we assume that artists are wiser than men of mere experience (which implies that in all cases wisdom depends rather upon knowledge);

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and this is because the former know the cause, whereas the latter do not. For the experienced know the fact, but not the wherefore; but the artists know the wherefore and the cause. For the same reason we consider that the master craftsmen in every profession are more estimable and know more and are wiser than the artisans, because they know the reasons of the things which are done; but we think that the artisans, like certain inanimate objects, do things, but without knowing what they are doing (as, for instance, fire burns);

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only whereas inanimate objects perform all their actions in virtue of a certain natural quality, artisans perform theirs through habit. Thus the master craftsmen are superior in wisdom, not because they can do things, but because they possess a theory and know the causes.

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In general the sign of knowledge or ignorance is the ability to teach, and for this reason we hold that art rather than experience is scientific knowledge; for the artists can teach, but the others cannot.

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Further, we do not consider any of the senses to be Wisdom. They are indeed our chief sources of knowledge about particulars, but they do not tell us the reason for anything, as for example why fire is hot, but only that it is hot.

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It is therefore probable that at first the inventor of any art which went further than the ordinary sensations was admired by his fellow-men, not merely because some of his inventions were useful, but as being a wise and superior person.

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And as more and more arts were discovered, some relating to the necessities and some to the pastimes of life, the inventors of the latter were always considered wiser than those of the former, because their branches of knowledge did not aim at utility.

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Hence when all the discoveries of this kind were fully developed, the sciences which relate neither to pleasure nor yet to the necessities of life were invented, and first in those places where men had leisure. Thus the mathematical sciences originated in the neighborhood of Egypt, because there the priestly class was allowed leisure.Cf. Plat. Phaedrus 274, Hdt. 2.109.

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The difference between art and science and the other kindred mental activities has been stated in theEthicsAristot. Nic. Eth. 6.1139b 14-1141b 8.; the reason for our present discussion is that it is generally assumed that what is called Wisdomi.e. Metaphysics. is concerned with the primary causes and principles, so that, as has been already stated, the man of experience is held to be wiser than the mere possessors of any power of sensation, the artist than the man of experience, the master craftsman than the artisan; and the speculative sciences to be more learned than the productive. Thus it is clear that Wisdom is knowledge of certain principles and causes.

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Since we are investigating this kind of knowledge, we must consider what these causes and principles are whose knowledge is Wisdom. Perhaps it will be clearer if we take the opinions which we hold about the wise man.

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We consider first, then, that the wise man knows all things, so far as it is possible, without having knowledge of every one of them individually; next, that the wise man is he who can comprehend difficult things, such as are not easy for human comprehension (for sense-perception, being common to all, is easy, and has nothing to do with Wisdom); and further that in every branch of knowledge a man is wiser in proportion as he is more accurately informed and better able to expound the causes.

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Again among the sciences we consider that that science which is desirable in itself and for the sake of knowledge is more nearly Wisdom than that which is desirable for its results, and that the superior is more nearly Wisdom than the subsidiary; for the wise man should give orders, not receive them; nor should he obey others, but the less wise should obey him.

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Such in kind and in number are the opinions which we hold with regard to Wisdom and the wise. Of the qualities there described the knowledge of everything must necessarily belong to him who in the highest degree possesses knowledge of the universal, because he knows in a sense all the particulars which it comprises. These things, viz. the most universal, are perhaps the hardest for man to grasp, because they are furthest removed from the senses.

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Again, the most exact of the sciences are those which are most concerned with the first principles; for those which are based on fewer principles are more exact than those which include additional principles; e.g., arithmetic is more exact than geometry.

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Moreover, the science which investigates causes is more instructive than one which does not, for it is those who tell us the causes of any particular thing who instruct us. Moreover, knowledge and understanding which are desirable for their own sake are most attainable in the knowledge of that which is most knowable. For the man who desires knowledge for its own sake will most desire the most perfect knowledge, and this is the knowledge of the most knowable, and the things which are most knowable are first principles and causes; for it is through these and from these that other things come to be known, and not these through the particulars which fall under them.

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And that science is supreme, and superior to the subsidiary, which knows for what end each action is to be done; i.e. the Good in each particular case, and in general the highest Good in the whole of nature.

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Thus as a result of all the above considerations the term which we are investigating falls under the same science, which must speculate about first principles and causes; for the Good, i.e. the end , is one of the causes.

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That it is not a productive science is clear from a consideration of the first philosophers.

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It is through wonder that men now begin and originally began to philosophize; wondering in the first place at obvious perplexities, and then by gradual progression raising questions about the greater matters too, e.g. about the changes of the moon and of the sun, about the stars and about the origin of the universe.

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Now he who wonders and is perplexed feels that he is ignorant (thus the myth-lover is in a sense a philosopher, since myths are composed of wonders); therefore if it was to escape ignorance that men studied philosophy, it is obvious that they pursued science for the sake of knowledge, and not for any practical utility.

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The actual course of events bears witness to this; for speculation of this kind began with a view to recreation and pastime, at a time when practically all the necessities of life were already supplied. Clearly then it is for no extrinsic advantage that we seek this knowledge; for just as we call a man independent who exists for himself and not for another, so we call this the only independent science, since it alone exists for itself.

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For this reason its acquisition might justly be supposed to be beyond human power, since in many respects human nature is servile; in which case, as SimonidesSimon. Fr. 3 (Hiller). says, God alone can have this privilege, and man should only seek the knowledge which is within his reach.

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Indeed if the poets are right and the Deity is by nature jealous, it is probable that in this case He would be particularly jealous, and all those who excel in knowledge unfortunate. But it is impossible for the Deity to be jealous (indeed, as the proverbCf. Solon, Fr. 26 (Hiller); Leutsch and Schneidwin, Paroemiographi, 1.371. says, poets tell many a lie), nor must we suppose that any other form of knowledge is more precious than this; for what is most divine is most precious.

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Now there are two ways only in which it can be divine. A science is divine if it is peculiarly the possession of God, or if it is concerned with divine matters. And this science alone fulfils both these conditions; for (a) all believe that God is one of the causes and a kind of principle, and (b) God is the sole or chief possessor of this sort of knowledge. Accordingly, although all other sciences are more necessary than this, none is more excellent.

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The acquisition of this knowledge, however, must in a sense result in something which is the reverse of the outlook with which we first approached the inquiry. All begin, as we have said, by wondering that things should be as they are, e.g. with regard to marionettes, or the solstices, or the incommensurabilityi.e. the fact that the diagonal of a square cannot be rationally expressed in terms of the side. of the diagonal of a square; because it seems wonderful to everyone who has not yet perceived the cause that a thing should not be measurable by the smallest unit.

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But we must end with the contrary and (according to the proverb)i.e. δευτέρον ἀμεινόνων(second thoughts are better). Leutsch and Schneidwin 1.62. the better view, as men do even in these cases when they understand them; for a geometrician would wonder at nothing so much as if the diagonal were to become measurable.

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Thus we have stated what is the nature of the science which we are seeking, and what is the object which our search and our whole investigation must attain.

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It is clear that we must obtain knowledge of the primary causes, because it is when we think that we understand its primary cause that we claim to know each particular thing. Now there are four recognized kinds of cause. Of these we hold that one is the essence or essential nature of the thing (since the reason why of a thing is ultimately reducible to its formula, and the ultimate reason why is a cause and principle); another is the matter or substrate; the third is the source of motion; and the fourth is the cause which is opposite to this, namely the purpose or good;

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for this is the end of every generative or motive process. We have investigated these sufficiently in the PhysicsPhys. 2.3, Phys. 2.7; however, let us avail ourselves of the evidence of those who have before us approached the investigation of reality and philosophized about Truth. For clearly they too recognize certain principles and causes, and so it will be of some assistance to our present inquiry if we study their teaching; because we shall either discover some other kind of cause, or have more confidence in those which we have just described.

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Most of the earliest philosophers conceived only of material principles as underlying all things. That of which all things consist, from which they first come and into which on their destruction they are ultimately resolved, of which the essence persists although modified by its affections—this, they say, is an element and principle of existing things. Hence they believe that nothing is either generated or destroyed, since this kind of primary entity always persists. Similarly we do not say that Socrates comes into being absolutely when he becomes handsome or cultured, nor that he is destroyed when he loses these qualities; because the substrate, Socrates himself, persists.

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In the same way nothing else is generated or destroyed; for there is some one entity (or more than one) which always persists and from which all other things are generated.

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All are not agreed, however, as to the number and character of these principles. Thales,Thales of Miletus, fl. 585 B.C. the founder of this school of philosophy,That of the Ionian monists, who sought a single material principle of everything. says the permanent entity is water (which is why he also propounded that the earth floats on water). Presumably he derived this assumption from seeing that the nutriment of everything is moist, and that heat itself is generated from moisture and depends upon it for its existence (and that from which a thing is generated is always its first principle). He derived his assumption, then, from this; and also from the fact that the seeds of everything have a moist nature, whereas water is the first principle of the nature of moist things.

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There are someCf. Plat. Crat. 402b, Plat. Theaet. 152e, Plat. Theaet. 180c,d. who think that the men of very ancient times, long before the present era, who first speculated about the gods, also held this same opinion about the primary entity. For theycf. Hom. Il. 14. 201, Hom. Il. 14.246. represented Oceanus and Tethys to be the parents of creation, and the oath of the gods to be by water— Styx,Cf. Hom. Il. 2.755, Hom. Il. 14.271, Hom. Il.15.37. as they call it. Now what is most ancient is most revered, and what is most revered is what we swear by.

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Whether this view of the primary entity is really ancient and time-honored may perhaps be considered uncertain; however, it is said that this was Thales’ opinion concerning the first cause. (I say nothing of Hippo,Hippo of Samos, a medical writer and eclectic philosopher who lived in the latter half of the fifth century B.C. Cf.Aristot. De Anima 405b 2. because no one would presume to include him in this company, in view of the paltriness of his intelligence.)

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AnaximenesThe third Milesian monist; fl. circa 545 B.C. and DiogenesDiogenes of Apollonia, an eclectic philosopher roughly contemporary with Hippo. held that air is prior to water, and is of all corporeal elements most truly the first principle. HippasusA Pythagorean, probably slightly junior to Heraclitus. of Metapontum and HeraclitusFl. about 500 B.C. of Ephesus hold this of fire; and EmpedoclesOf Acragas; fl. 450 B.C.—adding earth as a fourth to those already mentioned—takes all four. These, he says, always persist, and are only generated in respect of multitude and paucity, according as they are combined into unity or differentiated out of unity.Cf. Empedocles, Fr. 17 (Diels), R.P. 166; Burnet, E.G.P. 108-109.

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Anaxagoras of Clazomenae—prior to Empedocles in point of age, but posterior in his activities—says that the first principles are infinite in number. For he says that as a general rule all things which are, like fire and water,This is Aristotle’s illustration; apparently Anaxagoras did not regard the elements as homoeomerous (i.e. composed of parts which are similar to one another and to the whole). Cf. Aristot. De Caelo 302a 28, Aristot. De Gen. et Corr. 314a 24. homoeomerous, are generated and destroyed in this sense only, by combination and differentiation; otherwise they are neither generated nor destroyed, but persist eternally.Cf. Anaxagoras Fr. 4 (Diels); and see Burnet, E.G.P. 130.

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From this account it might be supposed that the only cause is of the kind called material. But as men proceeded in this way, the very circumstances of the case led them on and compelled them to seek further; because if it is really true that all generation and destruction is out of some one entity or even more than one, why does this happen, and what is the cause?

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It is surely not the substrate itself which causes itself to change. I mean, e.g., that neither wood nor bronze is responsible for changing itself; wood does not make a bed, nor bronze a statue, but something else is the cause of the change. Now to investigate this is to investigate the second type of cause: the source of motion, as we should say.

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Those who were the very first to take up this inquiry, and who maintained that the substrate is one thing, had no misgivings on the subject; but some of thosei.e. the Eleatic school. who regard it as one thing, being baffled, as it were, by the inquiry, say that that one thing (and indeed the whole physical world) is immovable in respect not only of generation and destruction (this was a primitive belief and was generally admitted) but of all other change. This belief is peculiar to them.

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None of those who maintained that the universe is a unity achieved any conception of this type of cause, except perhaps ParmenidesFounder of the above; fl. about 475.; and him only in so far as he admits, in a sense, not one cause only but two.i.e. in the Δόξα. Parmenides Fr. 8 (Diels); R.P. 121.

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But those who recognize more than one entity, e.g. hot and cold, or fire and earth, are better able to give a systematic explanation, because they avail themselves of fire as being of a kinetic nature, and of water, earth, etc., as being the opposite.Aristotle is probably thinking of Empedocles. Cf. Aristot. Met. 4.8.

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After these thinkers and the discovery of these causes, since they were insufficient to account for the generation of the actual world, men were again compelled (as we have said) by truth itself to investigate the next first principle.

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For presumably it is unnatural that either fire or earth or any other such element should cause existing things to be or become well and beautifully disposed; or indeed that those thinkers should hold such a view. Nor again was it satisfactory to commit so important a matter to spontaneity and chance.

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Hence when someoneAnaxagoras. said that there is Mind in nature, just as in animals, and that this is the cause of all order and arrangement, he seemed like a sane man in contrast with the haphazard statements of his predecessors.Cf. Plat. Phaedo 97b-98b.

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We know definitely that Anaxagoras adopted this view; but HermotimusA semi-mythical person supposed to have been a preincarnation of Pythagoras. of Clazomenae is credited with having stated it earlier. Those thinkers, then, who held this view assumed a principle in things which is the cause of beauty, and the sort of cause by which motion is communicated to things.

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It might be inferred that the first person to consider this question was Hesiod, or indeed anyone else who assumed Love or Desire as a first principle in things; e.g. Parmenides. For he says, where he is describing the creation of the universe, Love sheProbably Aphrodite (so Simplicius, Plutarch). created first of all the gods . . . Parmenides Fr. 13 (Diels)And Hesiod says,Hes. Th. 116-20. The quotation is slightly inaccurate. First of all things was Chaos made, and then/Broad-bosomed Earth . . ./And Love, the foremost of immortal beings, thus implying that there must be in the world some cause to move things and combine them.

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The question of arranging these thinkers in order of priority may be decided later. Now since it was apparent that nature also contains the opposite of what is good, i.e. not only order and beauty, but disorder and ugliness; and that there are more bad and common things than there are good and beautiful: in view of this another thinker introduced Love and StrifeEmpedocles Fr. 17, 26 (Diels); R.P. 166. Cf. Burnet, E.G.P. 108 ff. as the respective causes of these things—

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because if one follows up and appreciates the statements of Empedocles with a view to his real meaning and not to his obscure language, it will be found that Love is the cause of good, and Strife of evil. Thus it would perhaps be correct to say that Empedocles in a sense spoke of evil and good as first principles, and was the first to do so—that is, if the cause of all good things is absolute good.

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These thinkers then, as I say, down to the time of Empedocles, seem to have grasped two of the causes which we have defined in the PhysicsAristot. Phys. 2.3, 7.: the material cause and the source of motion; but only vaguely and indefinitely. They are like untrained soldiers in a battle, who rush about and often strike good blows, but without science; in the same way these thinkers do not seem to understand their own statements, since it is clear that upon the whole they seldom or never apply them.

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Anaxagoras avails himself of Mind as an artificial device for producing order, and drags it in whenever he is at a loss to explain some necessary result; but otherwise he makes anything rather than Mind the cause of what happens.Cf. Plat. Phaedo 98b, Plat. Laws 967b; also Aristot. Met. 7.5. Again, Empedocles does indeed use causes to a greater degree than Anaxagoras, but not sufficiently; nor does he attain to consistency in their use.

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At any rate Love often differentiates and Strife combines: because whenever the universe is differentiated into its elements by Strife, fire and each of the other elements are agglomerated into a unity; and whenever they are all combined together again by Love, the particles of each element are necessarily again differentiated.

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Empedocles, then, differed from his predecessors in that he first introduced the division of this cause, making the source of motion not one but two contrary forces.

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Further, he was the first to maintain that the so-called material elements are four—not that he uses them as four, but as two only, treating fire on the one hand by itself, and the elements opposed to it—earth, air and water—on the other, as a single nature.Cf. 3.14. This can be seen from a study of his writings.e.g. Empedocles, Fr. 62 (Diels).

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Such, then, as I say, is his account of the nature and number of the first principles.

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Leucippus,Of Miletus; fl. circa 440 (?) B.C. See Burnet, E.G.P. 171 ff. however, and his disciple DemocritusOf Abdera; fl. circa 420 B.C. E.G.P loc. cit. hold that the elements are the Full and the Void—calling the one what is and the other what is not. Of these they identify the full or solid with what is, and the void or rare with what is not (hence they hold that what is not is no less real than what is,For the probable connection between the Atomists and the Eleatics see E.G.P. 173, 175, and cf. De Gen. et Corr. 324b 35-325a 32. because Void is as real as Body); and they say that these are the material causes of things.

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And just as those who make the underlying substance a unity generate all other things by means of its modifications, assuming rarity and density as first principles of these modifications, so these thinkers hold that the differencesi.e., of the atoms. are the causes of everything else.

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These differences, they say, are three: shape, arrangement, and position; because they hold that what is differs only in contour, inter-contact, and inclination .Cf. R.P. 194.(Of these contour means shape, inter-contact arrangement, and inclination position.) Thus, e.g., A differs from N in shape, AN from NA in arrangement, and Z from NThese letters will convey Aristotle’s point better to the English reader, but see critical note. in position.

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As for motion, whence and how it arises in things, they casually ignored this point, very much as the other thinkers did. Such, then, as I say, seems to be the extent of the inquiries which the earlier thinkers made into these two kinds of cause.

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At the same time, however, and even earlier the so-calledAristotle seems to have regarded Pythagoras as a legendary person. Pythagoreans applied themselves to mathematics, and were the first to develop this sciencePythagoras himself (fl. 532 B.C.) is said by Aristoxenus (ap. Stobaeus 1.20.1) to have been the first to make a theoretical study of arithmetic.; and through studying it they came to believe that its principles are the principles of everything.

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And since numbers are by nature first among these principles, and they fancied that they could detect in numbers, to a greater extent than in fire and earth and water, many analoguesCf. Aristot. Met. 14.6ff.. of what is and comes into being—such and such a property of number being justice ,Apparently (cf. infra, Aristot. Met. 1.17) they identified these not only with properties of number but with numbers themselves. Thus justice (properly=squareness)=4, the first square number; soul or mind=1, opportunity=7 (Alexander). and such and such soul or mind , another opportunity , and similarly, more or less, with all the rest—and since they saw further that the properties and ratios of the musical scales are based on numbers,Pythagoras himself is credited with having discovered the ratios of the octave (2 : 1), the fifth (3 : 2) and the fourth (4 : 3). Burnet, E.G.P. 51. and since it seemed clear that all other things have their whole nature modelled upon numbers, and that numbers are the ultimate things in the whole physical universe, they assumed the elements of numbers to be the elements of everything, and the whole universe to be a proportionOr harmony. Cf. Aristot. De Caelo 2.9, and E.G.P. 152. or number. Whatever analogues to the processes and parts of the heavens and to the whole order of the universe they could exhibit in numbers and proportions, these they collected and correlated;

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and if there was any deficiency anywhere, they made haste to supply it, in order to make their system a connected whole. For example, since the decad is considered to be a complete thing and to comprise the whole essential nature of the numerical system, they assert that the bodies which revolve in the heavens are ten; and there being only nineEarth, sun, moon, five planets, and the sphere of the fixed stars. that are visible, they make the antichthoni.e. counter-earth; a planet revolving round the central fire in such a way as to be always in opposition to the earth. the tenth.

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We have treated this subject in greater detail elsewhereIn the lost work On the Pythagoreans; but cf. Aristot. De Caelo 2.13.; but the object of our present review is to discover from these thinkers too what causes they assume and how these coincide with our list of causes.

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Well, it is obvious that these thinkers too consider number to be a first principle, both as the materialSee Burnet, E.G.P 143-146. of things and as constituting their properties and states.i.e., as a formal principle. Cf. Ross ad loc. The elements of number, according to them, are the Even and the Odd. Of these the former is limited and the latter unlimited; Unity consists of both (since it is both odd and even)Either because by addition it makes odd numbers even and even odd (Alexander, Theo Smyrnaeus) or because it was regarded as the principle of both odd and even numbers (Heath).; number is derived from Unity; and numbers, as we have said, compose the whole sensible universe.

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OthersZeller attributes the authorship of this theory to Philolaus. of this same school hold that there are ten principles, which they enunciate in a series of corresponding pairs: (1.) Limit and the Unlimited; (2.) Odd and Even; (3.) Unity and Plurality; (4.) Right and Left; (5.) Male and Female; (6.) Rest and Motion; (7.) Straight and Crooked; (8.) Light and Darkness; (9.) Good and Evil; (10.) Square and Oblong.

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Apparently Alcmaeon of Croton speculated along the same lines, and either he derived the theory from them or they from him; for [Alcmaeon was contemporary with the old age of Pythagoras, and]This statement is probably true, but a later addition. his doctrines were very similar to theirs.He was generally regarded as a Pythagorean. He says that the majority of things in the world of men are in pairs; but the contraries which he mentions are not, as in the case of the Pythagoreans, carefully defined, but are taken at random, e.g. white and black, sweet and bitter, good and bad, great and small.

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Thus Alcmaeon only threw out vague hints with regard to the other instances of contrariety, but the Pythagoreans pronounced how many and what the contraries are. Thus from both these authoritiesThe section of Pythagoreans mentioned in 6, and Alcmaeon. we can gather thus much, that the contraries are first principles of things; and from the former, how many and what the contraries are.

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How these can be referred to our list of causes is not definitely expressed by them, but they appear to reckon their elements as material; for they say that these are the original constituents of which Being is fashioned and composed.

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From this survey we can sufficiently understand the meaning of those ancients who taught that the elements of the natural world are a plurality. Others, however, theorized about the universe as though it were a single entity; but their doctrines are not all alike either in point of soundness or in respect of conformity with the facts of nature.

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For the purposes of our present inquiry an account of their teaching is quite irrelevant, since they do not, while assuming a unity, at the same time make out that Being is generated from the unity as from matter, as do some physicists, but give a different explanation; for the physicists assume motion also, at any rate when explaining the generation of the universe; but these thinkers hold that it is immovable. Nevertheless thus much is pertinent to our present inquiry.

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It appears that Parmenides conceived of the Unity as one in definition,His argument was Everything that is is one, if what is has one meaning (πάντα ἕν, εἰ τὸ ὂν ἓν σημαίνει, Aristot. Phys. 187a 1); but he probably believed, no less than Melissus, in the material unity of reality. Cf. Melissus Fr. 8 (Diels). It has been suggested, however (by the Rev. C. F. Angus), that he was simply trying to convey in figurative language a conception of absolute existence. but MelissusOf Samos; defeated the Athenian fleet in 441 B.C. as materially one. Hence the former says that it is finite,Melissus Fr. 8, ll. 32-3, 42-3. and the latter that it is infinite.Melissus Fr. 3. But Xenophanes,Of Colophon, b. 565 (?) B.C. Criticized and ridiculed most of the views of his day, especially the anthropomorphic conception of the gods. Burnet, E.G.P. 55 ff., esp. 61-62. Cf. Xenophanes Fr. 23 (Diels). the first exponent of the Unity (for Parmenides is said to have been his disciple), gave no definite teaching, nor does he seem to have grasped either of these conceptions of unity; but regarding the whole material universe he stated that the Unity is God.

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This school then, as we have said, may be disregarded for the purposes of our present inquiry; two of them, Xenophanes and Melissus, may be completely ignored, as being somewhat too crude in their views. Parmenides, however, seems to speak with rather more insight. For holding as he does that Not-being, as contrasted with Being, is nothing, he necessarily supposes that Being is one and that there is nothing else (we have discussed this point in greater detail in the Physics Aristot. Phys. 1.3 ); but being compelled to accord with phenomena, and assuming that Being is one in definition but many in respect of sensation, he posits in his turn two causes, i.e. two first principles, Hot and Cold; or in other words, Fire and Earth. Of these he ranks Hot under Being and the other under Not-being.Cf. note on Aristot. Met. 3.13.

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From the account just given, and from a consideration of those thinkers who have already debated this question, we have acquired the following information. From the earliest philosophers we have learned that the first principle is corporeal (since water and fire and the like are bodies); some of them assume one and others more than one corporeal principle, but both parties agree in making these principles material. Others assume in addition to this cause the source of motion, which some hold to be one and others two.

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Thus down to and apart from the ItalianThe Pythagoreans; so called because Pythagoras founded his society at Croton. philosophers the other thinkers have expressed themselves vaguely on the subject, except that, as we have said, they actually employ two causes, and one of these—the source of motion —some regard as one and others as two. The Pythagoreans, while they likewise spoke of two principles, made this further addition, which is peculiar to them: they believed, not that the Limited and the Unlimited are separate entities, like fire or water or some other such thing, but that the Unlimited itself and the One itself are the essence of those things of which they are predicated, and hence that number is the essence of all things.

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Such is the nature of their pronouncements on this subject. They also began to discuss and define the what of things; but their procedure was far too simple. They defined superficially, and supposed that the essence of a thing is that to which the term under consideration first applies—e.g. as if it were to be thought that double and 2 are the same, because 2 is the first number which is double another.

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But presumably to be double a number is not the same as to be the number 2. Otherwise, one thing will be many—a consequence which actually followed in their system.i.e., the same number might be the first to which each of several definitions applied; then that number would be each of the concepts so defined. This much, then, can be learned from other and earlier schools of thought.

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The philosophies described above were succeeded by the system of Plato,Compare Aristot. Met. 12.4.2-5. which in most respects accorded with them, but contained also certain peculiar features distinct from the philosophy of the Italians.

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In his youth Plato first became acquainted with CratylusCf. Aristot. Met. 4.5.18. and the Heraclitean doctrines—that the whole sensible world is always in a state of flux,Plat. Crat. 402a (fr. 41 Bywater). and that there is no scientific knowledge of it—and in after years he still held these opinions. And when Socrates, disregarding the physical universe and confining his study to moral questions, sought in this sphere for the universal and was the first to concentrate upon definition, Plato followed him and assumed that the problem of definition is concerned not with any sensible thing but with entities of another kind; for the reason that there can be no general definition of sensible things which are always changing.

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These entities he called Ideas,I have translated ἰδέα by Idea and εἶδος by Form wherever Aristotle uses the words with reference to the Platonic theory. Plato apparently uses them indifferently, and so does Aristotle in this particular connection, but he also uses εἶδος in the sense of form in general. For a discussion of the two words see Taylor, Varia Socratica, 178-267, and Gillespie, Classical Quarterly, 6.179-203. and held that all sensible things are named afterFor this interpretation of παρὰ ταῦτα see Ross’s note ad loc. them sensible and in virtue of their relation to them; for the plurality of things which bear the same name as the Forms exist by participation in them. (With regard to the participation, it was only the term that he changed; for whereas the Pythagoreans say that things exist by imitation of numbers, Plato says that they exist by participation—merely a change of term.

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As to what this participation or imitation may be, they left this an open question.)

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Further, he states that besides sensible things and the Forms there exists an intermediate class, the objects of mathematics,i.e. arithmetical numbers and geometrical figures. which differ from sensible things in being eternal and immutable, and from the Forms in that there are many similar objects of mathematics, whereas each Form is itself unique.

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Now since the Forms are the causes of everything else, he supposed that their elements are the elements of all things. Accordingly the material principle is the Great and Small, and the essence <or formal principle> is the One, since the numbers are derived from the Great and Small by participation in the the One.

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In treating the One as a substance instead of a predicate of some other entity, his teaching resembles that of the Pythagoreans, and also agrees with it in stating that the numbers are the causes of Being in everything else; but it is peculiar to him to posit a duality instead of the single Unlimited, and to make the Unlimited consist of the Great and Small. He is also peculiar in regarding the numbers as distinct from sensible things, whereas they hold that things themselves are numbers, nor do they posit an intermediate class of mathematical objects.

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His distinction of the One and the numbers from ordinary things (in which he differed from the Pythagoreans) and his introduction of the Forms were due to his investigation of logic (the earlier thinkers were strangers to Dialectic)See Aristot. Met. 4.2.19-20, and cf. Aristot. Met. 8.4.4.; his conception of the other principle as a duality to the belief that numbers other than primesἔξω τῶν πρώτων is very difficult, but it can hardly be a gloss, and no convincing emendation has been suggested. Whatever the statement means, it is probably (as the criticism which follows is certainly) based upon a misunderstanding. From Plat. Parm. 143c, it might be inferred that the Great and Small (the Indeterminate Dyad) played no part in the generation of numbers; but there the numbers are not Ideal, as here they must be. In any case Aristotle is obsessed with the notion that the Dyad is a duplicative principle (Aristot. Met. 13.8.14), which if true would imply that it could generate no odd number. Hence Heinze proposed reading περιττῶν(odd) for πρώτων(which may be right, although the corruption is improbable) and Alexander tried to extract the meaning of odd from πρώτων by understanding it as prime to 2. However, as Ross points out (note ad loc.), we may keep πρώτων in the sense of prime if we suppose Aristotle to be referring either (a) to the numbers within the decad (Aristot. Met. 13.8.17) and forgetting 9—the other odd numbers being primes; or (b) to numbers in general, and forgetting the entire class of compound odd numbers. Neither of these alternatives is very satisfactory, but it seems better to keep the traditional text. can be readily generated from it, as from a matrix.For a similar use of the word ἐκμαγεῖον cf. Plat. Tim. 50c.

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The fact, however, is just the reverse, and the theory is illogical; for whereas the Platonists derive multiplicity from matter although their Form generates only once,Aristotle’s objection is that it is unreasonable that a single operation of the formal upon the material principle should result in more than one product; i.e. that the material principle should be in itself duplicative. it is obvious that only one table can be made from one piece of timber, and yet he who imposes the form upon it, although he is but one, can make many tables. Such too is the relation of male to female: the female is impregnated in one coition, but one male can impregnate many females. And these relations are analogues of the principles referred to.

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This, then, is Plato’s verdict upon the question which we are investigating. From this account it is clear that he only employed two causesPlato refers several times in the dialogues to an efficient cause (e.g. the Demiurgus,Plat. Soph. 265b-d, Plat. Tim. 28c ff.) and a final cause (e.g. Plat. Phil. 20d, 53e, Plat. Tim. 29d ff.); but Aristotle does not seem to take these allusions seriously.: that of the essence, and the material cause; for the Forms are the cause of the essence in everything else, and the One is the cause of it in the Forms.

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He also tells us what the material substrate is of which the Forms are predicated in the case of sensible things, and the One in that of the Forms—that it is this the duality, the Great and Small. Further, he assigned to these two elements respectively the causation of goodCf. Plat. Phil. 25e-26b. and of evil; a problem which, as we have said,Aristot. Met. 3.17; 4.3. had also been considered by some of the earlier philosophers, e.g. Empedocles and Anaxagoras.

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We have given only a concise and summary account of those thinkers who have expressed views about the causes and reality, and of their doctrines. Nevertheless we have learned thus much from them: that not one of those who discuss principle or cause has mentioned any other type than those which we we have distinguished in the Physics. Aristot. Phys. 2.3 Clearly it is after these types that they are groping, however uncertainly.

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Some speak of the first principle as material, whether they regard it as one or several, as corporeal or incorporeal: e.g. Plato speaks of the Great and Small; the ItaliansSee note on Aristot. Met. 5.15. of the Unlimited; Empedocles of Fire, Earth, Water and Air; Anaxagoras of the infinity of homoeomeries.

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All these have apprehended this type of cause; and all those too who make their first principle air or water or something denser than fire but rarer than airThe various references in Aristotle to material principles intermediate between certain pairs of elements have been generally regarded as applying to Anaximander’s ἄπειρον or Indeterminate; but the references are so vague (cf. Aristot. Met. 7.6, Aristot. Phys.187a 14, 189b 3, 203a 18) that it seems better to connect them with later and minor members of the Milesian school. Cf. Ross’s note ad loc.(for some have so described the primary element). These, then, apprehended this cause only, but others apprehended the source of motion—e.g. all such as make Love and Strife, or Mind, or Desire a first principle.

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As for the essence or essential nature, nobody has definitely introduced it; but the inventors of the Forms express it most nearly. For they do not conceive of the Forms as the matter of sensible things (and the One as the matter of the Forms), nor as producing the source of motion (for they hold that they are rather the cause of immobility and tranquillity); but they adduce the Forms as the essential nature of all other things, and the One as that of the Forms.

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The end towards which actions, changes and motions tend they do in a way treat as a cause, but not in this sense, i.e. not in the sense in which it is naturally a cause. Those who speak of Mind or Love assume these causes as being something good; but nevertheless they do not profess that anything exists or is generated for the sake of them, but only that motions originate from them.Cf. Aristot. Met. 3.17.

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Similarly also those who hold that Unity or Being is an entity of this kind state that it is the cause of existence, but not that things exist or are generated for the sake of it. So it follows that in a sense they both assert and deny that the Good is a cause; for they treat it as such not absolutely, but incidentally.

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It appears, then, that all these thinkers too (being unable to arrive at any other cause) testify that we have classified the causes rightly, as regards both number and nature. Further, it is clear that all the principles must be sought either along these lines or in some similar way.

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Let us next examine the possible difficulties arising out of the statements of each of these thinkers, and out of his attitude to the first principles.

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All those who regard the universe as a unity, and assume as its matter some one nature, and that corporeal and extended, are clearly mistaken in many respects. They only assume elements of corporeal things, and not of incorporeal ones, which also exist. They attempt to state the causes of generation and destruction, and investigate the nature of everything; and at the same time do away with the cause of motion.

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Then there is their failure to regard the essence or formula as a cause of anything; and further their readiness to call any one of the simple bodies—except earth—a first principle, without inquiring how their reciprocal generation is effected. I refer to fire, water, earth and air. Of these some are generated from each other by combination and others by differentiation;

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and this difference is of the greatest importance in deciding their relative priority. In one way it might seem that the most elementary body is that from which first other bodies are produced by combination; and this will be that body which is rarest and composed of the finest particles.

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Hence all who posit Fire as first principle will be in the closest agreement with this theory. However, even among the other thinkers everyone agrees that the primary corporeal element is of this kind. At any rate none of the Monists thought earth likely to be an element—obviously on account of the size of its particles—

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but each of the other three has had an advocate; for some name fire as the primary element, others water, and others air.Cf. Aristot. Met. 3.5, 8. And yet why do they not suggest earth too, as common opinion does? for people say Everything is earth.

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And Hesiod too saysCf. Aristot. Met. 4.1. that earth was generated first of corporeal things—so ancient and popular is the conception found to be. Thus according to this theory anyone who suggests any of these bodies other than fire, or who assumes something denser than air but rarer than water,Cf. Aristot. Met. 7.3 n. will be wrong.

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On the other hand if what is posterior in generation is prior in nature, and that which is developed and combined is posterior in generation, then the reverse will be the case; water will be prior to air, and earth to water. So much for those who posit one cause such as we have described.

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The same will apply too if anyone posits more than one, as e.g. Empedocles says that matter consists of four bodies;

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objections must occur in his case also, some the same as before, and some peculiar to him. First, we can see things being generated from each other in a way which shows that fire and earth do not persist as the same corporeal entity. (This subject has been treated in my works on Natural Science.Aristot. De Caelo, 3.7; Aristot. De Gen. et Corr. 2.6.) Again with regard to the cause of motion in things, whether one or two should be assumed, it must not be thought that his account is entirely correct or even reasonable.Cf. Aristot. Met. 4.6.

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And in general those who hold such views as these must of necessity do away with qualitative alteration; for on such a theory cold will not come from hot nor hot from cold, because to effect this there must be something which actually takes on these contrary qualities: some single element which becomes both fire and water—which Empedocles denies.

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If one were to infer that Anaxagoras recognized twoMind, and the mixture of homoeomerous particles. elements, the inference would accord closely with a view which, although he did not articulate it himself, he must have accepted as developed by others.

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To say that originally everything was a mixture is absurd for various reasons, but especially since (a) it follows that things must have existed previously in an unmixed state; (b) it is contrary to nature for anything to mix with anything ; (c) moreover affections and attributes would then be separable from their substances (because what is mixed can also be separated). At the same time, if one were to follow his doctrine carefully and interpret its meaning, perhaps it would be seen to be more up-to-date;

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because when nothing was yet differentiated, obviously nothing could be truly predicated of that substance—e.g. that it was white or black or buff or any other color. It must necessarily have been colorless, since otherwise it would have had one of these colors.

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Similarly by the same argument it had no taste or any other such attribute; for it cannot have had any quality or magnitude or individuality. Otherwise some particular form would have belonged to it; but this is impossible on the assumption that everything was mixed together, for then the form would have been already differentiated, whereas he says that everything was mixed together except Mind, which alone was pure and unmixed.Anaxagoras. Fr. 12 (Diels).

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It follows from this that he recognizes as principles the One (which is simple and unmixed) and the Other, which is such as we suppose the Indeterminate to be before it is determined and partakes of some form. Thus his account is neither correct nor clear, but his meaning approximates to more recent theories and what is now more obviously true.

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However, these thinkers are really concerned only with the theories of generation and destruction and motion (for in general it is only with reference to this aspect of reality that they look for their principles and causes).

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Those, however, who make their study cover the whole of reality, and who distinguish between sensible and non-sensible objects, clearly give their attention to both kinds; hence in their case we may consider at greater length what contributions, valuable or otherwise, they make to the inquiry which is now before us.

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The so-called Pythagoreans employ abstruser principles and elements than the physicists. The reason is that they did not draw them from the sensible world; for mathematical objects, apart from those which are connected with astronomy, are devoid of motion.

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Nevertheless all their discussions and investigations are concerned with the physical world. They account for the generation of the sensible universe, and observe what happens in respect of its parts and affections and activities, and they use up their principles and causes in this connection, as though they agreed with the others—the physicists—that reality is just so much as is sensible and is contained in the so-called heavens.

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All the same, as we have said,Aristot. Met. 1.8.17. the causes and principles which they describe are capable of application to the remoter class of realities as well, and indeed are better fitted to these than to their physical theories.

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But as to how there is to be motion, if all that is premissed is Limit and the Unlimited, and Odd and Even, they do not even hint; nor how, without motion and change, there can be generation and destruction, or the activities of the bodies which traverse the heavens.

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And further, assuming that it be granted to them or proved by them that magnitudeAristotle uses the word μέγεθος both of magnitude in general and of spatial magnitude or extension. Here the meaning seems to be the former. Numbers obviously have magnitude, and might be regarded as causing it; but (except on the Number-Atomism theory,) they are no more the cause of extension than that of gravity. is composed of these factors, yet how is it to be explained that some bodies are light, and others have weight? For in their premisses and statements they are speaking just as much about sensible as about mathematical objects; and this is why they have made no mention of fire or earth or other similar bodies, because, I presume, they have no separate explanation of sensible things.

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Again, how are we to understand that number and the modifications of number are the causes of all being and generation, both in the beginning and now, and at the same time that there is no other number than the number of which the universe is composed?i.e., how can number be both reality and the cause of reality?

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Because when they make out that Opinion and Opportunity are in such and such a region, and a little above or below them Injustice and Separation or Mixture, and when they state as proof of this that each of these abstractions is a number; and that also in this region there is already a plurality of the magnitudes composed of number, inasmuch as these modifications of number correspond to these several regions,—is the number which we must understand each of these abstractions to be the same number which is present in the sensible universe, or another kind of number?The point seems to be this. The Pythagoreans say that Opinion is a number, 3 (or 2, according to another version), and is located in a certain region of the universe because that region is proper to a corporeal magnitude composed of the number 3 (air was so composed according to Syrianus). Are we to understand, says Aristotle, that the abstract number identified with Opinion is the same as the concrete number of which air consists? The difficulty is probably due to an attempt to combine two different Pythagorean views of number.

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Plato at least says that it is another. It is true that he too supposes that numbers are both these magnitudes and their causes; but in his view the causative numbers are intelligible and the others sensible.

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The Pythagoreans, then, may be dismissed for the present, for it is enough to touch upon them thus briefly. As for those who posit the Forms as causes,For a discussion of the Ideal theory and Aristotle’s conception of it see Introduction; and with the whole contents of Aristot. Met. 9.1-15 cf. Aristot. Met. 13.4.6-5. in the first place in their attempt to find the causes of things in our sensible world, they introduced an equal number of other entities—as though a man who wishes to count things should suppose that it would be impossible when they are few, and should attempt to count them when he has added to them. For the Forms are as many as, or not fewer than, the things in search of whose causes these thinkers were led to the Forms; because corresponding to each thing there is a synonymous entity apart from the substances (and in the case of non-substantial things there is a One over the ManyAn Idea which represents their common denominator.), both in our everyday world and in the realm of eternal entities.The heavenly bodies.

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Again, not one of the arguments by which weAristotle is here speaking as a Platonist. Contrast the language of Aristot. Met. 13.4.7ff., and see Introduction. try to prove that the Forms exist demonstrates our point: from some of them no necessary conclusion follows, and from others it follows that there are Forms of things of which we hold that there are no Forms.

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For according to the arguments from the sciencesScientific knowledge must have a permanent object (cf. Aristot. Met. 1.4.2. there will be Forms of all things of which there are sciencesIncluding artificial products; cf. Aristot. Met. 1.15.; and according to the One-over-Many argument,The fact that several particulars can have a common quality or nature implies a single Idea of which they all partake (Plat. Rep. 596a). of negations too; and according to the argument that we have some conception of what has perished, of perishable things; because we have a mental picture of these things.The theory always admitted Ideas of perishable things, e.g. man. The objection here is that if the memory of dead men establishes the Idea of man, the memory of a dead individual establishes an Idea of that (perishable) individual. Again, of Plato’s more exact arguments some establish Ideas of relations,Plat. Phaedo 74a-77a, Plat. Rep. 479a-480a. which we do not hold to form a separate genus;

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and others state the Third Man. Several arguments bore this name. Here the reference is probably to the following: If X is a man because he resembles the Idea of Man, there must be a third man in whom the humanity of these two is united. Cf.Plat. Parm. 132a-133a. And in general the arguments for the Forms do away with things which are more important to us exponents of the Forms than the existence of the Ideas; for they imply that it is not the Dyad that is primary, but NumberThe Indeterminate Dyad, being to Aristotle a glorified 2, falls under the Idea of Number, which is therefore prior to it.; and that the relative is prior to the absoluteThis seems to be a development of the same objection. Number, which is relative, becomes prior to the supposedly self-subsistent Dyad.; and all the other conclusions in respect of which certain persons, by following up the views held about the Ideas, have gone against the principles of the theory.

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Again, according to the assumption by which we hold that the Ideas exist, there will be Forms not only of substances but of many other things (since the concept is one not only in the case of substances, but also in the case of all other things; and there are sciences not only of substances but of other things as well; and there are a thousand other similar consequences); but according to logical necessity, and from the views generally held about them, it follows that if the Forms are participated in, then there can only be Ideas of substances. For they are not participated in qua accidents; each Form can only be participated in in so far as it is not predicated of a subject.

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I mean, e.g., that if anything participates in absolute Doubleness it participates also in eternal, but only accidentally; because it is an accident of Doubleness to be eternal.Sensible double things are not eternal; therefore they do not, in the proper sense of participation, participate in the Idea of Doubleness qua having the accidental attribute eternal. Therefore Ideas, qua participated in, are not attributes but substances.

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Thus the Forms must be substance. But the same names denote substance in the sensible as in the Ideal world; otherwise what meaning will there be in saying that something exists beside the particulars, i.e. the unity comprising their multiplicity?

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If the form of the Ideas and of the things which participate in them is the same, they will have something in common (for why should Duality mean one and the same thing in the case of perishable twosi.e. pairs of sensible objects. and the twos which are many but eternal,i.e. mathematical 2s. and not in the case of the Idea of Duality and a particular two?); but if the form is not the same, they will simply be homonyms; just as though one were to call both Callias and a piece of wood man, without remarking any property common to them.The argument of 7-8 is: Ideas are substances. The common name which an idea shares with its particulars must mean the same of both; otherwise participation is merely homonymy. But as applied to Ideas it denotes substance; therefore particulars must be substances.

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Above all we might examine the question what on earth the Forms contribute to sensible things, whether eternal or subject to generation and decay; for they are not the cause of any motion or change in them.

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Again, they are no help towards the knowledge of other thingsThis objection, like the next, is chiefly directed against the transcendence of the Ideas. It is anticipated by Plato in Plat. Parm. 134d.(for they are not the substance of things, otherwise they would be in things), nor to their existence, since they are not present in the things which partake of them. If they were, it might perhaps seem that they are causes, in the sense in which the admixture of white causes a thing to be white;

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but this theory, which was first stated by AnaxagorasAnaxagoras Fr. 12ad fin. and later by EudoxusSee note on Aristot. Met. 12.8.9. Apparently he was a Platonist who regarded the Ideas as immanent in particulars. and others, is very readily refutable, for it is easy to adduce plenty of impossibilities against such a view. Again, other things are not in any accepted sense derived from the Forms.

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To say that the Forms are patterns, and that other things participate in them, is to use empty phrases and poetical metaphors; for what is it that fashions things on the model of the IdeasPlato says the Demiurgus?Plat. Tim. 28c, Plat. Tim. 29a. Besides, anything may both be and become like something else without being imitated from it; thus a man may become just like Socrates whether Socrates exists or not,

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and even if Socrates were eternal, clearly the case would be the same. Also there will be several patterns, and hence Forms, of the same thing; e.g. animal and two-footed will be patterns of man, and so too will the Idea of Man.Why this consequence is objectionable is not quite clear. Perhaps it is on the ground that to account for appearances in this way is not economical.

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Further, the Forms will be patterns not only of sensible things but of themselves (e.g. genus in the sense of genus of species), and thus the same thing will be both pattern and copy.The species will be the pattern of individuals, and the genus of the species. Further, it would seem impossible that the substance and the thing of which it is the substance exist in separation; hence how can the Ideas, if they are the substances of things, exist in separation from them?Cf. Aristot. Met. 1.10. It is stated in the PhaedoPlat. Phaedo 100d. that the Forms are the causes both of existence and of generation.

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Yet, assuming that the Forms exist, still the things which participate in them are not generated unless there is something to impart motion; while many other things are generated (e.g. house, ring) of which we hold that there are no Forms. Thus it is clearly possible that all other things may both exist and be generated for the same causes as the things just mentioned.

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Further, if the Forms are numbers, in what sense will they be causes? Is it because things are other numbers, e.g. such and such a number Man, such and such another Socrates, such and such another Callias? then why are those numbers the causes of these? Even if the one class is eternal and the other not, it will make no difference.

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And if it is because the things of our world are ratios of numbers (e.g. a musical concord), clearly there is some one class of things of which they are ratios. Now if there is this something, i.e. their matter , clearly the numbers themselves will be ratios of one thing to another.

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I mean, e.g., that if Callias is a numerical ratio of fire, earth, water and air, the corresponding Idea too will be a number of certain other things which are its substrate. The Idea of Man, too, whether it is in a sense a number or not, will yet be an arithmetical ratio of certain things, and not a mere number; nor, on these grounds, will any Idea be a number.The point, which is not very clearly expressed, is that the Ideas will not be pure numerical expressions or ratios, but will have a substrate just as particulars have.

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Again, one number can be composed of several numbers, but how can one Form be composed of several Forms? And if the one number is not composed of the other numbers themselves, but of their constituents (e.g. those of the number 10,000), what is the relation of the units? If they are specifically alike, many absurdities will result, and also if they are not (whether (a) the units in a given number are unlike, or (b) the units in each number are unlike those in every other number).That the words in brackets give the approximate sense seems clear from Aristot. Met. 13.6.2-3, Aristot. Met. 13.7.15; but it is difficult to get it out of the Greek. For in what can they differ, seeing that they have no qualities? Such a view is neither reasonable nor compatible with our conception of units.

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Further, it becomes necessary to set up another kind of number (with which calculation deals), and all the objects which are called intermediate by some thinkers.Cf. vi. 4. But how or from what principles can these be derived? or on what grounds are they to be considered intermediate between things here and Ideal numbers? Further, each of the units in the number 2 comes from a prior 2; but this is impossible.i.e., if 2 is derived from a prior 2 (the Indeterminate Dyad; Aristotle always regards this as a number 2), and at the same time consists of two units or 1s, 2 will be prior both to itself and to 1.

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Further, why should a number <of units>, taken together, be one thing? And further, in addition to the above objections, if the units are unlike, they should be treated as the thinkers who assume two or four elements treat those elements; for not one of them applies the term element to the common substrate, e.g. body, but to fire and earth—whether there is a common substrate (i.e. body) or not.In the Aristot. De Gen. et Corr. 320b 23Aristotle says that there is not.

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As it is, the One is spoken of as though it were homogeneous, like fire or water. But if this is so, the numbers will not be substances. And if there is an absolute One which is a principle, clearly the term one is ambiguous; otherwise this is impossible.This last sentence shows that in what goes before A. has been regarding the Platonic One as a unit. If this is so, he says, substance cannot be composed of it. If on the other hand the One is something different from the unit, they ought to make this clear.

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When we wish to refer substances to their principles we derive linesThe lines, planes, and solids here discussed are probably the Ideal lines, etc., which are immediately posterior to the Idea-Numbers. Cf. 30, Aristot. Met. 13.6.10, Aristot. Met. 13.9.2, and see Introduction. from Long and Short, a kind of Great and Small; and the plane from Wide and Narrow, and the solid body from Deep and Shallow. But in this case how can the plane contain a line,

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or the solid a line and a plane? for Wide and Narrow and Deep and Shallow are different genera. Nor is Number contained in these objects (because Many and Few is yet another class); and in the same way it is clear that none of the other higher genera will be contained in the lower. Nor, again, is the Broad the genus of which the Deep is a species; for then body would be a kind of plane.

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Further, how will it be possible for figures to contain points?Lines, planes, and solids are generated from varieties of the Great and Small, but points cannot be, having no magnitude; how, then, can the latter be present in the former? Plato steadily rejected this class of objects as a geometrical fiction, but he recognized the beginning of a line, and he frequently assumed this latter class, i.e. the indivisible lines. That Plato denied the existence of the point and asserted that of indivisible lines is not directly stated elsewhere, but the same views are ascribed to Xenocrates, and were attacked in the treatise Xenocrates De lineis insecabilibus. See Ross ad loc. But these must have some limit; and so by the same argument which proves the existence of the line, the point also exists.Sc. if the point is the limit of the line.

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In general, although Wisdom is concerned with the cause of visible things, we have ignored this question (for we have no account to give of the cause from which change arises),Cf. Aristot. Met. 7.5 and Aristot. Met. 1.9. and in the belief that we are accounting for their substance we assert the existence of other substances; but as to how the latter are the substances of the former, our explanation is worthless—for participation, as we have said before,Aristot. Met. 1.12. means nothing.

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And as for that which we can see to be the cause in the sciences, and through which all mind and all nature works—this causeThe final cause. Cf. Aristot. Met. 1.6.9-10. which we hold to be one of the first principles—the Forms have not the slightest bearing upon it either. Philosophy has become mathematics for modern thinkers,e.g. Speusippus, for whom see Aristot. Met. 7.2.4. although they professCf. Plat. Rep.531c-d that mathematics is only to be studied as a means to some other end.

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Further, one might regard the substance which they make the material substrate as too mathematical, and as being a predicate and differentia of substance or matter rather than as matter itself, I mean the Great and Small, which is like the Rare and Dense of which the physicists speak,Cf. iv. 10. holding that they are the primary differentiae of the substrate; because these qualities are a species of excess and defect.

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Also with regard to motion, if the Great and Small is to constitute motion, obviously the Forms will be moved; if not, whence did it come? On this view the whole study of physics is abolished. And what is supposed to be easy, to prove that everything is One, does not follow; because from their expositionThe word ἔκθεσις has various technical meanings. The process referred to here apparently consisted in taking, e.g., particular men, and reducing them with reference to their common nature to a single unit or universal, man; then taking man, horse, dog, etc. and treating them in the same way, until a unit is reached which embraces everything (Alexander). it does not follow, even if you grant them all their assumptions that everything is One, but only that there is an absolute One—

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and not even this, unless you grant that the universal is a class; which is impossible in some cases.Probably those of relative or negative terms. Cf. Aristot. Met. 1.3. Nor is there any explanation of the lines, planes and solids which come after the NumbersSee note on Aristot. Met. 1.23.: neither as to how they exist or can exist, nor as to what their importance is. They cannot be Forms (since they are not numbers) or Intermediates (which are the objects of mathematics) or perishables; clearly they form yet another fourth class.

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In general, to investigate the elements of existing things without distinguishing the various senses in which things are said to exist is a hopeless task; especially when one inquires along these lines into the nature of the elements of which things are composed. For (a) we cannot surely conceive of the elements of activity or passivity or straightness; this is possible, if at all, only in the case of substances. Hence to look for, or to suppose that one has found, the elements of everything that exists, is a mistake.

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(b) How can one apprehend the elements of everything ? Obviously one could not have any previous knowledge of anything; because just as a man who is beginning to learn geometry can have previous knowledge of other facts, but no previous knowledge of the principles of that science or of the things about which he is to learn, so it is in the case of all other branches of knowledge.

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Hence if there is a science which embraces everythinge.g. Plato’s Dialectic.(as some say), the student of it can have no previous knowledge at all. But all learning proceeds, wholly or in part, from what is already known; whether it is through demonstration or through definition—since the parts of the definition must be already known and familiar. The same is true of induction.

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On the other hand, assuming that this knowledge should turn out to be innate,Cf. the doctrine of ἀνάμνησις (recollection), Plat. Meno 81c, Plat. Phaedo 72e. it is astonishing that we should possess unawares the most important of the sciences. Further, how is one to know of what elements things consist? how is it to be established?

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Even this presents a difficulty, because the facts might be disputed, as happens in the case of certain syllables—for some say that ZA is composed of S, D and A, while others say that it is a distinct sound and not any one of those which are familiar to us.στοιχεῖον means both an element and a letter of the alphabet; hence letters are often used as analogues of the material elements. The point here is: Is Z or rather the Greek ζ) a στοιχεῖον, or is it further analyzable? Since this can be disputed, we must expect differences of opinion about the elements in general.

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Further, how can one gain knowledge of the objects of a particular sense-perception without possessing that sense? Yet it should be possible, that if the elements of which all things consist, as composite sounds consist of their peculiar Peculiar to them as sounds, not as individual sounds. If sights and sounds had the same elements, sight, which knows those elements as composing sights, would know them as composing sounds; i.e., we could see sounds. elements, are the same.

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Thus it is obvious, from the statements of earlier thinkers also, that all inquiry is apparently directed towards the causes described in the Physics,Aristot. Phys. 2.3, 7. and that we cannot suggest any other cause apart from these. They were, however, only vaguely conceived; and although in one sense they have all been stated before, in another they have not been stated at all.

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For the earliest philosophy speaks falteringly, as it were, on all subjects; being new and in its infancy. Even Empedocles says that bone exists by virtue of its ratio,Empedocles Fr. 96, 98 (Diels), Ritter and Preller 175. Aristotle says that Empedocles had some idea of the essence or formal cause, but did not apply it generally. which is the definition or essence of a thing.

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But by similar reasoning both flesh and every other thing, or else nothing at all, must be ratio; for it must be because of this, and not because of their matter—which he calls fire, earth, water and air—that flesh and bone and every other thing exists.

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If anyone else had stated this, he would necessarily have agreed, but his own statement was not clear.

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These and similar points have been explained already. We will now return to the difficulties which might be raised about these same questions, for they may throw some light upon subsequent difficulties.The reference is to Book 3. See Introduction.

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The study of Truth is in one sense difficult, in another easy. This is shown by the fact that whereas no one person can obtain an adequate grasp of it, we cannot all fail in the attempt; each thinker makes some statement about the natural world, and as an individual contributes little or nothing to the inquiry; but a combination of all conjectures results in something considerable.

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Thus in so far as it seems that Truth is like the proverbial door which no one can miss,Leutsch and Schneidewin, Paroemiographi, 2.678. in this sense our study will be easy; but the fact that we cannot, although having some grasp of the whole, grasp a particular part, shows its difficulty. However, since difficulty also can be accounted for in two ways, its cause may exist not in the objects of our study but in ourselves:

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just as it is with bats’ eyes in respect of daylight, so it is with our mental intelligence in respect of those things which are by nature most obvious.

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It is only fair to be grateful not only to those whose views we can share but also to those who have expressed rather superficial opinions. They too have contributed something; by their preliminary work they have formed our mental experience.

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If there had been no Timotheus,Of Miletus, 446 (?)—357 B.C. we should not possess much of our music; and if there had been no Phrynis,Of Mytilene; he is referred to as still alive in Aristoph. Cl. 971. Both Phrynis and Timotheus are criticized in the fragment of Pherecrates Chirontranslated by Rogers in the appendix to his ed. of the Clouds. there would have been no Timotheus. It is just the same in the case of those who have theorized about reality: we have derived certain views from some of them, and they in turn were indebted to others.

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Moreover, philosophy is rightly called a knowledge of Truth. The object of theoretic knowledge is truth, while that of practical knowledge is action; for even when they are investigating how a thing is so, practical men study not the eternal principle but the relative and immediate application.

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But we cannot know the truth apart from the cause. Now every thing through which a common quality is communicated to other things is itself of all those things in the highest degree possessed of that quality (e.g. fire is hottest, because it is the cause of heat in everything else); hence that also is most true which causes all subsequent things to be true.

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Therefore in every case the first principles of things must necessarily be true above everything else—since they are not merely sometimes true, nor is anything the cause of their existence, but they are the cause of the existence of other things,—and so as each thing is in respect of existence, so it is in respect of truth.

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Moreover, it is obvious that there is some first principle, and that the causes of things are not infinitely many either in a direct sequence or in kind. For the material generation of one thing from another cannot go on in an infinite progression (e.g. flesh from earth, earth from air, air from fire, and so on without a stop); nor can the source of motion (e.g. man be moved by air, air by the sun, the sun by Strife,Aristotle is evidently thinking of Empedocles’ system. with no limit to the series).

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In the same way neither can the Final Cause recede to infinity—walking having health for its object, and health happiness, and happiness something else: one thing always being done for the sake of another.

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And it is just the same with the Formal Cause. For in the case of all intermediate terms of a series which are contained between a first and last term, the prior term is necessarily the cause of those which follow it; because if we had to say which of the three is the cause, we should say the first. At any rate it is not the last term, because what comes at the end is not the cause of anything. Neither, again, is the intermediate term, which is only the cause of one

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(and it makes no difference whether there is one intermediate term or several, nor whether they are infinite or limited in number). But of series which are infinite in this way, and in general of the infinite, all the parts are equally intermediate, down to the present moment. Thus if there is no first term, there is no cause at all.

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On the other hand there can be no infinite progression downwards (where there is a beginning in the upper direction) such that from fire comes water, and from water earth, and in this way some other kind of thing is always being produced. There are two senses in which one thing comes from another—apart from that in which one thing is said to come after another, e.g. the Olympian fromἐκ means not only from but after; Aristotle dismisses this latter meaning. The Isthmian fell alternatively in the same year as the Olympian festival; when this happened the former was held in the spring and the latter in the summer. Cf. Aristot. Met. 5.24.5. the Isthmian games—either as a man comes from a child as it develops, or as air comes from water.

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Now we say that a man comes from a child in the sense that that which has become something comes from that which is becoming: i.e. the perfect from the imperfect. (For just as becoming is always intermediate between being and not-being, so is that which is becoming between what is and what is not. The learner is becoming informed, and that is the meaning of the statement that the informed person comes from the learner.)

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On the other hand A comes from B in the sense that water comes from air by the destruction of B. Hence the former class of process is not reversible (e.g. a child cannot come from a man, for the result of the process of becoming is not the thing which is becoming, but that which exists after the process is complete. So day comes from early dawn, because it is after dawn; and hence dawn does not come from day). But the other class is reversible.

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In both cases progression to infinity is impossible; for in the former the intermediate terms must have an end, and in the second the process is reversible, for the destruction of one member of a pair is the generation of the other. At the same time the first cause, being eternal, cannot be destroyed; because, since the process of generation is not infinite in the upper direction, that cause which first, on its destruction, became something else, cannot possibly be eternal.The argument is elliptical and confused. The meaning is this: Since there is an upward limit, there is a first cause which is eternal, being independent of any other cause. Therefore this cause cannot cause other things by its destruction, in the manner just described.

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Further, the Final cause of a thing is an end , and is such that it does not happen for the sake of some thing else, but all other things happen for its sake. So if there is to be a last term of this kind, the series will not be infinite; and if there is no such term, there will be no Final cause. Those who introduce infinity do not realize that they are abolishing the nature of the Good (although no one would attempt to do anything if he were not likely to reach some limit);

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nor would there be any intelligence in the world, because the man who has intelligence always acts for the sake of something, and this is a limit, because the end is a limit.

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Nor again can the Formal cause be referred back to another fuller definition;

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for the prior definition is always closer, and the posterior is not; and where the original definition does not apply, neither does the subsequent one. Further, those who hold such a view do away with scientific knowledge, for on this view it is impossible to know anything until one comes to terms which cannot be analyzed.

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Understanding, too, is impossible; for how can one conceive of things which are infinite in this way? It is different in the case of the line, which, although in respect of divisibility it never stops, yet cannot be conceived of unless we make a stop (which is why, in examining an infinitei.e. infinitely divisible. line, one cannot count the sections).It does not follow that we can apprehend that which is infinite because we can apprehend a line which is infinitely divisible. We can only really apprehend the line by setting a limit to its divisibility and regarding it simply as divisible into a very great (but not infinite) number of sections. An infinite number of sections can neither be apprehended nor counted.

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Even matter has to be conceived under the form of something which changes,Matter too, which is infinite in its varieties, can only be apprehended in the form of concrete sensible objects which are liable to change. This seems to be the meaning of the text, but Ross’s reading and interpretation may be right: see his note ad loc. and there can be nothing which is infinite.i.e. not actually, but only potentially. In any case the concept of infinity is not infinite.Cf. the third note above.

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Again, if the kinds of causes were infinite in number it would still be impossible to acquire knowledge; for it is only when we have become acquainted with the causes that we assume that we know a thing; and we cannot, in a finite time, go completely through what is additively infinite.

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The effect of a lecture depends upon the habits of the listener; because we expect the language to which we are accustomed, and anything beyond this seems not to be on the same level, but somewhat strange and unintelligible on account of its unfamiliarity; for it is the familiar that is intelligible. The powerful effect of familiarity is clearly shown by the laws, in which the fanciful and puerile survivals prevail, through force of habit, against our recognition of them.

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Thus some people will not accept the statements of a speaker unless he gives a mathematical proof; others will not unless he makes use of illustrations; others expect to have a poet adduced as witness. Again, some require exactness in everything, while others are annoyed by it, either because they cannot follow the reasoning or because of its pettiness; for there is something about exactness which seems to some people to be mean, no less in an argument than in a business transaction.

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Hence one must have been already trained how to take each kind of argument, because it is absurd to seek simultaneously for knowledge and for the method of obtaining it; and neither is easy to acquire. Mathematical accuracy is not to be demanded in everything, but only in things which do not contain matter.

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Hence this method is not that of natural science, because presumably all nature is concerned with matter. Hence we should first inquire what nature is; for in this way it will become clear what the objects of natural science are [and whether it belongs to one science or more than one to study the causes and principles of things].These words have evidently been inserted to form a kind of link with the subject matter of the Metaphysics. The book is almost certainly part of a quite independent treatise; see Introduction.

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It is necessary, with a view to the science which we are investigating, that we first describe the questions which should first be discussed. These consist of all the divergent views which are held about the first principles; and also of any other view apart from these which happens to have been overlooked.

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Now for those who wish to get rid of perplexities it is a good plan to go into them thoroughly; for the subsequent certainty is a release from the previous perplexities, and release is impossible when we do not know the knot. The perplexity of the mind shows that there is a knot in the subject; for in its perplexity it is in much the same condition as men who are fettered: in both cases it is impossible to make any progress.

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Hence we should first have studied all the difficulties, both for the reasons given and also because those who start an inquiry without first considering the difficulties are like people who do not know where they are going; besides, one does not even know whether the thing required has been found or not. To such a man the end is not clear; but it is clear to one who has already faced the difficulties.

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Further, one who has heard all the conflicting theories, like one who has heard both sides in a lawsuit, is necessarily more competent to judge.

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The first difficulty is concerned with the subjectsThe principles and causes referred to in Book I. which we discussed in our prefatory remarks. (1.) Does the study of the causes belong to one science or to more than one?The problem is discussed Aristot. Met. 3.2.1-10, and answered Aristot. Met. 4.1.(2.) Has that science only to contemplate the first principles of substance, or is it also concerned with the principles which all use for demonstration—e.g. whether it is possible at the same time to assert and deny one and the same thing, and other similar principles?Discussed Aristot. Met. 3.2.10-15; answered Aristot. Met. 4.2.

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And if it is concerned with substance, (3.) is there one science which deals with all substances, or more than one; and if more than one, are they all cognate, or should we call some of them kinds of Wisdom and others something different?Discussed Aristot. Met. 3.2.15-17; answered Aristot. Met. 4.2.9-10, Aristot. Met. 6.1.

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This too is a question which demands inquiry: (iv.) should we hold that only sensible substances exist, or that there are other besides? And should we hold that there is only one class of non-sensible substances, or more than one (as do those who posit the Forms and the mathematical objects as intermediate between the Forms and sensible things)?Discussed Aristot. Met. 3.2.20-30 answered Aristot. Met. 12.6-10, and also by the refutation of the Platonic Ideas and Intermediates in Books 13 and 14.

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These questions, then, as I say, must be considered; and also (v.) whether our study is concerned only with substances, or also with the essential attributes of substance;

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and further, with regard to Same and Other, and Like and Unlike and Contrariety, and Prior and Posterior, and all other such terms which dialecticians try to investigate, basing their inquiry merely upon popular opinions; we must consider whose province it is to study all of these.

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Further, we must consider all the essential attributes of these same things, and not merely what each one of them is, but also whether each one has one oppositeDiscussed Aristot. Met. 3.2.18-19; answered Aristot. Met. 4.2.8-25.; and (vi.) whether the first principles and elements of things are the genera under which they fall or the pre-existent parts into which each thing is divided; and if the genera, whether they are those which are predicated ultimately of individuals, or the primary genera—e.g., whether animal or man is the first principle and the more independent of the individual.DiscussedAristot. Met. 3.3; answered Aristot. Met. 7.10, 12-13

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Above all we must consider and apply ourselves to the question (7.) whether there is any other cause per se besides matter, and if so whether it is dissociable from matter, and whether it is numerically one or several; and whether there is anything apart from the concrete thing (by the concrete thing I mean matter together with whatever is predicated of it) or nothing; or whether there is in some cases but not in others; and what these cases are.Discussed iv. 1-8. For answers to these questions see Aristot. Met. 7.8, 13-14; Aristot. Met. 12.6-10; Aristot. Met. 13.10.

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Further, (8.) we must ask whether the first principles are limited in number or in kindDiscussed Aristot. Met. 3.4.8-10; answered Aristot. Met. 12.4-5, Aristot. Met. 13.10.—both those in the definitions and those in the substrate—and (ix.) whether the principles of perishable and of imperishable things are the same or different; and whether all are imperishable, or those of perishable things are perishable.Discussed Aristot. Met. 3.4.11-23; for Aristotle’s general views on the subject see Aristot. Met. 7.7-10, Aristot. Met. 12.1-7.

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Further, there is the hardest and most perplexing question of all: (x.) whether Unity and Being (as the Pythagoreans and Plato maintained) are not distinct, but are the substance of things; or whether this is not so, and the substrate is something distinctDiscussed Aristot. Met. 3.4.24-34; answered Aristot. Met. 7.16.3-4, Aristot. Met. 10.2.(as Empedocles holds of Love,Actually Love was no more the universal substrate than was any other of Empedocles’ elements; Aristotle appears to select it on account of its unifying function. another thinkerHeraclitus. of fire, and another Thales. of water or airAnaximenes.);

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and (xi.) whether the first principles are universal or like individual thingsDiscussed Aristot. Met. 3.6.7-9; for the answer see Aristot. Met. 7.13-15, Aristot. Met. 13.10.; and (12.) whether they exist potentially or actually; and further whether their potentiality or actuality depends upon anything other than motionDiscussed Aristot. Met. 3.6.5-6; for the relation of potentiality to actuality see Aristot. Met. 9.1-9; for actuality and motion see Aristot. Met. 12.6-7.; for these questions may involve considerable difficulty.

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Moreover we must ask (13.) whether numbers and lines and figures and points are substances in any sense, or not; and if they are, whether they are separate from sensible things or inherent in them.Discussed Aristot. Met. 3.5; answered Aristot. Met. 13.1-3, 6-9; Aristot. Met. 14.1-3, 5, 6. With regard to these problems not only is it difficult to attain to the truth, but it is not even easy to state all the difficulties adequately.For another statement of the problems sketched in this chapter see Aristot. Met. 9.1, 2.

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(1.) Firstly, then, with respect to the first point raised: whether it is the province of one science or of more than one to study all the kinds of causes. How can one science comprehend the first principles unless they are contraries? Again, in many things they are not all present.

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How can a principle of motion be in immovable things? or the nature of the Good? for everything which is good in itself and of its own nature is an end and thus a cause, because for its sake other things come to be and exist; and the end and purpose is the end of some action, and all actions involve motion; thus it would be impossible either for this principle to exist in motionless things or for there to be any absolute Good.

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Hence in mathematics too nothing is proved by means of this cause, nor is there any demonstration of the kind because it is better or worse; indeed no one takes any such consideration into account.

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And so for this reason some of the sophists, e.g. Aristippus,Founder of the Cyrenaic school in the early fourth century. spurned mathematics, on the ground that in the other arts, even the mechanical ones such as carpentry and cobbling, all explanation is of the kind because it is better or worse, while mathematics takes no account of good and bad.For a defense of mathematics see Aristot. Met. 13.3.10-12.

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On the other hand if there are several sciences of the causes, and a different one for each different principle, which of them shall we consider to be the one which we are seeking, or whom of the masters of these sciences shall we consider to be most learned in the subject which we are investigating?

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For it is possible for all the kinds of cause to apply to the same object; e.g. in the case of a house the source of motion is the art and the architect; the final cause is the function; the matter is earth and stones, and the form is the definition. Now to judge from our discussion some time agoCf. Aristot. Met. 1.2.5-6. as to which of the sciences should be called Wisdom, there is some case for applying the name to each of them.

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Inasmuch as Wisdom is the most sovereign and authoritative kind of knowledge, which the other sciences, like slaves, may not contradict, the knowledge of the end and of the Good resembles Wisdom (since everything else is for the sake of the end ); but inasmuch as it has been defined as knowledge of the first principles and of the most knowable, the knowledge of the essence will resemble Wisdom.

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For while there are many ways of understanding the same thing, we say that the man who recognizes a thing by its being something knows more than he who recognizes it by its not being something; and even in the former case one knows more than another, and most of all he who knows what it is, and not he who knows its size or quality or natural capacity for acting or being acted upon.

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Further, in all other cases too, even in such as admit of demonstration, we consider that we know a particular thing when we know what it is (e.g. what is the squaring of a rectangle? answer, the finding of a mean proportional to its sides; and similarly in other instances); but in the case of generations and actions and all kinds of change, when we know the source of motion.

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This is distinct from and opposite to the end . Hence it might be supposed that the study of each of these causes pertained to a different science.See Aristot. Met. 4.1

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(2.) Again, with respect to the demonstrative principles as well, it may be disputed whether they too are the objects of one sciencesc. the science which studies the four causes. or of several.Cf. Aristot. Met. 3.1.5.

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By demonstrative I mean the axioms from which all demonstration proceeds, e.g. everything must be either affirmed or denied, and it is impossible at once to be and not to be, and all other such premisses. Is there one science both of these principles and of substance, or two distinct sciences? and if there is not one, which of the two should we consider to be the one which we are now seeking?

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It is not probable that both subjects belong to one science; for why should the claim to understand these principles be peculiar to geometry rather than to any other science? Then if it pertains equally to any science, and yet cannot pertain to all, comprehension of these principles is no more peculiar to the science which investigates substances than to any other science.

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Besides, in what sense can there in be a science of these principles? We know already just what each of them is; at any rate other sciences employ them as being known to us.sc. and so there can be no science which defines them. If, however there is a demonstrative science of them, there will have to be some underlying genus, and some of the principles will be derived from axioms, and others will be unproved

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(for there cannot be demonstration of everything), since demonstration must proceed from something, and have some subject matter, and prove something. Thus it follows that there is some one genus of demonstrable things; for all the demonstrative sciences employ axioms.

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On the other hand, if the science of substance is distinct from the science of these principles, which is of its own nature the more authoritative and ultimate?

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The axioms are most universal, and are the first principles of everything. And whose province will it be, if not the philosopher’s, to study truth and error with respect to them?For the answer see Aristot. Met. 4.3.

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(3.) And in general, is there one science of all substances, or more than one?Cf. Aristot. Met. 3.1.6. if there is not one, with what sort of substance must we assume that this science is concerned?

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On the other hand, it is not probable that there is one science of all substances; for then there would be one demonstrative of all attributes—assuming that every demonstrative science proceeds from accepted beliefs and studies the essential attributes concerned with some definite subject matter.

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Thus to study the essential attributes connected with the same genus is the province of the same science proceeding from the same beliefs. For the subject matter belongs to one science, and so do the axioms, whether to the same science or to a different one; hence so do the attributes, whether they are studied by these sciences themselves or by one derived from them.For the answer see Aristot. Met. 4.2.9-10, Aristot. Met. 6.1.

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(v.) Further, is this study concerned only with substances, or with their attributes as well?Cf. Aristot. Met. 3.1.8-10. I mean, e.g., if the solid is a kind of substance, and so too lines and planes, is it the province of the same science to investigate both these and their attributes, in every class of objects about which mathematics demonstrates anything, or of a different science?

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If of the same, then the science of substance too would be in some sense demonstrative; but it does not seem that there is any demonstration of the what is it? And if of a different science, what will be the science which studies the attributes of substance? This is a very difficult question to answer.This problem, together with the appendix to it stated in Aristot. Met. 3.1.9-10, is answered in Aristot. Met. 4.2.8-25.

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(iv.) Further, are we to say that only sensible substances exist, or that others do as well? and is there really only one kind of substance, or more than one (as they hold who speak of the Forms and the Intermediates, which they maintain to be the objects of the mathematical sciences)?

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In what sense we Platonists hold the Forms to be both causes and independent substances has been statedAristot. Met. 1.6. in our original discussion on this subject. But while they involve difficulty in many respects, not the least absurdity is the doctrine that there are certain entities apart from those in the sensible universe, and that these are the same as sensible things except in that the former are eternal and the latter perishable.As it stands this is a gross misrepresentation; but Aristotle’s objection is probably directed against the conception of Ideas existing independently of their particulars. See Introduction.

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For Platonists say nothing more or less than that there is an absolute Man, and Horse, and Health; in which they closely resemble those who state that there are Gods, but of human form; for as the latter invented nothing more or less than eternal men, so the former simply make the Forms eternal sensibles.

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Again, if anyone posits Intermediates distinct from Forms and sensible things, he will have many difficulties;

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because obviously not only will there be lines apart from both Ideal and sensible lines, but it will be the same with each of the other classes.sc. of objects of mathematical sciences. Thus since astronomy is one of the mathematical sciences, there will have to be a heaven besides the sensible heaven, and a sun and moon, and all the other heavenly bodies.

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But how are we to believe this? Nor is it reasonable that the heaven should be immovable; but that it should move is utterly impossible.The reference is to the supposed intermediate heaven. A heaven (including heavenly bodies) without motion is unthinkable; but a non-sensible heaven can have no motion. It is the same with the objects of optics and the mathematical theory of harmony; these too, for the same reasons, cannot exist apart from sensible objects. Because if there are intermediate objects of sense and sensations, clearly there will also be animals intermediate between the Ideal animals and the perishable animals.If there are intermediate, i.e. non-sensible, sights and sounds, there must be intermediate faculties of sight and hearing, and intermediate animals to exercise these faculties; which is absurd.

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One might also raise the question with respect to what kind of objects we are to look for these sciences. For if we are to take it that the only difference between mensuration and geometry is that the one is concerned with things which we can perceive and the other with things which we cannot, clearly there will be a science parallel to medicine (and to each of the other sciences), intermediate between Ideal medicine and the medicine which we know.

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Yet how is this possible? for then there would be a class of healthy things apart from those which are sensible and from the Ideally healthy. Nor, at the same time, is it true that mensuration is concerned with sensible and perishable magnitudes; for then it would perish as they do. Nor, again, can astronomy be concerned with sensible magnitudes or with this heaven of ours;

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for as sensible lines are not like those of which the geometrician speaks (since there is nothing sensible which is straight or curved in that sense; the circlei.e., the visible circle which we draw. Like the ruler, it is geometrically imperfect; thus they touch at more than one point. touches the ruler not at a point, but <along a line> as Protagoras used to say in refuting the geometricians), so the paths and orbits of our heaven are not like those which astronomy discusses, nor have the symbols of the astronomer the same nature as the stars.

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Some, however, say that these so-called Intermediates between Forms and sensibles do exist: not indeed separately from the sensibles, but in them. It would take too long to consider in detail all the impossible consequences of this theory, but it will be sufficient to observe the following.

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On this view it is not logical that only this should be so; in clearly it would be possible for the Forms also to be in sensible things; for the same argument applies to both. Further, it follows necessarily that two solids must occupy the same space; and that the Forms cannot be immovable, being present in sensible things, which move.

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And in general, what is the object of assuming that Intermediates exist, but only in sensible things? The same absurdities as before will result: there will be a heaven besides the sensible one, only not apart from it, but in the same place; which is still more impossible.The problem is dealt with partly in Aristot. Met. 12.6-10, where Aristotle describes the eternal moving principles, and partly in Books 13 and 14, where he argues against the Platonic non-sensible substances.

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Thus it is very difficult to say, not only what view we should adopt in the foregoing questions in order to arrive at the truth, but also in the case of the first principles (vi.) whether we should assume that the genera, or the simplest constituents of each particular thing, are more truly the elements and first principles of existing things. E.g., it is generally agreed that the elements and first principles of speech are those things of which, in their simplest form, all speech is composed; and not the common term speech; and in the case of geometrical propositions we call those the elementsCf. Aristot. Met. 5.3.3. whose proofs are embodied in the proofs of all or most of the rest.

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Again, in the case of bodies, both those who hold that there are several elements and those who hold that there is one call the things of which bodies are composed and constituted first principles. E.g., Empedocles states that fire and water and the other things associated with them are the elements which are present in things and of which things are composed; he does not speak of them as genera of things.

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Moreover in the case of other things too, if a man wishes to examine their nature he observes, e.g., of what parts a bed consists and how they are put together; and then he comprehends its nature. Thus to judge from these arguments the first principles will not be the genera of things.

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But from the point of view that it is through definitions that we get to know each particular thing, and that the genera are the first principles of definitions, the genera must also be the first principles of the things defined.

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And if to gain scientific knowledge of things is to gain it of the species after which things are named, the genera are first principles of the species. And apparently some even of thoseThe Pythagoreans and Plato. who call Unity or Being or the Great and Small elements of things treat them as genera.

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Nor again is it possible to speak of the first principles in both senses.

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The formula of substance is one; but the definition by genera will be different from that which tells us of what parts a thing is composed.

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Moreover, assuming that the genera are first principles in the truest sense, are we to consider the primary genera to be first principles, or the final terms predicated of individuals? This question too involves some dispute.

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For if universals are always more truly first principles, clearly the answer will be the highest genera, since these are predicated of everything. Then there will be as many first principles of things as there are primary genera, and so both Unity and Being will be first principles and substances, since they are in the highest degree predicated of all things.

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But it is impossible for either Unity or Being to be one genus of existing things. For there must be differentiae of each genus, and each differentia must be onei.e., each differentia must have Being and Unity predicated of it.; but it is impossible either for the species of the genus to be predicated of the specific differentiae, or for the genus to be predicated without its species.The reasons are given in Aristot. Topica, 144a 36-b11. Hence if Unity or Being is a genus, there will be no differentia Being or Unity.

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But if they are not genera, neither will they be first principles, assuming that it is the genera that are first principles. And further, the intermediate terms, taken together with the differentiae, will be genera, down to the individuals; but in point of fact, although some are thought to be such, others are not. Moreover the differentiae are more truly principles than are the genera; and if they also are principles, we get an almost infinite number of principles, especially if one makes the ultimate genus a principle.

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Moreover, if Unity is really more of the nature of a principle, and the indivisible is a unity, and every thing indivisible is such either in quantity or in kind, and the indivisible in kind is prior to the divisible, and the genera are divisible into species, then it is rather the lowest predicate that will be a unity (for man is not the genussc. but the species. of individual men).

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Further, in the case of things which admit of priority and posteriority, that which is predicated of the things cannot exist apart from them. E.g., if 2 is the first number, there will be no Number apart from the species of number; and similarly there will be no Figure apart from the species of figures. But if the genera do not exist apart from the species in these cases, they will scarcely do so in others; because it is assumed that genera are most likely to exist in these cases.

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In individuals, however, there is no priority and posteriority. Further, where there is a question of better or worse, the better is always prior; so there will be no genus in these cases either.

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From these considerations it seems that it is the terms predicated of individuals, rather than the genera, that are the first principles. But again on the other hand it is not easy to say in what sense we are to understand these to be principles;

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for the first principle and cause must be apart from the things of which it is a principle, and must be able to exist when separated from them. But why should we assume that such a thing exists alongside of the individual, except in that it is predicated universally and of all the terms? And indeed if this is a sufficient reason, it is the more universal concepts that should rather be considered to be principles; and so the primary genera will be the principles.For partial solutions to the problem see Aristot. Met. 7.10, 12-13.

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In this connection there is a difficulty which is the hardest and yet the most necessary of all to investigate, and with which our inquiry is now concerned. (7.) If nothing exists apart from individual things, and these are infinite in number, how is it possible to obtain knowledge of the numerically infinite? For we acquire our knowledge of all things only in so far as they contain something universal, some one and identical characteristic.

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But if this is essential, and there must be something apart from individual things, it must be the genera; either the lowest or the highest; but we have just concluded that this is impossible.In Aristot. Met. 3.3.

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Further, assuming that when something is predicated of matter there is in the fullest sense something apart from the concrete whole, if there is something, must it exist apart from all concrete wholes, or apart from some but not others, or apart from none?

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If nothing exists apart from individual things, nothing will be intelligible; everything will be sensible, and there will be no knowledge of anything—unless it be maintained that sense-perception is knowledge. Nor again will anything be eternal or immovable, since sensible things are all perishable and in motion.

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Again, if nothing is eternal, even generation is impossible; for there must be something which becomes something, i.e. out of which something is generated, and of this series the ultimate term must be ungenerated; that is if there is any end to the series and generation cannot take place out of nothing.

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Further, if there is generation and motion, there must be limit too. For (a) no motion is infinite, but every one has an end; (b) that which cannot be completely generated cannot begin to be generated, and that which has been generated must be as soon as it has been generated.

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Further, if matter exists apart in virtue of being ungenerated, it is still more probable that the substance, i.e. that which the matter is at any given time becoming, should exist. And if neither one nor the other exists, nothing will exist at all. But if this is impossible, there must be something, the shape or form, apart from the concrete whole.

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But again, if we assume this, there is a difficulty: in what cases shall we, and in what shall we not, assume it? Clearly it cannot be done in all cases; for we should not assume that a particular house exists apart from particular houses. Moreover, are we to regard the essence of all things, e.g. of men, as one? This is absurd; for all things whose essence is one are one.

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Then is it many and diverse? This too is illogical. And besides, how does the matter become each individual one of these things, and how is the concrete whole both matter and form?For answers to these questions see Aristot. Met. 7.8, 13-14; Aristot. Met. 12.6-10; Aristot. Met. 13.10.

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(8.) Further, the following difficulty might be raised about the first principles. If they are one in kind, none of them will be one in number, not even the Idea of Unity or of Being. And how can there be knowledge unless there is some universal term?If the principles are one in kind only, particular things cannot be referred to the same principle but only to like principles; i.e., there will be no universal terms, without which there can be no knowledge.

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On the other hand if they are numerically one, and each of the principles is one, and not, as in the case of sensible things, different in different instances (e.g. since a given syllable is always the same in kind, its first principles are always the same in kind, but only in kind, since they are essentially different in number)—if the first principles are one, not in this sense, but numerically, there will be nothing else apart from the elements; for numerically one and individual are identical in meaning. This is what we mean by individual: the numerically one; but by universal we mean what is predicable of individuals.

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Hence just as, if the elements of languageOr letters of the alphabet. Cf. Aristot. Met. 1.9.36n. were limited in number, the whole of literature would be no more than those elements—that is, if there were not two nor more than two of the same <so it would be in the case of existing things and their principles>.For the answer to the problem see Aristot. Met. 12.4-5, Aristot. Met. 13.10.

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(ix.) There is a difficulty, as serious as any, which has been left out of account both by present thinkers and by their predecessors: whether the first principles of perishable and imperishable things are the same or different. For if they are the same, how is it that some things are perishable and others imperishable, and for what cause?

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The school of Hesiod, and all the cosmologists, considered only what was convincing to themselves, and gave no consideration to us. For they make the first principles Gods or generated from Gods, and say that whatever did not taste of the nectar and ambrosia became mortal—clearly using these terms in a sense significant to themselves;

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but as regards the actual applications of these causes their statements are beyond our comprehension. For if it is for pleasure that the Gods partake of them, the nectar and ambrosia are in no sense causes of their existence; but if it is to support life, how can Gods who require nourishment be eternal?

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However, it is not worth while to consider seriously the subtleties of mythologists; we must ascertain by cross-examining those who offer demonstration of their statements why exactly things which are derived from the same principles are some of an eternal nature and some perishable. And since these thinkers state no reason for this view, and it is unreasonable that things should be so, obviously the causes and principles of things cannot be the same.

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Even the thinker who might be supposed to speak most consistently, Empedocles, is in the same case; for he posits Strife as a kind of principle which is the cause of destruction, but none the less Strife would seem to produce everything except the One; for everything except GodThe expressions the One and God refer to Empedocles’ Sphere: the universe as ordered and united by Love. Cf. Empedocles, Fr. 26-29 (Diels). proceeds from it.

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At any rate he says

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From which grew all that was and is and shall be

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In time to come: the trees, and men and women,

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The beasts and birds and water-nurtured fish,

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And the long-living Gods.Empedocles, Fr. 21. 9-12.

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And it is obvious even apart from this; for if there had not been Strife in things, all things would have been one, he says; for when they came together then Strife came to stand outermost. Empedocles, Fr. 36. 7. Hence it follows on his theory that God, the most blessed being, is less wise than the others, since He does not know all the elements; for He has no Strife in Him, and knowledge is of like by like:

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By earth (he says) we earth perceive, by water water,

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By air bright air, by fire consuming fire,

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Love too by love, and strife by grievous strife.Empedocles, Fr. 109.

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But—and this is the point from which we started—thus much is clear: that it follows on his theory that Strife is no more the cause of destruction than it is of Being. Nor, similarly, is Love the cause of Being; for in combining things into one it destroys everything else.Cf. Aristot. Met. 1.4.6.

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Moreover, of the actual process of change he gives no explanation, except that it is so by nature:

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But when Strife waxing great among the membersi.e., of the Sphere.

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Sprang up to honor as the time came round

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Appointed them in turn by a mighty oath,Empedocles, Fr. 30.

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as though change were a necessity; but he exhibits no cause for the necessity.

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However, thus much of his theory is consistent: he does not represent some things to be perishable and others imperishable, but makes everything perishable except the elements. But the difficulty now being stated is why some things are perishable and others not, assuming that they are derived from the same principles.

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The foregoing remarks may suffice to show that the principles cannot be the same.

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If however they are different, one difficulty is whether they too are to be regarded as imperishable or as perishable. For if they are perishable, it is clearly necessary that they too must be derived from something else, since everything passes upon dissolution into that from which it is derived. Hence it follows that there are other principles prior to the first principles;

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but this is impossible, whether the series stops or proceeds to infinity. And further, how can perishable things exist if their principles are abolished? On the other hand if the principles are imperishable, why should some imperishable principles produce perishable things, and others imperishable things? This is not reasonable; either it is impossible or it requires much explanation.

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Further, no one has so much as attempted to maintain different principles; they maintain the same principles for everything. But they swallow down the difficulty which we raised firsti.e., whether all things have the same principles. as though they took it to be trifling.For Aristotle’s views about the principles of perishable and imperishable things see Aristot. Met. 7.7-10, Aristot. Met. 12.1-7.

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But the hardest question of all to investigate and also the most important with a view to the discovery of the truth, is whether after all Being and Unity are substances of existing things, and each of them is nothing else than Being and Unity respectively, or whether we should inquire what exactly Being and Unity are, there being some other nature underlying them.

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Some take the former, others the latter view of the nature of Being and Unity. Plato and the Pythagoreans hold that neither Being nor Unity is anything else than itself, and that this is their nature, their essence being simply Being and Unity.

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But the physicists, e.g. Empedocles, explain what Unity is by reducing it to something, as it were, more intelligible—or it would seem that by Love Empedocles means Unity; at any rate Love is the cause of Unity in all things. Others identify fire and others air with this Unity and Being of which things consist and from which they have been generated.

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Those who posit more numerous elements also hold the same view; for they too must identify Unity and Being with all the principles which they recognize. And it follows that unless one assumes Unity and Being to be substance in some sense, no other universal term can be substance; for Unity and Being are the most universal of all terms,

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and if there is no absolute Unity or absolute Being, no other concept can well exist apart from the so-called particulars. Further, if Unity is not substance, clearly number cannot be a separate characteristic of things; for number is units, and the unit is simply a particular kind of one.

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On the other hand, if there is absolute Unity and Being, their substance must be Unity and Being; for no other term is predicated universally of Unity and Being, but only these terms themselves. Again, if there is to be absolute Being and absolute Unity, it is very hard to see how there can be anything else besides these; I mean, how things can be more than one.

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For that which is other than what is, is not; and so by Parmenides’ argumentBy τὸ ὄν Parmenides meant what is, i.e. the real universe, which he proved to be one thing because anything else must be what is not, or non-existent. The Platonists meant by it being in the abstract. Aristotle ignores this distinction. it must follow that all things are one, i.e. Being. In either case there is a difficulty; for whether Unity is not a substance or whether there is absolute Unity, number cannot be a substance.

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It has already been stated why this is so if Unity is not a substance; and if it is, there is the same difficulty as about Being. For whence, if not from the absolute One or Unity, can there be another one? It must be not-one; but all things are either one, or many of which each is one. Further, if absolute Unity is indivisible, by Zeno’s axiom it will be nothing.

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For that which neither when added makes a thing greater nor when subtracted makes it smaller is not an existent thing, he saysCf. Zeno, Fr. 2, and see Burnet, E.G.P. sects. 157 ff.; clearly assuming that what exists is spatial magnitude. And if it is a spatial magnitude it is corporeal, since the corporeal exists in all dimensions, whereas the other magnitudes, the plane or line, when added to a thing in one way will increase it, but when added in another will not; and the point or unit will not increase a thing in any way whatever.

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But since Zeno’s view is unsound, and it is possible for a thing to be indivisible in such a way that it can be defended even against his argument (for such a thinge.g., a point is indivisible and has no magnitude, yet added to other points it increases their number. when added will increase a thing in number though not in size)—still how can a magnitude be composed of one or more such indivisible things? It is like saying that the line is composed of points.

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Moreover, even if one supposes the case to be such that number is generated, as some say, from the One itself and from something else which is not one, we must none the less inquire why and how it is that the thing generated will be at one time number and at another magnitude, if the not-one was inequality and the same principle in both cases.The reference is to the Platonists. Cf. Aristot. Met. 14.1.5, 6; Aristot. Met. 14.2.13, 14. For it is not clear how magnitude can be generated either from One and this principle, or from a number and this principle.For the answer to this problem see Aristot. Met. 7.16.3, 4; Aristot. Met. 10.2; and cf. Aristot. Met. 13.8.

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(13.) Out of this arises the question whether numbers, bodies, planes and points are substances or not. If not, the question of what Being is, what the substances of things are, baffles us; for modifications and motions and relations and dispositions and ratios do not seem to indicate the substance of anything; they are all predicated of a substrate, and none of them is a definite thing.

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As for those things which might be especially supposed to indicate substance—water, earth, fire and air, of which composite bodies are composed— their heat and cold and the like are modifications, not substances; and it is only the body which undergoes these modifications that persists as something real and a kind of substance.

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Again, the body is less truly substance than the plane, and the plane than the line, and the line than the unit or point; for it is by these that the body is defined, and it seems that they are possible without the body, but that the body cannot exist without them.

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This is why the vulgar and the earlier thinkers supposed that substance and Being are Body, and everything else the modifications of Body; and hence also that the first principles of bodies are the first principles of existing things; whereas later thinkers with a greater reputation for wisdom supposed that substance and Being are numbers.

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As we have said, then, if these things are not substance, there is no substance or Being at all; for the attributes of these things surely have no right to be called existent things. On the other hand, if it be agreed that lines and points are more truly substance than bodies are, yet unless we can see to what kind of bodies they belong (for they cannot be in sensible bodies) there will still be no substance.

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Further, it is apparent that all these lines are divisions of Body, either in breadth or in depth or in length. Moreover every kind of shape is equally present in a solid, so that if Hermes is not in the stone,Apparently a proverbial expression. neither is the half-cube in the cube as a determinate shape.

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Hence neither is the plane; for if any kind of plane were in it, so would that plane be which defines the half-cube. The same argument applies to the line and to the point or unit. Hence however true it may be that body is substance, if planes, lines and points are more truly substance than Body is, and these are not substance in any sense, the question of what Being is and what is the substance of things baffles us.

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Because, in addition to the above arguments, absurd results follow from a consideration of generation and destruction; for it seems that if substance, not having existed before, now exists, or having existed before, subsequently does not exist it suffers these changes in the process of generation and destruction. But points, lines and planes, although they exist at one time and at another do not, cannot be in process of being either generated or destroyed;

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for whenever bodies are joined or divided, at one time, when they are joined one surface is instantaneously produced, and at another, when they are divided, two. Thus when the bodies are combined the surface does not exist but has perished; and when they are divided, surfaces exist which did not exist before. (The indivisible point is of course never divided into two.) And if they are generated and destroyed, from what are they generated?

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It is very much the same with the present moment in time. This too cannot be generated and destroyed; but nevertheless it seems always to be different, not being a substance. And obviously it is the same with points, lines and planes, for the argument is the same; they are all similarly either limits or divisions.For arguments against the substantiality of numbers and mathematical objects see Aristot. Met. 13.1-3, 6-9; Aristot. Met. 14.1-3, 5, 6.

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In general one might wonder why we should seek for other entities apart from sensible things and the Intermediates:Cf. Aristot. Met. 3.2.20ff.. e.g., for the Forms which we Platonists assume.

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If it is for the reason that the objects of mathematics, while differing from the things in our world in another respect, resemble them in being a plurality of objects similar in form, so that their principles cannot be numerically determined (just as the principles of all language in this world of ours are determinate not in number but in kind—unless one takes such and such a particular syllable or sound, for the principles of these are determinate in number too—

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and similarly with the Intermediates, for in their case too there is an infinity of objects similar in form), then if there is not another set of objects apart from sensible and mathematical objects, such as the Forms are said to be, there will be no substance which is one both in kind and in number, nor will the principles of things be determinate in number, but in kind only.

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Thus if this is necessarily so, it is necessary for this reason to posit the Forms also. For even if their exponents do not articulate their theory properly, still this is what they are trying to express, and it must be that they maintain the Forms on the ground that each of them is a substance, and none of them exists by accident.

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On the other hand, if we are to assume that the Forms exist, and that the first principles are one in number but not in kind, we have already statedAristot. Met. 3.4.9, 10. the impossible consequences which must follow.This problem is not stated in ch. 1., but is akin to problems 5. and 8., which see.

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(12.) Closely connected with these questions is the problem whether the elements exist potentially or in some other sense.

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If in some other sense, there will be something else prior to the first principles. For the potentiality is prior to the actual cause, and the potential need not necessarily always become actual. On the other hand, if the elements exist potentially, it is possible for nothing to exist; for even that which does not yet exist is capable of existing. That which does not exist may come to be, but nothing which cannot exist comes to be.For the relation of potentiality to actuality see Aristot. Met. 9.1-9. The second point raised in this connection in ch. 1 is not discussed here; for actuality and motion see Aristot. Met. 12.6, 7.

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(xi.) Besides the foregoing problems about the first principles we must also raise the question whether they are universal or such as we describe the particulars to be. For if they are universal, there will be no substances; for no common term denotes an individual thing, but a type; and substance is an individual thing.

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But if the common predicate be hypostatized as an individual thing, Socrates will be several beings: himself, and Man, and Animal—that is, if each predicate denotes one particular thing.

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These then are the consequences if the principles are universal. If on the other hand they are not universal but like particulars, they will not be knowable; for the knowledge of everything is universal. Hence there will have to be other universally predicated principles prior to the first principles, if there is to be any knowledge of them.For the answer to this problem see Aristot. Met. 7.13-15, Aristot. Met. 13.10.

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There is a science which studies Being qua Being, and the properties inherent in it in virtue of its own nature. This science is not the same as any of the so-called particular sciences, for none of the others contemplates Being generally qua Being; they divide off some portion of it and study the attribute of this portion, as do for example the mathematical sciences.

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But since it is for the first principles and the most ultimate causes that we are searching, clearly they must belong to something in virtue of its own nature. Hence if these principles were investigated by those also who investigated the elements of existing things, the elements must be elements of Being not incidentally, but qua Being. Therefore it is of Being qua Being that we too must grasp the first causes.

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The term being is used in various senses, but with reference to one central idea and one definite characteristic, and not as merely a common epithet. Thus as the term healthy always relates to health (either as preserving it or as producing it or as indicating it or as receptive of it),

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and as medical relates to the art of medicine (either as possessing it or as naturally adapted for it or as being a function of medicine)—and we shall find other terms used similarly to these—

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so being is used in various senses, but always with reference to one principle. For some things are said to be because they are substances; others because they are modifications of substance; others because they are a process towards substance, or destructions or privations or qualities of substance, or productive or generative of substance or of terms relating to substance, or negations of certain of these terms or of substance. (Hence we even say that not-being is not-being.)

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And so, just as there is one science of all healthy things, so it is true of everything else. For it is not only in the case of terms which express one common notion that the investigation belongs to one science, but also in the case of terms which relate to one particular characteristic; for the latter too, in a sense, express one common notion. Clearly then the study of things which are, qua being, also belongs to one science.

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Now in every case knowledge is principally concerned with that which is primary, i.e. that upon which all other things depend, and from which they get their names. If, then, substance is this primary thing, it is of substances that the philosopher must grasp the first principles and causes.

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Now of every single class of things, as there is one perception, so there is one science: e.g., grammar, which is one science, studies all articulate sounds.

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Hence the study of all the species of Being qua Being belongs to a science which is generically one, and the study of the several species of Being belongs to the specific parts of that science.

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Now if Being and Unity are the same, i.e. a single nature, in the sense that they are associated as principle and cause are, and not as being denoted by the same definition (although it makes no difference but rather helps our argument if we understand them in the same sense),

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since one man and man and existent man and man are the same thing, i.e. the duplication in the statement he is a man and an existent man gives no fresh meaning (clearly the concepts of humanity and existence are not dissociated in respect of either coming to be or ceasing to be), and similarly in the case of the term one, so that obviously the additional term in these phrases has the same significance, and Unity is nothing distinct from Being;

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and further if the substance of each thing is one in no accidental sense, and similarly is of its very nature something which is—then there are just as many species of Being as of Unity. And to study the essence of these species (I mean, e.g., the study of Same and Other and all the other similar concepts—

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roughly speaking all the contraries are reducible to this first principle; but we may consider that they have been sufficiently studied in the Selection of ContrariesIt is uncertain to what treatise Aristotle refers; in any case it is not extant.) is the province of a science which is generically one.

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And there are just as many divisions of philosophy as there are kinds of substance; so that there must be among them a First Philosophy and one which follows upon it.

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For Being and Unity at once entail genera, and so the sciences will correspond to these genera. The term philosopher is like the term mathematician in its uses; for mathematics too has divisions—there is a primary and a secondary science, and others successively, in the realm of mathematics.

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Now since it is the province of one science to study opposites, and the opposite of unity is plurality, and it is the province of one science to study the negation and privation of Unity, because in both cases we are studying Unity, to which the negation (or privation) refers, stated either in the simple form that Unity is not present, or in the form that it is not present in a particular class; in the latter case Unity is modified by the differentia, apart from the content of the negation (for the negation of Unity is its absence); but in privation there is a substrate of which the privation is predicated.—

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The opposite of Unity, then, is Plurality; and so the opposites of the above-mentioned concepts—Otherness, Dissimilarity, Inequality and everything else which is derived from these or from Plurality or Unity— fall under the cognizance of the aforesaid science. And one of them is Oppositeness; for this is a form of Difference, and Difference is a form of Otherness.

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Hence since the term one is used in various senses, so too will these terms be used; yet it pertains to one science to take cognizance of them all. For terms fall under different sciences, not if they are used in various senses, but if their definitions are neither identical nor referable to a common notion.

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And since everything is referred to that which is primary, e.g. all things which are called one are referred to the primary One, we must admit that this is also true of Identity and Otherness and the Contraries. Thus we must first distinguish all the senses in which each term is used, and then attribute them to the primary in the case of each predicate, and see how they are related to it; for some will derive their name from possessing and others from producing it, and others for similar reasons.

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Thus clearly it pertains to one science to give an account both of these concepts and of substance (this was one of the questions raised in the DifficultiesSee Aristot. Met. 3.1.8-10, Aristot. Met. 3.2.18, 19.), and it is the function of the philosopher to be able to study all subjects.

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If this is not so, who is it who in will investigate whether Socrates and Socrates seated are the same thing; or whether one thing has one contrary, or what the contrary is, or how many meanings it has?Cf. Aristot. Met. 10.4. and similarly with all other such questions.

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Thus since these are the essential modifications of Unity qua Unity and of Being qua Being, and not qua numbers or lines or fire, clearly it a pertains to that sciencei.e., Philosophy or Metaphysics. to discover both the essence and the attributes of these concepts.

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And those who investigate them err, not in being unphilosophical, but because the substance, of which they have no real knowledge, is prior. For just as number qua number has its peculiar modifications, e.g. oddness and evenness, commensurability and equality, excess and defect, and these things are inherent in numbers both considered independently and in relation to other numbers; and as similarly other peculiar modifications are inherent in the solid and the immovable and the moving and the weightless and that which has weight; so Being qua Being has certain peculiar modifications, and it is about these that it is the philosopher’s function to discover the truth. And here is evidence of this fact.

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Dialecticians and sophists wear the same appearance as the philosopher, for sophistry is Wisdom in appearance only, and dialecticians discuss all subjects, and Being is a subject common to them all; but clearly they discuss these concepts because they appertain to philosophy.

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For sophistry and dialectic are concerned with the same class of subjects as philosophy, but philosophy differs from the former in the nature of its capability and from the latter in its outlook on life. Dialectic treats as an exercise what philosophy tries to understand, and sophistry seems to be philosophy; but is not.

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Further, the second column of contraries is privative, and everything is reducible to Being and Not being, and Unity and Plurality; e.g. Rest falls under Unity and Motion under Plurality. And nearly everyone agrees that substance and existing things are composed of contraries; at any rate all speak of the first principles as contraries—

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some as Odd and Even,The Pythagoreans. some as Hot and Cold,Perhaps Parmenides. some as Limit and Unlimited,The Platonists. some as Love and Strife.Empedocles. And it is apparent that all other things also are reducible to Unity and Plurality (we may assume this reduction); and the principles adduced by other thinkers fall entirely under these as genera.

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It is clear, then, from these considerations also, that it pertains to a single science to study Being qua Being; for all things are either contraries or derived from contraries, and the first principles of the contraries are Unity and Plurality. And these belong to one science, whether they have reference to one common notion or not. Probably the truth is that they have not; but nevertheless even if the term one is used in various senses, the others will be related to the primary sense (and similarly with the contraries)—

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even if Being or Unity is not a universal and the same in all cases, or is not separable from particulars (as it presumably is not; the unity is in some cases one of reference and in others one of succession). For this very reason it is not the function of the geometrician to inquire what is Contrariety or Completeness or Being or Unity or Identity or Otherness, but to proceed from the assumption of them.

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Clearly, then, it pertains to one science to study Being qua Being, and the attributes inherent in it qua Being; and the same science investigates, besides the concepts mentioned above, Priority and Posteriority, Genus and Species, Whole and Part, and all other such concepts.

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We must pronounce whether it pertains to the same science to study both the so-called axioms in mathematics and substance, or to different sciences. It is obvious that the investigation of these axioms too pertains to one science, namely the science of the philosopher; for they apply to all existing things, and not to a particular class separate and distinct from the rest. Moreover all thinkers employ them—because they are axioms of Being qua Being, and every genus possesses Being—

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but employ them only in so far as their purposes require; i.e., so far as the genus extends about which they are carrying out their proofs. Hence since these axioms apply to all things qua Being (for this is what is common to them), it is the function of him who studies Being qua Being to investigate them as well.

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For this reason no one who is pursuing a particular inquiry—neither a geometrician nor an arithmetician—attempts to state whether they are true or false; but some of the physicists did so, quite naturally; for they alone professed to investigate nature as a whole, and Being.

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But inasmuch as there is a more ultimate type of thinker than the natural philosopher (for nature is only a genus of Being), the investigation of these axioms too will belong to the universal thinker who studies the primary reality. Natural philosophy is a kind of Wisdom, but not the primary kind.

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As for the attempts of some of those who discuss how the truth should be received, they are due to lack of training in logic; for they should understand these things before they approach their task, and not investigate while they are still learning.

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Clearly then it is the function of the philosopher, i.e. the student of the whole of reality in its essential nature, to investigate also the principles of syllogistic reasoning. And it is proper for him who best understands each class of subject to be able to state the most certain principles of that subject; so that he who understands the modes of Being qua Being should be able to state the most certain principles of all things.

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Now this person is the philosopher, and the most certain principle of all is that about which one cannot be mistaken; for such a principle must be both the most familiar (for it is about the unfamiliar that errors are always made), and not based on hypothesis.

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For the principle which the student of any form of Being must grasp is no hypothesis; and that which a man must know if he knows anything he must bring with him to his task.

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Clearly, then, it is a principle of this kind that is the most certain of all principles. Let us next state what this principle is.

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It is impossible for the same attribute at once to belong and not to belong to the same thing and in the same relation; and we must add any further qualifications that may be necessary to meet logical objections. This is the most certain of all principles, since it possesses the required definition;

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for it is impossible for anyone to suppose that the same thing is and is not, as some imagine that Heraclitus saysFor examples of Heraclitus’s paradoxes cf. Heraclitus Fr. 36, 57, 59 (Bywater); and for their meaning see Burnet, E.G.P. 80.—for what a man says does not necessarily represent what he believes.

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And if it is impossible for contrary attributes to belong at the same time to the same subject (the usual qualifications must be added to this premiss also), and an opinion which contradicts another is contrary to it, then clearly it is impossible for the same man to suppose at the same time that the same thing is and is not; for the man who made this error would entertain two contrary opinions at the same time.

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Hence all men who are demonstrating anything refer back to this as an ultimate belief; for it is by nature the starting-point of all the other axioms as well.

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There are some, however, as we have said, who both state themselves that the same thing can be and not be, and say that it is possible to hold this view. Many even of the physicists adopt this theory. But we have just assumed that it is impossible at once to be and not to be, and by this means we have proved that this is the most certain of all principles.

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Some, indeed, demand to have the law proved, but this is because they lack educationsc., in logic.; for it shows lack of education not to know of what we should require proof, and of what we should not. For it is quite impossible that everything should have a proof; the process would go on to infinity, so that even so there would be no proof.Every proof is based upon some hypothesis, to prove which another hypothesis must be assumed, and so on ad infinitum.

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If on the other hand there are some things of which no proof need be sought, they cannot say what principle they think to be more self-evident. Even in the case of this law, however, we can demonstrate the impossibility by refutation, if only our opponent makes some statement. If he makes none, it is absurd to seek for an argument against one who has no arguments of his own about anything, in so far as he has none; for such a person, in so far as he is such, is really no better than a vegetable.

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And I say that proof by refutation differs from simple proof in that he who attempts to prove might seem to beg the fundamental question, whereas if the discussion is provoked thus by someone else, refutation and not proof will result.

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The starting-point for all such discussions is not the claim that he should state that something is or is not so (because this might be supposed to be a begging of the question), but that he should say something significant both to himself and to another (this is essential if any argument is to follow; for otherwise such a person cannot reason either with himself or with another);

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and if this is granted, demonstration will be possible, for there will be something already defined. But the person responsible is not he who demonstrates but he who acquiesces; for though he disowns reason he acquiesces to reason. Moreover, he who makes such an admission as this has admitted the truth of something apart from demonstration [so that not everything will be so and not so].

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Thus in the first place it is obvious that this at any rate is true: that the term to be or not to be has a definite meaning; so that not everything can be so and not so. Again, if man has one meaning, let this be two-footed animal.

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By has one meaning I mean this: if X means man, then if anything is a man, its humanity will consist in being X. And it makes no difference even if it be said that man has several meanings, provided that they are limited in number; for one could assign a different name to each formula.

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For instance, it might be said that man has not one meaning but several, one of which has the formula two-footed animal, and there might be many other formulae as well, if they were limited in number; for a particular name could be assigned to each for formula.

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If on the other hand it be said that man has an infinite number of meanings, obviously there can be no discourse; for not to have one meaning is to have no meaning, and if words have no meaning there is an end of discourse with others, and even, strictly speaking, with oneself; because it is impossible to think of anything if we do not think of one thing; and even if this were possible, one name might be assigned to that of which we think.

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Now let this name, as we said at the beginning, have a meaning; and let it have one meaning. Now it is impossible that being man should have the same meaning as not being man, that is, if man is not merely predicable of one subject but has one meaning

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(for we do not identify having one meaning with being predicable of one subject, since in this case cultured and white and man would have one meaning, and so all things would be one; for they would all have the same meaning). And it will be impossible for the same thing to be and not to be, except by equivocation, as e.g. one whom we call man others might call not-man;

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but the problem is whether the same thing can at once be and not be man, not in name , but in fact . If man and not-man have not different meanings, clearly not being a man will mean nothing different from being a man; and so being a man will be not being a man; they will be one.

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For to be one means, as in the case of garment and coat, that the formula is one. And if being man and being not-man are to be one, they will have the same meaning; but it has been proved above that they have different meanings. If then anything can be truly said to be man, it must be two-footed animal; for this is what man was intended to mean.

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And if this is necessarily so, it is impossible that at the same time the same thing should not be two-footed animal. For to be necessarily so means this: that it is impossible not to be so. Thus it cannot be true to say at the same time that the same thing is and is not man.

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And the same argument holds also in the case of not being man; because being man and being not-man have different meanings if being white and being man have different meanings (for the opposition is much stronger in the former case so as to produce different meanings).

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And if we are told that white too means one and the same thing,i.e. the same as man. we shall say again just what we said before,Aristot. Met. 4.4.12. that in that case all things, and not merely the opposites, will be one. But if this is impossible, what we have stated follows; that is, if our opponent answers our question; but if when asked the simple question he includes in his answer the negations, he is not answering our question.

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There is nothing to prevent the same thing from being man and white and a multitude of other things; but nevertheless when asked whether it is true to say that X is man, or not, one should return an answer that means one thing, and not add that X is white and large. It is indeed impossible to enumerate all the infinity of accidents; and so let him enumerate either all or none.

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Similarly therefore, even if the same thing is ten thousand times man and not-man, one should not include in one’s answer to the question whether it is man that it is at the same time also not-man, unless one is also bound to include in one’s answer all the other accidental things that the subject is or is not. And if one does this, he is not arguing properly.

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In general those who talk like this do away with substance and essence,

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for they are compelled to assert that all things are accidents, and that there is no such thing as being essentially man or animal. For if there is to be such a thing as being essentially man, this will not be being not-man nor not-being man (and yet these are negations of it); for it was intended to have one meaning, i.e. the substance of something.

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But to denote a substance means that the essence is that and nothing else; and if for it being essentially man is the same as either being essentially not-man or essentially not-being man, the essence will be something else.

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Thus they are compelled to say that nothing can have such a definition as this, but that all things are accidental; for this is the distinction between substance and accident: white is an accident of man, because although he is white, he is not white in essence.

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And since the accidental always implies a predication about some subject, if all statements are accidental, there will be nothing primary about which they are made; so the predication must proceed to infinity. But this is impossible, for not even more than two accidents can be combined in predication. An accident cannot be an accident of an accident unless both are accidents of the same thing.

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I mean, e.g., that white is cultured and cultured white merely because both are accidents of a man. But it is not in this sense—that both terms are accidents of something else—that Socrates is cultured. Therefore since some accidents are predicated in the latter and some in the former sense, such as are predicated in the way that white is of Socrates cannot be an infinite series in the upper direction; e.g. there cannot be another accident of white Socrates, for the sum of these predications does not make a single statement.

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Nor can white have a further accident, such as cultured; for the former is no more an accident of the latter than vice versa; and besides we have distinguished that although some predicates are accidental in this sense, others are accidental in the sense that cultured is to Socrates; and whereas in the former case the accident is an accident of an accident, it is not so in the latter; and thus not all predications will be of accidents.

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Therefore even so there will be something which denotes substance. And if this is so, we have proved that contradictory statements cannot be predicated at the same time.

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Again, if all contradictory predications of the same subject at the same time are true, clearly all things will be one.

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For if it is equally possible either to affirm or deny anything of anything, the same thing will be a trireme and a wall and a man; which is what necessarily follows for those who hold the theory of Protagoras.i.e., that all appearances and opinions are true. For if anyone thinks that a man is not a trireme, he is clearly not a trireme; and so he also is a trireme if the contradictory statement is true.

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And the result is the dictum of Anaxagoras, all things mixed together Fr. 1 (Diels). ; so that nothing truly exists. It seems, then, that they are speaking of the Indeterminate; and while they think that they are speaking of what exists, they are really speaking of what does not; for the Indeterminate is that which exists potentially but not actually.

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But indeed they must admit the affirmation or negation of any predicate of any subject, for it is absurd that in the case of each term its own negation should be true, and the negation of some other term which is not true of it should not be true. I mean, e.g., that if it is true to say that a man is not a man, it is obviously also true to say that he is or is not a trireme.

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Then if the affirmation is true, so must the negation be true; but if the affirmation is not true the negation will be even truer than the negation of the original term itself. Therefore if the latter negation is true, the negation of trireme will also be true; and if this is true, the affirmation will be true too.

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And not only does this follow for those who hold this theory, but also that it is not necessary either to affirm or to deny a statement.

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For if it is true that X is both man and not-man, clearly he will be neither man nor not-man; for to the two statements there correspond two negations, and if the former is taken as a single statement compounded out of two, the latter is also a single statement and opposite to it.

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Again, either this applies to all terms, and the same thing is both white and not-white, and existent and non-existent, and similarly with all other assertions and negations; or it does not apply to all, but only to some and not to others.

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And if it does not apply to all, the exceptions will be admittedi.e., it will be admitted that in certain cases where an attribute is true of a subject, the negation is not true; and therefore some propositions are indisputable.; but if it does apply to all, again either (a) the negation will be true wherever the affirmation is true, and the affirmation will be true wherever the negation is true, or (d) the negation will be true wherever the assertion is true, but the assertion will not always be true where the negation is true.

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And in the latter case there will be something which definitely is not, and this will be a certain belief; and if that it is not is certain and knowable, the opposite assertion will be still more knowable. But if what is denied can be equally truly asserted, it must be either true or false to state the predicates separately and say, e.g., that a thing is white, and again that it is not-white.

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And if it is not-true to state them separately, our opponent does not say what he professes to say, and nothing exists; and how can that which does not exist speak or walk?If our opponent holds that you can only say A is B and not B, (1) he contradicts every statement that he makes; (2) he must say that what exists does not exist. Therefore nothing exists, and so he himself does not exist; but how can he speak or walk if he does not exist? And again all things will be one, as we said before,Aristot. Met. 4.4.27. and the same thing will be man and God and trireme and the negations of these terms.

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For if it is equally possible to assert or deny anything of anything, one thing will not differ from another; for if anything does differ, it will be true and unique. And similarly even if it is possible to make a true statement while separating the predicates, what we have stated follows. Moreover it follows that all statements would be true and all false; and that our opponent himself admits that what he says is false. Besides, it is obvious that discussion with him is pointless, because he makes no real statement.

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For he says neither yes nor no, but yes and no; and again he denies both of these and says neither yes nor no; otherwise there would be already some definite statement.

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Again, if when the assertion is true the negation is false, and when the latter is true the affirmation is false, it will be impossible to assert and deny with truth the same thing at the same time.

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But perhaps it will be said that this is the point at issue.

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Again, is the man wrong who supposes that a thing is so or not so, and he who supposes both right? If he is right, what is the meaning of saying that such is the nature of reality?If everything is both so and not so, nothing has any definite nature. And if he is not right, but is more right than the holder of the first view, reality will at once have a definite nature, and this will be true, and not at the same time not-true.

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And if all men are equally right and wrong, an exponent of this view can neither speak nor mean anything, since at the same time he says both yes and no. And if he forms no judgement, but thinks and thinks not indifferently, what difference will there be between him and the vegetables?

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Hence it is quite evident that no one, either of those who profess this theory or of any other school, is really in this position.

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Otherwise, why does a man walk to Megara and not stay at home, when he thinks he ought to make the journey? Why does he not walk early one morning into a well or ravine, if he comes to it, instead of clearly guarding against doing so, thus showing that he does not think that it is equally good and not good to fall in? Obviously then he judges that the one course is better and the other worse.

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And if this is so, he must judge that one thing is man and another not man, and that one thing is sweet and another not sweet. For when, thinking that it is desirable to drink water and see a man, he goes to look for them, he does not look for and judge all things indifferently; and yet he should, if the same thing were equally man and not-man.

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But as we have said, there is no one who does not evidently avoid some things and not others. Hence, as it seems, all men form unqualified judgements, if not about all things, at least about what is better or worse.

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And if they do this by guesswork and without knowledge, they should be all the more eager for truth; just as a sick man should be more eager for health than a healthy man; for indeed the man who guesses, as contrasted with him who knows, is not in a healthy relation to the truth.

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Again, however much things may be so and not so, yet differences of degree are inherent in the nature of things. For we should not say that 2 and 3 are equally even; nor are he who thinks that 4 is 5, and he who thinks it is 1000, equally wrong: hence if they are not equally wrong, the one is clearly less wrong, and so more right.

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If then that which has more the nature of something is nearer to that something, there will be some truth to which the more true is nearer. And even if there is not, still there is now something more certain and true, and we shall be freed from the undiluted doctrine which precludes any mental determination.

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From the same view proceeds the theory of Protagoras, and both alike must be either true or false. For if all opinions and appearances are true, everything must be at once true and false; for many people form judgements which are opposite to those of others, and imagine that those who do not think the same as themselves are wrong: hence the same thing must both be and not be.

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And if this is so, all opinions must be true; for those who are wrong and those who are right think contrarily to each other. So if reality is of this nature, everyone will be right.

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Clearly then both these theories proceed from the same mental outlook. But the method of approach is not the same for all cases; for some require persuasion and others compulsion.

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The ignorance of those who have formed this judgement through perplexity is easily remedied, because we are dealing not with the theory but with their mental outlook; but those who hold the theory for its own sake can only be cured by refuting the theory as expressed in their own speech and words.

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This view comes to those who are perplexed from their observation of sensible things. (1.) The belief that contradictions and contraries can be true at the same time comes to them from seeing the contraries generated from the same thing.

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Then if what is not cannot be generated, the thing must have existed before as both contraries equally—just as Anaxagoras saysCf. Aristot. Met. 4.4.28. that everything is mixed in everything; and also Democritus, for he too saysCf. Aristot. Met. 1.4.9. that Void and Plenum are present equally in any part, and yet the latter is , and the former is not.

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To those, then, who base their judgement on these considerations, we shall say that although in one sense their theory is correct, in another they are mistaken. For being has two meanings, so that there is a sense in which something can be generated from not-being, and a sense in which it cannot; and a sense in which the same thing can at once be and not be; but not in the same respect. For the same thing can be contraries at the same time potentially, but not actually.

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And further, we shall request them to conceive another kind also of substance of existing things, in which there is absolutely no motion or destruction or generation. And (2.) similarly the theory that there is truth in appearances has come to some people from an observation of sensible things.

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They think that the truth should not be judged by the number or fewness of its upholders; and they say that the same thing seems sweet to some who taste it, and bitter to others; so that if all men were diseased or all insane, except two or three who were healthy or sane, the latter would seem to be diseased or insane, and not the others.

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And further they say that many of the animals as well get from the same things impressions which are contrary to ours, and that the individual himself does not always think the same in matters of sense-perception. Thus it is uncertain which of these impressions are true or false; for one kind is no more true than another, but equally so. And hence Democritus saysCf. Ritter and Preller, 204. that either there is no truth or we cannot discover it.

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And in general it is because they suppose that thought is sense-perception, and sense-perception physical alteration, that they say that the impression given through sense-perception is necessarily true; for it is on these grounds that both Empedocles and Democritus and practically all the rest have become obsessed by such opinions as these.

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For Empedocles says that those who change their bodily condition change their thought:

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For according to that which is present to them doth thought increase in men.Empedocles Fr. 106.

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And in another passage he says:

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And as they change into a different nature, so it ever comes to them to think differently.Empedocles Fr. 108.

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And Parmenides too declares in the same way:

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For as each at any time hath the temperament of his many-jointed limbs, so thought comes to men. For for each and every man the substance of his limbs is that very thing which thinks; for thought is that which preponderates.Empedocles Fr. 16; quoted also (in a slightly different form; see critical notes) by Theophrastus, De Sensu 3.

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There is also recorded a saying of Anaxagoras to some of his disciples, that things would be for them as they judged them to be.

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And they say that in Homer too clearly held this view, because he made Hector,The only passage in our text of Homer to which this reference could apply isHom. Il. 23.698; but there the subject is Euryalus, not Hector. when he was stunned by the blow, lie with thoughts deranged—thus implying that even those who are out of their minds still think, although not the same thoughts. Clearly then, if both are kinds of thought, reality also will be both so and not so.

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It is along this path that the consequences are most difficult; for if those who have the clearest vision of such truth as is possible (and these are they who seek and love it most) hold such opinions and make these pronouncements about the truth, surely those who are trying to be philosophers may well despair; for the pursuit of truth will be chasing birds in the air. Cf. Leutsch and Schneidewin, Paroemiographi Graeci, 2.677.

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But the reason why these men hold this view is that although they studied the truth about reality, they supposed that reality is confined to sensible things, in which the nature of the Indeterminate, i.e. of Being in the sense which we have explained,Aristot. Met. 4.4.28. is abundantly present. (Thus their statements, though plausible, are not true;

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this form of the criticism is more suitable than that which EpicharmusFl. early 5th century; held views partly Pythagorean, partly Heraclitean. applied to Xenophanes.) And further, observing that all this indeterminate substance is in motion, and that no true predication can be made of that which changes, they supposed that it is impossible to make any true statement about that which is in all ways and entirely changeable.

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For it was from this supposition that there blossomed forth the most extreme view of those which we have mentioned, that of the professed followers of Heraclitus, and such as Cratylus held, who ended by thinking that one need not say anything, and only moved his finger; and who criticized Heraclitus for saying that one cannot enter the same river twice,Heraclitus Fr. 41 (Bywater). for he himself held that it cannot be done even once.

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But we shall reply to this theory also that although that which is changeable supplies them, when it changes, with some real ground for supposing that it is not, yet there is something debatable in this; for that which is shedding any quality retains something of that which is being shed, and something of that which is coming to be must already exist.

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And in general if a thing is ceasing to be, there will be something there which is ; and if a thing is coming to be, that from which it comes and by which it is generated must be ; and this cannot go on to infinity. But let us leave this line of argument and remark that quantitative and qualitative change are not the same.

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Let it be granted that there is nothing permanent in respect of quantity; but it is by the form that we recognize everything. And again those who hold the theory that we are attacking deserve censure in that they have maintained about the whole material universe what they have observed in the case of a mere minority of sensible things.

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For it is only the realm of sense around us which continues subject to destruction and generation, but this is a practically negligible part of the whole; so that it would have been fairer for them to acquit the former on the ground of the latter than to condemn the latter on account of the former.

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Further, we shall obviously say to these thinkers too the same as we said some time agoAristot. Met. 4.5.7.; for we must prove to them and convince them that there is a kind of nature that is not moved

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(and yet those who claim that things can at once be and not be are logically compelled to admit rather that all things are at rest than that they are in motion; for there is nothing for them to change into, since everything exists in everything). And as concerning reality, that not every appearance is real, we shall say, first, that indeed the perception, at least of the proper object of a sense, is not false, but the impression we get of it is not the same as the perception.

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And then we may fairly express surprise if our opponents raise the question whether magnitudes and colors are really such as they appear at a distance or close at hand, as they appear to the healthy or to the diseased; and whether heavy things are as they appear to the weak or to the strong; and whether truth is as it appears to the waking or to the sleeping.

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For clearly they do not really believe the latter alternative—at any rate no one, if in the night he thinks that he is at Athens whereas he is really in Africa, starts off to the Odeum.A concert-hall (used also for other purposes) built by Pericles. It lay to the south-east of the Acropolis. And again concerning the future (as indeed Plato saysPlat. Theaet. 171e, 178cff..) the opinion of the doctor and that of the layman are presumably not equally reliable, e.g. as to whether a man will get well or not.

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And again in the case of the senses themselves, our perception of a foreign object and of an object proper to a given sense, or of a kindred object and of an actual object of that sense itself, is not equally reliableAn object of taste is foreign to the sense of sight; a thing may look sweet without tasting sweet. Similarly although the senses of taste and smell (and therefore their objects) are kindred (Aristot. De Sensu 440b 29), in judging tastes the sense of taste is the more reliable.; but in the case of colors sight, and not taste, is authoritative, and in the case of flavor taste, and not sight. But not one of the senses ever asserts at the same time of the same object that it is so and not so.

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Nor even at another time does it make a conflicting statement about the quality, but only about that to which the quality belongs. I mean, e.g., that the same wine may seem, as the result of its own change or of that of one’s body, at one time sweet and at another not; but sweetness, such as it is when it exists, has never yet changed, and there is no mistake about it, and that which is to be sweet is necessarily of such a nature.

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Yet all these theories destroy the possibility of anything’s existing by necessity, inasmuch as they destroy the existence of its essence; for the necessary cannot be in one way and in another; and so if anything exists of necessity, it cannot be both so and not so.

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And in general, if only the sensible exists, without animate things there would be nothing; for there would be no sense-faculty.

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That there would be neither sensible qualities nor sensations is probably trueCf. Aristot. De Anima 425b 25-426b 8.(for these depend upon an effect produced in the percipient), but that the substrates which cause the sensation should not exist even apart from the sensation is impossible.

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For sensation is not of itself, but there is something else too besides the sensation, which must be prior to the sensation; because that which moves is by nature prior to that which is moved, and this is no less true if the terms are correlative.

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But there are some, both of those who really hold these convictions and of those who merely profess these views, who raise a difficulty; they inquire who is to judge of the healthy man, and in general who is to judge rightly in each particular case. But such questions are like wondering whether we are at any given moment asleep or awake;

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and all problems of this kind amount to the same thing. These people demand a reason for everything. They want a starting-point, and want to grasp it by demonstration; while it is obvious from their actions that they have no conviction. But their case is just what we have stated beforeAristot. Met. 4.4.2.; for they require a reason for things which have no reason, since the starting-point of a demonstration is not a matter of demonstration.

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The first class, then, may be readily convinced of this, because it is not hard to grasp. But those who look only for cogency in argument look for an impossibility, for they claim the right to contradict themselves, and lose no time in doing so.

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Yet if not everything is relative, but some things are self-existent, not every appearance will be true; for an appearance is an appearance to someone. And so he who says that all appearances are true makes everything relative.

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Hence those who demand something cogent in argument, and at the same time claim to make out a case, must guard themselves by saying that the appearance is true; not in itself, but for him to whom it appears, and at, the time when it appears, and in the way and manner in which it appears. And if they make out a case without this qualification, as a result they will soon contradict themselves;

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for it is possible in the case of the same man for a thing to appear honey to the sight, but not to the taste, and for things to appear different to the sight of each of his two eyes, if their sight is unequal. For to those who assert (for the reasons previously stated Aristot. Met. 4.5.7-17. ) that appearances are true, and that all things are therefore equally false and true, because they do not appear the same to all, nor always the same to the same person, but often have contrary appearances at the same time

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(since if one crosses the fingers touch says that an object is two, while sight says that it is only oneCf. Aristot. Problemata 958b 14, 959a 5, 965a 36.), we shall say but not to the same sense or to the same part of it in the same way and at the same time; so that with this qualification the appearance will be true. But perhaps it is for this reason that those who argue not from a sense of difficulty but for argument’s sake are compelled to say that the appearance is not true in itself, but true to the percipient;

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and, as we have said before, are compelled also to make everything relative and dependent upon opinion and sensation, so that nothing has happened or will happen unless someone has first formed an opinion about it; otherwise clearly all things would not be relative to opinion.

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Further, if a thing is one, it is relative to one thing or to something determinate. And if the same thing is both a half and an equal, yet the equal is not relative to the double.

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If to the thinking subject man and the object of thought are the same, man will be not the thinking subject but the object of thought; and if each thing is to be regarded as relative to the thinking subject, the thinking subject will be relative to an infinity of specifically different things.

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That the most certain of all beliefs is that opposite statements are not both true at the same time, and what follows for those who maintain that they are true, and why these thinkers maintain this, may be regarded as adequately stated. And since the contradiction of a statement cannot be true at the same time of the same thing, it is obvious that contraries cannot apply at the same time to the same thing.

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For in each pair of contraries one is a privation no less than it is a contrary—a privation of substance. And privation is the negation of a predicate to some defined genus. Therefore if it is impossible at the same time to affirm and deny a thing truly, it is also impossible for contraries to apply to a thing at the same time; either both must apply in a modified sense, or one in a modified sense and the other absolutely.

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Nor indeed can there be any intermediate between contrary statements, but of one thing we must either assert or deny one thing, whatever it may be. This will be plain if we first define truth and falsehood. To say that what is is not, or that what is not is, is false; but to say that what is is, and what is not is not, is true; and therefore also he who says that a thing is or is not will say either what is true or what is false.

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But neither what is nor what is not is said not to be or to be. Further, an intermediate between contraries will be intermediate either as grey is between black and white, or as neither man nor horse is between man and horse. If in the latter sense, it cannot change (for change is from not-good to good, or from good to not-good);

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but in fact it is clearly always changing; for change can only be into the opposite and the intermediate. And if it is a true intermediate, in this case too there would be a kind of change into white not from not-white; but in fact this is not seen.It is not qua grey (i.e. intermediate between white and black) that grey changes to white, but qua not-white (i.e. containing a certain proportion of black). Further, the understanding either affirms or denies every object of understanding or thought (as is clear from the definitionAristot. Met. 4.7.1.)

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whenever it is right or wrong. When, in asserting or denying, it combines the predicates in one way, it is right; when in the other, it is wrong.

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Again, unless it is maintained merely for argument’s sake, the intermediate must exist beside all contrary terms; so that one will say what is neither true nor false. And it will exist beside what is and what is not; so that there will be a form of change beside generation and destruction.

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Again, there will also be an intermediate in all classes in which the negation of a term implies the contrary assertion; e.g., among numbers there will be a number which is neither odd nor not-odd. But this is impossible, as is clear from the definition.What definition Aristotle had in mind we cannot tell; but it must have stated that every number is either even or odd.

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Again, there will be an infinite progression, and existing things will be not only half as many again, but even more.

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For again it will be possible to deny the intermediate in reference both to its assertion and to its negation, and the result will be somethingIf besides A and not-A there is an intermediate B, besides B and not-B there will be an intermediate C which is neither B nor not-B; and so on.; for its essence is something distinct.

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Again, when a man is asked whether a thing is white and says no, he has denied nothing except that it is <white>, and its not-being <white> is a negation.

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Now this view has occurred to certain people in just the same way as other paradoxes have also occurred; for when they cannot find a way out from eristic arguments, they submit to the argument and admit that the conclusion is true. Some, then, hold the theory for this kind of reason, and others because they require an explanation for everything. In dealing with all such persons the starting-point is from definition;

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and definition results from the necessity of their meaning something; because the formula, which their term implies, will be a definition.Cf. Aristot. Met. 4.4.5, 6. The doctrine of Heraclitus, which says that everything is and is not,Cf. Aristot. Met. 4.3.10. seems to make all things true; and that of AnaxagorasCf. Aristot. Met. 4.4.28. seems to imply an intermediate in contradiction, so that all things are false; for when things are mixed, the mixture is neither good nor not-good; and so no statement is true.

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It is obvious from this analysis that the one-sided and sweeping statements which some people make cannot be substantially true—some maintaining that nothing is true (for they say that there is no reason why the same rule should not apply to everything as applies to the commensurability of the diagonal of a squareA stock example of impossibility and falsity; see Index.), and some that everything is true.

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These theories are almost the same as that of Heraclitus. For the theory which says that all things are true and all false also makes each of these statements separately; so that if they are impossible in combination they are also impossible individually. And again obviously there are contrary statements, which cannot be true at the same time. Nor can they all be false, although from what we have said, this might seem more possible.

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But in opposing all such theories we must demand, as was said in our discussion above,Aristot. Met. 4.4.5. not that something should be or not be, but some significant statement; and so we must argue from a definition, having first grasped what falsehood or truth means. And if to assert what is true is nothing else than to deny what is false, everything cannot be false; for one part of the contradiction must be true.

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Further, if everything must be either asserted or denied, both parts cannot be false; for one and only one part of the contradiction is false. Indeed, the consequence follows which is notorious in the case of all such theories, that they destroy themselves;

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for he who says that everything is true makes the opposite theory true too, and therefore his own untrue (for the opposite theory says that his is not true); and he who says that everything is false makes himself a liar.

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And if they make exceptions, the one that the opposite theory alone is not true, and the other that his own theory alone is not false, it follows none the less that they postulate an infinite number of true and false statements. For the statement that the true statement is true is also true; and this will go on to infinity.

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Nor, as is obvious, are those right who say that all things are at rest; nor those who say that all things are in motion. For if all things are at rest, the same things will always be true and false, whereas this state of affairs is obviously subject to change; for the speaker himself once did not exist, and again he will not exist. And if all things are in motion, nothing will be true, so everything will be false; but this has been proved to be impossible.

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Again, it must be that which is that changes, for change is from something into something. And further, neither is it true that all things are at rest or in motion sometimes, but nothing continuously; for there is something The sphere of the fixed stars; cf. Aristot. Met. 12.6, 12.7.1, 12.8.18. which always moves that which is moved, and the prime mover is itself unmoved.Cf. Aristot. Met. 12.7.

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Beginningἀρχή means starting-point, principle, rule or ruler. means: (a) That part of a thing from which one may first move; eg., a line or a journey has one beginning here , and another at the opposite extremity. (b) The point from which each thing may best come into being; e.g., a course of study should sometimes be begun not from what is primary or from the starting-point of the subject, but from the point from which it is easiest to learn. (c) That thing as a result of whose presence something first comes into being; e.g., as the keel is the beginning of a ship, and the foundation that of a house, and as in the case of animals some thinkers suppose the heartThis was Aristotle’s own view,Aristot. De Gen. An. 738b 16. to be the beginning, others the brain,So Plato held,Plat. Tim. 44 d. and others something similar, whatever it may be. (d) That from which, although not present in it, a thing first comes into being, and that from which motion and change naturally first begin, as the child comes from the father and mother, and fighting from abuse. (e) That in accordance with whose deliberate choice that which is moved is moved, and that which is changed is changed; such as magistracies, authorities, monarchies and despotisms.

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(f) Arts are also called beginnings,As directing principles. especially the architectonic arts. (g) Again, beginning means the point from which a thing is first comprehensible, this too is called the beginning of the thing; e.g. the hypotheses of demonstrations. (Cause can have a similar number of different senses, for all causes are beginnings. )

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It is a common property, then, of all beginnings to be the first thing from which something either exists or comes into being or becomes known; and some beginnings are originally inherent in things, while others are not. Hence nature is a beginning, and so is element and understanding and choice and essence and final cause—for in many cases the Good and the Beautiful are the beginning both of knowledge and of motion.

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Cause means: (a) in one sense, that as the result of whose presence something comes into being—e.g. the bronze of a statue and the silver of a cup, and the classessc. of material—metal, wood, etc. which contain these; (b) in another sense, the form or pattern; that is, the essential formula and the classes which contain it—e.g. the ratio 2:1 and number in general is the cause of the octave—and the parts of the formula.

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(c) The source of the first beginning of change or rest; e.g. the man who plans is a cause, and the father is the cause of the child, and in general that which produces is the cause of that which is produced, and that which changes of that which is changed. (d) The same as end; i.e. the final cause; e.g., as the end of walking is health.

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For why does a man walk? To be healthy, we say, and by saying this we consider that we have supplied the cause. (e) All those means towards the end which arise at the instigation of something else, as, e.g. fat-reducing, purging, drugs and instruments are causes of health; for they all have the end as their object, although they differ from each other as being some instruments, others actions.

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These are roughly all the meanings of cause, but since causes are spoken of with various meanings, it follows that there are several causes (and that not in an accidental sense) of the same thing. E.g., both statuary and bronze are causes of the statue; not in different connections, but qua statue. However, they are not causes in the same way, but the one as material and the other as the source of motion. And things are causes of each other; as e.g. labor of vigor, and vigor of labor—but not in the same way; the one as an end , and the other as source of motion .

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And again the same thing is sometimes the cause of contrary results; because that which by its presence is the cause of so-and-so we sometimes accuse of being, by its absence, the cause of the contrary—as, e.g., we say that the absence of the pilot is the cause of a capsize, whereas his presence was the cause of safety.

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And both, presence and privation, are moving causes.

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Now there are four senses which are most obvious under which all the causes just described may be classed.

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The components of syllables; the material of manufactured articles; fire, earth and all such bodies; the parts of a whole; and the premisses of a syllogistic conclusion; are causes in the material sense. Of these some are causes as substrate: e.g. the parts; and others as essence : the whole, and the composition, and the form.

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The seed and the physician and the contriver and in general that which produces, all these are the source of change or stationariness. The remainder represent the end and good of the others; for the final cause tends to be the greatest good and end of the rest.

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Let it be assumed that it makes no difference whether we call it good or apparent good. In kind , then, there are these four classes of cause.

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The modes of cause are numerically many, although these too are fewer when summarized.

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For causes are spoken of in many senses, and even of those which are of the same kind, some are causes in a prior and some in a posterior sense; e.g., the physician and the expert are both causes of health; and the ratio 2:1 and number are both causes of the octave; and the universals which include a given cause are causes of its particular effects.

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Again, a thing may be a cause in the sense of an accident, and the classes which contain accidents; e.g., the cause of a statue is in one sense Polyclitus and in another a sculptor, because it is an accident of the sculptor to be Polyclitus. And the universal terms which include accidents are causes; e.g., the cause of a statue is a man, or even, generally, an animal; because Polyclitus is a man, and man is an animal.

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And even of accidental causes some are remoter or more proximate than others; e.g., the cause of the statue might be said to be white man or cultured man, and not merely Polyclitus or man.

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And besides the distinction of causes as proper and accidental , some are termed causes in a potential and others in an actual sense; e.g., the cause of building is either the builder or the builder who builds.

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And the same distinctions in meaning as we have already described will apply to the effects of the causes; e.g. to this statue, or a statue, or generally an image; and to this bronze, or bronze, or generally material.Effects, just like causes (10), may be particular or general. The metal-worker produces (a) the bronze for a particular statue by the sculptor, (b) bronze for a statue, (c) metal for an image. And it is the same with accidental effects. Again, the proper and accidental senses will be combined; e.g., the cause is neither Polyclitus nor a sculptor but the sculptor Polyclitus.

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However, these classes of cause are in all six in number, each used in two senses. Causes are (1.) particular, (2.) generic, (3.) accidental, (4.) generically accidental; and these may be either stated singly or (5, 6) in combinationThe cause of a statue may be said to be (1) a sculptor, (2) an artist, (3) Polyclitus, (4) a man, (5) the sculptor Polyclitus (combination of (1) and (3)), (6) an artistic man (combination of (2) and (4)).; and further they are all either actual or potential.

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And there is this difference between them, that actual and particular causes coexist or do not coexist with their effects (e.g. this man giving medical treatment with this man recovering his health, and this builder with this building in course of erection); but potential causes do not always do so; for the house and the builder do not perish together.

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Element means (a) the primary immanent thing, formally indivisible into another form, of which something is composed. E.g., the elements of a sound are the parts of which that sound is composed and into which it is ultimately divisible, and which are not further divisible into other sounds formally different from themselves. If an element be divided, the parts are formally the same as the whole: e.g., a part of water is water; but it is not so with the syllable.

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(b) Those who speak of the elements of bodies similarly mean the parts into which bodies are ultimately divisible, and which are not further divisible into other parts different in form. And whether they speak of one such element or of more than one, this is what they mean.

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(c) The term is applied with a very similar meaning to the elements of geometrical figures, and generally to the elements of demonstrations; for the primary demonstrations which are contained in a number of other demonstrations are called elements of demonstrations.Cf. Aristot. Met. 3.3.1. Such are the primary syllogisms consisting of three terms and with one middle term.

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(d) The term element is also applied metaphorically to any small unity which is useful for various purposes; and so that which is small or simple or indivisible is called an element.

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(e) Hence it comes that the most universal things are elements; because each of them, being a simple unity, is present in many things—either in all or in as many as possible. Some too think that unity and the point are first principles.

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(f) Therefore since what are called generaThis must refer to the highest genera, which have no definition because they cannot be analyzed into genus and differentia ( Ross). are universal and indivisible (because they have no formula), some people call the genera elements, and these rather than the differentia, because the genus is more universal. For where the differentia is present, the genus also follows; but the differentia is not always present where the genus is. And it is common to all cases that the element of each thing is that which is primarily inherent in each thing.

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NatureOn the meaning of φύσις cf. Burnet, E.G.P. pp. 10-12, 363-364. means: (a) in one sense, the genesis of growing things—as would be suggested by pronouncing the υ of φύσις long—and (b) in another, that immanent thingProbably the seed (Bonitz). from which a growing thing first begins to grow. (c) The source from which the primary motion in every natural object is induced in that object as such. All things are said to grow which gain increase through something else by contact and organic unity (or adhesion, as in the case of embryos).

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Organic unity differs from contact; for in the latter case there need be nothing except contact, but in both the things which form an organic unity there is some one and the same thing which produces, instead of mere contact, a unity which is organic, continuous and quantitative (but not qualitative).

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Again, nature means (d) the primary stuff, shapeless and unchangeable from its own potency, of which any natural object consists or from which it is produced; e.g., bronze is called the nature of a statue and of bronze articles, and wood that of wooden ones, and similarly in all other cases.

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For each article consists of these natures, the primary material persisting. It is in this sense that men call the elements of natural objects the nature, some calling it fire, others earth or air or water, others something else similar, others some of these, and others all of them.

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Again in another sense nature means (e) the substance of natural objects; as in the case of those who say that the nature is the primary composition of a thing, or as Empedocles says: Of nothing that exists is there nature, but only mixture and separation of what has been mixed; nature is but a name given to these by men.Empedocles Fr. 8 (Diels).

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Hence as regards those things which exist or are produced by nature, although that from which they naturally are produced or exist is already present, we say that they have not their nature yet unless they have their form and shape.

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That which comprises both of these exists by nature; e.g. animals and their parts. And nature is both the primary matter (and this in two senses: either primary in relation to the thing, or primary in general; e.g., in bronze articles the primary matter in relation to those articles is bronze, but in general it is perhaps water—that is if all things which can be melted are water) and the form or essence, i.e. the end of the process, of generation. Indeed from this sense of nature, by an extension of meaning, every essence in general is called nature, because the nature of anything is a kind of essence.

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From what has been said, then, the primary and proper sense of nature is the essence of those things which contain in themselves as such a source of motion; for the matter is called nature because it is capable of receiving the nature, and the processes of generation and growth are called nature because they are motions derived from it. And nature in this sense is the source of motion in natural objects, which is somehow inherent in them, either potentially or actually.

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Necessary means: (a) That without which, as a concomitant condition, life is impossible; e.g. respiration and food are necessary for an animal, because it cannot exist without them. (b) The conditions without which good cannot be or come to be, or without which one cannot get rid or keep free of evil—e.g., drinking medicine is necessary to escape from ill-health, and sailing to Aegina is necessary to recover one’s money.

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(c) The compulsory and compulsion; i.e. that which hinders and prevents, in opposition to impulse and purpose. For the compulsory is called necessary, and hence the necessary is disagreeable; as indeed EvenusOf Poros; sophist and poet, contemporary with Socrates. says: For every necessary thing is by nature grievous. Evenus Fr. 8 (Hiller).

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And compulsion is a kind of necessity, as Sophocles says: Compulsion makes me do this of necessity. Soph. El. 256 (the quotation is slightly inaccurate).

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And necessity is held, rightly, to be something inexorable; for it is opposed to motion which is in accordance with purpose and calculation. (d) Again, what cannot be otherwise we say is necessarily so.

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It is from this sense of necessary that all others are somehow derived; for the term compulsory is used of something which it is necessary for one to do or suffer only when it is impossible to act according to impulse, because of the compulsion: which shows that necessity is that because of which a thing cannot be otherwise; and the same is true of the concomitant conditions of living and of the good. For when in the one case good, and in the other life or existence, is impossible without certain conditions, these conditions are necessary, and the cause is a kind of necessity.

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(e) Again, demonstration is a necessary thing, because a thing cannot be otherwise if the demonstration has been absolute. And this is the result of the first premisses, when it is impossible for the assumptions upon which the syllogism depends to be otherwise.

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Thus of necessary things, some have an external cause of their necessity, and others have not, but it is through them that other things are of necessity what they are.

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Hence the necessary in the primary and proper sense is the simple , for it cannot be in more than one condition. Hence it cannot be in one state and in another; for if so it would ipso facto be in more than one condition. Therefore if there are certain things which are eternal and immutable, there is nothing in them which is compulsory or which violates their nature.

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The term one is used (1.) in an accidental, (2.) in an absolute sense. (1.) In the accidental sense it is used as in the case of CoriscusCoriscus of Scepsis was a Platonist with whom Aristotle was probably acquainted; but the name is of course chosen quite arbitrarily. and cultured and cultured Coriscus (for Coriscus and cultured and cultured Coriscus mean the same);

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and cultured and upright and cultured upright Coriscus. For all these terms refer accidentally to one thing; upright and cultured because they are accidental to one substance, and cultured and Coriscus because the one is accidental to the other.

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And similarly in one sense cultured Coriscus is one with Coriscus, because one part of the expression is accidental to the other, e.g. cultured to Coriscus; and cultured Coriscus is one with upright Coriscus,

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because one part of each expression is one accident of one and the same thing. It is the same even if the accident is applied to a genus or a general term; e.g., man and cultured man are the same, either because cultured is an accident of man, which is one substance, or because both are accidents of some individual, e.g. Coriscus.

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But they do not both belong to it in the same way; the one belongs presumably as genus in the substance, and the other as condition or affection of the substance. Thus all things which are said to be one in an accidental sense are said to be so in this way.

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(2.) Of those things which are said to be in themselves one, (a) some are said to be so in virtue of their continuity; e.g., a faggot is made continuous by its string, and pieces of wood by glue; and a continuous line, even if it is bent, is said to be one, just like each of the limbs; e.g. the leg or arm. And of these things themselves those which are naturally continuous are one in a truer sense than those which are artificially continuous.

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Continuous means that whose motion is essentially one, and cannot be otherwise; and motion is one when it is indivisible, i.e. indivisible in time . Things are essentially continuous which are one not by contact only; for if you put pieces of wood touching one another you will not say that they are one piece of wood, or body, or any other continuous thing.

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And things which are completely continuous are said to be one even if they contain a joint, and still more those things which contain no joint; e.g., the shin or the thigh is more truly one than the leg, because the motion of the leg may not be one.

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And the straight line is more truly one than the bent. We call the line which is bent and contains an angle both one and not one, because it may or may not move all at once; but the straight line always moves all at once, and no part of it which has magnitude is at rest while another moves, as in the bent line.

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(b) Another sense of one is that the substrate is uniform in kind.

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Things are uniform whose form is indistinguishable to sensation; and the substrate is either that which is primary, or that which is final in relation to the end. For wine is said to be one, and water one, as being something formally indistinguishable. And all liquids are said to be one (e.g. oil and wine), and melted things; because the ultimate substrate of all of them is the same, for all these things are water or vapor.

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(c) Things are said to be one whose genus is one and differs in its opposite differentiae. All these things too are said to be one because the genus, which is the substrate of the differentiae, is one (e.g., horse, man and dog are in a sense one, because they are all animals); and that in a way very similar to that in which the matter is one.

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Sometimes these things are said to be one in this sense, and sometimes their higher genus is said to be one and the same (if they are final species of their genus)—the genus, that is, which is above the genera of which their proximate genus is one; e.g., the isosceles and equilateral triangles are one and the same figure (because they are both triangles), but not the same triangles.

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(d) Again, things are said to be one when the definition stating the essence of one is indistinguishable from a definition explaining the other; for in itself every definition is distinguishable <into genus and differentiae>. In this way that which increases and decreases is one, because its definition is one; just as in the case of planes the definition of the form is one.

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And in general those things whose concept, which conceives the essence, is indistinguishable and cannot be separated either in time or in place or in definition, are in the truest sense one; and of these such as are substances are most truly one. For universally such things as do not admit of distinction are called one in so far as they do not admit of it; e.g., if man qua man does not admit of distinction, he is one man; and similarly if qua animal, he is one animal; and if qua magnitude, he is one magnitude.

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Most things, then, are said to be one because they produce, or possess, or are affected by, or are related to, some other one thing; but some are called one in a primary sense, and one of these is substance. It is one either in continuity or in form or in definition; for we reckon as more than one things which are not continuous, or whose form is not one, or whose definition is not one.

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Again, in one sense we call anything whatever one if it is quantitative and continuous; and in another sense we say that it is not one unless it is a whole of some kind, i.e. unless it is one in form (e.g., if we saw the parts of a shoe put together anyhow, we should not say that they were one — except in virtue of their continuity; but only if they were so put together as to be a shoe, and to possess already some one form).

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Hence the circumference of a circle is of all lines the most truly one, because it is whole and complete.

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The essence of one is to be a kind of starting point of number; for the first measure is a starting point, because that by which first we gain knowledge of a thing is the first measure of each class of objects. The one, then, is the starting-point of what is knowable in respect of each particular thing. But the unit is not the same in all classes,

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for in one it is the quarter-tone, and in another the vowel or consonant; gravity has another unit, and motion another. But in all cases the unit is indivisible, either quantitatively or formally.

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Thus that which is quantitatively and qua quantitative wholly indivisible and has no position is called a unit; and that which is wholly indivisible and has position, a point; that which is divisible in one sense, a line; in two senses, a plane; and that which is quantitatively divisible in all three senses, a body.

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And reversely that which is divisible in two senses is a plane, and in one sense a line; and that which is in no sense quantitatively divisible is a point or a unit; if it has no position, a unit, and if it has position, a point.

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Again, some things are one numerically, others formally, others generically, and others analogically; numerically, those whose matter is one; formally, those whose definition is one; generically, those which belong to the same category; and analogically, those which have the same relation as something else to some third object.

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In every case the latter types of unity are implied in the former: e.g., all things which are one numerically are also one formally, but not all which are one formally are one numerically; and all are one generically which are one formally, but such as are one generically are not all one formally, although they are one analogically; and such as are one analogically are not all one generically.

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It is obvious also that many will have the opposite meanings to one. Some things are called many because they are not continuous; others because their matter (either primary or ultimate) is formally divisible; others because the definitions of their essence are more than one.

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Being means (1.) accidental being, (2.) absolute being. (1.) E.g., we say that the upright person is cultured, and that the man is cultured, and that the cultured person is a man; very much as we say that the cultured person builds, because the builder happens to be cultured, or the cultured person a builder; for in this sense X is Y means that Y is an accident of X.

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And so it is with the examples cited above; for when we say that the man is cultured and the cultured person is a man or the white is cultured or the cultured is white, in the last two cases it is because both predicates are accidental to the same subject, and in the first case because the predicate is accidental to what is ; and we say that the cultured is a man because the cultured is accidental to a man.

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(Similarly not-white is said to be, because the subject of which not-white is an accident, is .) These, then, are the senses in which things are said to be accidentally: either because both predicates belong to the same subject, which is ; or because the predicate belongs to the subject, which is ; or because the subject to which belongs that of which it is itself predicated itself is .

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(2.) The senses of essential being are those which are indicated by the figures of predicationThe categories. For the full list of these see Aristot. Categories 1b 25-27.; for being has as many senses as there are ways of predication. Now since some predicates indicate (a) what a thing is, and others its (b) quality, (c) quantity, (d) relation, (e) activity or passivity, (f) place, (g) time, to each of these corresponds a sense of being.

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There is no difference between the man is recovering and the man recovers; or between the man is walking or cutting and the man walks or cuts; and similarly in the other cases.

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(3.) Again, to be and is mean that a thing is true, and not to be that it is false.

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Similarly too in affirmation and negation; e.g., in Socrates is cultured is means that this is true; or in Socrates is not-white that this is true; but in the diagonal is not commensurableCf. Aristot. Met. 1.2.15.is not means that the statement is false. (4.) Again, to be <or is> means that some of these statements can be made in virtue of a potentiality and others in virtue of an actuality.

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For we say that both that which sees potentially and that which sees actually is a seeing thing. And in the same way we call understanding both that which can use the understanding, and that which does ; and we call tranquil both that in which tranquillity is already present, and that which is potentially tranquil.

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Similarly too in the case of substances. For we say that Hermes is in the stone,Cf. Aristot. Met. 3.5.6. and the half of the line in the whole; and we call corn what is not yet ripe. But when a thing is potentially existent and when not, must be defined elsewhere.Aristot. Met. 9.9.

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Substance means (a) simple bodies, e.g. earth, fire, water and the like; and in general bodies, and the things, animal or divine, including their parts, which are composed of bodies. All these are called substances because they are not predicated of any substrate, but other things are predicated of them.

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(b) In another sense, whatever, being immanent in such things as are not predicated of a substrate, is the cause of their being; as, e.g., the soul is the cause of being for the animal.

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(c) All parts immanent in things which define and indicate their individuality, and whose destruction causes the destruction of the whole; as, e.g., the plane is essential to the body (as someThe Pythagoreans and Platonists. hold) and the line to the plane. And number in general is thought by someThe Pythagoreans and Platonists. to be of this nature, on the ground that if it is abolished nothing exists, and that it determines everything.

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(d) Again, the essence , whose formula is the definition, is also called the substance of each particular thing.

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Thus it follows that substance has two senses: the ultimate subject, which cannot be further predicated of something else; and whatever has an individual and separate existence. The shape and form of each particular thing is of this nature.

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The same means (a) accidentally the same. E.g., white and cultured are the same because they are accidents of the same subject; and man is the same as cultured, because one is an accident of the other; and cultured is the same as man because it is an accident of man; and cultured man is the same as each of the terms cultured and man, and vice versa; for both man and cultured are used in the same way as cultured man, and the latter in the same way as the former.

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Hence none of these predications can be made universally. For it is not true to say that every man is the same as the cultured; because universal predications are essential to things, but accidental predications are not so, but are made of individuals and with a single application. Socrates and cultured Socrates seem to be the same; but Socrates is not a class-name, and hence we do not say every Socrates as we say every man.

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Some things are said to be the same in this sense, but (b) others in an essential sense, in the same number of senses as the one is essentially one; for things whose matter is formally or numerically one, and things whose substance is one, are said to be the same. Thus sameness is clearly a kind of unity in the being, either of two or more things, or of one thing treated as more than one; as, e.g., when a thing is consistent with itself; for it is then treated as two.

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Things are called other of which either the forms or the matter or the definition of essence is more than one; and in general other is used in the opposite senses to same.

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Things are called different which, while being in a sense the same, are other not only numerically, but formally or generically or analogically; also things whose genus is not the same; and contraries; and all things which contain otherness in their essence.

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Things are called like which have the same attributes in all respects; or more of those attributes the same than different; or whose quality is one. Also that which has a majority or the more important of those attributes of something else in respect of which change is possible (i.e. the contraries) is like that thing. And unlike is used in the opposite senses to like.

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The term opposite is applied to (a) contradiction; (b) contraries; (c) relative terms; (d) privation; (e) state; (f) extremes; e.g. in the process of generation and destruction. And (g) all things which cannot be present at the same time in that which admits of them both are called opposites; either themselves or their constituents. Grey and white do not apply at the same time to the same thing, and hence their constituents are opposite.

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Contrary means: (a) attributes, generically different, which cannot apply at the same time to the same thing. (b) The most different attributes in the same genus; or (c) in the same subject; or (d) falling under the same faculty. (e) Things whose difference is greatest absolutely, or in genus, or in species.

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Other things are called contrary either because they possess attributes of this kind, or because they are receptive of them, or because they are productive of or liable to them, or actually produce or incur them, or are rejections or acquisitions or possessions or privations of such attributes.

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And since one and being have various meanings, all other terms which are used in relation to one and being must vary in meaning with them; and so same, other and contrary must so vary, and so must have a separate meaning in accordance with each category.

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Things are called other in species (a) which belong to the same genus and are not subordinate one to the other; or (b) which are in the same genus and contain a differentia; or (c) which contain a contrariety in their essence.

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(d) Contraries, too (either all of them or those which are called so in a primary sense), are other in species than one another; and (e) so are all things of which the formulae are different in the final species of the genus (e.g., man and horse are generically indivisible, but their formulae are different); and (f) attributes of the same substance which contain a difference. The same in species has the opposite meanings to these.

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Prior and posterior mean: (1.) (a) In one sense (assuming that there is in each genus some primary thing or starting-point) that which is nearer to some starting-point, determined either absolutely and naturally, or relatively, or locally, or by some agency; e.g., things are prior in space because they are nearer either to some place naturally determined, such as the middle or the extreme, or to some chance relation; and that which is further is posterior.

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(b) In another sense, prior or posterior in time . Some things are prior as being further from the present, as in the case of past events (for the Trojan is prior to the Persian war, because it is further distant from the present); and others as being nearer the present, as in the case of future events (for the Nemean are prior to the Pythian games because they are nearer to the present, regarded as a starting-point and as primary).

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(c) In another sense, in respect of motion (for that which is nearer to the prime mover is prior; e.g., the boy is prior to the man). This too is a kind of starting point in an absolute sense. (d) In respect of potency; for that which is superior in potency, or more potent, is prior. Such is that in accordance with whose will the other, or posterior, thing must follow, so that according as the former moves or does not move, the latter is or is not moved. And the will is a starting-point.

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(e) In respect of order; such are all things which are systematically arranged in relation to some one determinate object. E.g., he who is next to the leader of the chorus is prior to him who is next but one, and the seventh string is prior to the eighthThe octachord to which Aristotle refers was composed of the following notes: E (ὑπάτη ) F (παρυπάτη) G (λιχανός) A (μέση) B (παραμέση) C (τρίτη) D (παρανήτη) E (νήτη).; for in one case the leader is the starting-point, and in the other the middleStrictly speaking there was no middle string in the octachord; the name was taken over from the earlier heptachord EFGABbCD, in which there was no παραμέση. The μέση was apparently what we should call the tonic. Cf. Aristot. Met. 14.6.5; Aristot. Problemata 919b 20. string.

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In these examples prior has this sense; but (2.) in another sense that which is prior in knowledge is treated as absolutely prior; and of things which are prior in this sense the prior in formula are different from the prior in perception . Universals are prior in formula, but particulars in perception. And in formula the attribute is prior to the concrete whole: e.g. cultured to the cultured man; for the formula will not be a whole without the part.

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Yet cultured cannot exist apart from some cultured person.

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Again, (3.) attributes of prior subjects are called prior; e.g., straightness is prior to smoothness, because the former is an attribute of the line in itself, and the latter of a surface.

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Some things, then, are called prior and posterior in this sense; but others (iv.) in virtue of their nature and substance, namely all things which can exist apart from other things, whereas other things cannot exist without them. This distinction was used by Plato.Not, apparently, in his writings.(And since being has various meanings, (a) the substrate, and therefore substance, is prior; (b) potential priority is different from actual priority.

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Some things are prior potentially, and some actually; e.g., potentially the half-line is prior to the whole, or the part to the whole, or the matter to the substance; but actually it is posterior, because it is only upon dissolution that it will actually exist.)

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Indeed, in a sense all things which are called prior or posterior are so called in this connection; for some things can exist apart from others in generation (e.g. the whole without the parts), and others in destruction (e.g. the parts without the whole). And similarly with the other examples.

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PotencyOr capacity or potentiality. means: (a) the source of motion or change which is in something other than the thing changed, or in it qua other. E.g., the science of building is a potency which is not present in the thing built; but the science of medicine, which is a potency, may be present in the patient, although not qua patient.

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Thus potency means the source in general of change or motion in another thing, or in the same thing qua other; or the source of a thing’s being moved or changed by another thing, or by itself qua other (for in virtue of that principle by which the passive thing is affected in any way we call it capable of being affected; sometimes if it is affected at all, and sometimes not in respect of every affection, but only if it is changed for the better).

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(b) The power of performing this well or according to intention; because sometimes we say that those who can merely take a walk, or speak, without doing it as well as they intended, cannot speak or walk. And similarly in the case of passivity.

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(c) All states in virtue of which things are unaffected generally, or are unchangeable, or cannot readily deteriorate, are called potencies. For things are broken and worn out and bent and in general destroyed not through potency but through impotence and deficiency of some sort; and things are unaffected by such processes which are scarcely or slightly affected because they have a potency and are potent and are in a definite state.

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Since potency has all these meanings, potent (or capable) will mean (a) that which contains a source of motion or change (for even what is static is potent in a sense) which takes place in another thing, or in itself qua other. (b) That over which something else has a potency of this kind. (c) That which has the potency of changing things, either for the worse or for the better (for it seems that even that which perishes is capable of perishing; otherwise, if it had been incapable, it would not have perished. As it is, it has a kind of disposition or cause or principle which induces such an affection.

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Sometimes it seems to be such as it is because it has something, and sometimes because it is deprived of something; but if privation is in a sense a state or habit, everything will be potent through having something; and so a thing is potent in virtue of having a certain habit or principle, and also in virtue of having the privation of that habit, if it can have privation; and if privation is not in a sense habit, the term potent is equivocal).

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(d) A thing is potent if neither any other thing nor itself qua other contains a potency or principle destructive of it. (e) All these things are potent either because they merely might chance to happen or not to happen, or because they might do so well . Even in inanimate things this kind of potency is found; e.g. in instruments; for they say that one lyre can be played, and another not at all, if it has not a good tone.

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Impotence is a privation of potency—a kind of abolition of the principle which has been described—either in general or in something which would naturally possess that principle, or even at a time when it would naturally already possess it (for we should not use impotence—in respect of begetting—in the same sense of a boy, a man and a eunuch). Again, there is an impotence corresponding to each kind of potency; both to the kinetic and to the successfully kinetic.

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Some things are said to be impotent in accordance with this meaning of impotence, but others in a different sense, namely possible and impossible. Impossible means: (a) that whose contrary is necessarily true; e.g., it is impossible that the diagonal of a square should be commensurable with the sides, because such a thing is a lie, whose contrary is not only true but inevitable. Hence that it is commensurable is not only a lie but necessarily a lie.

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And the contrary of the impossible, i.e. the possible, is when the contrary is not necessarily a lie; e.g., it is possible that a man should be seated, for it is not necessarily a lie that he should not be seated. Possible, then, means in one sense, as we have said, that which is not necessarily a lie; in another, that which is true; and in another, that which may be true.

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(The power in geometryA square was called a δύναμις. Plat. Rep 587d; Plat. Tim. 31c. is so called by an extension of meaning.)

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These are the senses of potent which do not correspond to potency. Those which do correspond to it all refer to the first meaning, i.e. a source of change which exists in something other than that in which the change takes place, or in the same thing qua other.

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Other things are said to be potentsc. in a passive sense, which the English word potent cannot bear. because something else has such a potency over them; others because it does not possess it; others because it possesses it in a particular way. The term impotent is similarly used. Thus the authoritative definition of potency in the primary sense will be a principle producing change, which is in something other than that in which the change takes place, or in the same thing qua other.

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Quantity means that which is divisible into constituent parts, eachi.e., if there are only two. or every one of which is by nature some one individual thing. Thus plurality, if it is numerically calculable, is a kind of quantity; and so is magnitude, if it is measurable. Plurality means that which is potentially divisible into non-continuous parts; and magnitude that which is potentially divisible into continuous parts. Of kinds of magnitude, that which is continuous in one direction is length; in two directions, breadth; in three, depth.

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And of these, plurality, when limited, is a number; length, a line; breadth, a plane; depth, a body. Again, some things are essentially quantitative, but others only accidentally; e.g. the line is essentially, but cultured accidentally quantitative.

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And of the former class some are quantitative in virtue of their substance, e.g. the fine (because the definition which describes it is quantitative in some form); and others are attributes and conditions of a substance of this kind— e.g., much and little, long and short, broad and narrow, deep and shallow, heavy and light, etc.

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Moreover, great and small, and greater and smaller, whether used absolutely or relatively to one another, are essential attributes of quantity; by an extension of meaning, however, these terms are also applied to other things.

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Of things called quantitative in an accidental sense, one kind is so called in the sense in which we said above that cultured or white is quantitative—because the subject to which they belong is quantitative; and others in the sense that motion and time are so called—for these too are said in a sense to be quantitative and continuous, since the subjects of which they are attributes are divisible. I mean, not the thing moved, but that through or along which the motion has taken place; for it is because the latter is quantitative that the motion is quantitative, and because the motion is quantitative that the time is also.

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Quality means (a) in one sense, the differentia of essence; e.g., a man is an animal of a certain quality because he is two-footed; and so is a horse, because it is four-footed. Also a circle is a geometrical figure of a certain quality, because it has no angles; which shows that the essential differentia is quality.

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In this one sense, then, quality means differentia of essence; but (b) in another it is used as of immovable and mathematical objects, in the sense that numbers are in a way qualitative—e.g. such as are composite and are represented geometrically not by a line but by a plane or solid (these are products respectively of two and of three factors)—and in general means that which is present besides quantity in the essence. For the essence of each number is that which goes into it once; e.g. that of 6 is not what goes twice or three times, but what goes once; for 6 is once 6.

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(c) All affections of substance in motion in respect of which bodies become different when they (the affections) change—e.g. heat and cold, whiteness and blackness, heaviness and lightness, etc. (d) The term is used with reference to goodness and badness, and in general to good and bad.

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Thus there are, roughly speaking, two meanings which the term quality can bear, and of these one is more fundamental than the other. Quality in the primary sense is the differentia of the essence; and quality in numbers falls under this sense, because it is a kind of differentia of essences, but of things either not in motion or not qua in motion. Secondly, there are the affections of things in motion qua in motion, and the differentiae of motions.

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Goodness and badness fall under these affections, because they denote differentiae of the motion or functioning in respect of which things in motion act or are acted upon well or badly. For that which can function or be moved in such-and-such a way is good, and that which can function in such-and-such a way and in the contrary way is bad. Quality refers especially to good and bad in the case of living things, and of these especially in the case of such as possess choice.

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Things are called relative (a) In the sense that the double is relative to the half, and the triple to the third; and in general the many times greater to the many times smaller, and that which exceeds to the thing exceeded. (b) In the sense that the thing which heats or cuts is relative to the thing heated or cut; and in general the active to the passive. (c) In the sense that the measurable is relative to the measure, and the knowable to knowledge, and the sensible to sensation.

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(a) In the first sense they are said to be numerically relative; either simply, or in a definite relation to numbers or to 1. E.g., the double in relation to 1 is a definite number; the many times as great is in a numerical relation to 1, but not in a definite relation such as this or that;

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the relation of that which is 1.5 times something else to that something is a definite numerical relation to a number; and that which is (n+1)/n times something else is in an indefinite relation to a number, just as the many times as great is in an indefinite relation to 1.

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The relation of that which exceeds to that which is exceeded is numerically quite indefinite, for number is commensurate, and is not predicated of the incommensurate; whereas that which exceeds, in relation to that which is exceeded, is so much plus something more; and this something more is indefinite, for it is indifferently equal or not equal to the so much.

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Thus not only are all these things said to be relative in respect of number, but also the equal and like and same, though in another way: for all these terms are used in respect of one. Things are the same whose essence is one; like whose quality is one; equal whose quantity is one. Now one is the starting-point and standard of number; and so all these relations involve number, though not all in the same way.

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(b) Active and passive things are called relative in virtue of an active or passive potentiality or actualization of the potentialities; e.g., that which can heat is called relative to that which can be heated, because it can heat; and again the thing heating is called relative to the thing heated, and the thing cutting to the thing cut, because their potentialities are actualized. Numerical relations, on the other hand, are not actualized (except as has been described elsewhere)The reference is quite uncertain, but cf. Aristot. Met. 9.9.4, 5. The point is that the actualization of a numerical (or geometrical) relation does not imply an active functioning, as in the case of the potentialities just described.; they have no actualizations in respect of motion.

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Of things potentially relative, some are further relative in respect of particular times; as, e.g., that which has made or will make is relative to that which has been or will be made. It is in this way that a father is called father of a son; the one has acted, and the other has been acted upon, in a particular way. Again, some things are relative in virtue of a privation of their potentiality; such is the impossible and all similar terms, e.g. the invisible.

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Thus relative terms which involve number and potentiality are all relative because their very essence contains a reference to something else; but not because something else is related to their essence. But (c) that which is measurable or knowable or thinkable is called relative because something else is related to its essence.

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For thinkable signifies that there is a thought which thinks it; but thought is not relative to that of which it is the thought (for then the same thing would have been said twice). And similarly sight is the sight of something; not of that of which it is the sight, although this is of course true—it is relative to some color or other similar thing.

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To describe it in the other way—the sight of the object of sight—would be to say the same thing twice. Things, then, which are called relative of their own nature are so called, some in these senses, and others because the classes which contain them are of this kind. E.g., medicine is reckoned as relative because its genus, science, is thought to be a relative thing.

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Further, there are the properties in virtue of which the things which possess them are called relative; e.g., equality is relative because the equal is relative, and similarity because the similar is relative. Other things are accidentally relative; e.g., a man is relative because he happens to be double something else, and double is a relative term; or white is relative if the same thing happens to be white as well as double.

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Perfect <or complete> means: (a) That outside which it is impossible to find even a single one of its parts; e.g., the complete time of each thing is that outside which it is impossible to find any time which is a part of it. (b) That which, in respect of goodness or excellence, cannot be surpassed in its kind; e.g., a doctor and a musician are perfect when they have no deficiency in respect of the form of their peculiar excellence.

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And thus by an extension of the meaning we use the term in a bad connection, and speak of a perfect humbug and a perfect thief; since indeed we call them good— e.g. a good thief and a good humbug.

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(c) And goodness is a kind of perfection. For each thing, and every substance, is perfect when, and only when, in respect of the form of its peculiar excellence, it lacks no particle of its natural magnitude. (d) Things which have attained their end, if their end is good, are called perfect; for they are perfect in virtue of having attained the end.

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Hence, since the end is an ultimate thing, we extend the meaning of the term to bad senses, and speak of perishing perfectly or being perfectly destroyed, when the destruction or calamity falls short in no respect but reaches its extremity. Hence, by an extension of the meaning, death is called an end, because they are both ultimate things. And the ultimate object of action is also an end.

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Things, then, which are called perfect in themselves are so called in all these senses; either because in respect of excellence they have no deficiency and cannot be surpassed, and because no part of them can be found outside them; or because, in general, they are unsurpassed in each particular class, and have no part outside. All other things are so called in virtue of these, because they either produce or possess something of this kind, or conform to it, or are referred in some way or other to things which are perfect in the primary sense.

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Limit means: (a) The furthest part of each thing, and the first point outside which no part of a thing can be found, and the first point within which all parts are contained. (b) Any form of magnitude or of something possessing magnitude.

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(c) The end of each thing. (This end is that to which motion and action proceed, and not the end from which. But sometimes it is both the end from which and the end to which, i.e. the final cause.) (d) The reality or essence of each thing; for this is the limit of our knowledge of it, and if it is a limit of the knowledge, it is also a limit of the thing. Thus it is obvious that limit has not only as many senses as beginning but even more; because the beginning is a kind of limit, but not every limit is a beginning.

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That in virtue of which has various meanings. (a) The form or essence of each individual thing; e.g., that in virtue of which a man is good is goodness itself. (b) The immediate substrate in which a thing is naturally produced; as, e.g., color is produced in the surface of things. Thus that in virtue of which in the primary sense is the form , and in the secondary sense, as it were, the matter of each thing, and the immediate substrate.

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And in general that in virtue of which will exist in the same number of senses as cause. For we say indifferently in virtue of what has he come? or for what reason has he come? and in virtue of what has he inferred or inferred falsely? or what is the cause of his inference or false inference? (And further, there is the positional sense of καθ’ ὅ, in which he stands, or in which he walks; all these examples denote place or position.)

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Hence in virtue of itself must also have various meanings. It denotes (a) The essence of each particular; e.g., Callias is in virtue of himself Callias and the essence of Callias. (b) Everything contained in the definition; e.g., Callias is in virtue of himself an animal, because animal is present in the definition, since Callias is a kind of animal.

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(c) Any attribute which a thing has received directly in itself or in any of its parts; e.g., the surface is white in virtue of itself; and man lives in virtue of himself, because the soul is a part of the man, and life is directly contained in it. (d) That which has no other cause. Man has many causes: animal, twofooted, etc.; but nevertheless man is in virtue of himself man. (e) All things which belong to a thing alone and qua alone; and hence that which is separate is in virtue of itself. This seems to be a slightly irrelevant reference to καθ’ ἁυτό in the sense of independent; but corruption in the text has made the true reading uncertain.

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Disposition means arrangement of that which has parts, either in space or in potentiality or in form. It must be a kind of position, as indeed is clear from the word, disposition.

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Havingἕξις means not only having but habit or state. Cf. Latin, habitus. means (a) In one sense an activity, as it were, of the haver and the thing had, or as in the case of an action or motion; for when one thing makes and another is made, there is between them an act of making. In this way between the man who has a garment and the garment which is had, there is a having. Clearly, then, it is impossible to have a having in this sense; for there will be an infinite series if we can have the having of what we have.

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But (b) there is another sense of having which means a disposition, in virtue of which the thing which is disposed is disposed well or badly, and either independently or in relation to something else. E.g., health is a state, since it is a disposition of the kind described. Further, any part of such a disposition is called a state; and hence the excellence of the parts is a kind of state.

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Affection means (a) In one sense, a quality in virtue of which alteration is possible; e.g., whiteness and blackness, sweetness and bitterness, heaviness and lightness, etc. (b) The actualizations of these qualities; i.e. the alterations already realized. (c) More particularly, hurtful alterations and motions, and especially hurts which cause suffering. (d) Extreme cases of misfortune and suffering are called affections. The English equivalent for πάθος in this sense would be calamity or disaster.

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We speak of privation: (a) In one sense, if a thing does not possess an attribute which is a natural possession, even if the thing itself would not naturally possess itThis is not a proper sense of privation, as Aristotle implies by choosing an example from everyday speech.; e.g., we say that a vegetable is deprived of eyes. (b) If a thing does not possess an attribute which it or its genus would naturally possess. E.g., a blind man is not deprived of sight in the same sense that a mole is; the latter is deprived in virtue of its genus, but the former in virtue of himself.i.e., a mole is blind as being a member of a blind genus, whereas a man is blind only as an individual. Of course moles are not really blind, but we still speak as though they were.

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(c) If a thing has not an attribute which it would naturally possess, and when it would naturally possess it (for blindness is a form of privation; but a man is not blind at any age, but only if he lacks sight at the age when he would naturally possess itThe qualification refers, I suppose, to the fact that an embryo does not naturally possess sight.), and similarly if itThe subject seems to be indefinite, but no doubt Aristotle is thinking primarily of the particular example which he has just given. A man is not called blind if he does not see in the dark, or if he does not see with his ears, or if he does not see sound, or if he does not see what is behind him or too far away ( Ross). lacks an attribute in the medium and organ and relation and manner in which it would naturally possess it.

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(d) The forcible removal of anything is called privation. (e) Privation has as many senses as there are senses of negation derived from the negative affix (ἀ-). For we call a thing unequal because it does not possess equality (though it would naturally do so); and invisible either because it has no color at all or because it has only a faint one; and footless either because it has no feet at all or because it has rudimentary feet.

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Again, a negative affix may mean having something in a small degree—e.g. stoneless— that is, having it in some rudimentary manner. Again, it may mean having it not easily or not well; e.g., uncutable means not only that which cannot be cut, but that which cannot be cut easily or well. And again, it may mean not having a thing at all; for it is not the one-eyed man, but the man who lacks sight in both eyes, who is called blind. Hence not every man is good or bad, moral or immoral; there is also the intermediate state.

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To have <or possess> is used in various senses. (a) To direct in accordance with one’s own nature or impulse; whence we say that fever possesses a man, and despots possess cities, and people who wear clothes possess them. (b) We speak of anything as having in which, as receptive material, something is present. E.g., the bronze has the shape of the statue, and the body has the disease.

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(c) In the sense that the container holds the contained; for when A is contained in B, we say that A is held by B. E.g., we say that the vessel holds the liquid, and the city holds men, and the ship holds sailors, and so too that the whole holds the parts.

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(d) The same term is applied to that which prevents anything from moving or acting in accordance with its own impulse; as pillars hold <up> the weights which are imposed upon them, and as the poets make AtlasCf. Hes. Th. 517. hold up the heaven, because otherwise it would fall upon the earth (as some of the physicistse.g., Empedocles held that the heavens were kept in place by the velocity of their rotation;Aristot. De Caelo 284a 24, 295a 16 (Ritter and Preller, 170 b). maintain also).

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It is in this sense that we say that that which holds together holds what it holds together; because otherwise the latter would disperse, each part in accordance with its own impulse.

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To be in a thing is used similarly in senses corresponding to those of to have.

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To come from something means: (a) In one sense, to come from something as matter, and this in two ways: in respect either of the primary genus or of the ultimate species. E.g., in the one sense everything liquefiable comes from water, and in the other the statue comes from bronze.

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(b) To come from something as the first moving principle; e.g., from what comes fighting? From abuse; because this is the beginning of a fight. (c) To come from the combination of matter and form (as the parts come from the whole, and the verse from the Iliad , and the stones from the house); for the shape is an end, and that is a complete thing which has attained its end.

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(d) In the sense that the form is made out of the part of its definition; as, e.g., man is made out of two-footed and the syllable out of its elementIn the sense that στοιχεῖον(letter) forms part of the definition of syllable. (this is a different way from that in which the statue is made out of the bronze; for the composite entity is made out of perceptible material, but the form is also made out of the material of the form).

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These, then, are some of the meanings of from <or out of>, but (e) sometimes one of these senses only partially applies; e.g., the child comes from the father and mother, and plants from the earth, because they come from some part of those things. (f) It means after in time; e.g., we say that night comes from day, and storm from fine weather, because one comes after the other.

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And we speak thus of some of these things in view of their alternation with each other, as in the examples just mentioned, and of others in view merely of their succession in time; e.g., the voyage was made from the equinox, meaning that it was made after it; and the Thargelia are from the Dionysia, meaning after the Dionysia.The (city) Dionysia were celebrated in March; the Thargelia (a festival in honor of Apollo and Artemis) at the end of May.

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Part means: (a) That into which a quantity can be in any way divided; for that which is taken from a quantity qua quantity is always called a part of that quantity—e.g., we call 2 part (in a sense) of 3. (b) In another sense the term is only applied to those parts in sense (a) which measure the whole; hence in one sense we call 2 part of 3, and in another not.

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Again, (c) those divisions into which the form, apart from quantity, can be divided, are also called parts of the form. Hence species are called parts of their genus. (d) That into which the whole (either the form or that which contains the form) is divided, or of which it is composed. E.g., of a bronze sphere or cube not only is the bronze

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(i.e. the material which contains the form) a part, but also the angle. (e) The elements in the definition of each thing are also called parts of the whole. Hence the genus is even called a part of the species, whereas in another sense the species is part of the genus.

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Whole means: (a) That from which no part is lacking of those things as composed of which it is called a natural whole. (b) That which so contains its contents that they form a unity; and this in two ways, either in the sense that each of them is a unity, or in the sense that the unity is composed of them.

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For (i) the universal, or term generally applied as being some whole thing, is universal in the sense that it contains many particulars; because it is predicated of each of them, and each and all of them (e.g. man, horse, god) are one; because they are all living things. And (2) that which is continuous and limited is a whole when it is a unity composed of several parts (especially if the parts are only potentially present in it; but otherwise even if they are present actually).

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And of these things themselves, those which are so naturally are more truly wholes than those which are so artificially; just as we said of the one, because wholeness is a kind of oneness. Again, since a quantity has a beginning, middle and end, those to which position makes no difference we describe as all, and those to which position makes a difference we describe as whole, and those to which both descriptions can be applied, as both all and whole.

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These are all things whose nature remains the same in transposition, but whose shape does not; e.g. wax or a coat. They are described as both whole and all; for they have both characteristics. Water, however, and all liquids, and number, are described as all; we do not speak of a whole number or whole water except by an extension of meaning. Things are described as all in the plural qua differentiated which are described as all in the singular qua one; all this number, all these units.

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We do not describe any chance quantity as mutilated; it must have parts, and must be a whole. The number 2 is not mutilated if one of its 1’s is taken away—because the part lost by mutilation is never equal to the remainder—nor in general is any number mutilated; because the essence must persist. If a cup is mutilated, it must still be a cup; but the number is no longer the same.

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Moreover, not even all things which have dissimilar parts are mutilated; for a number has in a sense dissimilar as well as similar parts—e.g. 2, 3. But in general of things whose position makes no difference, e.g. water or fire, none is mutilated;— to be mutilated, things must be such as have their position according to their essence.

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Further, they must be continuous; for a musical scale is composed of dissimilar parts, and has position; but it does not become mutilated. Moreover, even things which are wholes are not mutilated by the removal of any of their parts; the parts removed must be neither proper to their essence nor in any chance location. E.g., a cup is not mutilated if a hole is made in it, but only if the handle or some projection is broken;

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and a man is not mutilated if he loses flesh or his spleen, but if he loses some extremity; and not every extremity, but only such as cannot grow again when completely removed. Hence bald people are not mutilated.

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The term genus <or race> is used: (a) When there is a continuous generation of things of the same type; e.g., as long as the human race exists means as long as the generation of human beings is continuous. (b) Of anything from which things derive their being as the prime mover of them into being. Thus some are called Hellenes by race, and others Ionians, because some have Hellen and others Ion as their first ancestor.

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(Races are called after the male ancestor rather than after the material.Aristotle regards the mother as providing the material, and the father the formal element of the child. Cf. Aristot. Met. 1.6.8, Aristot. Met. 8.4.5. Some derive their race from the female as well; e.g. the descendants of PyrrhaWife of Deucalion, the Greek Noah.. ) (c) In the sense that the plane is the genus of plane figures, and the solid of solids (for each one of the figures is either a particular plane or a particular solid); i.e., that which underlies the differentiae.

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(d) In the sense that in formulae the first component, which is stated as part of the essence, is the genus, and the qualities are said to be its differentiae. The term genus, then, is used in all these senses—(a) in respect of continuous generation of the same type; (b) in respect of the first mover of the same type as the things which it moves; (c) in the sense of material. For that to which the differentia or quality belongs is the substrate, which we call material.

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Things are called generically different whose immediate substrates are different and cannot be resolved one into the other or both into the same thing. E.g., form and matter are generically different, and all things which belong to different categories of being; for some of the things of which being is predicated denote the essence, others a quality, and others the various other things which have already been distinguished. For these also cannot be resolved either into each other or into any one thing.

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False means: (i) false as a thing ; (a) because it is not or cannot be substantiated; such are the statements that the diagonal of a square is commensurable, or that you are sitting. Of these one is false always, and the other sometimes; it is in these senses that these things are not facts.

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(b) Such things as really exist, but whose nature it is to seem either such as they are not, or like things which are unreal; e.g. chiaroscuro and dreams. For these are really something, but not that of which they create the impression. Things, then, are called false in these senses: either because they themselves are unreal, or because the impression derived from them is that of something unreal.

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(2.) A false statement is the statement of what is not, in so far as the statement is false. Hence every definition is untrue of anything other than that of which it is true; e.g., the definition of a circle is untrue of a triangle. Now in one sense there is only one definition of each thing, namely that of its essence; but in another sense there are many definitions,Here Aristotle is using the word λόγος not in the strict sense of definition but in the looser sense of a statement about something. since the thing itself, and the thing itself qualified (e.g. Socrates and cultured Socrates) are in a sense the same.

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But the false definition is not strictly a definition of anything. Hence it was foolish of AntisthenesThe Cynic; contemporary and renegade disciple of Socrates. He taught that definition, and even predication, are strictly speaking impossible. A simple entity can only be named; a complex entity can only be defined by naming its simple constituents. Cf. Aristot. Met. 8.3.7, 8; Plat. Theaet. 201d-202c, Plat. Soph. 251b, c. to insist that nothing can be described except by its proper definition: one predicate for one subject; from which it followed that contradiction is impossible, and falsehoodCf. Plat. Euthyd. 283e-284c, 286c, d. nearly so. But it is possible to describe everything not only by its own definition but by that of something else; quite falsely, and yet also in a sense truly—e.g., 8 may be described as double by the definition of 2.

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Such are the meanings of false in these cases. (3.) A false man is one who readily and deliberately makes such statements, for the sake of doing so and for no other reason; and one who induces such statements in others—just as we call things false which induce a false impression. Hence the proof in the HippiasPlat. Hipp. Min 365-375. that the same man is false and true is misleading;

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for it assumes (a) that the false man is he who is able to deceive, i.e. the man who knows and is intelligent; (b) that the man who is willingly bad is better. This false assumption is due to the induction; for when he says that the man who limps willingly is better than he who does so unwillingly, he means by limping pretending to limp. For if he is willingly lame, he is presumably worse in this case just as he is in the case of moral character.

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Accident <or attribute> means that which applies to something and is truly stated, but neither necessarily nor usually; as if, for example, while digging a hole for a plant one found a treasure. Then the finding of treasure is an accident to the man who is digging the hole; for the one thing is not a necessary consequence or sequel of the other, nor does one usually find treasure while planting.

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And a cultured man might be white; but since this does not happen necessarily or usually, we call it an accident. Thus since there are attributes and subjects, and some attributes apply to their subjects only at a certain place and time, any attribute which applies to a subject, but not because it was a particular subject or time or place, will be an accident.

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Nor is there any definite cause for an accident, but only a chance, i.e. indefinite, cause. It was by accident that X went to Aegina if he arrived there, not because he intended to go there but because he was carried out of his course by a storm, or captured by pirates.

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The accident has happened or exists, but in virtue not of itself but of something else; for it was the storm which was the cause of his coming to a place for which he was not sailing—i.e. Aegina.

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Accident has also another sense,i.e. property. namely, whatever belongs to each thing in virtue of itself, but is not in its essence; e.g. as having the sum of its angles equal to two right angles belongs to the triangle. Accidents of this kind may be eternal, but none of the former kind can be. There is an account of this elsewhere.The reference is probably to the Aristot. Analytica Posteriora 75a 18, 39-41.

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It is the principles and causes of the things which are that we are seeking; and clearly of the things which are qua being. There is a cause of health and physical fitness; and mathematics has principles and elements and causes; and in general every intellectual science or science which involves intellect deals with causes and principles, more or less exactly or simply considered.

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But all these sciences single out some existent thing or class, and concern themselves with that; not with Being unqualified, nor qua Being, nor do they give any account of the essence; but starting from it, some making it clear to perception, and others assuming it as a hypothesis, they demonstrate, more or less cogently, the essential attributes of the class with which they are dealing.

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Hence obviously there is no demonstration of substance or essence from this method of approach, but some other means of exhibiting it. And similarly they say nothing as to whether the class of objects with which they are concerned exists or not; because the demonstration of its essence and that of its existence belong to the same intellectual process.

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And since physical science also happens to deal with a genus of Being (for it deals with the sort of substance which contains in itself the principle of motion and rest), obviously it is neither a practical nor a productive science.

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For in the case of things produced the principle of motion (either mind or art or some kind of potency) is in the producer; and in the case of things done the will is the agent—for the thing done and the thing willed are the same. Thus if every intellectual activity is either practical or productive or speculative, physics will be a speculative science; but speculative about that kind of Being which can be moved, and about formulated substance for the most part only qua inseparable from matter.

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But we must not fail to observe how the essence and the formula exist, since without this our inquiry is ineffectual.

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Now of things defined, i.e. of essences, some apply in the sense that snub does, and some in the sense that concave does. The difference is that snub is a combination of form with matter; because the snub is a concave nose , whereas concavity is independent of sensible matter.

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Now if all physical terms are used in the same sense as snub—e.g. nose, eye, face, flesh, bone, and in general animal; leaf, root, bark, and in general vegetable (for not one of these has a definition without motion; the definition invariably includes matter)—it is clear how we should look for and define the essence in physical things, and why it is the province of the physicist to study even some aspects of the soul, so far as it is not independent of matter.

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It is obvious, then, from these considerations, that physics is a form of speculative science. And mathematics is also speculative; but it is not clear at present whether its objects are immutable and separable from matter; it is clear, however, that some branches of mathematics study their objects qua immutable and qua separable from matter. Obviously it is the province of a speculative science to discover whether a thing is eternal and immutable and separable from matter;

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not, however, of physics (since physics deals with mutable objects) nor of mathematics, but of a science prior to both. For physics deals with things which exist separately but are not immutable; and some branches of mathematics deal with things which are immutable, but presumably not separable, but present in matter; but the primary science treats of things which are both separable and immutable.

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Now all causes must be eternal, but these especially; since they are the causes of what is visible of things divine. Hence there will be three speculative philosophies: mathematics, physics, and theology— since it is obvious that if the divine is present anywhere, it is present in this kind of entity; and also the most honorable science must deal with the most honorable class of subject.

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The speculative sciences, then, are to be preferred to the other sciences, and theology to the other speculative sciences. One might indeed raise the question whether the primary philosophy is universal or deals with some one genus or entity; because even the mathematical sciences differ in this respect—geometry and astronomy deal with a particular kind of entity, whereas universal mathematics applies to all kinds alike.

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Then if there is not some other substance besides those which are naturally composed, physics will be the primary science; but if there is a substance which is immutable, the science which studies this will be prior to physics, and will be primary philosophy, and universal in this sense, that it is primary. And it will be the province of this science to study Being qua Being; what it is, and what the attributes are which belong to it qua Being.

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But since the simple term being is used in various senses, of which we saw that one was accidental , and another true (not-being being used in the sense of false); and since besides these there are the categories, e.g. the what, quality, quantity, place, time, and any other similar meanings; and further besides all these the potential and actual : since the term being has various senses, it must first be said of what is accidentally, that there can be no speculation about it.

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This is shown by the fact that no science, whether practical, productive or speculative, concerns itself with it. The man who produces a house does not produce all the attributes which are accidental to the house in its construction; for they are infinite in number. There is no reason why the house so produced should not be agreeable to some, injurious to others, and beneficial to others, and different perhaps from every other existing thing; but the act of building is productive of none of these results.

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In the same way the geometrician does not study the accidental attributes of his figures, nor whether a triangle is different from a triangle the sum of whose angles is equal to two right angles. And this accords with what we should reasonably expect, because accident is only, as it were, a sort of name. Hence in a way PlatoCf. Plat. Soph. 254a. was not far wrong in making sophistry deal with what is nonexistent;

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because the sophists discuss the accident more, perhaps, than any other people—whether cultured and grammatical,i.e. able to read and write. The sophistic argument is given by Alexander as follows: A is grammatical; therefore grammatical A=A. A is cultured; therefore cultured A=A. Therefore grammatical=cultured, and he who is grammatical must be cultured. But B, though grammatical, is not cultured. Therefore the grammatical is not the same as the cultured. and cultured Coriscus and Coriscus,If Coriscus is the same as cultured Coriscus, he is the same as cultured cultured Coriscus, and soad infinitum. Cf. Soph. Elench. 173a 34. are the same or different; and whether everything that is, but has not always been, has come into being, so that if a man who is cultured has become grammatical, he has also, being grammatical, become culturedIf A, being cultured, has become grammatical, then being cultured he is grammatical. Then being grammatical he is cultured. But he has not always, being grammatical, been cultured. So if that which is but has not always been must have come to be, then being grammatical he has become cultured; i.e., he must have been both grammatical before he was cultured and cultured before he was grammatical; which is absurd ( Ross).; and all other such discussions. Indeed it seems that the accidental is something closely akin to the nonexistent.

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This is clear too from such considerations as the following: of things which are in other senses there is generation and destruction, but of things which are accidentally there is not.i.e., the process of becoming or change takes place in the subject—the man , who is accidentally cultured, becomes grammatical, and when the process is complete the cultured is accidentally grammatical; but it does not become so. Nevertheless we must state further, so far as it is possible, with regard to the accidental, what its nature is and through what cause it exists. At the same time it will doubtless also appear why there is no science of it.

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Since, then, there are among existing things some which are invariable and of necessity (not necessity in the sense of compulsion,Cf. Aristot. Met. 5.5.2. but that by which we mean that it cannot be otherwise Aristot. Met. 5.5.3 ), and some which are not necessarily so, nor always, but usually: this is the principle and this the cause of the accidental. For whatever is neither always nor usually so, we call an accident.

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E.g., if in the dog-daysThe period from July 3 to August 11, during which the dog-star Sirius rises and sets with the sun. we have storm and cold, we call it an accident; but not if we have stifling and intense heat, because the latter always or usually comes at this time, but not the former. It is accidental for a man to be white (since this is neither always nor usually so), but it is not accidental for him to be an animal.

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It is by accident that a builder restores to health, because it is not a builder but a doctor who naturally does this; but the builder happened accidentally to be a doctor. A confectioner, aiming at producing enjoyment, may produce something health-giving; but not in virtue of his confectioner’s art. Hence, we say, it was accidental; and he produces it in a sense, but not in an unqualified sense.

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For there are potencies which produce other things, but there is no art or determinate potency of accidents, since the cause of things which exist or come to be by accident is also accidental.

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Hence, since not everything is or comes to be of necessity and always, but most things happen usually, the accidental must exist. E.g., the white man is neither always nor usually cultured; but since this sometimes happens, it must be regarded as accidental. Otherwise, everything must be regarded as of necessity.

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Therefore the cause of the accidental is the matter, which admits of variation from the usual.

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We must take this as our starting-point: Is everything either always or usually? This is surely impossible. Then besides these alternatives there is something else: the fortuitous and accidental. But again, are things usually so, but nothing always , or are there things which are eternal? These questions must be inquired into laterCf. Aristot. Met. 12.6-8.; but it is clear that there is no science of the accidental—because all scientific knowledge is of that which is always or usually so. How else indeed can one learn it or teach it to another? For a fact must be defined by being so always or usually; e.g., honey-water is usually beneficial in case of fever.

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But science will not be able to state the exception to the rule: when it is not beneficial—e.g. at the new moon; because that which happens at the new moon also happens either always or usually; but the accidental is contrary to this. We have now explained the nature and cause of the accidental, and that there is no science of it.

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It is obvious that there are principles and causes which are generable and destructible apart from the actual processes of generation and destructionOn the analogy of accidental events; see 2. 5.; for if this is not true, everything will be of necessity: that is, if there must necessarily be some cause, other than accidental, of that which is generated and destroyed. Will A be, or not? Yes, if B happens; otherwise not. And B will happen if C does.

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It is clear that in this way, as time is continually subtracted from a limited period, we shall come to the present. Accordingly So-and-so will die by disease or violence if he goes out; and this if he gets thirsty; and this if something else happens; and thus we shall come to what is the case now, or to something which has already happened. E.g. if he is thirsty; this will happen if he is eating pungent food, and this is either the case or not.

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Thus of necessity he will either die or not die. And similarly if one jumps over to the past, the principle is the same; for this—I mean that which has just happened—is already present in something. Everything, then, which is to be, will be of necessity; e.g., he who is alive must die—for some stage of the process has been reached already; e.g., the contraries are present in the same body—but whether by disease or violence is not yet determined; it depends upon whether so-and-so happens.

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Clearly, then, the series goes back to some starting-point, which does not go back to something else. This, therefore, will be the starting-point of the fortuitous, and nothing else is the cause of its generation. But to what sort of starting-point and cause this process of tracing back leads, whether to a material or final or moving cause, is a question for careful consideration.

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So much, then, for the accidental sense of being; we have defined it sufficiently. As for being qua truth, and not-being qua falsity, since they depend upon combination and separation, and taken together are concerned with the arrangement of the parts of a contradiction (since the true has affirmation when the subject and predicate are combined, and negation where they are divided; but the false has the contrary arrangement.

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How it happens that we combine or separate in thought is another question. By combining or separating in thought I mean thinking them not as a succession but as a unitysc., or not as a unity but as a succession (this is separating in thought).); for falsity and truth are not in things —the good, for example, being true, and the bad false—but in thought ; and with regard to simple concepts and essences there is no truth or falsity even in thought;

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—what points we must study in connection with being and not-being in this sense, we must consider later. But since the combination and separation exists in thought and not in things, and this sense of being is different from the proper senses (since thought attaches or detaches essence or quality or quantity or some other category), we may dismiss the accidental and real sensesi.e., the senses in which the verb to be is used to express an accidental or a true relation. of being.

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For the cause of the one is indeterminate and of the other an affection of thought; and both are connected with the remaining genus of being, and do not indicate any objective reality. Let us therefore dismiss them, and consider the causes and principles of Being itself qua Being. [We have made it clear in our distinction of the number of senses in which each term is used that being has several senses.]This sentence is almost certainly a later and clumsy addition to show the connection with the following book.

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The term being has several senses, which we have classified in our discussionAristot. Met. 5.7. of the number of senses in which terms are used. It denotes first the what of a thing, i.e. the individuality; and then the quality or quantity or any other such category. Now of all these senses which being has, the primary sense is clearly the what, which denotes the substance

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(because when we describe the quality of a particular thing we say that it is good or bad, and not five feet high or a man; but when we describe what it is, we say not that it is white or hot or five feet high, but that it is a man or a god), and all other things are said to be because they are either quantities or qualities or affections or some other such thing.

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Hence one might raise the question whether the terms to walk and to be well and to sit signify each of these things as being, or not; and similarly in the case of any other such terms; for not one of them by nature has an independent existence or can be separated from its substance. Rather, if anything it is the thing which walks or sits or is well that is existent.

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The reason why these things are more truly existent is because their subject is something definite; i.e. the substance and the individual, which is clearly implied in a designation of this kind, since apart from it we cannot speak of the good or sitting. Clearly then it is by reason of the substance that each of the things referred to exists.

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Hence that which is primarily, not in a qualified sense but absolutely, will be substance.

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Now primary has several meanings; but nevertheless substance is primary in all senses, both in definition and in knowledge and in time. For none of the other categories can exist separately, but substance alone;

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and it is primary also in definition, because in the formula of each thing the formula of substance must be inherent; and we assume that we know each particular thing most truly when we know what man or fire is— rather than its quality or quantity or position; because we know each of these points too when we know what the quantity or quality is.

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Indeed, the question which was raised long ago, is still and always will be, and which always baffles us—What is Being?—is in other words What is substance? Some say that it is oneThe Milesians and Eleatics.; others, more than one; some, finiteThe Pythagoreans and Empedocles.; others, infinite.Anaxagoras and the Atomists. And so for us too our chief and primary and practically our only concern is to investigate the nature of being in the sense of substance.

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Substance is thought to be present most obviously in bodies. Hence we call animals and plants and their parts substances, and also natural bodies, such as fire, water, earth, etc., and all things which are parts of these or composed of these, either of parts or them or of their totality; e.g. the visible universe and its parts, the stars and moon and sun.

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We must consider whether (a) these are the only substances, or (b) these and some others, or (c) some of these, or (d) some of these and some others, or (e) none of these, but certain others. SomeThe Pythagoreans. hold that the bounds of body—i.e. the surface, line, point and unit—are substances, and in a truer sense than body or the solid.

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Again, someThe pre-Socratics. believe that there is nothing of this kind besides sensible things, while others believe in eternal entities more numerous and more real than sensible things. Thus Plato posited the Forms and the objects of mathematics as two kinds of substance, and as a third the substance of sensible bodies;

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and SpeusippusPlato’s nephew and successor as the head of the Academy. assumed still more kinds of substances, starting with the One, and positing principles for each kind: one for numbers, another for magnitudes, and then another for the soul. In this way he multiplies the kinds of substance. SomeThe followers of Xenocrates, successor to Speusippus. again hold that the Forms and numbers have the same nature, and that other things—lines and planes—are dependent upon them; and soon back to the substance of the visible universe and sensible things.

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We must consider, then, with regard to these matters, which of the views expressed is right and which wrong; and what things are substances; and whether there are any substances besides the sensible substances, or not; and how sensible substances exist; and whether there is any separable substance (and if so, why and how) or no substance besides the sensible ones. We must first give a rough sketch of what substance is.

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The term substance is used, if not in more, at least in four principal cases; for both the essence and the universal and the genus are held to be the substance of the particular, and fourthly the substrate. The substrate is that of which the rest are predicated, while it is not itself predicated of anything else. Hence we must first determine its nature, for the primary substrate is considered to be in the truest sense substance.

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Now in one sense we call the matter the substrate; in another, the shape ; and in a third, the combination of the two. By matter I mean, for instance, bronze; by shape, the arrangement of the form; and by the combination of the two, the concrete thing: the statue. Thus if the form is prior to the matter and more truly existent, by the same argument it will also be prior to the combination.

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We have now stated in outline the nature of substance—that it is not that which is predicated of a subject, but that of which the other things are predicated. But we must not merely define it so, for it is not enough. Not only is the statement itself obscure, but also it makes matter substance; for if matter is not substance, it is beyond our power to say what else is.

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For when everything else is removed, clearly nothing but matter remains; because all the other things are affections, products and potencies of bodies, and length, breadth and depth are kinds of quantity, and not substances. For quantity is not a substance; rather the substance is that to which these affections primarily belong.

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But when we take away length and breadth and depth we can see no thing remaining, unless it be the something bounded by them; so that on this view matter must appear to be the only substance. By matter I mean that which in itself is neither a particular thing nor a quantity nor designated by any of the categories which define Being.

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For there is something of which each of these is predicated, whose being is different from that of each one of the categories; because all other things are predicated of substance, but this is predicated of matter. Thus the ultimate substrate is in itself neither a particular thing nor a quantity nor anything else. Nor indeed is it the negations of these; for the negations too will only apply to it accidentally.

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If we hold this view, it follows that matter is substance. But this is impossible; for it is accepted that separability and individuality belong especially to substance. Hence it would seem that the form and the combination of form and matter are more truly substance than matter is.

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The substance, then, which consists of both—I mean of matter and form—may be dismissed, since it is posterior and obvious. Matter too is in a sense evident. We must consider the third type, for this is the most perplexing.

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Now it is agreed that some sensible things are substances, and so we should begin our inquiry in connection with these.

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It is convenient to advance to the more intelligiblesc. by nature. All learning proceeds by induction from that which is intelligible to us (i.e., the complex facts and objects of our experience, which are bound up with sensation and therefore less intelligible in themselves), to that which is intelligible in itself (i.e., the simple universal principles of scientific knowledge).; for learning is always acquired in this way, by advancing through what is less intelligible by nature to what is more so. And just as in actions it is our task to start from the good of the individual and make absolute good good for the individual,Cf. Aristot. Ethics 1129b 5. so it is our task to start from what is more intelligible to oneself and make what is by nature intelligible intelligible to oneself.

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Now that which is intelligible and primary to individuals is often but slightly intelligible, and contains but little reality; but nevertheless, starting from that which is imperfectly intelligible but intelligible to oneself, we must try to understand the absolutely intelligible; advancing, as we have said, by means of these very things which are intelligible to us.

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Since we distinguished at the beginningAristot. Met. 7.3.1. the number of ways in which substance is defined, and since one of these appeared to be essence, we must investigate this.

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First, let us make certain linguistic statements about it.

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The essence of each thing is that which it is said to be per se. To be you is not to be cultured, because you are not of your own nature cultured. Your essence, then, is that which you are said to be

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of your own nature. But not even all of this is the essence; for the essence is not that which is said to be per se in the sense that whiteness is said to belong to a surface,Cf. Aristot. Met. 5.18.3, 4. because being a surface is not being white.

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Nor is the essence the combination of both, being a white surface. Why? Because the word itself is repeated. Hence the formula of the essence of each thing is that which defines the term but does not contain it. Thus if being a white surface is the same as being a smooth surface, white and smooth are one and the same.The statement that to be a white surface is the same as to be a smooth surface tells us nothing fresh about surface; it simply identifies white with smooth. Aristotle has in mind Democritus’s theory of color (that it is an impression conveyed to our eyes from the superficial texture of the object; Theophrastus, De Sensu 73-75); cf.Aristot. De Sensu 442b 11, Aristot. De Gen. et Corr. 316a 1.

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But since in the other categories too there are compounds with substance (because there is a substrate for each category, e.g. quality, quantity, time, place and motion), we must inquire whether there is a formula of the essence of each one of them; whether these compounds, e.g. white man, also have an essence.

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Let the compound be denoted by X.Literally cloak, but the word is chosen quite arbitrarily. Cf. Aristot. Met. 8.6.4. What is the essence of X?

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But this is not even a per se expression. We reply that there are two ways in which a definition can be not per se true of its subject: (a) by an addition, and (b) by an omission.

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In one case the definition is not per se true because the term which is being defined is combined with something else; as if, e.g., in defining whiteness one were to state the definition of a white man. In the other, because something else (which is not in the definition) is combined with the subject; as if, e.g., X were to denote white man, and X were defined as white. White man is white, but its essence is not to be white. But is to be X an essence at all?

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Surely not. The essence is an individual type; but when a subject has something distinct from it predicated of it, it is not an individual type. E.g., white man is not an individual type; that is, assuming that individuality belongs only to substances. Hence essence belongs to all things the account of which is a definition.

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We have a definition, not if the name and the account signify the same (for then all accounts would be definitions; because any account can have a name, so that even the Iliad will be a definition), but if the account is of something primary. Such are all statements which do not involve the predication of one thing of another.

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Hence essence will belong to nothing except species of a genus, but to these only; for in these the predicate is not considered to be related to the subject by participation or affection, nor as an accident. But of everything else as well, if it has a name, there will be a formula of what it means—that X belongs to Y; or instead of a simple formula one more exact—but no definition, nor essence.

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Or perhaps definition, like the what, has more than one sense. For the what in one sense means the substance and the individual, and in another each one of the categories: quantity, quality, etc.

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Just as is applies to everything, although not in the same way, but primarily to one thing and secondarily to others; so what it is applies in an unqualified sense to substance, and to other things in a qualified sense. For we might ask also what quality is, so that quality also is a what it is; not however without qualification, but just as in the case of not-being some say by a verbal quibble that not-being is—not in an unqualified sense, but is not-being—so too with quality.

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Now although we must also consider how we should express ourselves in each particular case, it is still more important to consider what the facts are. Hence now, since the language which we are using is clear, similarly essence also will belong primarily and simply to substance, and secondarily to other things as well; just as the what it is is not essence simply, but the essence of a quality or quantity.

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For it must be either by equivocation that we say that these things are , or by adding and subtracting qualifications, as we say that the unknowable is knownsc. to be unknowable.; since the truth is that we use the terms neither equivocally nor in the same sense, but just as we use the term medical in relation to one and the same thing; but not of one and the same thing, nor yet equivocally. The term medical is applied to a body and a function and an instrument, neither equivocally nor in one sense, but in relation to one thing.Cf. Aristot. Met. 4.2.2.

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However, in whichever way one chooses to speak of these things, it matters nothing; but this point is clear: that the primary and unqualified definition, and the essence, belong to substances. It is true that they belong equally to other things too, but not primarily . For if we assume this, it does not necessarily follow that there is a definition of anything which means the same as any formula; it must mean the same as a particular kind of formula, i.e. the formula of one thing—

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one not by continuity like the Iliad, or things which are arbitrarily combined, but in one of the proper senses of one. And one has the same variety of senses as being. Being means sometimes the individual thing, sometimes the quantity, sometimes the quality. Hence even white man will have a formula and definition; but in a different sense from the definition of whiteness and substance.

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The question arises: If one denies that a formula involving an added determinant is a definition, how can there be a definition of terms which are not simple but coupled? Because they can only be explained by adding a determinant.

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I mean, e.g., there is nose and concavity and snubness, the term compounded of the two, because the one is present in the other. Neither concavity nor snubness is an accidental, but a per se affection of the nose.Snubness is a per se affection of the nose, because it applies only to the nose and cannot be explained apart from it, but the same can hardly be said of concavity. Aristotle himself uses the word (κοιλότης) elsewhere in other connections. Nor are they attributes in the sense that white is of Callias or a man, because Callias is white and is by accident a man; but in the sense that male is an attribute of animal, and equality of quantity, and all other attributes which we say belong per se.

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That is, all things which involve the formula or name of the subject of the affection, and cannot be explained apart from it. Thus white can be explained apart from man, but not female apart from animal. Thus either these terms have no essence or definition, or else they have it in a different sense, as we have said.

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But there is also another difficulty about them. If snub nose is the same as concave nose, snub will be the same as concave. But if not, since it is impossible to speak of snub apart from the thing of which it is a per se affection (because snub means a concavity in the nose), either it is impossible to call the nose snub, or it will be a tautology, concave-nose nose because snub nose will equal concave-nose nose.

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Hence it is absurd that such terms as these should have an essence. Otherwise there will be an infinite regression; for in snub-nose nose there will be yet another nose. Clearly, then, there is definition of substance alone. If there were definition of the other categories also, it would have to involve an added determinant, as in the case of the qualitative; and of the odd, for this cannot be defined apart from number; nor can female apart from animal.

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By involving an added determinant I mean descriptions which involve a tautology, as in the above examples. Now if this is true, there will be no definition of compound expressions either; e.g., odd number. We fail to realize this because our terms are not used accurately. If on the other hand there are definitions of these too, either they are defined in a different way, or, as we have said, definition and essence must be used in more than one sense;

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thus in one sense there will be no definition of anything, and nothing will have an essence, except substances; and in another those other things will have a definition and essence. It is obvious, then, that the definition is the formula of the essence, and that the essence belongs either only to substances, or especially and primarily and simply.

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We must inquire whether the essence is the same as the particular thing, or different. This is useful for our inquiry about substance; because a particular thing is considered to be nothing other than its own substance, and the essence is called the substance of the thing.

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In accidental predications, indeed, the thing itself would seem to be different from its essence; e.g., white man is different from essence of white man. If it were the same, essence of man and essence of white man would be the same. For man and white man are the same, they say, and therefore essence of white man is the same as essence of man.

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But perhaps it is not necessarily true that the essence of accidental combinations is the same as that of the simple terms; because the extremes of the syllogism are not identical with the middle term in the same way.The argument consists of two syllogisms: White=essence of white man. Man=white man. Therefore man=essence of white man. But essence of man=man. Therefore essence of man=essence of white man. The conclusion is faulty because whereas the first identity is assumed to be absolute, the second is accidental. Perhaps it might be thought to follow that the accidental extremes are identical; e.g. essence of white and essence of cultured; but this is not admitted.Aristotle seems to mean that both essence of white man and essence of cultured man might be proved by the former syllogism to be identical in the same way with the middle term man, in which case it would seem that essence of white and essence of cultured are the same. There is, however, the same fallacy as before.

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But in per se expressions, is the thing necessarily the same as its essence, e.g., if there are substances which have no other substances or entities prior to them, such as some hold the Ideas to be?

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For if the Ideal Good is to be different from the essence of good, and the Ideal Animal and Being from the essence of animal and being, there will be other substances and entities and Ideas besides the ones which they describe; and prior to them, if essence is substance. And if they are separate from each other, there will be no knowledge of the Ideas, and the essences will not exist

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(by being separate I mean if neither the essence of good is present in the Ideal Good, nor being good in the essence of good); for it is when we know the essence of it that we have knowledge of a thing. And it is the same with other essences as with the essence of good; so that if the essence of good is not good, neither will the essence of being be, nor the essence of one be one.

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Either all essences exist alike, or none of them; and so if not even the essence of being is, neither will any other essence exist. Again that to which essentially good does not apply cannot be good. Hence the good must be one with the essence of good, the beautiful with the essence of beauty, and so with all terms which are not dependent upon something else, but self-subsistent and primary.The example of the Ideas as per se terms is used by Aristotle to show incidentally the fallacy of the Ideal theory: there can be no self-subsistent entity apart from the essence.

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For it is enough if this is so, even if they are not Forms; or perhaps rather even if they are. (At the same time it is clear also that if the Ideas are such as some hold, the substrate will not be substance; for the Ideas must be substances, but not involving a substrate, because if they did involve one they would exist in virtue of its participation in them.)This criticism is irrelevant to the point under discussion. It simply points out that the Ideal theory conflicts with received opinion (cf. Aristot. Met. 7.3.1).

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That each individual thing is one and the same with its essence, and not merely accidentally so, is apparent, not only from the foregoing considerations, but because to have knowledge of the individual is to have knowledge of its essence; so that by setting out examples it is evident that both must be identical.

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But as for the accidental term, e.g. cultured or white, since it has two meanings, it is not true to say that the term itself is the same as its essence; for both the accidental term and that of which it is an accident are white, so that in one sense the essence and the term itself are the same, and in another they are not, because the essence is not the same as the man or the white man, but it is the same as the affection.

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The absurdity <of separating a thing from its essence> will be apparent also if one supplies a name for each essence; for then there will be another essence besides the original one, e.g. the essence of horse will have a further essence. Yet why should not some things be identified with their essence from the outset,i.e. to avoid the infinite series implied in the last sentence. if essence is substance? Indeed not only are the thing and its essence one, but their formula is the same, as is clear from what we have just stated; for it is not by accident that the essence of one, and the one, are one.

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Moreover, if they are different, there will be an infinite series; for the essence of one and the one will both exist; so that in that case too the same principle will apply.i.e. since there is a distinct term essence of one besides one, there will be a third distinct term essence of essence of one; and so on as in the case of horse above. Clearly, then, in the case of primary and self-subsistent terms, the individual thing and its essence are one and the same.

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It is obvious that the sophistical objections to this thesis are met in the same way as the question whether Socrates is the same as the essence of Socrates; for there is no difference either in the grounds for asking the question or in the means of meeting it successfully. We have now explained in what sense the essence is, and in what sense it is not, the same as the individual thing.

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Of things which are generated, some are generated naturally, others artificially, and others spontaneously; but everything which is generated is generated by something and from something and becomes something. When I say becomes something I mean in any of the categories; it may come to be either a particular thing or of some quantity or quality or in some place.

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Natural generation is the generation of things whose generation is by nature.

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That from which they are generated is what we call matter; that by which, is something which exists naturally; and that which they become is a man or a plant or something else of this kind, which we call substance in the highest degree. All things which are generated naturally or artificially have matter; for it is possible for each one of them both to be and not to be, and this possibility is the matter in each individual thing.

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And in general both that from which and that in accordance with which they are generated, is nature; for the thing generated, e.g. plant or animal, has a nature. And that by which they are generated is the so-called formal nature, which has the same form as the thing generated (although it is in something else); for man begets man.

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Such is the generation of things which are naturally generated; the other kinds of generation are called productions. All productions proceed from either art or potency or thought.

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Some of them are also generated spontaneously and by chance in much the same way as things which are naturally generated; for sometimes even in the sphere of nature the same things are generated both from seed and without it.e.g. fish (Aristot. Hist. An. 569a 11) and insects (Aristot. Hist. An. 539a 24). We shall consider cases of this kind later.In Aristot. Met. 7.9. Things are generated artificially whose form is contained in the soul (by form I mean the essence of each thing, and its primary substance);

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for even contraries have in a sense the same form.The logical connection is: It is sufficient to say that the form of objects which are artificially produced is contained in the soul; for although artificial production can produce contrary effects, the form of the positive effect is the absence of the form of the negative effect, so that in a sense they have the same form. For the substance of the privation is the opposite substance; e.g., health is the substance of disease; for disease is the absence of health, and health is the formula and knowledge in the soul. Now the healthy subject is produced as the result of this reasoning: since health is so-and-so, if the subject is to be healthy, it must have such-and-such a quality, e.g. homogeneity; and if so, it must have heat.

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And the physician continues reasoning until he arrives at what he himself finally can do; then the process from this point onwards, i.e. the process towards health, is called production. Therefore it follows in a sense that health comes from health and a house from a house; that which has matter from that which has not (for the art of medicine or of building is the form of health or the house). By substance without matter I mean the essence.

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In generations and motions part of the process is called cogitation, and part production—that which proceeds from the starting-point and the form is cogitation, and that which proceeds from the conclusion of the cogitation is production. Each of the other intermediate measures is carried out in the same way. I mean, e.g., that if A is to be healthy, his physical condition will have to be made uniform. What, then, does being made uniform entail? So-and-so; and this will be achieved if he is made hot. What does this entail? So-and-so; now this is potentially present, and the thing is now in his power.

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The thing which produces, and from which the process of recovering health begins, is the form in the soul, if the process is artificial; if spontaneous, it is whatever is the starting-point of the production for the artificial producer; as in medical treatment the starting-point is, perhaps, the heating of the patient; and this the doctor produces by friction. Heat in the body, then, is either a part of health, or is followed (directly or through several intermediaries) by something similar which is a part of health. This is the ultimate thing, namely that produces, and in this sense is a part of, health—or of the house

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(in the form of stones)There is no real analogy between the casual relationship of heat to health and of stones to a house. The former is both material and efficient; the latter only material. Cf. Aristot. Met. 7.9.1. or of other things. Therefore, as we say, generation would be impossible if nothing were already existent. It is clear, then, that some part must necessarily pre-exist; because the matter is a part, since it is matter which pre-exists in the product and becomes something. But then is matter part of the formula? Well, we define bronze circles in both ways; we describe the matter as bronze, and the form as such-and-such a shape; and this shape is the proximate genus in which the circle is placed.

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The bronze circle, then, has its matter in its formula. Now as for that from which, as matter, things are generated, some things when they are generated are called not so-and-so, but made of so-and-so; e.g., a statue is not called stone, but made of stone. But the man who becomes healthy is not called after that from which he becomes healthy. This is because the generation proceeds from the privation and the substrate, which we call matter (e.g., both the man and the invalid become healthy),

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but it is more properly said to proceed from the privation; e.g., a man becomes healthy from being an invalid rather than from being a man. Hence a healthy person is not called an invalid, but a man, and a healthy man. But where the privation is obscure and has no name—e.g. in bronze the privation of any given shape, or in bricks and wood the privation of the shape of a house—the generation is considered to proceed from these materials, as in the former case from the invalid.

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Hence just as in the former case the subject is not called that from which it is generated, so in this case the statue is not called wood, but is called by a verbal change not wood, but wooden; not bronze, but made of bronze; not stone, but made of stone; and the house is called not bricks, but made of bricks. For if we consider the matter carefully, we should not even say without qualification that a statue is generated from wood, or a house from bricks; because that from which a thing is generated should not persist, but be changed. This, then, is why we speak in this way.

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Now since that which is generated is generated by something (by which I mean the starting-point of the process of generation), and from something (by which let us understand not the privation but the matter; for we have already distinguished the meanings of these), and becomes something (i.e. a sphere or circle or whatever else it may be); just as the craftsman does not produce the substrate, i.e. the bronze, so neither does he produce the sphere; except accidentally, inasmuch as the bronze sphere is a sphere, and he makes the former.

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For to make an individual thing is to make it out of the substrate in the fullest sense. I mean that to make the bronze round is not to make the round or the sphere, but something else; i.e. to produce this form in another medium. For if we make the form, we must make it out of something else; for this has been assumed. E.g., we make a bronze sphere; we do this in the sense that from A, i.e. bronze, we make B, i.e. a sphere.

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If, then, we make the spherical form itself, clearly we shall have to make it in the same way; and the processes of generation will continue to infinity.

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It is therefore obvious that the form (or whatever we should call the shape in the sensible thing) is not generated—generation does not apply to it— nor is the essence generated; for this is that which is induced in something else either by art or by nature or by potency.

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But we do cause a bronze sphere to be, for we produce it from bronze and a sphere; we induce the form into this particular matter, and the result is a bronze sphere. But if the essence of sphere in general is generated, something must be generated from something; for that which is generated will always have to be divisible, and be partly one thing and partly another; I mean partly matter and partly form.

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If then a sphere is the figure whose circumference is everywhere equidistant from the center, part of this will be the medium in which that which we produce will be contained, and part will be in that medium; and the whole will be the thing generated, as in the case of the bronze sphere. It is obvious, then, from what we have said, that the thing in the sense of form or essence is not generated, whereas the concrete whole which is called after it is generated; and that in everything that is generated matter is present, and one part is matter and the other form.

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Is there then some sphere besides the particular spheres, or some house besides the bricks? Surely no individual thing would ever have been generated if form had existed thus independently.If forms are self-subsistent substances, individual substances cannot be generated from them; for the individual contains the form, but one substance cannot contain another actually existing substance (Aristot. Met. 7.8.8). Form, however, is not a substance but a characteristic. Form means of such a kind; it is not a definite individual, but we produce or generate from the individual something of such a kind; and when it is generated it is an individual of such a kind.

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The whole individual, Callias or Socrates, corresponds to this bronze sphere, but man and animal correspond to bronze sphere in general.

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Obviously therefore the cause which consists of the Forms (in the sense in which some speak of them, assuming that there are certain entities besides particulars), in respect at least of generation and destruction, is useless; nor, for this reason at any rate, should they be regarded as self-subsistent substances.

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Indeed in some cases it is even obvious that that which generates is of the same kind as that which is generated—not however identical with it, nor numerically one with it, but formally one—e.g. in natural productions (for man begets man), unless something happens contrary to nature, as when a horse sires a mule. And even these cases are similar; for that which would be common to both horse and ass, the genus immediately above them, has no name; but it would probably be both, just as the mule is both.Normally the sire communicates his form to the offspring. In the case of a mule, the material element contributed by the dam, which is an ass, limits the effect of the formal element contributed bu the sire, which is a horse; but even so the form of the sire is generically the same as that of the offspring.

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Thus obviously there is no need to set up a form as a pattern (for we should have looked for Forms in these cases especially, since living things are in a special sense substances); the thing which generates is sufficient to produce, and to be the cause of the form in the matter. The completed whole, such-and-such a form induced in this flesh and these bones, is Callias or Socrates. And it is different from that which generated it, because the matter is different but identical in form, because the form is indivisible.

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The question might be raised why some things are generated both artificially and spontaneously—e.g. health—and others not; e.g. a house. The reason is that in some cases the matter—which is the starting-point of the process in the production and generation of artificial things, and in which some part of the result is already existent—is such that it can initiate its own motion, and in other cases it is not; and of the former kind some can initiate motion in a particular way, and some cannot. For many things can move themselves, but not in a particular way, e.g. so as to dance.

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It is impossible, then, for any things whose matter is of this kind (e.g. stones) to be moved in this particular way except by something else; but in that particular way it is possible. And it is so with fire.Stones can fall by themselves, but cannot by themselves build a house; fire can rise by itself, but cannot boil a kettle. For this reason some things cannot exist apart from the possessor of the art, and others can; because the motion can be initiated by those things which do not indeed possess the art, but can themselves be moved either by other things which do not possess the art, or by the motion from the part of the product which pre-exists in them.e.g., health can be produced as the result of the activity set up by heat in the body.

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It is clear also from what we have said that in a sense all artificial things are generated either from something which bears the same name (as is the case with natural objects) or from a part of themselves which bears the same name as themselves (e.g. a house from a house, inasmuch as it is generated by mind; for the art is the form), or from something which contains some part; that is if the generation is not accidental; for the direct and independent cause of the production is a part of the product.

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Heat in the motion produces heat in the body; and either this is health or a part of health, or a part of health or health accompanies it. And this is why heat is said to produce health, because it produces that of which health is a concomitant and consequence. Therefore as essence is the starting-point of everything in syllogisms (because syllogisms start from the what of a thing), so too generation proceeds from it.

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And it is the same with natural formations as it is with the products of art. For the seed produces just as do those things which function by art. It contains the form potentially, and that from which the seed comes has in some sense the same name as the product (for we must not expect that all should have the same name in the sense that man is produced by man—since woman is also produced by man); unless the product is a freak. This is why a mule is not produced by a mule.

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Those natural objects which are produced, like artificial objects, spontaneously, are those whose matter can also initiate for itself that motion which the seed initiates. Those whose matter cannot do this cannot be generated otherwise than by their proper parents.

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It is not only with reference to substance that our argument shows that the form is not generated; the same argument is common in its application to all the primary divisions, i.e. quantity, quality and the other categories.

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For just as the bronze sphere is generated, but not the sphere nor the bronze; and as in the case of bronze, if it is generated the form and matter are not (because they must always pre-exist), so it is too with the what and the quality and quantity and the other categories similarly; for it is not the quality that is generated, but the wood of that quality; nor is it the size, but the wood or animal of that size.

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But a peculiarity of substance may be gathered from this: that some other substance must pre-exist in actuality which produces it; e.g. an animal, if an animal is being generated; but a quality or quantity need not pre-exist otherwise than potentially.

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Since a definition is a formula, and every formula has parts; and since the formula is related to the thing in the same way as the part of the formula to the part of the thing, the questionThe questions discussed in chs. 10-12 arise out of the consideration of essence as definition. now arises: Must the formula of the parts be contained in the formula of the whole, or not? It seems clear that it is so in some cases, but not in others.

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The formula of the circle does not include that of the segments, but the formula of the syllable includes that of the letters. And yet the circle is divisible into its segments in just the same way as the syllable into its letters.

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Again, if the parts are prior to the whole, and the acute angle is part of the right angle, and the finger part of the animal, the acute angle will be prior to the right angle, and the finger to the man.

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But it is considered that the latter are prior; for in the formula the parts are explained from them; and the wholes are prior also in virtue of their ability to exist independently. The truth probably is that part has several meanings, one of which is that which measures in respect of quantity. However, let us dismiss this question and consider of what, in the sense of parts, substance consists.

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If then matter, form, and the combination of the two are distinct, and if both matter and form and their combination are substance, there is one sense in which even matter may be called part of a thing; and another in which it is not, but the only parts are those elements of which the formula of the form consists. E.g., flesh is not a part of concavity, because flesh is the matter in which concavity is induced; but it is a part of snubness. And bronze is part of the statue as a concrete whole, but not of the statue in the sense of form.

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We may speak of the form (or the thing as having a form) as an individual thing, but we may never so speak of that which is material by itself. This is why the formula of the circle does not contain that of the segments, whereas the formula of the syllable does contain that of the letters; for the letters are parts of the formula of the form; they are not matter; but the segments are parts in the sense of matter in which the form is induced. They approximate, however, more closely to the form than does the bronze when roundness is engendered in bronze.

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But there is a sense in which not even all the letters will be contained in the formula of the syllable; e.g. particular letters on waxi.e. written on a waxed tablet. or sounds in the air; for these too are part of the syllable in the sense that they are its sensible matter.

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For even if the line is divided and resolved into its halves, or if the man is resolved into bones and muscles and flesh, it does not follow that they are composed of these as parts of their essence, but as their matter; and these are parts of the concrete whole, but not of the form, or that to which the formula refers. Hence they are not in the formulae.

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Accordingly in some cases the formula will include the formula of such parts as the above, but in others it need not necessarily contain their formula, unless it is the formula of the concrete object. It is for this reason that some things are composed of parts in the sense of principles into which they can be resolved, while others are not.

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All things which are concrete combinations of form and matter (e.g. the snub or the bronze circle) can be resolved into form and matter, and the matter is a part of them; but such as are not concrete combinations with matter, but are without matter—whose formulae refer to the form only—cannot be resolved; either not at all, or at least not in this way.

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Thus these material components are principles and parts of the concrete objects, but they are neither parts nor principles of the form. For this reason the clay statue can be resolved into clay, and the sphere into bronze, and Callias into flesh and bones, and the circle too into segments, because it is something which is combined with matter. For we use the same name for the absolute circle and for the particular circle, since there is no special name for the particular circles.

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We have now stated the truth; nevertheless let us recapitulate and state it more clearly. All constituents which are parts of the formula, and into which the formula can be divided, are prior to their wholes—either all or some of them. But the formula of the right angle is not divisible into the formula of an acute angle, but vice versa; since in defining the acute angle we use the right angle, because the acute angle is less than a right angle.

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It is the same with the circle and the semicircle; for the semicircle is defined by means of the circle. And the finger is defined by means of the whole body; for a finger is a particular kind of part of a man. Thus such parts as are material, and into which the whole is resolved as into matter, are posterior to the whole; but such as are parts in the sense of parts of the formula and of the essence as expressed in the formula, are prior; either all or some of them.

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And since the soul of animals (which is the substance of the living creature) is their substance in accordance with the formula, and the form and essence of that particular kind of body (at least each part, if it is to be properly defined, will not be defined apart from its function; and this will not belong to it apart from perceptionWhich implies soul.); therefore the parts of the soul are prior, either all or some of them, to the concrete animal; and similarly in other individual cases.

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But the body and its parts are posterior to this substance, and it is not the substance, but the concrete whole, which is resolved into these parts as into matter. Therefore in one sense these parts are prior to the concrete whole, and in another not; for they cannot exist in separation. A finger cannot in every state be a part of a living animal; for the dead finger has only the name in common with the living one.

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Some parts are contemporary with the whole: such as are indispensable and in which the formula and the essence are primarily present; e.g. the heart or perhaps the brain,Cf. Aristot. Met. 5.1.1. for it does not matter which of them is of this nature. But man and horse and terms which are applied in this way to individuals, but universally, are not substance, but a kind of concrete whole composed of this particular formula and this particular matter regarded as universal. But individually Socrates is already composed of ultimate matter; and similarly in all other cases.

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A part, then, may be part of the form (by form I mean essence), or of the concrete whole composed of form and matter, or of the matter itself. But only the parts of the form are parts of the formula, and the formula refers to the universal; for circle is the same as essence of circle, and soul the same as essence of soul.

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But when we come to the concrete thing, e.g. this circle—which is a particular individual, either sensible or intelligible (by intelligible circles I mean those of mathematics,i.e., something very similar to the Platonic intermediates. Cf. Introduction. and by sensible those which are of bronze or wood)—of these individuals there is no definition;

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we apprehend them by intelligence or perception; and when they have passed from the sphere of actuality it is uncertain whether they exist or not, but they are always spoken of and apprehended by the universal formula. But the matter is in itself unknowable. Some matter is sensible and some intelligible; sensible, such as bronze and wood and all movable matter; intelligible, that which is present in sensible things not qua sensible, e.g. the objects of mathematics.See Aristot. Met. 13.2, 3.

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We have now discussed the case of the whole and part, and of prior and posterior. But we must answer the question, when we are asked which is prior—the right angle and circle and animal, or that into which they are resolved and of which they are composed, i.e. their parts—by saying that neither is absolutely prior.

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For if the soul also is the animal or living thing, or the soul of the individual is the individual, and being a circle is the circle, and being a right angle or the essence of the right angle is the right angle, then we must admit that the whole in one sense is posterior to the part in one sense: e.g. to the parts in the formula and the parts of a particular right angle

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(since both the material right angle of bronze and the right angle included by individual lines are posterior to their parts), but the immaterial angle is posterior to the parts in the formula, but prior to the parts in the individual. We must not give an unqualified answer. And if the soul is not the animal but something else, even so we must say that some wholes are prior and some are not, as has been stated.

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The question naturally presents itself, what sort of parts belong to the form and what sort belong not to it but to the concrete object. Yet if this is not plain it is impossible to define the particular; because the definition refers to the universal and the form. Therefore if it is not clear what kind of parts are material and what kind are not, the formula of the thing will not be clear either.

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In the case of things which can be seen to be induced in specifically different materials, as, e.g., a circle is in bronze and stone and wood, it seems clear that these things, the bronze and the stone, are in no sense part of the essential substance of the circle, because it is separable from them.

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As for things which are not visibly separable, there is no reason why the same should not apply to them; e.g., if all the circles that had ever been seen were bronze; for the bronze would be none the less no part of the form, but it is difficult to separate it in thought.

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For example, the form of man is always manifested in flesh and bones and elements of this kind; then are these actually parts of the form and formula, or are they not so, but matter, though since the form is not induced in other materials, we cannot separate it?

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Now since this seems to be possible, but it is not clear when, some thinkersThe Pythagoreans. are doubtful even in the case of the circle and the triangle, considering that it is not proper to define them by lines and continuous space, but that all these are to the circle or triangle as flesh or bone is to man, and bronze or stone to the statue; and they reduce everything to numbers, and say that the formula of line is the formula of 2.

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And of the exponents of the Forms, some make 2 the Ideal line, and some the form of the lineThe distinction seems to be that given in Aristot. Met. 8.3.1. Some held that the line, considered absolutely, is simply twoness; others that it is twoness in length. ; for they say that in some cases the form and that of which it is the form, e.g. 2 and the form of 2, are the same; but in the case of line this is no longer so.

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It follows, then, that there is one form of many things whose form is clearly different (a consequence which confronted the Pythagoreans tooCf. Aristot. Met. 1.5.17.), and that it is possible to make one supreme Form of everything, and not to regard the rest as forms. In this way, however, all things would be one.

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Now we have stated that the question of definitions involves some difficulty, and have shown why this is so. Hence to reduce everything in this way and to dispose of the matter is going too far; for some things are presumably a particular form in particular matter, or particular things in a particular state.

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And the analogy in the case of the living thing which the younger SocratesA disciple of the great Socrates; one of the speakers in the PoliticusPlat. Stat. and referred to in Plat. Theaet. 147c, Plat. Soph. 218b. used to state is not a good one; for it leads one away from the truth, and makes one suppose that it is possible for a man to exist without his parts, as a circle does without the bronze. But the case is not similar; for the animal is sensible and cannot be defined without motion, and hence not unless its parts are in some definite condition;

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for it is not the hand in any condition that is a part of a man, but only when it can perform its function, and so has life in it. Without life in it it is not a part.

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And with respect to mathematical objects, why are the formulae of the parts not parts of the formulae of the whole; e.g., why are the formulae of the semicircles not parts of the formula of the circle? for they are not sensible.

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Probably this makes no difference; because there will be matter even of some things which are not sensible. Indeed there will be matter in some sense in everything which is not essence or form considered independently, but a particular thing. Thus the semicircles will be parts not of the universal circle but of the particular circles, as we said beforeAristot. Met. 7.10.17.—for some matter is sensible, and some intelligible.

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It is clear also that the soul is the primary substance, and the body matter; and man or animal is the combination of both taken universally. And Socrates or Coriscus has a double sense, that is if the soul too can be called Socrates (for by Socrates some mean the soul and some the concrete person); but if Socrates means simply this soul and this body, the individual is composed similarly to the universal.

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Whether there is some other material component of these substances besides their matter, and whether we should look for some further substance in them, such as numbers or something of that kind, must be considered later.In Books 13 and 14. It is with a view to this that we are trying to determine the nature of sensible substances, since in a sense the study of sensible substances belongs to physics or secondary philosophy; for the physicist must know not only about the matter, but also about the substance according to the formula; this is even more essential.

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And in the case of definitions, in what sense the elements in the formula are parts of the definition, and why the definition is one formula (for the thing is clearly one, but in virtue of what is it one, seeing that it has parts?); this must be considered later.Aristot. Met. 8.6.

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We have stated, then, in a general account which covers all cases, what essence is, and how it is independent; and why the formula of the essence of some things contains the parts of the thing defined, while that of others does not; and we have shown that the material parts of a thing cannot be present in the formula of the substance (since they are not even parts of the substance in that sense, but of the concrete substance; and of this in one sense there is a formula, and in another sense there is not.

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There is no formula involving the matter, for this is indeterminate; but there is a formula in accordance with the primary substance, e.g., in the case of a man, the formula of the soul; because the substance is the indwelling form, of which and of the matter the so called concrete substance is composed. E.g., concavity is such a form, since from this and nose is derived snub nose and snubness—for nose will be present twice over in these expressions);

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but in the concrete substance, e.g. snub nose or Callias, matter will be present too.Chapters. 10-11; and cf. Aristot. Met. 7.4. We have stated also that the essence and the individual are in some cases the same, as in the case of the primary substances; e.g. crookedness and essence of crookedness, if this is primary.

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By primary I mean that which does not imply the presence of something in something else as a material substrate. But such things as are material or are compounded with matter are not the same as their essence; not even if they are accidentally one, e.g. Socrates and cultured; for these are only accidentally the same.

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Now let us first deal with definition, in so far as it has not been dealt with in the Analytics; for the problem stated thereAristot. An. Post. 92a 29. has a bearing upon our discussion of substance. The problem I mean is this: what constitutes the unity of the thing of which we say that the formula is a definition? E.g., in the case of man, two-footed animal; for let us take this as the formula of man.

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Why, then, is this a unity and not a plurality, animal and two-footed? For in the case of man and white we have a plurality when the latter does not refer to the former, but a unity when it does refer to it, and the subject, man, has an attribute; for then they become a unity and we have the white man.

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But in the case before us one term does not partake of the other; the genus is not considered to partake of its differentiae, for then the same thing would be partaking simultaneously of contraries, since the differentiae by which the genus is distinguished are contrary. And even if it does partake of them, the same argument applies, since the differentiae are many; e.g. terrestrial, two-footed, wingless.

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Why is it that these are a unity and not a plurality? Not because they are present in one genus, for in that case all the differentiae of the genus will form a unity. But all the elements in the definition must form a unity, because the definition is a kind of formula which is one and defines substance, so that it must be a formula of one particular thing; because the substance denotes one thing and an individual, as we say.

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We must firstThe other type of definition, that which states the constituent parts of a thing, is not discussed here. examine definitions which are reached by the process of division.

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For there is nothing else in the definition but the primary genus and the differentiae; the other genera consist of the primary genus together with the differentiae which are taken with it. E.g., the primary genus is animal; the next below it, two-footed animal; and again, two-footed wingless animal; and similarly also if the expression contains more terms still.

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In general it does not matter whether it contains many or few terms, nor, therefore, whether it contains few or two. Of the two one is differentia and the other genus; e.g., in two-footed animal animal is genus, and the other term differentia.

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If, then, the genus absolutely does not exist apart from the species which it includes, or if it exists, but only as matter (for speech is genus and matter, and the differentiae make the species, i.e. the letters, out of it), obviously the definition is the formula composed of the differentiae.

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But further we must also divide by the differentia of the differentia. E.g., having feet is a differentia of animal; then in turn we must discover the differentia of animal having feet qua having feet. Accordingly we should not say that of that which has feet one kind is winged and another wingless, (that is if we are to speak correctly; if we say this it will be through incapability), but only that one kind is cloven-footed and another not; because these are differentiae of foot, since cloven-footedness is a kind of footedness.

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And thus we tend always to progress until we come to the species which contain no differentiae. At this point there will be just as many species of foot as there are differentiae, and the kinds of animals having feet will be equal in number to the differentiae. Then, if this is so, obviously the ultimate differentia will be the substance and definition of the thing, since we need not state the same things more than once in definitions, because this is superfluous.

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However, it does happen; for when we say footed two-footed animal we have simply said animal having feet, having two feet. And if we divide this by its proper division, we shall be stating the same thing several times, as many times as there are differentiae.

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If, then, we keep on taking a differentia of a differentia, one of them, the last, will be the form and the substance. But if we proceed with reference to accidental qualities—e.g. if we divide that which has feet into white and black—there will be as many differentiae as there are divisions. It is therefore obvious that the definition is the formula derived from the differentiae, and strictly speaking from the last of them.

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This will be clear if we change the order of such definitions, e.g. that of man, saying two-footed footed animal; for footed is superfluous when we have already said two-footed. But there is no question of order in the substance; for how are we to think of one part as posterior and the other prior?

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With regard, then, to definitions by division, let this suffice as a preliminary statement of their nature.

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Since the subject of our inquiry is substance, let us return to it. Just as the substrate and the essence and the combination of these are called substance, so too is the universal. With two of these we have already dealt, i.e. with the essenceChs. 4-5.,10-12. and the substrateCh. 3.; of the latter we have said that it underlies in two senses—either being an individual thing (as the animal underlies its attributes), or as matter underlies the actuality.

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The universal also is thought by someThe Platonists. to be in the truest sense a cause and a principle. Let us therefore proceed to discuss this question too; for it seems impossible that any universal term can be substance.

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First, the substance of an individual is the substance which is peculiar to it and belongs to nothing else; whereas the universal is common; for by universal we mean that which by nature appertains to several things.

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Of what particular, then, will the universal be the substance? Either of all or of none. But it cannot be the substance of all; while, if it is to be the substance of one, the rest also will be that one; because things whose substance is one have also one essence and are themselves one.

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Again, substance means that which is not predicated of a subject, whereas the universal is always predicated of some subject.

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But perhaps although the universal cannot be substance in the sense that essence is, it can be present in the essence, as animal can be present in man and horse.

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Then clearly there is in some sense a formula of the universal. It makes no difference even if there is not a formula of everything that is in the substance; for the universal will be none the less the substance of something; e.g., man will be the substance of the man in whom it is present. Thus the same thing will happen againi.e., the argument in ch. 3 will apply to this case also.; e.g. animal will be the substance of that in which it is present as peculiar to it.

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Again, it is impossible and absurd that the individual or substance, if it is composed of anything, should be composed not of substances nor of the individual, but of a quality; for then non-substance or quality will be prior to substance or the individual. Which is impossible; for neither in formula nor in time nor in generation can the affections of substance be prior to the substance, since then they would be separable.

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Again, a substance will be present in Socrates, who is a substance; so that it will be the substance of two things. And in general it follows that if man and all terms used in this way are substance, none of the elements in the formula is the substance of anything, nor can it exist apart from the species or in anything else; I mean, e.g., that neither animal nor any other element of the formula can exist apart from the particular species.

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If we look at the question from this standpoint it is obvious that no universal attribute is substance; and it is also clear from the fact that none of the common predicates means so-and-so, but such and-such. Otherwise amongst many other awkward consequences we have the third man. See note on Aristot. Met. 1.9.3.

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Again, it is clear in this way too. Substance can not consist of substances actually present in it; for that which is actually two can never be actually one, whereas if it is potentially two it can be one. E.g., the double consists of two halves—that is, potentially; for the actualization separates the halves.

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Thus if substance is one, it cannot consist of substances present in it even in this sense, as Democritus rightly observes; he says that it is impossible for two to come from one, or one from two, because he identifies substance with the atoms.Cf. Aristot. De Caelo 303a 6, Aristot. De Gen. et Corr. 325a 35.

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Clearly then the same will also hold good in the case of number (assuming that number is a composition of units, as it is said to be by some); because either 2 is not 1, or there is not actually a unit in it.

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The consequence involves a difficulty; for if no substance can consist of universals, because they mean of such a kind, and not a particular thing; and if no substance can be actually composed of substances, every substance will be incomposite, and so there will be no formula of any substance.

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But in point of fact it is universally held, and has been previously stated,Aristot. Met. 7.5.5-7. that substance is the only or chief subject of definition; but on this showing there is no definition even of substance. Then there can be no definition of anything; or rather in a sense there can, and in a sense cannot. What this means will be clearer from what follows later.Aristot. Met. 7.15, Aristot. Met. 8.6.

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From these same considerations it is clear also what consequence follows for those who maintain that the Forms are substances and separable, and who at the same time make the species consist of the genus and the differentiae. If there are Forms, and if animal is present in the man and the horse, it is either numerically one and the same with them, or not.

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(In formula they are clearly one; for in each case the speaker will enunciate the same formula.) If, then, there is in some sense an Absolute Man, who is an individual and exists separately, then the constituents, e.g. animal and two-footed, must have an individual meaning and be separable and substances. Hence there must be an Absolute Animal too.

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(i) Then if the animal which is in the horse and the man is one and the same, as you are one and the same with yourself, how can the one which in things that exist separately be one, and why should not this animal also be separated from itself? Again, if it is to partake of two-footed and of many-footed, an impossibility follows; for contrary attributes will belong to it although it is one and individual.

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But if it does not, in what sense is it that one calls an animal two-footed or terrestrial? Perhaps the terms are combined and in contact or mixed. But all these expressions are absurd.

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(2) But there is a different animal in each species. Then there will be practically an infinity of things of which animal is the substance, since it is not in an accidental sense that man is derived from animal.

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Again, the Absolute Animal will be a plurality. For (a) the animal in each species will be the substance of that species, since the species is called after it and no other thing. Otherwise man would be derived from that other thing, which would be the genus of man. (b) Further, all the constituents of man will be Ideas. Then, since nothing can be the Idea of one thing and the substance of another (for this is impossible),

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each and every animal in the various species will be the Absolute Animal.

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Further, from what will these Forms be derived, and how can they be derived from the Absolute Animal? Or how can the animal, whose very essence is animal, exist apart from the Absolute Animal? And further, in the case of sensible things both these and still more absurd consequences follow. If, then, these consequences are impossible, clearly there are not Forms of sensible things in the sense in which some hold that there are.

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Since substance is of two kinds, the concrete thing and the formula (I mean that one kind of substance is the formula in combination with the matter, and the other is the formula in its full sense), substances in the former sense admit of destruction, for they also admit of generation. But the formula does not admit of destruction in the sense that it is ever being destroyed, since neither does it so admit of generation (for the essence of house is not generated, but only the essence of this house); formulae are , and are not, independently of generation and destruction; for it has been shownCf. Aristot. Met. 7.8.3. that no one either generates or creates them.

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For this reason also there is no definition or demonstration of particular sensible substances, because they contain matter whose nature is such that it can both exist and not exist. Hence all the individual instances of them are perishable.

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If, then, the demonstration and definition of necessary truths requires scientific knowledge, and if, just as knowledge cannot be sometimes knowledge and sometimes ignorance (it is opinion that is of this nature), so too demonstration and definition cannot vary (it is opinion that is concerned with that which can be otherwise than it is)— then clearly there can be neither definition nor demonstration of individual sensible substances.

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For (a) things which perish are obscure to those who have knowledge of them when they are removed from the sphere of their perception, and (b) even though their formulae are preserved in the soul, there will no longer be either definition or demonstration of them. Therefore in cases relating to definition, when we are trying to define any individual, we must not fail to realize that our definition may always be upset; because it is impossible to define these things.

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Nor, indeed, can any Idea be defined; for the Idea is an individual, as they say, and separable; and the formula must consist of words, and the man who is defining must not coin a word, because it would not be comprehensible. But the words which are in use are common to all the things which they denote; and so they must necessarily apply to something else as well. E.g., if a man were to define you, he would say that you are an animal which is lean or white or has some other attribute, which will apply to something else as well.

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And if it should be said that there is no reason why all the attributes separately should not belong to several things, and yet in combination belong to this alone, we must reply, (1.) that they also belong to both the elements; e.g., two-footed animal belongs both to animal and to two-footed (and in the case of eternal elements this is even necessarily so; since they are prior to the compound, and parts of it.

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Indeed they are also separable, if the term man is separable—for either neither can be separable, or both are so. If neither, the genus will not exist apart from the species, or if it is so to exist, so will the differentia); (2.) that animal and two-footed are prior in being to two-footed animal, and that which is prior to something else is not destroyed together with it.

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Again, if the Ideas are composed of Ideas (for constituents are less composite than that which they compose), still the elements of which the Idea is composed (e.g. animal and two-footed) will have to be predicated of many particulars. Otherwise, how can they be known? For there would be an Idea which cannot be predicated of more than one thing. But this is not considered possible; every Idea is thought to admit of participation.

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Thus, as we have said,The statement has only been implied in the preceding arguments. the impossibility of defining individuals is hard to realize when we are dealing with eternal entities, especially in the case of such as are unique, e.g. the sun and moon. For people go wrong not only by including in the definition attributes on whose removal it will still be sun—e.g., that which goes round the earth, or night-hidden (for they suppose that if it stops or becomes visiblesc. in the night. it will no longer be sun; but it is absurd that this should be so, since the sun denotes a definite substance)—they also mention attributes which may apply to something else; e.g., if another thing with those attributes comes into being, clearly it will be a sun. The formula, then, is general; but the sun was supposed to be an individual, like Cleon or Socrates.

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Why does not one of the exponents of the Ideas produce a definition of them? If they were to try, it would become obvious that what we have just said is true.

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It is obvious that even of those things which are thought to be substances the majority are potentialities; both the parts of living things (for none of them has a separate substantial existence; and when they are separated, although they still exist, they exist as matter), and earth, fire and air; for none of these is one thing —they are a mere aggregate before they are digested and some one thing is generated from them.

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It might be supposed very reasonably that the parts of living things and the corresponding parts of their vital principle are both, i.e. exist both actually and potentially, because they contain principles of motion derived from something in their joints; and hence some animalse.g. wasps, bees, tortoises (P. Nat. 467a 18, 468a 25). live even when they are divided. Nevertheless it is only potentially that all of them will exist when they are one and continuous by nature and not by force or concretion; for this sort of thing is malformation.i.e., it is only when they do not properly constitute a unity that parts can be said to exist actually.

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And since unity has the same variety of senses as being, and the substance of Unity is one, and things whose substance is numerically one are numerically one, evidently neither Unity nor Being can be the substance of things, just as neither being an element or principle can be the substance; but we ask what the principle is so that we may refer to something more intelligible.i.e., a thing is a principle in relation to something else which it explains; therefore a principle is less substantial than unity or being, which belong to a thing in itself.

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Now of these concepts Being and Unity are more nearly substance than are principle, element and cause; but not even the former are quite substance, since nothing else that is common is substance; for substance belongs to nothing except itself and that which contains it and of which it is the substance.

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Again, Unity cannot exist in many places at the same time, but that which is common is present in many things at the same time. Hence it is clear that no universal exists in separation apart from its particulars. The exponents of the Forms are partly right in their account when they make the Forms separate; that is, if the Forms are substances, but they are also partly wrong, since by Form they mean the one-over-many. i.e. universal; cf. Aristot. Met. 1.9.1.

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The reason for this is that they cannot explain what are the imperishable substances of this kind which exist besides particular sensible substances; so they make them the same in kind as perishable things (for these we know); i.e., they make Ideal Man and Ideal Horse, adding the word Ideal to the names of sensible things.

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However, I presume that even if we had never seen the stars, none the less there would be eternal substances besides those which we knew; and so in the present case even if we cannot apprehend what they are, still there must be eternal substances of some kind.

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It is clear, then, both that no universal term is substance and that no substance is composed of substances.

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As for what and what sort of thing we mean by substance, let us explain this by making, as it were, another fresh start. Perhaps in this way we shall also obtain some light upon that kind of substance which exists in separation from sensible substances. Since, then, substance is a kind of principle and cause, we had better pursue our inquiry from this point.

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Now when we ask why a thing is, it is always in the sense why does A belong to B?

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To ask why the cultured man is a cultured man is to ask either, as we have said, why the man is cultured, or something else. Now to ask why a thing is itself is no question; because when we ask the reason of a thing the fact must first be evident; e.g., that the moon suffers eclipse;

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and because it is itself is the one explanation and reason which applies to all questions such as why is man man? or why is the cultured person cultured? (unless one were to say that each thing is indivisible from itself, and that this is what being one really means); but this, besides being a general answer, is a summary one.The argument is: The question Why is the cultured man a cultured man? if it does not mean Why is the man cultured? can only mean Why is a thing itself? But when we ask a question the fact must be obvious; and since it is obvious that a thing is itself, because it is itself (or because each thing is indivisible from itself) is the one and only complete answer to all questions of this type. Since this answer (in either form) is clearly unsatisfactory, the question which it answers cannot be a proper question. We may, however, ask why a man is an animal of such-and-such a kind.

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It is clear, then, that we are not asking why he who is a man is a man; therefore we are asking why A, which is predicated of B, belongs to B. (The fact that A does belong to B must be evident, for if this is not so, the question is pointless.) E.g., Why does it thunder? means why is a noise produced in the clouds? for the true form of the question is one thing predicated in this way of another.

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Or again, why are these things, e.g. bricks and stones, a house? Clearly then we are inquiring for the cause (i.e., to speak abstractly, the essence); which is in the case of some things, e.g. house or bed, the end , and in others the prime mover—for this also is a cause. We look for the latter kind of cause in the case of generation and destruction, but for the former also in the case of existence.

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What we are now looking for is most obscure when one term is not predicated of another; e.g. when we inquire what man is; because the expression is a simple one not analyzed into subject and attributes. We must make the question articulate before we ask it; otherwise we get something which shares the nature of a pointless and of a definite question.

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Now since we must know that the fact actually exists, it is surely clear that the question is why is the matter so-and-so? e.g. why are these materials a house? Because the essence of house is present in them. And this matter, or the body containing this particular form, is man. Thus what we are seeking is the cause (i.e. the form) in virtue of which the matter is a definite thing; and this is the substance of the thing.

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Clearly then in the case of simple entitiesPure forms which contain no matter; in their case the method just described obviously will not apply. They can only be apprehended intuitively (cf. Aristot. Met. 9.10.). inquiry and explanation are impossible; in such cases there is a different mode of inquiry.

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Now since that which is composed of something in such a way that the whole is a unity; not as an aggregate is a unity, but as a syllable isThis sentence is not finished; the parenthesis which follows lasts until the end of the chapter.—the syllable is not the letters, nor is BA the same as B and A; nor is flesh fire and earth; because after dissolution the compounds, e.g. flesh or the syllable, no longer exist; but the letters exist, and so do fire and earth.

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Therefore the syllable is some particular thing; not merely the letters, vowel and consonant, but something else besides. And flesh is not merely fire and earth, or hot and cold, but something else besides.

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Since then this something else must be either an element or composed of elements, (a) if it is an element, the same argument applies again; for flesh will be composed of this and fire and earth, and again of another element, so that there will be an infinite regression. And (b) if it is composed of elements, clearly it is composed not of one (otherwise it will itself be that element) but of several; so that we shall use the same argument in this case as about the flesh or the syllable.

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It would seem, however, that this something else is something that is not an element, but is the cause that this matter is flesh and that matter a syllable, and similarly in other cases.

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And this is the substance of each thing, for it is the primary cause of its existence. And since, although some things are not substances, all substances are constituted in accordance with and by nature, substance would seem to be this nature, which is not an element but a principle.i.e. the formal cause. Cf. Aristot. Met. 5.4.4-6. An element is that which is present as matter in a thing, and into which the thing is divided; e.g., A and B are the elements of the syllable.

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We must now draw our conclusions from what has been said, and after summing up the result, bring our inquiry to a close. We have saidCf. Aristot. Met. 7.1. that the objects of our inquiry are the causes and principles and elements of substances. Now some substances are agreed upon by all; but about others certain thinkers have stated individual theories.

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Those about which there is agreement are natural substances: e.g. fire, earth, water, air and all the other simple bodies; next, plants and their parts, and animals and the parts of animals; and finally the sensible universe and its parts; and certain thinkers individually include as substances the Forms and the objects of mathematics.Cf. Aristot. Met. 7.2.

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And arguments show that there are yet other substances: the essence and the substrate.Cf. Aristot. Met. 7.3-4. Again, from another point of view, the genus is more nearly substance than the species, and the universal than the particularsCf. Aristot. Met. 7.13.; and there is a close connection between the universal and genus and the Ideas, for they are thought to be substance on the same grounds.Cf. Aristot. Met. 7.14.

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And since the essence is substance, and definition is the formula of the essence, we have therefore systematically examined definition and essential predication.Cf. Aristot. Met. 7.4-6, 12, 15. And since the definition is a formula, and the formula has parts, we have been compelled to investigate parts, and to discover what things are parts of the substance, and what are not; and whether the parts of the substance are also parts of the definition.Cf. Aristot. Met. 7.10, 11. Further, then, neither the universal nor the genus is substance.Cf. Aristot. Met. 7.13, 16.

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As for the Ideas and the objects of mathematics (for some say that these exist apart from sensible substances) we must consider them later.Books 13 and 14. But now let us proceed to discuss those substances which are generally accepted as such.

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Now these are the sensible substances, and all sensible substances contain matter.

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And the substrate is substance; in one sense matter (by matter I mean that which is not actually, but is potentially, an individual thing); and in another the formula and the specific shape (which is an individual thing and is theoretically separable); and thirdly there is the combination of the two, which alone admits of generation and destruction,Cf. Aristot. Met. 7.8. and is separable in an unqualified sense—for of substances in the sense of formula some are separableIn point of fact the only form which is absolutely separable is Mind or Reason. Cf. Aristot. Met. 12.7, 9. and some are not.

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That matter is also substance is evident; for in all opposite processes of change there is something that underlies those processes; e.g., if the change is of place , that which is now in one place and subsequently in another; and if the change is of magnitude , that which is now of such-and-such a size, and subsequently smaller or greater; and if the change is of quality , that which is now healthy and subsequently diseased.

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Similarly, if the change is in respect of being , there is something which is now in course of generation, and subsequently in course of destruction, and which is the underlying substrate, now as this individual thing, and subsequently as deprived of its individuality. In this last process of change the others are involved, but in either one or twoi.e., locomotion does not involve substantial change; alteration may or may not involve it (in Aristot. Met. 9.8.17 we find that it does not); increase or decrease does involve it. of the others it is not involved; for it does not necessarily follow that if a thing contains matter that admits of change of place, it also contains matter that is generable and destructible.e.g., the heavenly bodies, though imperishable, can move in space (Aristot. Met. 8.4.7, Aristot. Met. 12.2.4). The difference between absolute and qualified generation has been explained in the Physics.Aristot. Phys. 225a 12-20; cf. Aristot. De Gen. et Corr. 317a 17-31.

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Since substance in the sense of substrate or matter is admittedly substance, and this is potential substance, it remains to explain the nature of the actual substance of sensible things. Now DemocritusCf. Aristot. Met. 1.4.11. apparently assumes three differences in substance; for he says that the underlying body is one and the same in material, but differs in figure, i.e. shape; or inclination, i.e. position; or intercontact, i.e. arrangement.

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But evidently there are many differences; e.g. some things are defined by the way in which their materials are combined, as, for example, things which are unified by mixture, as honey-water; or by ligature, as a faggot; or by glue, as a book; or by clamping, as a chest; or by more than one of these methods. Other things are defined by their position, e.g. threshold and lintel (for these differ in being situated in a particular way); and others by place <or direction>, e.g. the winds; others by time, e.g. dinner and breakfast; and others by the attributes peculiar to sensible things, e.g. hardness and softness, density and rarity, dryness and humidity. Some are distinguished by some of these differences, and others by all of them; and in general some by excess and some by defect.

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Hence it is clear that is has the same number of senses; for a thing is a threshold because it is situated in a particular way, and to be a threshold means to be situated in this particular way, and to be ice means to be condensed in this particular way. Some things have their being defined in all these ways: by being partly mixed, partly blended, partly bound, partly condensed, and partly subjected to all the other different processes; as, for example, a hand or a foot.

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We must therefore comprehend the various kinds of differences—for these will be principles of being—i.e. the differences in degree, or in density and rarity, and in other such modifications, for they are all instances of excess and defect.

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And if anything differs in shape or in smoothness or roughness, all these are differences in straightness and curvature. For some things mixture will constitute being, and the opposite state not-being.

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From this it is evident that if substance is the cause of the existence of each thing, we must look among these differences for the cause of the being of each thing.

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No one of them, nor the combination of any two of them, is substance, but nevertheless each one of them contains something analogous to substance. And just as in the case of substances that which is predicated of the matter is the actuality itself, so in the other kinds of definition it is the nearest approximation to actuality. E.g., if we have to define a threshold, we shall call it a piece of wood or stone placed in such-and-such a way; and we should define a house as bricks and timber arranged in such-and-such a way;

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or again in some cases there is the final cause as well. And if we are defining ice, we shall describe it as water congealed or condensed in such-and-such a way; and a harmony is such-and-such a combination of high and low; and similarly in the other cases.

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From this it is evident that the actuality or formula is different in the case of different matter; for in some cases it is a combination, in others a mixture, and in others some other of the modes which we have described.

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Hence in defining the nature of a house, those who describe it as stones, bricks and wood, describe the potential house, since these things are its matter; those who describe it as a receptacle for containing goods and bodies, or something else to the same effect, describe its actuality; but those who combine these two definitions describe the third kind of substance, that which is composed of matter and form.

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For it would seem that the formula which involves the differentiae is that of the form and the actuality, while that which involves the constituent parts is rather that of the matter. The same is true of the kind of definitions which ArchytasA celebrated Pythagorean, contemporary with Plato. used to accept; for they are definitions of the combined matter and form. E.g., what is windlessness? Stillness in a large extent of air; for the air is the matter, and the stillness is the actuality and substance.

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What is a calm? Levelness of sea. The sea is the material substrate, and the levelness is the actuality or form.

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From the foregoing account it is clear what sensible substance is, and in what sense it exists; either as matter, or as form and actuality, or thirdly as the combination of the two.

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We must not fail to realize that sometimes it is doubtful whether a name denotes the composite substance or the actuality and the form—e.g. whether house denotes the composite thing, a covering made of bricks and stones arranged in such-and-such a way, or the actuality and form, a covering; and whether line means duality in length or dualityCf. Aristot. Met. 7.11.6.; and whether animal means a soul in a body or a soul; for the soul is the substance and actuality of some body.

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The term animal would be applicable to both cases; not as being defined by one formula, but as relating to one concept. These distinctions are of importance from another point of view, but unimportant for the investigation of sensible substance; because the essence belongs to the form and the actualization.

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Soul and essence of soul are the same, but man and essence of man are not, unless the soul is also to be called man; and although this is so in one sense, it is not so in another.

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It appears, then, upon inquiry into the matter,Cf. Plat. Theaet. 204aff. that a syllable is not derived from the phonetic elements plus combination, nor is a house bricks plus combination. And this is true; for the combination or mixture is not derived from the things of which it is a combination or mixture,

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nor, similarly, is any other of the differences. E.g., if the threshold is defined by its position, the position is not derived from the threshold, but rather vice versa. Nor, indeed, is man animal plus two-footed; there must be something which exists besides these, if they are matter; but it is neither an element nor derived from an element, but the substance; and those who offer the definition given above are omitting this and describing the matter.

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If, then, this something else is the cause of a man’s being, and this is his substance, they will not be stating his actual substance.

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Now the substance must be either eternal or perishable without ever being in process of perishing, and generated without ever being in process of generation. It has been clearly demonstrated elsewhereCf. Aristot. Met. 7.8. that no one generates or creates the form; it is the individual thing that is created, and the compound that is generated.

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But whether the substances of perishable things are separable or not is not yet at all clearCf. Aristot. Met. 8.1.6. n..; only it is clear that this is impossible in some cases, i.e. in the case of all things which cannot exist apart from the particular instances; e.g. house or implement.Cf. Aristot. Met. 7.8.6. Probably, then, neither these things themselves, nor anything else which is not naturally composed, are substances; for their nature is the only substance which one can assume in the case of perishable things.

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Hence the difficulty which perplexed the followers of AntisthenesCf. Aristot. Met. 5.29.4. and others similarly unlearned has a certain application; I mean the difficulty that it is impossible to define what a thing is (for the definition, they say, is a lengthy formula), but it is possible actually to teach others what a thing is like; e.g., we cannot say what silver is, but we can say that it is like tin.

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Hence there can be definition and formula of one kind of substance, i.e. the composite, whether it is sensible or intelligible; but not of its primary constituents, since the defining formula denotes something predicated of something, and this must be partly of the nature of matter and partly of the nature of form.

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It is also obvious that, if numbers are in any sense substances, they are such in this sense, and not, as someAristotle is referring to the Pythagoreans and Platonists, but seems as usual to misrepresent their views. His object in this section is to show that the relation of number to substance is only one of analogy. Cf. Aristot. Met. 13.6, 7, and see Introduction. describe them, aggregates of units. For (a) the definition is a kind of number, since it is divisible, and divisible into indivisible parts (for formulae are not infinite); and number is of this nature.

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And (b) just as when any element which composes the number is subtracted or added, it is no longer the same number but a different one, however small the subtraction or addition is; so neither the definition nor the essence will continue to exist if something is subtracted from or added to it. And (c) a number must be something in virtue of which it is a unity (whereas our opponents cannot say what makes it one); that is, if it is a unity.

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For either it is not a unity but a kind of aggregate, or if it is a unity, we must explain what makes a unity out of a plurality. And the definition is a unity; but similarly they cannot explain the definition either. This is a natural consequence, for the same reason applies to both, and substance is a unity in the way which we have explained, and not as some thinkers say: e.g. because it is a kind of unit or point; but each substance is a kind of actuality and nature.

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Also (d) just as a number does not admit of variation in degree, so neither does substance in the sense of form; if any substance does admit of this, it is substance in combination with matter.In Aristot. Categories 3b 33-4a 9 Aristotle does not allow this exception.

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Let this suffice as a detailed account of the generation and destruction of so-called substances, in what sense they are possible and in what sense they are not; and of the reference of things to number.

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As regards material substance, we must not fail to realize that even if all things are derived from the same primary cause, or from the same things as primary causesi.e. from prime matter or the four elements.; i.e. even if all things that are generated have the same matter for their first principle, nevertheless each thing has some matter peculiar to it; e.g., the sweet or the viscous is the proximate matter of mucus, and the bitter or some such thing is that of bile— although probably mucus and bile are derived from the same ultimate matter.

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The result is that there is more than one matter of the same thing, when one thing is the matter of the other; e.g., mucus is derived from the viscous; and from the sweet, if the viscous is derived from the sweet; and from bile, by the analysis of bile into its ultimate matter. For there are two senses in which X comes from Y; either because X will be found further on than Y in the process of development, or because X is produced when Y is analyzed into its original constituents.

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And different things can be generated by the moving cause when the matter is one and the same, e.g. a chest and a bed from wood. But some different things must necessarily have different matter; e.g., a saw cannot be generated from wood, nor does this lie in the power of the moving cause, for it cannot make a saw of wool or wood.

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If, then, it is possible to make the same thing from different matter, clearly the art, i.e. the moving principle, is the same; for if both the matter and the mover are different, so too is the product.

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So whenever we inquire what the cause is, since there are causes in several senses, we must state all the possible causes.

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E.g., what is the material cause of a man? The menses. What is the moving cause? The semen. What is the formal cause? The essence. What is the final cause? The end. (But perhaps both the latter are the same.) We must, however, state the most proximate causes. What is the matter? Not fire or earth, but the matter proper to man.

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Thus as regards generable natural substances we must proceed in this manner, if we are to proceed correctly; that is, if the causes are these and of this number, and it is necessary to know the causes. But in the case of substances which though natural are eternal the principle is different. For presumably some of them have no matter; or no matter of this kind, but only such as is spatially mobile.Cf. Aristot. Met. 8.1.8 n.

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Moreover, things which exist by nature but are not substances have no matter; their substrate is their substance. E.g., what is the cause of an eclipse; what is its matter? It has none; it is the moon which is affected. What is the moving cause which destroys the light? The earth. There is probably no final cause. The formal cause is the formula; but this is obscure unless it includes the efficient cause.

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E.g., what is an eclipse? A privation of light; and if we add caused by the earth’s intervention, this is the definition which includes the <efficient> cause. In the case of sleep it is not clear what it is that is proximately affected. Is it the animal? Yes; but in respect of what, and of what proximately? The heart, or some other part. Again, by what is it affected? Again, what is the affection which affects that part, and not the whole animal? A particular kind of immobility? Yes; but in virtue of what affection of the proximate subject is it this?

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Since some things both are and are not, without being liable to generation and destructionCf. Aristot. Met. 6.3.1, Aristot. Met. 7.8.3.—e.g. points,Cf. Aristot. Met. 3.5.8, 9. if they exist at all; and in general the forms and shapes of things (because white does not come to be, but the wood becomes white, since everything which comes into being comes from something and becomes something)—not all the contrariesi.e., we must distinguish contraries in the sense of contrary qualities from contraries in the sense of things characterized by contrary qualities. can be generated from each other. White is not generated from black in the same way as a white man is generated from a black man; nor does everything contain matter, but only such things as admit of generation and transformation into each other.

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And such things as, without undergoing a process of change, both are and are not, have no matter.

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There is a difficulty in the question how the matter of the individual is related to the contraries. E.g., if the body is potentially healthy, and the contrary of health is disease, is the body potentially both healthy and diseased? And is water potentially wine and vinegar? Probably in the one case it is the matter in respect of the positive state and form, and in the other case in respect of privation and degeneration which is contrary to its proper nature.

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There is also a difficulty as to why wine is not the matter of vinegar, nor potentially vinegar (though vinegar comes from it), and why the living man is not potentially dead. In point of fact they are not; their degeneration is accidental, and the actual matter of the living body becomes by degeneration the potentiality and matter of the dead body, and water the matter of vinegar; for the one becomes the other just as day becomes night.

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All things which change reciprocally in this way must return into the matter; e.g., if a living thing is generated from a dead one, it must first become the matter, and then a living thing; and vinegar must first become water, and then wine.

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With regard to the difficulty which we have describedAristot. Met. 7.12, Aristot. Met. 8.3.10, 11. in connection with definitions and numbers, what is the cause of the unification? In all things which have a plurality of parts, and which are not a total aggregate but a whole of some sort distinct from the parts, there is some cause ; inasmuch as even in bodies sometimes contact is the cause of their unity, and sometimes viscosity or some other such quality.

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But a definition is one account, not by connection, like the Iliad , but because it is a definition of one thing.

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What is it, then, that makes man one thing, and why does it make him one thing and not many, e.g. animal and two-footed, especially if, as some say, there is an Idea of animal and an Idea of two-footed?

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Why are not these Ideas man, and why should not man exist by participation, not in any man, but in two Ideas, those of animal and two-footed? And in general man will be not one, but two things—animal and two-footed. Evidently if we proceed in this way, as it is usual to define and explain, it will be impossible to answer and solve the difficulty.

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But if, as we maintain, man is part matter and part form—the matter being potentially, and the form actually man—, the point which we are investigating will no longer seem to be a difficulty. For this difficulty is just the same as we should have if the definition of XLiterally cloak; cf. Aristot. Met. 7.4.7 n. were round bronze; for this name would give a clue to the formula, so that the question becomes what is the cause of the unification of round and bronze?

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The difficulty is no longer apparent, because the one is matter and the other form. What then is it (apart from the active cause) which causes that which exists potentially to exist actually in things which admit of generation? There is no other cause of the potential sphere’s being an actual sphere; this was the essence of each.i.e., it was the essence of the potential sphere to become the actual sphere, and of the actual sphere to be generated from the potential sphere.

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Some matter is intelligible and some sensible, and part of the formula is always matter and part actuality; e.g., the circle is a plane figure.Even formulae contain matter in a sense (intelligible matter); i.e. the generic element in the species. Plane figure is the generic element of circle. But such thingThe highest genera, or categories. as have no matter, neither intelligible nor sensible, are ipso facto each one of them essentially something one; just as they are essentially something existent: an individual substance, a quality, or a quantity. Hence neither existent nor one is present in their definitions. And their essence is ipso facto something one, just as it is something existent.

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Hence also there is no other cause of the unity of any of these things, or of their existence; for each one of them is one and existent not because it is contained in the genus being or unity, nor because these genera exist separately apart from their particulars, but ipso facto.

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It is because of this difficulty that some thinkersThe Platonists. speak of participation, and raise the question of what is the cause of participation, and what participation means; and others speak of communion; e.g., LycophronA sophist, disciple of Gorgias. says that knowledge is a communion of the soul with knowing; and others call life a combination or connection of soul with body.

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The same argument, however, applies in every case; for being healthy will be the communion or connection or combination of soul and health; and being a bronze triangle a combination of bronze and triangle; and being white a combination of surface and whiteness. The reason for this is that people look for a unifying formula, and a difference, between potentiality and actuality.

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But, as we have said,Cf. sects. 4, 5. the proximate matter and the shape are one and the same; the one existing potentially, and the other actually. Therefore to ask the cause of their unity is like asking the cause of unity in general; for each individual thing is one, and the potential and the actual are in a sense one. Thus there is no cause other than whatever initiates the development from potentiality to actuality. And such things as have no matter are all, without qualification, essential unities.

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We have now dealt with Being in the primary sense, to which all the other categories of being are related; i.e. substance. For it is from the concept of substance that all the other modes of being take their meaning; both quantity and quality and all other such terms; for they will all involve the concept of substance, as we stated it in the beginning of our discussion.Aristot. Met. 7.1.

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And since the senses of being are analyzableCf. Aristot. Met. 6.2.1. not only into substance or quality or quantity, but also in accordance with potentiality and actuality and function, let us also gain a clear understanding about potentiality and actuality; and first about potentiality in the sense which is most proper to the word, but not most useful for our present purpose— for potentiality and actuality extend beyond the sphere of terms which only refer to motion.

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When we have discussed this sense of potentiality we will, in the course of our definitions of actuality,Chs. 6-10. explain the others also.

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We have made it plain elsewhereAristot. Met. 5.12. that potentiality and can have several senses.

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All senses which are merely equivocal may be dismissed; for some are used by analogy, as in geometry,Cf. Aristot. Met. 5.12.11. and we call things possible or impossible because they are or are not in some particular way. But the potentialities which conform to the same type are all principles, and derive their meaning from one primary sense of potency, which is the source of change in some other thing, or in the same thing qua other.

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One kind of potentiality is the power of being affected; the principle in the patient itself which initiates a passive change in it by the action of some other thing, or of itself qua other. Another is a positive state of impassivity in respect of deterioration or destruction by something else or by itself qua something else; i.e. by a transformatory principle—for all these definitions contain the formula of the primary sense of potentiality.

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Again, all these potentialities are so called either because they merely act or are acted upon in a particular way, or because they do so well . Hence in their formulae also the formulae of potentiality in the senses previously described are present in some degree.

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Clearly, then, in one sense the potentiality for acting and being acted upon is one (for a thing is capable both because it itself possesses the power of being acted upon, and also because something else has the power of being acted upon by it);

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and in another sense it is not; for it is partly in the patient (for it is because it contains a certain principle, and because even the matter is a kind of principle, that the patient is acted upon; i.e., one thing is acted upon by another: oily stuff is inflammable, and stuff which yields in a certain way is breakable, and similarly in other cases)—

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and partly in the agent; e.g. heat and the art of building: the former in that which produces heat, and the latter in that which builds. Hence in so far as it is a natural unity, nothing is acted upon by itself; because it is one, and not a separate thing.

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Incapacity and the incapable is the privation contrary to capacity in this sense; so that every capacity has a contrary incapacity for producing the same result in respect of the same subject.

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Privation has several sensesCf. Aristot. Met. 5.22.—it is applied (1.) to anything which does not possess a certain attribute; (2.) to that which would naturally possess it, but does not; either (a) in general, or (b) when it would naturally possess it; and either (1) in a particular way, e.g. entirely, or (2) in any way at all. And in some cases if things which would naturally possess some attribute lack it as the result of constraint, we say that they are deprived.

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Since some of these principles are inherent in inanimate things, and others in animate things and in the soul and in the rational part of the soul, it is clear that some of the potencies also will be irrational and some rational. Hence all arts, i.e. the productive sciences, are potencies; because they are principles of change in another thing, or in the artist himself qua other.

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Every rational potency admits equally of contrary results, but irrational potencies admit of one result only. E.g., heat can only produce heat, but medical science can produce disease and health. The reason of this is that science is a rational account, and the same account explains both the thing and its privation, though not in the same way; and in one sense it applies to both, and in another sense rather to the actual fact.

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Therefore such sciences must treat of contraries—essentially of the one, and non-essentially of the other; for the rational account also applies essentially to the one, but to the other in a kind of accidental way, since it is by negation and removal that it throws light on the contrary. For the contrary is the primary privation,Cf. Aristot. Met. 10.4.7. and this is the removal of that to which it is contrary.Literally of the other, i.e. the positive term.

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And since contrary attributes cannot be induced in the same subject, and science is a potency which depends upon the possession of a rational formula, and the soul contains a principle of motion, it follows that whereas the salutary can only produce health, and the calefactory only heat, and the frigorific only cold, the scientific man can produce both contrary results.

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For the rational account includes both, though not in the same way; and it is in the soul, which contains a principle of motion, and will therefore, by means of the same principle, set both processes in motion, by linking them with the same rational account. Hence things which have a rational potency produce results contrary to those of things whose potency is irrationalThe meaning of this awkward sentence is clearly shown in the latter part of 4.; for the results of the former are included under one principle, the rational account.

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It is evident also that whereas the power of merely producing (or suffering) a given effect is implied in the power of producing that effect well , the contrary is not always true; for that which produces an effect well must also produce it, but that which merely produces a given effect does not necessarily produce it well.

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There are some, e.g. the Megaric school,Founded by Euclides of Megara, an enthusiastic admirer of Socrates. The Megarics adopted the Eleatic system and developed it along dialectical lines. who say that a thing only has potency when it functions, and that when it is not functioning it has no potency. E.g., they say that a man who is not building cannot build, but only the man who is building, and at the moment when he is building; and similarly in the other cases.

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It is not difficult to see the absurd consequences of this theory. Obviously a man will not be a builder unless he is building, because to be a builder is to be capable of building; and the same will be true of the other arts.

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If, therefore, it is impossible to possess these arts without learning them at some time and having grasped them, and impossible not to possess them without having lost them at some time (through forgetfulness or some affection or the lapse of time; not, of course, through the destruction of the object of the art,i.e. the form of house. because it exists always), when the artist ceases to practice his art, he will not possess it;

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and if he immediately starts building again, how will he have re-acquired the art?

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The same is true of inanimate things. Neither the cold nor the hot nor the sweet nor in general any sensible thing will exist unless we are perceiving it (and so the result will be that they are affirming Protagoras’ theoryCf. IV. v., vi.). Indeed, nothing will have the faculty of sensation unless it is perceiving, i.e. actually employing the faculty.

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If, then, that is blind which has not sight, though it would naturally have it, and when it would naturally have it, and while it still exists, the same people will be blind many times a day; and deaf too.

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Further, if that which is deprived of its potency is incapable, that which is not happening will be incapable of happening; and he who says that that which is incapable of happening is or will be, will be in error, for this is what incapable meant.i.e., we have just said that that which is incapable is deprived of its potency—in this case, of its potency for happening.

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Thus these theories do away with both motion and generation; for that which is standing will always stand, and that which is sitting will always sit; because if it is sitting it will not get up, since it is impossible that anything which is incapable of getting up should get up.

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Since, then, we cannot maintain this, obviously potentiality and actuality are different. But these theories make potentiality and actuality identical; hence it is no small thing that they are trying to abolish.

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Thus it is possible that a thing may be capable of being and yet not be, and capable of not being and yet be; and similarly in the other categories that which is capable of walking may not walk, and that which is capable of not walking may walk.

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A thing is capable of doing something if there is nothing impossible in its having the actuality of that of which it is said to have the potentiality. I mean, e.g., that if a thing is capable of sitting and is not prevented from sitting, there is nothing impossible in its actually sitting; and similarly if it is capable of being moved or moving or standing or making to stand or being or becoming or not being or not becoming.

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The term actuality, with its implication of complete reality, has been extended from motions, to which it properly belongs, to other things; for it is agreed that actuality is properly motion.

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Hence people do not invest non-existent things with motion, although they do invest them with certain other predicates. E.g., they say that non-existent things are conceivable and desirable, but not that they are in motion. This is because, although these things do not exist actually, they will exist actually; for some non-existent things exist potentially; yet they do not exist, because they do not exist in complete reality.

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Now if, as we have said, that is possible which does not involve an impossibility, obviously it cannot be true to say that so-and-so is possible, but will not be, this view entirely loses sight of the instances of impossibility.If it is true to say that a thing which is possible will not be, anything may be possible, and nothing impossible. I mean, suppose that someone—i.e. the sort of man who does not take the impossible into account—were to say that it is possible to measure the diagonal of a square, but that it will not be measured, because there is nothing to prevent a thing which is capable of being or coming to be from neither being nor being likely ever to be.

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But from our premisses this necessarily follows: that if we are to assume that which is not, but is possible, to be or to have come to be, nothing impossible must be involved. But in this case something impossible will take place; for the measuring of the diagonal is impossible.

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The false is of course not the same as the impossible; for although it is false that you are now standing, it is not impossible.

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At the same time it is also clear that if B must be real if A is, then if it is possible for A to be real, it must also be possible for B to be real; for even if B is not necessarily possible, there is nothing to prevent its being possible. Let A, then, be possible. Then when A was possible, if A was assumed to be real, nothing impossible was involved; but B was necessarily real too. But ex hypothesi B was impossible. Let B be impossible.

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Then if B is impossible, A must also be impossible. But A was by definition possible. Therefore so is B.

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If, therefore, A is possible, B will also be possible; that is if their relation was such that if A is real, B must be real.

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Then if, A and B being thus related, B is not possible on this condition, A and B will not be related as we assumed; and if when A is possible B is necessarily possible, then if A is real B must be real too. For to say that B must be possible if A is possible means that if A is real at the time when and in the way in which it was assumed that it was possible for it to be real, then B must be real at that time and in that way.

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Since all potencies are either innate, like the senses, or acquired by practice, like flute-playing, or by study, as in the arts, some—such as are acquired by practice or a rational formula—we can only possess when we have first exercised themCf. Aristot. Met. 9.8.6, 7.; in the case of others which are not of this kind and which imply passivity, this is not necessary.

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Since anything which is possible is something possible at some time and in some way, and with any other qualifications which are necessarily included in the definition; and since some things can set up processes rationally and have rational potencies, while others are irrational and have irrational potencies; and since the former class can only belong to a living thing, whereas the latter can belong both to living and to inanimate things: it follows that as for potencies of the latter kind, when the agent and the patient meet in accordance with the potency in question, the one must act and the other be acted upon; but in the former kind of potency this is not necessary, for whereas each single potency of the latter kind is productive of a single effect, those of the former kind are productive of contrary effects,Cf. Aristot. Met. 9.2.4, 5. so that one potency will produce at the same time contrary effects.sc., if every potency must act automatically whenever agent and patient meet.

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But this is impossible. Therefore there must be some other deciding factor, by which I mean desire or conscious choice. For whichever of two things an animal desires decisively it will do, when it is in circumstances appropriate to the potency and meets with that which admits of being acted upon. Therefore everything which is rationally capable, when it desires something of which it has the capability, and in the circumstances in which it has the capability, must do that thing.

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Now it has the capability when that which admits of being acted upon is present and is in a certain state; otherwise it will not be able to act. (To add the qualification if nothing external prevents it is no longer necessary; because the agent has the capability in so far as it is a capability of acting; and this is not in all, but in certain circumstances, in which external hindrances will be excluded; for they are precluded by some of the positive qualifications in the definition.)

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Hence even if it wishes or desires to do two things or contrary things simultaneously, it will not do them, for it has not the capability to do them under these conditions, nor has it the capability of doing things simultaneously, since it will only do the things to which the capability applies and under the appropriate conditions.

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Since we have now dealt with the kind of potency which is related to motion, let us now discuss actuality; what it is, and what its qualities are. For as we continue our analysis it will also become clear with regard to the potential that we apply the name not only to that whose nature it is to move or be moved by something else, either without qualification or in some definite way, but also in other senses; and it is on this account that in the course of our inquiry we have discussed these as well.

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Actuality means the presence of the thing, not in the sense which we mean by potentially. We say that a thing is present potentially as Hermes is present in the wood, or the half-line in the whole, because it can be separated from it; and as we call even a man who is not studying a scholar if he is capable of studying. That which is present in the opposite sense to this is present actually.

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What we mean can be plainly seen in the particular cases by induction; we need not seek a definition for every term, but must comprehend the analogy: that as that which is actually building is to that which is capable of building, so is that which is awake to that which is asleep; and that which is seeing to that which has the eyes shut, but has the power of sight; and that which is differentiated out of matter to the matter; and the finished article to the raw material.

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Let actuality be defined by one member of this antithesis, and the potential by the other.

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But things are not all said to exist actually in the same sense, but only by analogy—as A is in B or to B, so is C in or to D; for the relation is either that of motion to potentiality, or that of substance to some particular matter.

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Infinity and void and other concepts of this kind are said to be potentially or actually in a different sense from the majority of existing things, e.g. that which sees, or walks, or is seen.

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For in these latter cases the predication may sometimes be truly made without qualification, since that which is seen is so called sometimes because it is seen and sometimes because it is capable of being seen; but the Infinite does not exist potentially in the sense that it will ever exist separately in actuality; it is separable only in knowledge. For the fact that the process of division never ceases makes this actuality exist potentially, but not separately.For Aristotle’s views about infinity and void see Aristot. Physics 3.4-8, 4.6-9 respectively.

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Since no action which has a limit is an end, but only a means to the end, as, e.g., the process of thinning; and since the parts of the body themselves, when one is thinning them, are in motion in the sense that they are not already that which it is the object of the motion to make them, this process is not an action, or at least not a complete one, since it is not an end; it is the process which includes the end that is an action.

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E.g., at the same time we see and have seen, understand and have understood, think and have thought; but we cannot at the same time learn and have learnt, or become healthy and be healthy. We are living well and have lived well, we are happy and have been happy, at the same time; otherwise the process would have had to cease at some time, like the thinning-process; but it has not ceased at the present moment; we both are living and have lived.

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Now of these processes we should call the one type motions, and the other actualizations.

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Every motion is incomplete—the processes of thinning, learning, walking, building—these are motions, and incomplete at that. For it is not the same thing which at the same time is walking and has walked, or is building and has built, or is becoming and has become, or is being moved and has been moved, but two different things; and that which is causing motion is different from that which has caused motion.

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But the same thing at the same time is seeing and has seen, is thinking and has thought. The latter kind of process, then, is what I mean by actualization, and the former what I mean by motion.

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What the actual is, then, and what it is like, may be regarded as demonstrated from these and similar considerations.

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We must, however, distinguish when a particular thing exists potentially, and when it does not; for it does not so exist at any and every time. E.g., is earth potentially a man? No, but rather when it has already become semen,This is inconsistent with Aristotle’s doctrine that the semen is the formal element in reproduction. Cf. Aristot. Met. 8.4.5, Aristot. Met. 6.9.5. and perhaps not even then; just as not everything can be healed by medicine, or even by chance, but there is some definite kind of thing which is capable of it, and this is that which is potentially healthy.

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The definition of that which as a result of thought comes, from existing potentially, to exist actually, is that, when it has been willed, if no external influence hinders it, it comes to pass; and the condition in the case of the patient, i.e. in the person who is being healed, is that nothing in him should hinder the process. Similarly a house exists potentially if there is nothing in X, the matter, to prevent it from becoming a house, i.e., if there is nothing which must be added or removed or changed; then X is potentially a house;

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and similarly in all other cases where the generative principle is external. And in all cases where the generative principle is contained in the thing itself, one thing is potentially another when, if nothing external hinders, it will of itself become the other. E.g., the semen is not yet potentially a man; for it must further undergo a change in some other medium.This is inconsistent with Aristotle’s doctrine that the semen is the formal element in reproduction. Cf. Aristot. Met. 8.4.5, Aristot. Met. 9.6.5. But when, by its own generative principle, it has already come to have the necessary attributes, in this state it is now potentially a man, whereas in the former state it has need of another principle;

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just as earth is not yet potentially a statue, because it must undergo a change before it becomes bronze.

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It seems that what we are describing is not a particular thing, but a definite material; e.g., a box is not wood, but wooden material,Cf. Aristot. Met. 7.7.10-12. and wood is not earth, but earthen material; and earth also is an illustration of our point if it is similarly not some other thing, but a definite material—it is always the latter term in this series which is, in the fullest sense, potentially something else.

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E.g., a box is not earth, nor earthen, but wooden; for it is this that is potentially a box, and this is the matter of the box—that is, wooden material in general is the matter of box in general, whereas the matter of a particular box is a particular piece of wood.

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If there is some primary stuff, which is not further called the material of some other thing, this is primary matter. E.g., if earth is made of air, and air is not fire, but made of fire, then fire is primary matter, not being an individual thing.

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For the subject or substrate is distinguishable into two kinds by either being or not being an individual thing. Take for example as the subject of the attributes man, or body or soul, and as an attribute cultured or white. Now the subject, when culture is induced in it, is called not culture but cultured, and the man is called not whiteness but white; nor is he called ambulation or motion, but walking or moving; just as we said that things are of a definite material.

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Thus where subject has this sense, the ultimate substrate is substance; but where it has not this sense, and the predicate is a form or individuality, the ultimate substrate is matter or material substance. It is quite proper that both matter and attributes should be described by a derivative predicate, since they are both indefinite.

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Thus it has now been stated when a thing should be said to exist potentially, and when it should not.

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Now since we have distinguishedAristot. Met. 5.11. the several senses of priority, it is obvious that actuality is prior to potentiality. By potentiality I mean not that which we have defined as a principle of change which is in something other than the thing changed, or in that same thing qua other, but in general any principle of motion or of rest; for nature also is in the same genus as potentiality, because it is a principle of motion, although not in some other thing, but in the thing itself qua itself.Cf. Aristot. Met. 5.4.1.

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To every potentiality of this kind actuality is prior, both in formula and in substance; in time it is sometimes prior and sometimes not.

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That actuality is prior in formula is evident; for it is because it can be actualized that the potential, in the primary sense, is potential, I mean, e.g., that the potentially constructive is that which can construct, the potentially seeing that which can see, and the potentially visible that which can be seen.

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The same principle holds in all other cases too, so that the formula and knowledge of the actual must precede the knowledge of the potential.

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In time it is prior in this sense: the actual is prior to the potential with which it is formally identical, but not to that with which it is identical numerically.

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What I mean is this: that the matter and the seed and the thing which is capable of seeing, which are potentially a man and corn and seeing, but are not yet so actually, are prior in time to the individual man and corn and seeing subject which already exist in actuality.

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But prior in time to these potential entities are other actual entities from which the former are generated; for the actually existent is always generated from the potentially existent by something which is actually existent—e.g., man by man, cultured by cultured—there is always some prime mover; and that which initiates motion exists already in actuality.

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We have saidAristot. Met. 7.7, 8. in our discussion of substance that everything which is generated is generated from something and by something; and by something formally identical with itself.

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Hence it seems impossible that a man can be a builder if he has never built, or a harpist if he has never played a harp; because he who learns to play the harp learns by playing it, and similarly in all other cases.

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This was the origin of the sophists’ quibble that a man who does not know a given science will be doing that which is the object of that science, because the learner does not know the science. But since something of that which is being generated is already generated, and something of that which is being moved as a whole is already moved (this is demonstrated in our discussion on MotionAristot. Physics, 6.6.), presumably the learner too must possess something of the science.

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At any rate from this argument it is clear that actuality is prior to potentiality in this sense too, i.e. in respect of generation and time.

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But it is also prior in substantiality; (a) because things which are posterior in generation are prior in form and substantiality; e.g., adult is prior to child, and man to semen, because the one already possesses the form, but the other does not;

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and (b) because everything which is generated moves towards a principle, i.e. its end . For the object of a thing is its principle; and generation has as its object the end . And the actuality is the end, and it is for the sake of this that the potentiality is acquired; for animals do not see in order that they may have sight, but have sight in order that they may see.

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Similarly men possess the art of building in order that they may build, and the power of speculation that they may speculate; they do not speculate in order that they may have the power of speculation—except those who are learning by practice; and they do not really speculate, but only in a limited sense, or about a subject about which they have no desire to speculate.

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Further, matter exists potentially, because it may attain to the form; but when it exists actually, it is then in the form. The same applies in all other cases, including those where the end is motion.

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Hence, just as teachers think that they have achieved their end when they have exhibited their pupil performing, so it is with nature. For if this is not so, it will be another case of Pauson’s HermesProbably a trick picture of some kind. So Pauson is said to have painted a picture of a horse galloping which when inverted showed the horse rolling on its back. Cf. Aelian, Var. Hist. 14.15; Lucian, Demosth. Enc. 24; Plut. Moralia, 396e; Pfuhl, Malerei und Zeichnung der Griechen, 763.; it will be impossible to say whether the knowledge is in the pupil or outside him, as in the case of the Hermes. For the activity is the end, and the actuality is the activity; hence the term actuality is derived from activity, and tends to have the meaning of complete reality.

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Now whereas in some cases the ultimate thing is the use of the faculty, as, e.g., in the case of sight seeing is the ultimate thing, and sight produces nothing else besides this; but in other cases something is produced, e.g. the art of building produces not only the act of building but a house; nevertheless in the one case the use of the faculty is the end, and in the other it is more truly the end than is the potentiality. For the act of building resides in the thing built; i.e., it comes to be and exists simultaneously with the house.

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Thus in all cases where the result is something other than the exercise of the faculty, the actuality resides in the thing produced; e.g. the act of building in the thing built, the act of weaving in the thing woven, and so on; and in general the motion resides in the thing moved. But where there is no other result besides the actualization, the actualization resides in the subject; e.g. seeing in the seer, and speculation in the speculator, and life in the soul

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(and hence also happiness, since happiness is a particular kind of life). Evidently, therefore, substance or form is actuality. Thus it is obvious by this argument that actuality is prior in substantiality to potentiality; and that in point of time, as we have said, one actuality presupposes another right back to that of the prime mover in each case.

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It is also prior in a deeper sense; because that which is eternal is prior in substantiality to that which is perishable, and nothing eternal is potential. The argument is as follows. Every potentiality is at the same time a potentiality for the opposite.Cf. 19. For whereas that which is incapable of happening cannot happen to anything, everything which is capable may fail to be actualized.

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Therefore that which is capable of being may both be and not be. Therefore the same thing is capable both of being and of not being. But that which is capable of not being may possibly not be; and that which may possibly not be is perishable; either absolutely, or in the particular sense in which it is said that it may possibly not be; that is, in respect either of place or of quantity or of quality. Absolutely means in respect of substance.

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Hence nothing which is absolutely imperishable is absolutely potential (although there is no reason why it should not be potential in some particular respect; e.g. of quality or place); therefore all imperishable things are actual. Nor can anything which is of necessity be potential; and yet these things are primary, for if they did not exist, nothing would exist. Nor can motion be potential, if there is any eternal motion. Nor, if there is anything eternally in motion, is it potentially in motion (except in respect of some starting-point or destination), and there is no reason why the matter of such a thing should not exist.

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Hence the sun and stars and the whole visible heaven are always active, and there is no fear that they will ever stop—a fear which the writerse.g. Empedocles; cf. Aristot. Met. 5.23.3 n. on physics entertain. Nor do the heavenly bodies tire in their activity; for motion does not imply for them, as it does for perishable things, the potentiality for the opposite, which makes the continuity of the motion distressing; this results when the substance is matter and potentiality, not actuality.

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Imperishable things are resembled in this respect by things which are always undergoing transformation, such as earth and fire; for the latter too are always active, since they have their motion independently and in themselves.Cf. Aristot. De Gen. et Corr. 337a 1-7. Other potentialities, according to the distinctions already made,Aristot. Met. 9.5.2. all admit of the opposite result; for that which is capable of causing motion in a certain way can also cause it not in that way; that is if it acts rationally.

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The same irrational potentialities can only produce opposite results by their presence or absence.

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Thus if there are any entities or substances such as the dialecticiansFor this description of the Platonists cf. Aristot. Met. 1.6.7. describe the Ideas to be, there must be something which has much more knowledge than absolute knowledge, and much more mobility than motion; for they will be in a truer sense actualities, whereas knowledge and motion will be their potentialities.This is a passing thrust at the Ideal theory. Absolute knowledge (the faculty of knowledge) will be a mere potentiality, and therefore substantially posterior to its actualization in particular instances. Thus it is obvious that actuality is prior both to potentiality and to every principle of change.

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That a good actuality is both better and more estimable than a good potentiality will be obvious from the following arguments. Everything of which we speak as capable is alike capable of contrary results; e.g., that which we call capable of being well is alike capable of being ill, and has both potentialities at once; for the same potentiality admits of health and disease, or of rest and motion, or of building and of pulling down, or of being built and of falling down.

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Thus the capacity for two contraries can belong to a thing at the same time, but the contraries cannot belong at the same time; i.e., the actualities, e.g. health and disease, cannot belong to a thing at the same time. Therefore one of them must be the good; but the potentiality may equally well be both or neither. Therefore the actuality is better.

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Also in the case of evils the end or actuality must be worse than the potentiality; for that which is capable is capable alike of both contraries.

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Clearly, then, evil does not exist apart from things ; for evil is by nature posterior to potentiality.The argument is presumably as follows (the fallacy, as pointed out by Bonitz, is indicated in parenthesis): That which has a separate substantial existence is actuality. Actuality is prior (substantially) to potentiality. Potentiality is prior to evil (in the moral scale. But since by evil Aristotle means the actualization of a potentiality for evil, potentiality is substantially posterior to evil). Therefore that which has a separate substantial existence is prior to evil; i.e., evil does not exist apart from particular instances of evil. The argument is directed against the Platonic Idea of evil (Plat. Rep. 476a); and the corollary which follows against the identification of Evil with one of the principles of the universe (Aristot. Met. 1.6.10, Aristot. Met. 12.10.6, Aristot. Met. 14.4.10, 11; cf. Plat. Laws 896e, Plat. Laws 898c). Nor is there in things which are original and eternal any evil or error, or anything which has been destroyed—for destruction is an evil.

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Geometrical constructions, too, are discovered by an actualization, because it is by dividing that we discover them. If the division were already done, they would be obvious; but as it is the division is only there potentially. Why is the sum of the interior angles of a triangle equal to two right angles? Because the angles about one point <in a straight line> are equal to two right angles. If the line parallel to the side had been already drawn, the answer would have been obvious at sight.The figure, construction and proof are as follows: ***

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Why is the angle in a semicircle always a right angle? If three lines are equal, the two forming the base, and the one set upright from the middle of the base, the answer is obvious to one who knows the former proposition.Aristotle implies a proof something after this fashion: FIGURE BAC is an angle in a semicircle. From D, the mid-point of the diameter BC, draw a perpendicular DE to meet the circumference at E. Join EB, EC.*** Thus it is evident that the potential constructions are discovered by being actualized. The reason for this is that the actualization is an act of thinking. Thus potentiality comes from actuality (and therefore it is by constructive action that we acquire knowledge). <But this is true only in the abstract>, for the individual actuality is posterior in generation to its potentiality.This whole passage (sects. 4, 5) should be compared with Aristot. Met. 9.8.3-7, where it logically belongs.

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The terms being and not-being are used not only with reference to the types of predication, and to the potentiality or actuality, or non-potentiality and non-actuality, of these types, but also (in the strictest senseThis appears to contradict Aristot. Met. 6.4.3. But it is just possible to interpret κυριώτατα(with Jaeger) as in the commonest sense. ) to denote truth and falsity. This depends, in the case of the objects, upon their being united or divided; so that he who thinks that what is divided is divided, or that what is united is united, is right; while he whose thought is contrary to the real condition of the objects is in error. Then when do what we call truth and falsity exist or not exist? We must consider what we mean by these terms.

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It is not because we are right in thinking that you are white that you are white; it is because you are white that we are right in saying so. Now if whereas some things are always united and cannot be divided, and others are always divided and cannot be united, others again admit of both contrary states, then to be is to be united, i.e. a unity; and not to be is to be not united, but a plurality.

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Therefore as regards the class of things which admit of both contrary states, the same opinion or the same statement comes to be false and true, and it is possible at one time to be right and at another wrong; but as regards things which cannot be otherwise the same opinion is not sometimes true and sometimes false, but the same opinions are always true or always false.

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But with regard to incomposite things, what is being or not-being, and truths or falsity? Such a thing is not composite, so as to be when it is united and not to be when it is divided, like the proposition that the wood is white, or the diagonal is incommensurable; nor will truth and falsity apply in the same way to these cases as to the previous ones.

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In point of fact, just as truth is not the same in these cases, so neither is being. Truth and falsity are as follows: contacti.e. direct and accurate apprehension. and assertion are truth (for assertion is not the same as affirmation), and ignorance is non-contact. I say ignorance, because it is impossible to be deceived with respect to what a thing is, except accidentallyi.e. we cannot be mistaken with regard to a simple term X. We either apprehend it or not. Mistake arises when we either predicate something wrongly of X, or analyze X wrongly.;

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and the same applies to incomposite substances, for it is impossible to be deceived about them. And they all exist actually, not potentially; otherwise they would be generated and destroyed; but as it is, Being itself is not generated (nor destroyed); if it were, it would be generated out of something. With respect, then, to all things which are essences and actual, there is no question of being mistaken, but only of thinking or not thinking them.

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Inquiry as to what they are takes the form of inquiring whether they are of such-and-such a nature or not.

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As for being in the sense of truth, and not-being in the sense of falsity, a unity is true if the terms are combined, and if they are not combined it is false. Again, if the unity exists, it exists in a particular way, and if it does not exist in that way, it does not exist at all.

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Truth means to think these objects, and there is no falsity or deception, but only ignorance—not, however, ignorance such as blindness is; for blindness is like a total absence of the power of thinking. And it is obvious that with regard to immovable things also, if one assumes that there are immovable things, there is no deception in respect of time.

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E.g., if we suppose that the triangle is immutable, we shall not suppose that it sometimes contains two right angles and sometimes does not, for this would imply that it changes; but we may suppose that one thing has a certain property and another has not; e.g., that no even number is a prime, or that some are primes and others are not. But about a single number we cannot be mistaken even in this way, for we can no longer suppose that one instance is of such a nature, and another not, but whether we are right or wrong, the fact is always the same.

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That one has several meanings has been already statedAristot. Met. 5.6. in our distinction of the various meanings of terms. But although it has a number of senses, the things which are primarily and essentially called one, and not in an accidental sense, may be summarized under four heads:

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(1.) That which is continuous, either absolutely or in particular that which is continuous by natural growth and not by contact or ligature; and of these things those are more strictly and in a prior sense one whose motion is more simple and indivisible.

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(2.) Of this kind in a still higher degree is that which is a whole and has a definite shape or form, particularly that which is such by nature and not by constraint (like things which are joined by glue or nails or by being tied together), but which contains in itself the cause of its continuity.

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A thing is of this kind if its motion is one and indivisible in respect of place and time; so that clearly if a thing has as its principle of motion the primary kind of motion (i.e. locomotion) in its primary form (i.e. circular locomotion), it is in the primary sense one spatial magnitude.This description applies to the celestial spheres.

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Some things, then, are one in this sense, qua continuous or whole; the other things which are one are those whose formula is one.

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Such are the things of which the concept is one, i.e. of which the concept is indivisible; and this is indivisible when the object is indivisible (3.) in form or (4.) in number. Now in number the individual is indivisible, and in form that which is indivisible in comprehension and knowledge; so that that which causes the unity of substances must be one in the primary sense.

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Such, then, in number are the meanings of one: the naturally continuous, the whole, the individual, and the universal. All these are one because they are indivisible; some in motion, and others in concept or formula. But we must recognize that the questions, What sort of things are called one? and What is essential unity, and what is the formula? must not be taken to be the same.

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One has these several meanings, and each thing to which some one of these senses applies will be one; but essential unity will have now one of these senses and now something else, which is still nearer to the term one, whereas they are nearer to its denotation . This is also true of element and cause, supposing that one had to explain them both by exhibiting concrete examples and by giving a definition of the term.

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There is a sense in which fire is an element (and no doubt so too is the indeterminateThe reference is undoubtedly to Anaximander. or some other similar thing, of its own nature), and there is a sense in which it is not; because to be fire and to be an element are not the same. It is as a concrete thing and as a stuff that fire is an element; but the term element denotes that it has this attribute: that something is made of it as a primary constituent.

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The same is true of cause or one and all other such terms.

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Hence to be one means to be indivisible (being essentially a particular thing, distinct and separate in place or form or thought), or to be whole and indivisible; but especially to be the first measure of each kind, and above all of quantity; for it is from this that it has been extended to the other categories.

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Measure is that by which quantity is known, and quantity qua quantity is known either by unity or by number, and all number is known by unity. Therefore all quantity qua quantity is known by unity, and that by which quantities are primarily known is absolute unity.

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Thus unity is the starting point of number qua number. Hence in other cases too measure means that by which each thing is primarily known, and the measure of each thing is a unit—in length, breadth, depth, weight and speed.

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(The terms weight and speed are common to both contraries, for each of them has a double meaning; e.g., weight applies to that which has the least amount of gravity and also to that which has excess of it, and speed to that which has the least amount of motion and also to that which has excess of it; for even the slow has some speed, and the light some weight.)

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In all these cases, then, the measure and starting-point is some indivisible unit (since even in the case of lines we treat the one-foot line as indivisible). For everywhere we require as our measure an indivisible unit; i.e., that which is simple either in quality or in quantity.

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Now where it seems impossible to take away or add, there the measure is exact. Hence the measure of number is most exact, for we posit the unit as in every way indivisible; and in all other cases we follow this example, for with the furlong or talent or in general with the greater measure an addition or subtraction would be less obvious than with a smaller one.

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Therefore the first thing from which, according to our perception, nothing can be subtracted is used by all men as their measure of wet and dry, weight and magnitude; and they think that they know the quantity only when they know it in terms of this measure. And they know motion too by simple motion and the most rapid, for this takes least time.

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Hence in astronomy a unit of this kind is the starting point and measure; for they assume that the motion of the heavens is uniform and the most rapid, and by it they judge the others. In music the measure is the quarter tone, because it is the smallest interval; and in language the letter. All these are examples of units in this sense—not in the sense that unity is something common to them all, but in the sense which we have described.

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The measure is not always numerically one, but sometimes more than one; e.g., there are two quarter tones, distinguished not by our hearing but by their theoretical ratiosi.e., the enharmonic (or quarter-tone proper) and the chromatic, which was 1/3 of a tone (Aristoxenus 1.21, 2.51). There was also the δίεσις ἡμιολία, which was 3/8 of a tone.; and the articulate sounds by which we measure speech are more than one; and the diagonal of a square is measured by two quantities,The meaning seems to be that the diameter consists of two parts, one equal to the side, and the other representing its excess over the side; the two parts being incommensurate are measured by different units (Ross). καὶ ἡ πλευρά must, I think, be a gloss. and so are all magnitudes of this kind. Thus unity is the measure of all things, because we learn of what the substance is composed by dividing it, in respect of either quantity or form.

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Hence unity is indivisible, because that which is primary in each class of things is indivisible. But not every unit is indivisible in the same sense—e.g. the foot and the arithmetical unit; but the latter is absolutely indivisible, and the former must be classed as indivisible with respect to our power of perception, as we have already stated; since presumably everything which is continuous is divisible.

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The measure is always akin to the thing measured. The measure of magnitude is magnitude, and in particular the measure of length is a length; of breadth, a breadth; of sounds, a sound; of weight, a weight; of units, a unit; for this is the view that we must take, and not that the measure of numbers is a number. The latter, indeed, would necessarily be true, if the analogy held good; but the supposition is not analogous—it is as though one were to suppose that the measure of units is units, and not a unit; for number is a plurality of units.

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We also speak of knowledge or sense perception as a measure of things for the same reason, because through them we come to know something; whereas really they are measured themselves rather than measure other things. But our experience is as though someone else measured us, and we learned our height by noticing to what extent he applied his foot-rule to us.

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Protagoras says that man is the measure of all things, meaning, as it were, the scholar or the man of perception; and these because they possess, the one knowledge, and the other perception, which we hold to be the measures of objects. Thus, while appearing to say something exceptional, he is really saying nothing.What Protagoras really meant was (apparently) that appearances are true relatively to the percipient. Cf. Aristot. Met. 4.4.27, and see Burnet, Greek Philosophy (Part I. Thales to Plato), 92.

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Obviously, then, unity in the strictest sense, if we make our definition in accordance with the meaning of the term, is a measure; particularly of quantity, and secondarily of quality. Some things will be of this kind if they are indivisible in quantity, and others if in quality. Therefore that which is one is indivisible, either absolutely or qua one.

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We must inquire, with regard to the substance and nature of unity, in which sense it exists. This is the same question which we approached in our discussion of difficultiesAristot. Met. 3.4.24-27.: what unity is, and what view we are to take of it; whether that unity itself is a kind of substance—as first the Pythagoreans, and later Plato, both maintain—or whether rather some nature underlies it, and we should give a more intelligible account of it, and more after the manner of the physicists; for of them oneEmpedocles. holds that the One is Love, anotherAnaximenes. Air, and anotherAnaximander. the Indeterminate.

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Now if no universal can be a substance (as we have stated in our discussionAristot. Met. 7.13. of substance and being), and being itself cannot be a substance in the sense of one thing existing alongside the many (since it is common to them), but only as a predicate, then clearly neither can unity be a substance; because being and unity are the most universal of all predicates.

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Therefore (a) genera are not certain entities and substances separate from other things; and (b) unity cannot be a genus, for the same reasons that being and substance cannot.Cf. Aristot. Met. 3.3.7.

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Further, the nature of unity must be the same for all categories.

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Now being and unity have the same number of meanings; so that since in the category of qualities unity is something definite, i.e. some definite entity, and similarly in the category of quantity, clearly we must also inquire in general what unity is, just as in the case of being; since it is not enough to say that its nature is simply unity or being.

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But in the sphere of colors unity is a color, e.g. white; that is if all the other colors are apparently derived from white and black, and black is a privation of white, as darkness is of light. Thus if all existing things were colors, all existing things would be a number; but of what?

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Clearly of colors. And unity would be some one color, e.g. white. Similarly if all existing things were tunes, there would be a number—of quarter-tones; but their substance would not be a number; and unity would be something whose substance is not unity but a quarter-tone. Similarly in the case of sounds, existing things would be a number of letters, and unity would be a vowel;

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and if existing things were right-lined figures, they would be a number of figures, and unity would be a triangle. And the same principle holds for all other genera. Therefore if in the categories of passivity and quality and quantity and motion there is in every category a number and a unity, and if the number is of particular things and the unity is a particular unity, and its substance is not unity, then the same must be true in the case of substances, because the same is true in all cases.

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It is obvious, then, that in every genus one is a definite entity, and that in no case is its nature merely unity; but as in the sphere of colors the One-itself which we have to seek is one color, so too in the sphere of substance the One-itself is one substance.

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And that in a sense unity means the same as being is clear (a) from the fact that it has a meaning corresponding to each of the categories, and is contained in none of them—e.g., it is contained neither in substance nor in quality, but is related to them exactly as being is; (b) from the fact that in one man nothing more is predicated than in manCf. Aristot. Met. 4.2.6-8.(just as Being too does not exist apart from some thing or quality or quantity); and (c) because to be one is to be a particular thing.

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One and Many are opposed in several ways. Unity and Plurality are opposed as being indivisible and divisible; for that which is divided or divisible is called a plurality, and that which is indivisible or undivided is called one. Then since opposition is of four kinds, and one of the present pairs of opposites is used in a privative sense, they must be contraries, and neither contradictories nor relative terms.

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Unity is described and explained by its contrary—the indivisible by the divisible—because plurality, i.e. the divisible, is more easily perceptible than the indivisible; and so in formula plurality is prior to the indivisible, on account of our powers of perception.

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To Unity belong (as we showed by tabulation in our distinction of the contrariesCf. Aristot. Met. 4.2.9.) Identity, Similarity and Equality; and to Plurality belong Otherness, Dissimilarity and Inequality.

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IdentityOr the same. Cf. Aristot. Met. 5.9. has several meanings. (a) Sometimes we speak of it in respect of number. (b) We call a thing the same if it is one both in formula and in number, e.g., you are one with yourself both in form and in matter; and again (c) if the formula of the primary substance is one, e.g., equal straight lines are the same, and equal quadrilaterals with equal angles, and there are many more examples; but in these equality means unity.

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Things are similarOr like. Cf. Aristot. Met. 5.9.5.(a) if, while not being the same absolutely or indistinguishable in respect of their concrete substance, they are identical in form; e.g the larger square is similar to the smaller, and unequal straight lines are similar. These are similar, but not absolutely the same. (b) If, having the same form, and being capable of difference in degree, they have no difference of degree.

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(c) If things have an attribute which is the same and one in form—e.g. white—in different degrees, we say that they are similar because their form is one. (d) If the respects in which they are the same are more than those in which they differ, either in general or as regards their more prominent qualities; e.g., tin is similar to silver, as being white; and gold to fire, as being yellow or flame-colored.

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Thus it is obvious that OtherCf. Aristot. Met. 5.9.4. and Unlike also have several meanings. (a) In one sense other is used in the sense opposite to the same; thus everything in relation to every other thing is either the same or other. (b) In another sense things are other unless both their matter and their formula are one; thus you are other than your neighbor. (c) The third sense is that which is found in mathematics.sc. as opposed to same in sense (a); 3 above. Therefore everything in relation to everything else is called either other or the same; that is, in the case of things of which unity and being are predicated;

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for other is not the contradictory of the same, and so it is not predicated of non-existent things (they are called not the same), but it is predicated of all things which exist; for whatever is by nature existent and one is either one or not one with something else.

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Other and same, then, are opposed in this way; but differenceCf. Aristot. Met. 5.9.4. is distinct from otherness.

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For that which is other than something need not be other in a particular respect, since everything which is existent is either other or the same. But that which is different from something is different in some particular respect, so that that in which they differ must be the same sort of thing; i.e. the same genus or species.

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For everything which is different differs either in genus or in species—in genus, such things as have not common matter and cannot be generated into or out of each other, e.g. things which belong to different categories; and in species, such things as are of the same genus (genus meaning that which is predicated of both the different things alike in respect of their substance).

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The contrariesCf. Aristot. Met. 5.10. are different, and contrariety is a kind of difference. That this is rightly premissed is made clear by induction; for the contraries are obviously all different, since they are not merely other, but some are other in genus, and others are in the same line of predication, and so are in the same genus and the same in genus. We have distinguished elsewhereAristot. Met. 5.28.4. what sort of things are the same or other in genus.

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Since things which differ can differ from one another in a greater or less degree, there is a certain maximum difference, and this I call contrariety. That it is the maximum difference is shown by induction. For whereas things which differ in genus have no means of passing into each other, and are more widely distant, and are not comparable, in the case of things which differ in species the contraries are the extremes from which generation takes place;

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and the greatest distance is that which is between the extremes, and therefore also between the contraries. But in every class the greatest thing is complete. For (a) that is greatest which cannot be exceeded, and (b) that is complete outside which nothing proper to it can be found. For complete difference implies an end, just as all other things are called complete because they imply an end.

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And there is nothing beyond the end; for in everything the end is the last thing, and forms the boundary. Thus there is nothing beyond the end, and that which is complete lacks nothing.

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From this argument, then, it is clear that contrariety is maximum difference; and since we speak of contraries in various senses, the sense of completeness will vary in accordance with the sense of contrariety which applies to the contraries.

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This being so, evidently one thing cannot have more than one contrary (since there can be nothing more extreme than the extreme, nor can there be more than two extremes of one interval); and in general this is evident, if contrariety is difference, and difference (and therefore complete difference) is between two things.

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The other definitions of contraries must also be true, for (1.) complete difference is the maximum difference; since (a) we can find nothing beyond it, whether things differ in genus or in species (for we have shown that difference in relation to things outside the genus is impossible; this is the maximum difference between them); and (b) the things which differ most in the same genus are contraries; for complete difference is the maximum difference between these.

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(2.) The things which differ most in the same receptive material are contraries; for contraries have the same matter. (3.) The most different things which come under the same faculty are contraries; for one science treats of one class of things, in which complete difference is the greatest.

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Positive state and Privation constitute primary contrariety—not every form of privation (for it has several senses), but any form which is complete. All other contraries must be so called with respect to these; some because they possess these, others because they produce them or are productive of them, and others because they are acquisitions or losses of these or other contraries.

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Now if the types of opposition are contradiction, privation, contrariety and relation, and of these the primary type is contradiction, and an intermediate is impossible in contradiction but possible between contraries, obviously contradiction is not the same as contrariety; and privation is a form of contradiction;

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for it is either that which is totally incapable of possessing some attribute,This is not a proper example of privation. Cf. Aristot. Met. 5.22. or that which would naturally possess some attribute but does not, that suffers privation—either absolutely or in some specified way. Here we already have several meanings, which we have distinguished elsewhere. Thus privation is a kind of contradiction or incapacity which is determinate or associated with the receptive material.

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This is why though there is no intermediate in contradiction there is one in some kinds of privation. For everything is either equal or not equal, but not everything is either equal or unequal; if it is, it is only so in the case of a material which admits of equality. If, then, processes of material generation start from the contraries, and proceed either from the form and the possession of the form, or from some privation of the form or shape, clearly all contrariety must be a form of privation, although presumably not all privation is contrariety.

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This is because that which suffers privation may suffer it in several senses; for it is only the extremes from which changes proceed that are contraries.

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This can also be shown by induction. Every contrariety involves privation as one of its contraries, but not always in the same way: inequality involves the privation of equality, dissimilarity that of similarity, evil that of goodness.

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And the differences are as we have stated: one case is, if a thing is merely deprived; another, if it is deprived at a certain time or in a certain part—e.g. at a certain age or in the important part—or entirely. Hence in some cases there is an intermediate (there are men who are neither good nor bad), and in others there is not—a thing must be either odd or even.

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Again, some have a determinate subject, and others have not. Thus it is evident that one of a pair of contraries always has a privative sense; but it is enough if this is true of the primary or generic contraries, e.g. unity and plurality; for the others can be reduced to them.

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Since one thing has one contrary, it might be asked in what sense unity is opposed to plurality, and the equal to the great and to the small. For if we always use the word whether in an antithesis—e.g., whether it is white or black, or whether it is white or not (but we do not ask whether it is a man or white, unless we are proceeding upon some assumption, and asking, for instance, whether it was Cleon who came or Socrates.

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This is not a necessary disjunction in any class of things, but is derived from the use in the case of opposites—for it is only opposites that cannot be true at the same time—and we have this same use here in the question which of the two came? for if both alternatives were possible, the question would be absurd; but even so the question falls into an antithesis: that of one or many—i.e., whether both came, or one)—

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if, then, the question whether is always concerned with opposites, and we can ask whether it is greater or smaller, or equal, what is the nature of the antithesis between equal and greater or smaller? It is contrary neither to one only, nor to both: for (a) it is no more contrary to the greater than to the smaller; (b) equal is contrary to unequal, and thus it will be contrary to more than one thing;

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(c) if unequal means the same as both greater and smaller at the same time, equal must still be opposed to them both: This difficulty supports the theoryHeld by the Platonists. Cf. Aristot. Met. 14.1.4, 5. that the unequal is a duality. But the result is that one thing is contrary to two; which is impossible.

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Further, it is apparent that equal is intermediate between great and small, but it is not apparent that any contrariety is intermediate, nor can it be, by definition; for it could not be complete if it were the intermediate of something, but rather it always has something intermediate between itself and the other extreme.

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It remains, then, that it is opposed either as negation or as privation. Now it cannot be so opposed to one of the two, for it is no more opposed to the great than to the small.

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Therefore it is a privative negation of both. For this reason we say whether with reference to both, and not to one of the two—e.g., whether it is greater or equal, or whether it is equal or smaller; there are always three alternatives. But it is not a necessary privation; for not everything is equal which is not greater or smaller, but only things which would naturally have these attributes.

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The equal, then, is that which is neither great nor small, but would naturally be either great or small; and it is opposed to both as a privative negation, and therefore is intermediate between them. And that which is neither good nor bad is opposed to both, but it has no name (for each of these terms has several meanings, and there is no one material which is receptive of both); that which is neither white nor black is better entitled to a name,

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although even this has no single name, but the colors of which this negation is privatively predicated are to a certain extent limited; for it must be either grey or buff or something similar.

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Therefore those persons are wrong in their criticism who imagine that all terms are used analogously, so that that which is neither a shoe nor a hand will be intermediate between shoe and hand, because that which is neither good nor bad is intermediate between good and bad—as though there must be an intermediate in all cases; but this does not necessarily follow.

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For the one is a joint negation of opposites where there is an intermediate and a natural interval; but in the other case there is no question of difference, since the joint negation applies to things which are in different genera, and therefore the substrate is not one.Cf. Aristot. Met. 10.3.8

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A similar question might be raised about one and many. For if many is absolutely opposed to one, certain impossibilities result. (1) One will be few; for many is also opposed to few.

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(2) Two will be many; since twofold is manifold, and twofold is derived from two. Therefore one will be few; for in what relation can two be many if not in relation to one, which must therefore be few? for there can be nothing less. (3) If much and little are in plurality what long and short are in length, and if whatever is much is also many,

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and many is much (unless indeed there is a difference in the case of a plastic continuumi.e., a fluid, which cannot be described as many. ), few will be a plurality. Therefore one will be a plurality, if it is few; and this necessarily follows if two is many. Presumably, however, although many in a sense means much, there is a distinction; e.g., water is called much but not many.

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To all things, however, which are divisible the term many is applicable: in one sense, if there is a plurality which involves excess either absolutely or relatively (and similarly few is a plurality involving defect); and in another in the sense of number, in which case it is opposed to one only. For we say one or many just as if we were to say one and ones, or white thing and white things, or were to compare the things measured with the measure.

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Multiples, too, are spoken of in this way; for every number is many, because it consists of ones, and because every number is measurable by one; and also as being the opposite of one, and not of few. In this sense even two is many; but as a plurality involving excess either relatively or absolutely it is not many, but the first plurality. Two is, however, absolutely few; because it is the first plurality involving defect

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(hence AnaxagorasCf. Aristot. Met. 1.3.9. was not right in leaving the subject by saying all things were together, infinite both in multitude and in smallness; instead of in smallness he should have said in fewness,sc. and then the absurdity of his view would have been apparent, for, etc. Aristotle assumes the Anaxagoras meant smallness (μικρότης) to be the opposite of multitude (πλῆθος); but he meant just what he said—that the particles of which things consist are infinitely many and infinitely small. See Bowman in Classical Review 30, 42-44. for things cannot be infinite in fewness), since fewness is constituted not by one, as some hold, but by two.

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In the sphere of numbers one is opposed to many as the measure to the measurable, i.e., as relative terms are opposed which are not of their own nature relative. We have distinguished elsewhereAristot. Met. 5.15.8, 9. that things are called relative in two senses—either as being contraries, or as knowledge is related to the knowable, A being related to B because B is described in relation to A.

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There is no reason why one should not be fewer than something, e.g. two; for if it is fewer it is not therefore few. Plurality is, as it were, a genus of number, since number is a plurality measurable by one. And in a sense one and number are opposed; not, however, as being contrary, but as we have said some relative terms to be; for it is qua measure and measurable that they are opposed.

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(Hence not everything which is one is a number—e.g., a thing which is indivisible.) But although the relation between knowledge and the knowable is said to be similar to this, it turns out not to be similar. For it would seem that knowledge is a measure, and the knowable that which is measurable by it; but it happens that whereas all knowledge is knowable, the knowable is not always knowledge, because in a way knowledge is measured by the knowable.Cf. Aristot. Met. 10.1.19.

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Plurality is contrary neither to the few (whose real contrary is the many, as an excessive plurality to an exceeded plurality) nor in all senses to one; but they are contrary in one sense (as has been said) as being the one divisible and the other indivisible; and in another as being relative (just as knowledge is relative to the knowable) if plurality is a number and one is the measure.

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Since there can be, and in some cases is, an intermediate between contraries, intermediates must be composed of contraries; for all intermediates are in the same genus as the things between which they are intermediate.

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By intermediates we mean those things into which that which changes must first change. E.g., if we change from the highest string to the lowest by the smallest gradations we shall first come to the intermediate notes; and in the case of colors if we change from white to black we shall come to red and grey before we come to black; and similarly in other cases.

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But change from one genus into another is impossible except accidentally; e.g., from color to shape. Therefore intermediates must be in the same genus as one another and as the things between which they are intermediate.

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But all intermediates are between certain opposites, for it is only from these per se that change is possible.

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Hence there can be no intermediate between things which are not opposites; for then there would be change also between things which are not opposites. Of things which are opposites, contradiction has no intermediate term (for contradiction means this: an antithesis one term of which must apply to any given thing, and which contains no intermediate term); of the remaining types of opposites some are relative, others privative, and others contrary.

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Those relative opposites which are not contrary have no intermediate. The reason for this is that they are not in the same genus— for what is intermediate between knowledge and the knowable?—but between great and small there is an intermediate. Now since intermediates are in the same genus, as has been shown, and are between contraries, they must be composed of those contraries. For the contraries must either belong to a genus or not. And if there is a genus in such a way

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that it is something prior to the contraries, then the differentiae which constitute the contrary species (for species consist of genus and differentiae) will be contraries in a prior sense.

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E.g., if white and black are contraries, and the one is a penetrativeThis is Plato’s definition. Cf. Plat. Tim. 67d, e. and the other a compressive color, these differentiae, penetrative and compressive, are prior, and so are opposed to each other in a prior sense.

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But it is the species which have contrary differentiae that are more truly contraries; the other, i.e. intermediate, species will consist of genus and differentiae. E.g., all colors which are intermediate between white and black should be described by their genus (i.e. color) and by certain differentiae.

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But these differentiae will not be the primary contraries; otherwise every thing will be either white or black. Therefore they will be different from the primary contraries. Therefore they will be intermediate between them, and the primary differentiae will be the penetrative and the compressive. Thus we must first investigate the contraries which are not contained in a genus, and discover of what their intermediates are composed.

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For things which are in the same genus must either be composed of differentiae which are not compounded with the genus, or be incomposite. Contraries are not compounded with one another, and are therefore first principles; but intermediates are either all incomposite or none of them. Now from the contraries something is generated in such a way that change will reach it before reaching the contraries themselves (for there must be something which is less in degree than one contrary and greater than the other). Therefore this also will be intermediate between the contraries.

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Hence all the other intermediates must be composite; for that which is greater in degree than one contrary and less than the other is in some sense a compound of the contraries of which it is said to be greater in degree than one and less than the other. And since there is nothing else homogeneous which is prior to the contraries, all intermediates must be composed of contraries.

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Therefore all the lower terms, both contraries and intermediates, must be composed of the primary contraries. Thus it is clear that intermediates are all in the same genus, and are between contraries, and are all composed of contraries.

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That which is other in species than something else is other in respect of something and that something must apply to both. E.g., if an animal is other in species than something else, they must both be animals. Hence things which are other in species must be in the same genus. The sort of thing I mean by genus is that in virtue of which two things are both called the same one thing; and which is not accidentally differentiated, whether regarded as matter or otherwise.

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For not only must the common quality belong to both, e.g., that they are both animals, but the very animality of each must be different; e.g., in one case it must be equinity and in the other humanity. Hence the common quality must for one be other in species than that which it is for the other. They must be, then, of their very nature, the one this kind of animal, and the other that ; e.g., the one a horse and the other a man.

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Therefore this difference must be otherness of genus (I say otherness of genus because by difference of genus I mean an otherness which makes the genus itself other); this, then, will be a form of contrariety. This is obvious by induction.Aristotle does not use induction to prove his point; indeed he does not prove it at all. For all differentiation is by opposites, and we have shownIn ch. 4. that contraries are in the same genus, because contrariety was shown to be complete difference. But difference in species is always difference from something in respect of something; therefore this is the same thing, i.e. the genus, for both.

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(Hence too all contraries which differ in species but not in genus are in the same line of predication,Or category. and are other than each other in the highest degree; for their difference is complete, and they cannot come into existence simultaneously.) Hence the difference is a form of contrariety.

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To be other in species, then, means this: to be in the same genus and involve contrariety, while being indivisible

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(and the same in species applies to all things which do not involve contrariety, while being indivisible); for it is in the course of differentiation and in the intermediate terms that contrariety appears, before we come to the indivisibles.i.e., indivisible species and individuals.

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Thus it is evident that in relation to what is called genus no species is either the same or other in species (and this is as it should be, for the matter is disclosed by negation, and the genus is the matter of that of which it is predicated as genus; not in the sense in which we speak of the genus or clan of the Heraclidae,Cf. Aristot. Met. 5.28.1. but as we speak of a genus in nature); nor yet in relation to things which are not in the same genus. From the latter it will differ in genus, but in species from things which are in the same genus. For the difference of things which differ in species must be a contrariety; and this belongs only to things which are in the same genus.

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The question might be raised as to why woman does not differ in species from man, seeing that female is contrary to male, and difference is contrariety; and why a female and a male animal are not other in species, although this difference belongs to animal per se, and not as whiteness or blackness does; male and female belong to it qua animal.

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This problem is practically the same as why does one kind of contrariety (e.g. footed and winged) make things other in species, while another (e.g. whiteness and blackness) does not? The answer may be that in the one case the attributes are peculiar to the genus, and in the other they are less so; and since one element is formula and the other matter, contrarieties in the formula produce difference in species, but contrarieties in the concrete whole do not.

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Hence the whiteness or blackness of a man does not produce this, nor is there any specific difference between a white man and a black man; not even if one term is assigned to each. For we are now regarding man as matter, and matter does not produce difference; and for this reason, too, individual men are not species of man, although the flesh and bones of which this and that man consist are different. The concrete whole is other, but not other in species, because there is no contrariety in the formula, and this is the ultimate indivisible species.

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But Callias is definition and matter. Then so too is white man, because it is the individual, Callias, who is white. Hence man is only white accidentally. Again, a bronze circle and a wooden one do not differ in species; and a bronze triangle and a wooden circle differ in species not because of their matter, but because there is contrariety in their formulae.

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But does not matter, when it is other in a particular way, make things other in species? Probably there is a sense in which it does. Otherwise why is this particular horse other in species than this particular man, although the definitions involve matter? Surely it is because there is contrariety in the definition, for so there also is in white man and black horse; and it is a contrariety in species, but not because one is white and the other black; for even if they had both been white, they would still be other in species.

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Male and female are attributes peculiar to the animal, but not in virtue of its substance; they ar material or physical. Hence the same semen may, as the result of some modification, become either female or male.

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We have now stated what to be other in species means, and why some things differ in species and others do not.

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Since contraries are other in form,It appears that in this chapter (apart from 5, which may be a later addition) the terms εἶδος and γένος are used in a non-technical sense. Cf. Ross on Aristot. Met. 1058b 28. and the perishable and imperishable are contraries (for privation is a definite incapacity), the perishable must be other in kind than the imperishable. But so far we have spoken only of the universal terms; and so it might appear to be unnecessary that anything perishable and imperishable should be other in form, just as in the case of white and black.

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For the same thing may be both at the same time, if it is a universal (e.g, man may be both white and black); and it may still be both if it is a particular, for the same person may be white and black, although not at the same time. Yet white is contrary to black. But although some contraries

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(e.g. those which we have just mentioned, and many others) can belong to certain things accidentally, others cannot; and this applies to the perishable and the imperishable. Nothing is accidentally perishable; for that which is accidental may not be applicable; but perishability is an attribute which applies necessarily when it is applicable at all. Otherwise one and the same thing will be imperishable as well as perishable, if it is possible for perishability not to apply to it.

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Thus perishability must be either the substance or in the substance of every perishable thing. The same argument also applies to the imperishable; for both perishability and imperishability are attributes which are necessarily applicable. Hence the characteristics in respect of which and in direct consequence of which one thing is perishable and another imperishable are opposed; and therefore they must be other in kind.

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Thus it is obvious that there cannot be Forms such as some thinkers maintain; for then there would be both a perishable and an imperishable man. i.e., the individual man is perishable and the Idea of man imperishable; and these must be other in kind (γένει non-technical). But the Platonists hold that the Idea is the same in species as the particular. This is impossible if it is other in genus (γένει technical). Yet the Forms are said to be the same in species as the particulars, and not merely to share a common predicate with them; but things which are other in genus differ more widely than things which are other in species.

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That wisdom is a science of first principles is clear from our Introductory remarks,Aristot. Met. 1.3-10. in which we of raised objections to the statements of other thinkers about the first principles. It might be asked, however, whether we should regard Wisdom as one science or as more than one.Cf. Aristot. Met. 3.1.5, Aristot. Met. 3.2.1-10. If as one, it may be objected that the objects of one science are always contraries; but the first principles are not contraries. And if it is not one, what sort of sciences are we to suppose them to be?

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Again, is it the province of one science, or of more than one, to study the principles of demonstration?Cf. Aristot. Met. 3.1.5, , Aristot. Met. 3.2.10-15, where the problem takes a slightly different form. If of one, why of it rather than of any other? And if of more than one, of what sort are we to suppose them to be?

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Again, are we to suppose that Wisdom deals with all substances or not?Cf. Aristot. Met. 3.1.6, Aristot. Met. 3.2.15-17. If not with all, it is hard to lay down with what kind it does deal; while if there is one science of them all, it is not clear how the same science can deal with more than one subject.

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Again, is this science concerned only with substances, or with attributes as well?Cf. Aristot. Met. 3.1.8-10, Aristot. Met. 3.2.18-19. For if it is a demonstration of attributes, it is not concerned with substances; and if there is a separate science of each, what is each of these sciences, and which of them is Wisdom? qua demonstrative, the science of attributes appears to be Wisdom; but qua concerned with that which is primary, the science of substances.

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Nor must we suppose that the science which we are seeking is concerned with the causes described in the Physics.Aristot. Physics 2.3. It is not concerned with the final cause; for this is the Good, and this belongs to the sphere of action and to things which are in motion; and it is this which first causes motion (for the end is of this nature); but there is no Prime Mover in the sphere of immovable things.

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And in general it is a difficult question whether the science which we are now seeking is concerned with sensible substances, or not with sensible substances, but with some other kind.Cf. Aristot. Met. 3.1.7, Aristot. Met.3.2.20-30. If with another kind, it must be concerned either with the Forms or with mathematical objects. Now clearly the Forms do not exist. (But nevertheless, even if we posit them, it is a difficult question as to why the same rule does not apply to the other things of which there are Forms as applies to the objects of mathematics.

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I mean that they posit the objects of mathematics as intermediate between the Forms and sensible things, as a third class besides the Forms and the things of our world; but there is no third manThis phrase has no technical sense here; cf. Aristot. Met. 1.9.4. or horse besides the Ideal one and the particulars. If on the other hand it is not as they make out, what sort of objects are we to suppose to be the concern of the mathematician? Not surely the things of our world; for none of these is of the kind which the mathematical sciences investigate.)

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Nor indeed is the science which we are now seeking concerned with the objects of mathematics; for none of them can exist separately. But it does not deal with sensible substances either; for they are perishable.

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In general the question might be raised, to what science it pertains to discuss the problems concerned with the matteri.e., intelligible matter (cf. Aristot. Met. 7.10.18). This problem is not raised in Book 3. of mathematical objects.

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It is not the province of physics, because the whole business of the physicist is with things which contain in themselves a principle of motion and rest; nor yet of the science which inquires into demonstration and

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scientific knowledge, for it is simply this sort of thing which forms the subject of its inquiry. It remains, therefore, that it is the science which we have set ourselves to find that treats of these subjects.

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One might consider the question whether we should regard the science which we are now seeking as dealing with the principles which by some are called elements.Cf. Aristot. Met. 3.1.10, Aristot. Met. 3.3. But everyone assumes that these are present in composite things; and it would seem rather that the science which we are seeking must be concerned with universals, since every formula and every science is of universals and not of ultimate species; so that in this case it must deal with the primary genera.

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These would be Being and Unity; for these, if any, might best be supposed to embrace all existing things, and to be most of the nature of first principles, because they are by nature primary; for if they are destroyed, everything else is destroyed with them, since everything exists and is one.

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But inasmuch as, if Being and Unity are to be regarded as genera, they must be predicable of their differentiae, whereas no genus is predicable of any of its differentiae, from this point of view it would seem that they should be regarded neither as genera nor as principles.

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Further, since the more simple is more nearly a principle than the less simple, and the ultimate subdivisions of the genus are more simple than the genera (because they are indivisible), and the genera are divided into a number of different species, it would seem that species are more nearly a principle than genera.

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On the other hand, inasmuch as species are destroyed together with their genera, it seems more likely that the genera are principles; because that which involves the destruction of something else is a principle. These and other similar points are those which cause us perplexity.

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Again, ought we to assume the existence of something else besides particular things, or are they the objects of the science which we are seeking?Cf. Aristot. Met. 3.1.11, Aristot. Met. 3.4.1-8. It is true that they are infinite in number; but then the things which exist besides particulars are genera or species, and neither of these is the object of the science which we are now seeking. We have explained Aristot. Met. 11.1.11-13 why this is impossible.

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Indeed, in general it is a difficult question whether we should suppose that there is some substance which exists separately besides sensible substances (i.e. the substances of our world), or that the latter constitute reality, and that it is with them that Wisdom is concerned. It seems that we are looking for some other kind of substance, and that this is the object of our undertaking: I mean, to see whether there is anything which exists separately and independently, and does not appertain to any sensible thing.

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But again, if there is another kind of substance besides sensible substances, to what kind of sensible things are we to suppose that it corresponds? Why should we suppose that it corresponds to men or horses rather than to other animals, or even to inanimate objects in general? And yet to manufacture a set of eternal substances equal in number to those which are sensible and perishable would seem to fall outside the bounds of plausibility.

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Yet if the principle which we are now seeking does not exist in separation from bodies, what can we suppose it to be if not matter? Yes, but matter does not exist actually, but only potentially. It might seem rather that a more appropriate principle would be form or shape; but this is perishableForms which are induced in matter are perishable, although not subject to the process of destruction; they are at one time and are not at another (cf. Aristot. Met. 7.15.1). The only pure form (i.e., the only form which is independent of matter in any and every sense) is the prime mover (Aristot. Met. 12.7).; and so in general there is no eternal substance which exists separately and independently.

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But this is absurd, because it seems natural that there should be a substance and principle of this kind, and it is sought for as existing by nearly all the most enlightened thinkers. For how can there be any order in the universe if there is not something eternal and separate and permanent?

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Again, if there is a substance and principle of such a nature as that which we are now seeking, and if it is one for all things, i.e. the same for both eternal and perishable things, it is a difficult question as to why, when the principle is the same, some of the things which come under that principle are eternal, and others not; for this is paradoxical.Cf. Aristot. Met. 3.1.12, Aristot. Met. 3.4.11-23.

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But if there is one principle of perishable things, and another of eternal things, if the principle of perishable things is also eternal, we shall still have the same difficulty; because if the principle is eternal, why are not the things which come under that principle eternal? And if it is perishable, it must have another principle behind it, and that principle must have another behind it; and the process will go on to infinity.

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On the other hand, if we posit the principles which seem most unchangeable, Being and Unity,Cf. Aristot. Met. 3.1.13, Aristot. Met. 3.4.24-34.(a) unless each of them denotes a particular thing and a substance, how can they be separate and independent? but the eternal and primary principles for which we are looking are of this nature.

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(b) If, however, each of them denotes a particular thing and a substance, then all existing things are substances; for Being is predicated of everything, and Unity also of some things.

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But that all things are substances is false. (c) As for those who maintain that Unity is the first principle and a substance, and who generate number from Unity and matter as their first product, and assert that it is a substance, how can their theory be true? How are we to conceive of 2 and each of the other numbers thus composed, as one? On this point they give no explanation; nor is it easy to give one.

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But if we posit lines or the things derived from them (I mean surfaces in the primary sensei.e., intelligible surfaces, etc.) as principles,Cf. Aristot. Met. 3.1.15, Aristot. Met. 3.5. these at least are not separately existing substances, but sections and divisions, the former of surfaces and the latter of bodies (and points are sections and divisions of lines); and further they are limits of these same things. All these things are integral parts of something else, and not one of them exists separately.

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Further, how are we to suppose that there is a substance of unity or a point? for in the case of every substancesc. which is liable to generation or destruction. there is a process of

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generation, but in the case of the point there is not; for the point is a division.

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It is a perplexing fact also that whereas every science treats of universals and types, substance is not a universal thing, but rather a particular and separable thing; so that if there is a science that deals with first principles, how can we suppose that substance is a first principle?Cf. Aristot. Met. 3.1.14, Aristot. Met. 3.6.7-9.

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Again, is there anything besides the concrete whole (I mean the matter and the form in combination) or not?This section belongs to the problem discussed in 1-5 above. If not, all things in the nature of matter are perishable; but if there is something, it must be the form or shape. It is hard to determine in what cases this is possible and in what it is not; for in some cases, e.g. that of a house, the form clearly does not exist in separation.

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Again, are the first principles formally or numerically the same?Cf. Aristot. Met. 3.1.12, Aristot. Met. 3.4.8-10. If they are numerically one, all things will be the same.

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Since the science of the philosopher is concerned with Being qua Being universally,This chapter corresponds to Aristot. Met. 4.1, 2, with which it should be compared. and not with some part of it, and since the term Being has several meanings and is not used only in one sense, if it is merely equivocal and has no common significance it cannot fall under one science (for there is no one class in things of this kind); but if it has a common significance it must fall under one science.

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Now it would seem that it is used in the sense which we have described, like medical and healthy, for we use each of these terms in several senses; and each is used in this way because it has a reference, one to the science of medicine, and another to health, and another to something else; but each refers always to the same concept. A diagnosis and a scalpel are both called medical, because the one proceeds from medical science and the other is useful to it.

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The same is true of healthy; one thing is so called because it is indicative, and another because it is productive, of health; and the same applies to all other cases. Now it is in this same way that everything which exists is said to be ; each thing is said to be because it is a modification or permanent or temporary state or motion or some other such affection of Being qua Being.

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And since everything that is can be referred to some one common concept, each of the contrarieties too can be referred to the primary differentiae and contrarieties of Being—whether the primary differentiae of Being are plurality and unity, or similarity and dissimilarity, or something else; for we may take them as already discussed.Cf. Aristot. Met. 4.2.9 n.

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It makes no difference whether that which is is referred to Being or Unity; for even if they are not the same but different, they are in any case convertible, since that which is one also in a sense is , and that which is is one.

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Now since the study of contraries pertains to one and the same science, and each contrary is so called in virtue of privation (although indeed one might wonder in what sense they can be called contraries in virtue of privation when they admit of a middle term—e.g. unjust and just), in all such cases we must regard the privation as being not of the whole definition but of the ultimate species. E.g., if the just man is one who is obedient to the laws in virtue of some volitional state, the unjust man will not be entirely deprived of the whole definition, but will be one who is in some respect deficient in obedience to the laws; and it is in this respect that the privation of justice will apply to him (and the same holds good in all other cases).

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And just as the mathematician makes a study of abstractions (for in his investigations he first abstracts everything that is sensible, such as weight and lightness, hardness and its contrary, and also heat and cold and all other sensible contrarieties, leaving only quantity and continuity—sometimes in one, sometimes in two and sometimes in three dimensions—and their affections qua quantitative and continuous, and does not study them with respect to any other thing; and in some cases investigates the relative positions of things and the properties of these, and in others their commensurability or incommensurability, and in others their ratios; yet nevertheless we hold that there is one and the same science of all these things, viz. geometry), so it is the same with regard to Being.

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For the study of its attributes in so far as it is Being, and of its contrarietiesi.e., identity, otherness, etc. qua Being, belongs to no other science than Philosophy; for to physics one would assign the study of things not qua Being but qua participating in motion, while dialectics and sophistry deal with the attributes of existing things, but not of things qua Being, nor do they treat of Being itself in so far as it is Being.

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Therefore it remains that the philosopher is the man who studies the things which we have described, in so far as they are Being. And since everything that is , although the term has several meanings, is so described in virtue of some one common concept, and the same is true of the contraries (since they can be referred to the primary contrarieties and differences of Being), and since things of this kind can fall under one science, the difficulty which we stated at the beginningAristot. Met. 11.1.1. may be regarded as solvedAlso the problem stated in ch. i. 3.—I mean the problem as to how there can be one science of several things which are different in genus.

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Since even the mathematician uses the common axioms only in a particular application, it will be the province of Primary Philosophy to study the principles of these as well.This chapter corresponds to Aristot. Met. 4.3.1-6, and answers the problem stated in Aristot. Met. 11.1.2.

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That when equals are taken from equals the remainders are equal is an axiom common to all quantities; but mathematics isolates a particular part of its proper subject matter and studies it separately; e.g. lines or angles or numbers or some other kind of quantity, but not qua Being, but only in so far as each of them is continuous in one, two or three dimensions. But philosophy does not investigate particular things in so far as each of them has some definite attribute, but studies that which is , in so far as each particular thing is .

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The same applies to the science of physics as to mathematics, for physics studies the attributes and first principles of things qua in motion, and not qua Being; but Primary Science, as we have said, deals with these things only in so far as the subjects which underlie them are existent, and not in respect of anything else. Hence we should regard both physics and mathematics as subdivisions of Wisdom.

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There is a principle in existing things about which we cannot make a mistakeThis chapter corresponds to Aristot. Met. 4.3.7-4.31.; of which, on the contrary, we must always realize the truth—viz. that the same thing cannot at one and the same time be and not be, nor admit of any other similar pair of opposites. Of such axioms although there is a proof ad hominem, there is no absolute proof;

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because there is no principle more convincing than the axiom itself on which to base an argument, whereas there must be such a principle if there is to be absolute proof.

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But he who wants to convince an opponent who makes opposite statements that he is wrong must obtain from him an admission which shall be identical with the proposition that the same thing cannot at one and the same time be and not be, but shall seem not to be identical with it. This is the only method of proof which can be used against one who maintains that opposite statements can be truly made about the same subject.

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Now those who intend to join in discussion must understand one another to some extent; for without this how can there be any common discussion between them? Therefore each of the terms which they use must be intelligible and signify something; not several things, but one only; or if it signifies more than one thing, it must be made clear to which of these the term is applied.

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Now he who says that A is and is not denies what he asserts, and therefore denies that the term signifies what it does signify. But this is impossible. Therefore if to be so-and-so has a definite meaning, the opposite statement about the same subject cannot be true.

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Again, if the term has a definite significance and this is truly stated, it must of necessity be so.sect. 6=Aristot. Met. 4.4.14-16. But that which of necessity is can never not be. Hence opposite statements about the same subject cannot be true.

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Again, if the assertion is no more true than the negation, it will be no more true to say A is man than to say A is not man. With this section cf. Aristot. Met. 4.4.26-30.

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But it would also be admitted that it is more or at least not less true to say that a man is not a horse than to say that he is not a man; and therefore, since it was assumed that opposite statements are equally true, it will be true to say that the same person is also a horse. It follows therefore, that the same person is a man and a horse, or any other animal.

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Thus, although there is no absolute proof of these axioms, there is an ad hominem proof where one’s opponent makes these assumptions.sect. 8=Aristot. Met. 4.3.10. Perhaps even Heraclitus himself, if he had been questioned on these lines, would have been compelled to admit that opposite statements can never be true of the same subjects; as it is, he adopted this theory through ignorance of what his doctrine implied.

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In general,sect. 9-11=Aristot. Met. 4.4.31. if what he says is true, not even this statement itself (I mean that the same thing can at one and the same time be and not be) will be true;

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because just as, when they are separated, the affirmation is no more true than the negation, so in the same way, if the complex statement is taken as a single affirmation, the negation will be just as true as the whole statement regarded as an affirmation.

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And further, if nothing can be truly affirmed, then this very statement—that there is no such thing as a true affirmation—will be false. But if there is such a thing, the contentions of those who raise objections of this kind and utterly destroy rational discourse may be considered to be refuted.Cf. Aristot. Met. 4.8.4, 5.

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Very similar to the views which we have just mentioned is the dictum of ProtagorasThis chapter forms a summary of Aristot. Met. 4.5-8. sect. 1-3=Aristot. Met. 4.5.1-5.; for he said that man is the measure of all things, by which he meant simply that each individual’s impressions are positively true.

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But if this is so, it follows that the same thing is and is not, and is bad and good, and that all the other implications of opposite statements are true; because often a given thing seems beautiful to one set of people and ugly to another, and that which seems to each individual is the measure.

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This difficulty will be solved if we consider the origin of the assumption. It seems probable that it arose in some cases from the doctrine of the natural philosophers, and in others from the fact that everyone does not form the same opinion about the same things, but to some a given thing seems sweet and to others the contrary.

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For that nothing comes from what is not, but everything from what is, is a doctrine common to nearly all natural philosophers.With sect. 4, 5 cf. Aristot. Met. 4.5.6. Since, then, a thing does not become white which was before completely white and in no respect not-white, that which becomes white must come from what was not-white. Hence according to this theory there would be generation from what is not, unless the same thing were originally white and not-white.

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However, it is not hard to solve this difficulty. We have explained in the PhysicsAristot. Physics 1.7-9. in what sense things which are generated are generated from what is not, and in what sense from what is.

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But to attach equal importance to the opinions and impressions of opposing parties is foolish, because clearly one side or the other must be wrong.sect. 5-7=Aristot. Met. 4.5.23-27.

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This is evident from what happens in the sphere of sensation; for the same thing never seems to some people sweet and to others to the contrary unless one of the parties has the organ of sense which distinguishes the said flavors injured or impaired. Such being the case, the one party should be taken as the measure, and the other not.

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And I hold the same in the case of good and bad, and of beautiful and ugly, and of all other such qualities. For to maintain this viewi.e., that the same thing has contrary qualities. is just the same as to maintain that what appears to us when we press the finger below the eye and make a thing seem two instead of one must be two because it appears to be so, and then afterwards that it must be one; because if we do not interfere with our sight that which is one appears to be one.

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And in general it is absurd to form our opinion of the truth from the appearances of things in this world of ours which are subject to change and never remain in the same statesect. 8, 9 (first half)=Aristot. Met. 4.5.21, 22.; for it is by reference to those things which are always the same state and undergo no change that we should prosecute our search for truth.

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Of this kind are the heavenly bodies; for these do not appear to be now of one nature and subsequently of another, but are manifestly always the same and have no change of any kind.

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Again, if there is motion there is also something which is moved; and everything is moved from something and into something. Therefore that which is moved must be in that from which it is to be moved, and must also not be in it; and must be moved into so-and-so and must also come to be in it; but the contradictory statements cannot be true at the same time, as our opponents allege.

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And if the things of our world are in a state of continuous flux and motion in respect of quantity, and we assume this although it is not true, why should they not be constant in respect of quality?Cf. Aristot. Met. 4.5.20, 21. It appears that not the least reason why our opponents predicate opposite statements of the same thing is that they start with the assumption that quantity is not constant in the case of bodies; hence they say that the same thing is and is not six feet long.

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But essence depends upon quality, and this is of a determinate, whereas quantity is of an indeterminate nature.

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Again, when the doctor orders them to adopt some article of diet, why do they adopt it?Cf. Aristot. Met. 4.4.39-42. For on their view it is no more true that a thing is bread than that it is not; and therefore it would make no difference whether they ate it or not. But as it is, they adopt a particular food as though they knew the truth about it and it were the food prescribed;

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yet they ought not to do so if there were no fixed and permanent nature in sensible things and everything were always in a state of motion and flux.

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Again, if we are always changing and never remain the same, is it any wonder that to us, as to the diseased, things never appear the same?With this section cf. Aristot. Met. 4.5.7-14.

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For to the diseased, since they are not in the same physical condition as when they were well, sensible qualities do not appear to be the same; although this does not mean that the sensible things themselves partake of any change, but that they cause different, and not the same, sensations in the diseased. Doubtless the same must be true if the change which we have referred to takes place in us.

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If, however, we do not change but remain always the same, there must be something permanent.

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As for those who raise the aforesaid difficulties on dialectical grounds,With this section cf. Aristot. Met. 4.5.3, 4, Aristot. Met. 4.6.1-3. it is not easy to find a solution which will convince them unless they grant some assumption for which they no longer require an explanation; for every argument and proof is possible only in this way. If they grant no assumption, they destroy discussion and reasoning in general.

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Thus there is no arguing with people of this kind; but in the case of those who are perplexed by the traditional difficulties it is easy to meet and refute the causes of their perplexity. This is evident from what has been already said.

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Thus from these considerations it is obvious that opposite statements cannot be true of the same thing at one time; nor can contrary statements, since every contrariety involves privation. This is clear if we reduce the formulae of contraries to their first principles.Cf. Aristot. Met. 4.6.10, 11.

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Similarly no middle term can be predicated of one and the same thing of which one of the contraries is predicated.Cf. Aristot. Met. 4.7 where, however, the point which is proved is that there can be no intermediate between contradictories.

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If, when the subject is white, we say that it is neither white nor black, we shall be in error; for it follows that it is and is not white, because the first of the two terms in the complex statement will be true of the subject, and this is the contradictory of white.

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Thus we cannot be right in holding the views either of HeraclitusCf. Aristot. Met. 11.5.8 or of Anaxagoras.Cf. Aristot. Met. 4.7.8-8.5

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If we could, it would follow that contraries are predicable of the same subject; for when heAnaxagoras. What he really meant was that even the sweetest things contain some bitter particles. Cf. Anaxagoras Fr. 11 (Diels); Burnet, E.G.P. 129. says that in everything there is a part of everything, he means that nothing is sweet any more than it is bitter, and similarly with any of the other pairs of contraries; that is, if everything is present in everything not merely potentially but actually and in differentiation.

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Similarly all statements cannot be false, nor all true. Among many other difficulties which might be adduced as involved by this supposition there is the objection that if all statements were false, not even this proposition itself would be true; while if they were all true it would not be false to say that they are all false.

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Every science inquires for certain principles and causes with respect to every knowable thing which comes within its scopeThis chapter corresponds to Aristot. Met. 6.1; cf. also Aristot. Met. 4.3.1-6 and ch. 4 above. It also answers the problem stated in ch. 1.2.; e.g., the sciences of medicine and physical culture do this, and so does each of the other productive and mathematical sciences. Each one of these marks out for itself some class of objects, and concerns itself with this as with something existent and real, but not qua real; it is another science distinct from these which does this.

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Each of the said sciences arrives in some way at the essence in a particular class of things, and then tries to prove the rest more or less exactly. Some arrive at the essence through sense-perception, and some by hypothesis; hence it is obvious from such a process of induction that there is no demonstration of the reality or essence.

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Now since there is a science of nature, clearly it must be different from both practical and productive science. In a productive science the source of motion is in the producer and not in the thing produced, and is either an art or some other kind of potency; and similarly in a practical science the motion is not in the thing acted upon but rather in the agent.

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But the science of the natural philosopher is concerned with things which contain in themselves a source of motion. From this it is clear that natural science must be neither practical nor productive, but speculative; since it must fall under one of these classes.

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And since every science must have some knowledge of the essence and must use it as a starting-point, we must be careful to observe how the natural philosopher should define, and how he should regard the formula of essence—whether in the same way as the term snub, or rather as the term concave.

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For of these the formula of snub is stated in conjunction with the matter of the object, whereas that of concave is stated apart from the matter; since snubness is only found in the nose, which is therefore included in the formula, for the snub is a concave nose . Thus it is obvious that the formula of flesh and eye and the other parts of the body must always be stated in conjunction with their matter.

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Since there is a science of Being qua Being and separately existent, we must inquire whether this should be regarded as identical with natural science or rather as a distinct branch of knowledge. Physics deals with things which contain a source of motion in themselves, and mathematics is speculative and is a science which deals with permanent things, but not with things which can exist separately.

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Hence there is a science distinct from both of these, which deals with that which exists separately and is immovable; that is, if there really is a substance of this kind—I mean separately existent and immovable—as we shall endeavor to prove.Aristot. Met. 12.6, 7. And if there is an entity of this kind in the world of reality, here surely must be the Divine, and this must be the first and most fundamental principle.

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Evidently, then, there are three kinds of speculative science: physics, mathematics, and theology. The highest class of science is the speculative, and of the speculative sciences themselves the highest is the last named, because it deals with the most important side of reality; and each science is reckoned higher or lower in accordance with the object of its study.

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The question might be raised as to whether the science of Being qua Being should be regarded as universal or not.

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Each of the mathematical sciences deals with some one class of things which is determinate, but universal mathematics is common to all alike. If, then, natural substances are the first of existing things, physics will be the first of the sciences; but if there is some other nature and substance which exists separately and is immovable, then the science which treats of it must be different from and prior to physics, and universal because of its priority.

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Since the term Being in its unqualified sense is used with several meanings, of which one is accidental Being, we must first consider Being in this sense.Sections 1-9 of this chapter correspond to Aristot. Met. 6.2-4. Clearly none of the traditional sciences concerns itself with the accidental; the science of building does not consider what will happen to the occupants of the house, e.g. whether they will find it unpleasant or the contrary to live in; nor does the science of weaving or of shoemaking or of confectionery.

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Each of these sciences considers only what is proper to it, i.e. its particular end. As for the question whether the cultured is also the lettered, or the quibbleThis is a different form of the quibble in Aristot. Met. 6.2.4. Here the fallacy obviously consists in the wrong application of the word ἅμα(at once or at the same time). that the man who is cultured, when he has become lettered, will be both at once although he was not before; but that which is but was not always so must have come to be; therefore he must have become at the same time cultured and lettered

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—none of the recognized sciences considers this, except sophistry. This is the only science which concerns itself with the accidental, and hence Plato was not far wrong in sayingPlat. Sop. 254a. that the sophist spends his time in the study of unreality. But that it is not even possible for there to be a science of the accidental will be apparent if we try to see what the accidental really is.

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Of some things we say that they are so always and of necessity (necessity having the sense not of compulsion, but that which we use in logical demonstrationCf. Aristot. Met. 6.2.6.), and of others that they are so usually, but of others that they are so neither usually nor always and of necessity, but fortuitously. E.g., there might be a frost at midsummer, although this comes about neither always and of necessity nor usually; but it might happen sometimes.

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The accidental, then, is that which comes about, but not always nor of necessity nor usually. Thus we have now stated what the accidental is; and it is obvious why there can be no science of such a thing, because every science has as its object that which is so always or usually, and the accidental falls under neither of these descriptions.

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Clearly there can be no causes and principles of the accidental such as there are of that which is per se; otherwise everything would be of necessity. For if A is when B is, and B is when C is, and C is not fortuitously but of necessity, then that of which C was the cause will also be of necessity, and so on down to the last causatum , as it is called.

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(But this was assumed to be accidental.) Therefore everything will be of necessity, and the element of chance, i.e. the possibility of a thing’s either happening or not, is entirely banished from the world of events. Even if we suppose the cause not to exist already but to be coming to be, the result will be the same; for everything will come to be of necessity.

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The eclipse tomorrow will come about if A does, and A will if B does, and B if C does; and in this way if we keep on subtracting time from the finite time between now and to-morrow, we shall at some point arrive at the present existing condition. Therefore since this exists, everything subsequent to it will happen of necessity, and so everything happens of necessity.

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As for what is in the sense of what is true or what is accidental , the former depends upon a combination in thought, and is an affection of thought (hence we do not look for the principles of Being in this sense, but only for those of objective and separable Being) the latter is not necessary but indeterminate (I mean the accidental); and of such a thing the causes are indefinite and cannot be reduced to a system.

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Teleology is found in events which come about in the course of nature or as a result of thought.This section is taken from Aristot. Physics 2.5, 6. It is chance <or luck> when one of these comes about by accident; for a thing may be a cause, just as it may exist, either per se or accidentally. Chance is an accidental cause of normally purposive teleological events.

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Hence chance and thought have the same sphere of action, for there is no purpose without thought. Causes from which chance results may come about are indeterminate; hence chance is inscrutable to human calculation, and is a cause only accidentally, but in the strictest sense is a cause of nothing.

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It is good or bad luck when the result is good or bad, and good or bad fortune when the result is on a large scale.

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Since nothing accidental is prior to that which is per se, neither are accidental causes prior. Therefore if chance or spontaneity is the cause of the universe, mind and nature are prior causes.The argument is stated more fully and clearly in Aristot. Physics 2.6ff.. Chance produces indirectly the effects produced directly by mind; and spontaneity is similarly related to nature. But the indirect cause presupposes the direct. The argument is directed against the Atomists. Cf. Aristot. Phys. 196a 24, Simplicius 327.24, Cicero De Nat. Deor. 1.66 (nulla cogente natura, sed concursu quodam fortuito).

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A thing may exist only actually or potentially, or actually and potentially; it may be a substance or a quantity or one of the other categories. There is no motionThe discussion of motion in this chapter consists of extracts from Aristot. Physics 3.1-3. apart from things, for change is always in accordance with the categories of Beingi.e., change is substantial (generation and destruction); quantitative (increase and decrease); qualitative (alteration); spatial (locomotion). Cf. Aristot. Met. 11.12.1, 2.; and there is nothing which is common to these and in no one category. Each category belongs to all its members in two ways—e.g. substance, for this is sometimes the form of the thing and sometimes its privation;

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and as regards quality there is white and black; and as regards quantity, complete and incomplete; and as regards spatial motion there is up and down or light and heavy—so that there are as many forms of motion and change as there are of Being.This is inaccurate; see previous note.

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Now since every kind of thing is divided into the potential and the real, I call the actualization of the potential as such,What Aristotle means by this is explained more clearly in the following sections, which may be summarized thus. The material substrate, e.g. bricks, etc., which is potentially a house, may be regarded (a) as potential material; in this sense it is actualized as bricks before building begins; (b) as potentially a house; in this sense when it is actualized it is no longer buildable but built, i.e., it is no longer potential; (c) as potentially buildable into a house. In this sense its actualization is conterminous with the process of building, and is incomplete (sect.11), and should not be described as ἐντελέχεια or complete reality. But Aristotle often uses this term as synonymous with the vaguer ἐνέργεια. motion.

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That this is a true statement will be clear from what follows. When the buildable in the sense in which we call it such exists actually, it is being built; and this is the process of building. The same is true of the processes of learning, healing, walking, jumping, ageing, maturing. Motion results when the complete reality itself exists, and neither sooner nor later.

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The complete reality, then, of that which exists potentially, when it is completely real and actual, not qua itself but qua movable, is motion. By qua I mean this. The bronze is potentially a statue; but nevertheless the complete reality of the bronze qua bronze is not motion. To be bronze is not the same as to be a particular potentiality; since if it were absolutely the same by definition the complete reality of the bronze would be a kind of motion; but it is not the same.

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(This is obvious in the case of contraries; for the potentiality for health and the potentiality for illness are not the same—for if they were, health and illness would be the same too—but the substrate which becomes healthy or ill, whether it is moisture or blood, is one and the same.) And since it is not the same, just as color and visible are not the same, it is the complete reality of the potential qua potential that is motion.

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It is evident that it is this, and that motion results when the complete reality itself exists, and neither sooner nor later. For everything may sometimes be actual, and sometimes not; e.g. the buildable qua buildable; and the actualization of the buildable qua buildable is the act of building.

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For the actualization is either this—the act of building—or a house. But when the house exists, it will no longer be buildable; the buildable is that which is being built. Hence the actualization must be the act of building, and the act of building is a kind of motion. The same argument applies to the other kinds of motion.

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That this account is correct is clear from what the other authorities say about motion, and from the fact that it is not easy to define it otherwise. For one thing, it could not be placed in any other class; this is clear from the fact that some peoplePythagoreans and Platonists. Cf. Aristot. Met. 1.5.6, Plat. Soph. 256d. identify it with otherness and inequality and not-being, none of which is necessarily moved;

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moreover change is no more into these or out of them than into or out of their opposites.The criticism implied is: If motion is identified with otherness, inequality, etc., then these concepts must be either (a) subjects of motion, which is absurd, or (b) termini of motion, in which case the same must be true of their contraries, since motion is between contraries. The reason for placing motion in this class is that it is considered to be indeterminate, and the principles in one of the columns of contraries are indeterminate, being privative; for none of them is a determinate thing or quality or any of the other categories.

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The reason for considering motion to be indeterminate is that it cannot be associated either with the potentiality or with the actuality of things; for neither that which is potentially nor that which is actually of a certain size is necessarily moved.

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And motion is considered to be a kind of actualization, but incompleteCf. note on sect. 2 (end) above, and Aristot. Met. 9.6.7-10.; the reason of this is that the potential, of which it is the actualization, is incomplete.

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Thus it is difficult to comprehend what motion is; for we must associate it either with privation or with potentiality or with absolute actuality; and apparently none of these is possible.

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There remains, then, the account which we have given; that it is an actuality, and an actuality of the kind which we have described, which is hard to visualize but capable of existing.

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That motion is in the movable is evident; for it is the complete realization of the movable by that which is capable of causing motion, and the actualization of that which is capable of causing motion is identical with that of the movable.

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For it must be a complete realization of them both; since a thing is capable of moving because it has the potentiality, but it moves only when it is active; but it is upon the movable that it is capable of acting. Thus the actuality of both alike is one; just as there is the same interval from one to two as from two to one, and the hill up and the hill down are one, although their being is not one; the case of the mover and the thing moved is similar.

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This chapter consists of extracts from Aristot. Physics 3.4, 5, 7.The infinite is either (a) that which cannot be traversed because it is not its nature to be traversed (just as sound is by nature invisible); or (b) that which admits of an endless traverse; or (c) scarcely admits of traverse; or (d) which, though it would naturally admit of traverse or limit, does not do so. Further, it may be infinite in respect of addition or of subtraction or of both.

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That the infinite should be a separate independent entity,The Pythagorean and Platonic view. and yet imperceptible, is impossible.

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For if it is neither magnitude nor plurality, but infinity itself is the essence of it, and not merely an accident, it must be indivisible; because that which is divisible is either magnitude or plurality. And if it is indivisible it cannot be infinite, except in the same way as sound is invisible. But this is not what people mean by infinite; and it is not the infinite in this sense that we are investigating, but the infinite in the sense of the untraversable.

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Again, how can the infinite exist independently unless number and magnitude, of which infinity is an attribute, also exist independently?Aristotle has argued that they do not in Aristot. Met. 1.9.16-25. And further, if the infinite is accidental, it cannot, qua infinite, be an element of things; just as the invisible is not an element of speech, although sound is invisible. It is clear also that the infinite cannot exist actually.

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Otherwise any part of it which we might take would be infinite; for infinity and the infinite are the same, if the infinite is substance and is not predicated of a subject. Therefore it is either indivisible, or if it is partible, the parts into which it is divisible are infinite. But the same thing cannot be many infinites; for just as a part of air is air, so a part of the infinite will be infinite, if the infinite is a substance and principle.

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Therefore it is impartible and indivisible. But this is impossible of the actually infinite, because it must be some quantity. Therefore infinity is an accidental attribute. But if so, as we have said, it cannot be it that is a principle, but that of which it is an accident: airAccording to Anaximenes; cf. Theophrastus, Phys. Opin. Fr. 2 (Ritter and Preller 26). or the even. According to the Pythagoreans. Cf. Aristot. Met. 1.5.5. n

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The foregoing inquiry is general; but what follows will show that the infinite does not exist in sensible things.

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If the definition of a body is that which is bounded by surfaces, then no body, whether sensible or intelligible, can be infinite nor can there be any separate and infinite number, since number or that which involves number is numerable. This is clearly shown by the following concrete argument. The infinite can neither be composite nor simple. For (a) it cannot be a composite body if the elements are limited in numberThis is proved in Aristot. Physics 1.6.;

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for the contraries must be equal, and no one of them must be infinite; for if the potency of one of the two corporeal elements is in any way inferior, the finite element will be destroyed by the infinite. And every element cannot be infinite, because body is that which has extension in all directions, and the infinite is that which is extended without limit; so that if the infinite is corporeal it will be infinite in all directions.sc. and so no other body can exist beside it.

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Nor (b) can the infinite be any simple body; neither, as someAnaximander. It seems, however, that by ἄπειρον he meant indeterminate or undifferentiated, although he no doubt regarded this principle as infinite as well. Cf. notes on Aristot. Met. 1.7.3, Aristot. Met. 12.2.3. hold, something which is apart from the elements and from which they suppose the elements to be generated (for there is no such body apart from the elements; everything can be resolved into that of which it consists, but we do not see things resolved into anything apart from the simple bodies), nor fire nor any other element.

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Apart from the question of how any of them could be infinite, the All, even if it is finite, cannot be or become any one of the elements, as Heraclitus saysCf. Hereclitus Fr. 20-22 (Bywater). all things at certain times become fire. The same argument applies as to the One which the physicists posit besides the elements; for all change proceeds from the contrary, e.g. from hot to cold.The argument seems to be: Since all change is from contrary to contrary, and it is impossible that either (a) one of the elements should be contrary to the rest, or (b) one material principle should be contrary to all four elements, it follows that no one element, and similarly that no one material principle apart from the elements, can be the ultimate material principle of the universe.

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Again, a sensible body is in some region, and the region of the whole and of the part (e.g. of the earth) is the same.i.e., the region of the universe which is proper to a given element is proper also to any part of that element. The proper region of earth is the center, of fire the circumference of the universe. Cf. Aristot. De Caelo 1.2. Therefore if the infinite body is homogeneous, it will be immovable or will always be in motionRoss is evidently right in taking this to refer to the rest or motion of the parts. An infinite body cannot move as a whole, because there is no space outside it.; but this is impossible, for why should there be rest or motion below rather than above or in any other region? E.g., if there were a clod, in what region would it move or be at rest?

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The region proper to the body which is homogeneous with the clod is infinite. Then will the clod occupy the whole of that region? How can it? Then what of its rest or motion? It will either rest everywhere—in which case it cannot move—or move everywhere; in which case it cannot rest.If earth is an infinite body, its region must be infinite. But the infinite has no center (cf. sect. 13). Therefore a clod, which cannot occupy the whole region proper to earth, will have no region proper to itself to which it can move or in which it can rest. And if the whole is not alike throughout, the regions proper to its parts are unlike also; and (a) the body of the whole is not one, except in virtue of contact; (b) the parts will be either finite or infinite in kind.

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Finite they cannot be, for then those of one kind would be infinitesc. in quantity. If the universe is infinite in quantity, and the elements are limited in kind, some of the elements (or at least one) must be infinite in quantity. But this is impossible, just as it is impossible that all the elements should be infinite in quantity. Cf. sect. 7 above and those of another would not (if the whole is infinite); e.g., fire or water would be infinite. But such a condition would involve the destruction of the contraries. But if the parts are infinitesc. in kind or number. and simple, the regions proper to them are infinite and the elements will be infinite. And since this is impossible,Cf. sect. 6 n. the regions are finiteCf. sect. 14 n. and the whole must be finite.

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In general, there cannot be an infinite body and a place for bodies if every body which is sensible has either weight or lightness; for it will have to move either towards the center or upwards, and the infinite—either the whole or the half—cannot do either; for how can you divide it? How can the infinite be part up and part down, or part extreme and part center?

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Further, every sensible body is in some place, and of place there are six kinds,i.e., above and below, before and behind, right and left (Aristot. Phys. 205b 31). but these cannot exist in an infinite body. In general, if an infinite place is impossible, so is an infinite body; because that which is in a place is somewhere, and this means either up or down or one of the other kinds of place, and each of these is a limit.

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The infinite is not the same in the sense that it is one nature whether it applies to magnitude or to motion or to time; the posterior is derived from the prior sense, e.g. motion is called infinite in virtue of the magnitude involved when a thing is moved or changed or increased, and time is so called on account of motion.Cf. Aristot. Met. 5.13.5.

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That which changes either changes accidentally, as when the cultured walks; or is said to change in general because something in it changes, as in the case of things which change in their parts; the body becomes healthy because the eye does.

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But there is something which is moved directly per se, i.e. the essentially movable. The same applies to that which moves, for it moves sometimes accidentally, sometimes partially, and sometimes per se. There is something that moves directly, and something that is moved; and also a time in which, and something from which, and something into which it is moved. But the forms and modifications and place into which moving things are moved are immovable; e.g. knowledge and warmth. It is not warmth that is motion, but the process of warming.

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Non-accidental change is not found in all things, but only between contraries and intermediates and contradictories. We can convince ourselves of this by means of induction. That which changes changes either from positive into positive, or from negative into negative, or from positive into negative, or from negative into positive.

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By positive I mean that which is denoted by an affirmation. Thus there must be three forms of change; for that which is from negative into negative is not change, because they are neither contraries nor contradictories, since they entail no opposition. The change from the negative into its contradictory positive is generation—absolute change absolute generation, and qualified change qualified generation; and the change from the positive to the negative is destruction—absolute change absolute destruction, and qualified change qualified destruction.The change from positive to positive is omitted here (but cf. sect. 7). Aristotle no doubt intended to use it as an example of non-substantial change, e.g. from poor man to rich man; but since this can be regarded as change from poor man to not-poor man, or not-rich man to rich man, he includes it as a qualified type of substantial change.

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Now if what is not has several meanings, and neither that which implies a combination or separation of terms,i.e., falsity. Cf. Aristot. Met. 9.10.1. nor that which relates to potentiality and is opposed to unqualified Being, admits of motion (not-white or not-good, however, admits of motion accidentally, because not-white may be a man; but that which is not so-and-so in an absolute sense does not admit of it at all), then what is not cannot be moved. If this is so, generation cannot be motion; for it is what is not that is generated.

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For even if the generation is in the highest degree accidental, still it is true to say that not-being is predicable of that which is generated absolutely. And the argument applies similarly to rest. Thus not only do these difficult conclusions follow, but also that everything which is moved is in a place, whereas what is not is not in a place; for then it would be somewhere. Nor is destruction motion; for the contrary of motion is motion or rest, but the contrary of destruction is generation.

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And since every motion is a kind of change, and the three kinds of change are those which we have described,sect. 3. and of these those which relate to generation and destruction are not motions, and these are the changes between contradictories, the change from positive to positive must alone be motion. The subjects are either contraries or intermediates (for privative terms may also be regarded as contraries) and are denoted by a positive term—e.g. naked or toothless or black.

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Now since the categories are distinguished as substance, quality, place, activity or passivity, relation and quantity,Aristotle generally distinguishes eight categories (originally ten, but he seems to have abandoned κεῖσθαιposition and ἔχεινstate at an early date); here he omits time as being relative to motion (it is that by which motion can be numerically estimated; cf. Aristot. Met. 12.6.2, Aristot. Phys. 219b 1) and therefore neither the subject nor the terminus of motion. Cf. Ross ad loc. there must be three kinds of motion, in respect of quality, quantity and place. There is no motionThere is, however, change in respect of substance (generation and destruction), but this is between contradictories and is not motion in the strict sense. Cf. Aristot. Met. 11.11.6, and sect. 4 below. The distinction between motion and change is not always maintained. in respect of substance, because substance has no contrary; nor of the relative, because it is possible that when one of two related things changes the relation to it of the other thing, even though the thing itself does not change, may become untrue; therefore the motion of these related things is accidental.

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Nor is there motion of the agent or patient, or of the mover and the thing moved, because there is no motion of motion nor no generation of generation, nor in general is there change of change. There are two ways in which there might be motion of motion: (1) Motion might be the subject of motion, as, e.g., a man is moved because he changes from white to black; in this way motion might be heated or cooled or might change its place or increase.

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But this is impossible, because the change is not a subject. Or (2) some other subject might change from change to some other form of existence, as, e.g., a man changes from sickness to health. But this is also impossible except accidentally.

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Every motion is a change from one thing into something else; and the same is true of generation and destruction, except that these are changes into opposites in one sense,sc. contradictories. while the other, i.e. motion, is a change into opposites in another sense.sc. contraries. Hence a thing changes at the same time from health to sickness, and from this change itself into another.

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Now clearly if it has fallen ill it will be already changed (for it cannot remain at rest) into that other change, whatever it may be; and further this cannot be, in any given case, any chance change; and it also must be from something into something else. Therefore it will be the opposite change, viz. becoming healthy. But this is so accidentally; just as there is change from recollecting to forgetting because the subject changes, now in the direction of knowledge and now in that of ignorance.

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Further, we shall have an infinite series if there is to be change of change and becoming of becoming, because if the latter of two becomings comes to be from the former, the former must come to be too. E.g., if simple becoming was once coming to be, that which comes to be something was also once coming to be. Therefore that which simply comes to be was not yet, but there was already something coming to be coming to be something.

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But this too was at one time coming to be, and therefore it was not at that time coming to be something. But in infinite series there is no first term, and therefore in this series the first term cannot exist, nor can any subsequent term. Therefore nothing can be either generated or moved or changed.

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Further, the same thing which admits of motion admits also of the contrary motion and of rest, and that which admits of generation admits also of destruction.

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Therefore that which comes to be, when it has come to be coming to be, is then in course of perishingsc. which is absurd.; for it does not perish as soon as it is coming to be coming to be, nor afterwards, because that which is perishing must exist .That which comes to be must cease to be, and it can cease to be only when it exists. Therefore if that which comes to be comes to be coming to be, it must cease to be when it is coming to be; before this it does not exist, but is only coming to be coming to be, and after this it is not that which comes to be but that which has come to be.

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Further, there must be some matter underlying that which is coming to be or changing. What then will it be? What is it that becomes motion or generation in the same way as it is body or soul that undergoes change? And moreover what is that which is the terminus of the motion? For that which we are considering must be a motion or generation of A from B into C.

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How then can these conditions be fulfilled? There can be no learning of learning, and therefore there can be no generation of generation.

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Since there is no motion of substance or of the relative or of activity and passivity, it remains that there is motion in respect of quality, quantity and place; for each of these admits of contrariety. By quality I mean not that which is in the substance (for indeed even the differentia is a quality), but the passive quality in virtue of which a thing is said to be acted upon or to be immune from being acted upon.Cf. Aristot. Met. 5.14.

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The immovable is either that which is wholly incapable of being moved, or that which is scarcely moved in the course of a long time or is slow in starting, or that which would naturally be moved but cannot be moved at the time when and from the place whence and in the way in which it would naturally be moved. This last is the only kind of immovable thing which I recognize as being at rest; for rest is contrary to motion, and so must be a privation of that which admits of motion.

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Things are together in place which are in the primary sensei.e., when they occupy one place to the exclusion of anything else. Cf. Aristot. Phys. 209a 33-b 1. in one place, and separate which are in different places. Contrary in place is that which is at a maximum distance in a straight line.I have transferred this sentence from the end of the section, where it is placed in the text, on the ground that it fits more naturally here. I suspect that it, like the displaced portion of sect. 13, was originally a marginal note which was later inserted in the body of the text, but in the wrong position. Things are said to be in contact whose extremes are together in place. An intermediate is that at which a changing thing which changes continuously in accordance with its nature naturally arrives before it arrives at the extreme into which it is changing. Since all change takes place between opposites, and these are either contraries or contradictories, and contradictories have no middle term, clearly it is to the sphere of contraries that the intermediate belongs.I have followed Prantl’s suggestion in transferring this sentence from the end of sect. 13.

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Successive is that which comes after the beginning (the order being determined by position or form or in some other way) and has nothing of the same class between itself and that which it succeeds; e.g. lines in the case of a line, and units in that of a unit, and a house in the case of a house (but there is nothing to prevent something else from coming between). For that which is successive is a thing which is successive and posterior to some other thing. 1 is not successive to 2, nor is the new mooni.e., the first day of the month. to the second day of the month.

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Contiguous is that which is successive and in contact. The continuous is a species of the contiguous.

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I call two things continuous when their respective boundaries, by which they are kept together in contact, become one and the same; hence clearly the continuous belongs to the sphere of things whose nature it is to become one by contiguity.

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Clearly successive is the most ultimate term; for the successive need not be in contact, but contact implies succession; and if there is continuity there is contact, but if there is contact there is not necessarily continuity;

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and where there is no contact there is no coalescence. Therefore a point is not the same as a unit; for points admit of contact, whereas units do not, but only of succession; and between points there is something intermediate, but between units there is not.

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Our inquiry is concerned with substance; for it is the principles and causes of substances that we are investigating. Indeed if the universe is to be regarded as a whole, substance is its first part; and if it is to be regarded as a succession,Cf. Aristot. Met. 12.10.14, Aristot. Met. 14.3.9. even so substance is first, then quality, then quantity. Moreover, the latter hardly exist at all in the full sense, but are merely qualifications and affections of Being. Otherwise not-white and not-straight would also exist; at any rate we say that they too are, e.g., it is not white.

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Further, none of the other categories is separately existent. Even the ancients in effect testify to this, for it was of substance that they sought the principles and elements and causes. Present-day thinkersPlatonists. tend to regard universals as substance, because genera are universal, and they hold that these are more truly principles and substances because they approach the question theoretically; but the ancients identified substance with particular things, e.g. fire and earth, and not with body in general.

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Now there are three kinds of substance. One is sensible (and may be either eternali.e., the celestial bodies. or perishable; the latter, e.g. plants and animals, is universally recognized); of this we must apprehend the elements, whether they are one or many.

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Another is immutable , which certain thinkers hold to exist separately; some dividing it into two classes, others combining the Forms and the objects of mathematics into a single class, and others recognizing only the objects of mathematics as of this nature.These three views were held respectively by Plato, Xenocrates and Speusippus. Cf. Aristot. Met. 7.2.3, 4; Aristot. Met. 13.1.4, and see Introduction. The first two kinds of substance come within the scope of physics, since they involve motion; the last belongs to some other science, if there is no principle common to all three.

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Sensible substance is liable to change. Now if change proceeds from opposites or intermediates—not however from all opposites (for speech is not white), but only from the contraryCf. Aristot. Met. 10.7.—then there must be something underlying which changes into the opposite contrary; for the contrariesi.e., contrary qualities. Cf. Aristot. Met. 8.5.1. do not change.

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Further, something persists, whereas the contrary does not persist. Therefore besides the contraries there is some third thing, the matter . Now if change is of four kinds, in respect either of substance or of quality or of quantity or of place, and if change of substance is generation or destruction in the simple sense, and change of quantity is increase or decrease, and change of affection is alteration, and change of place is locomotion, then changes must be in each case into the corresponding contrary state.

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It must be the matter, then, which admits of both contraries, that changes. And since that which is is twofold, everything changes from that which is potentially to that which is actually; e.g. from potentially white to actually white. The same applies to increase and decrease. Hence not only may there be generation accidentally from that which is not, but also everything is generated from that which is, but is potentially and is not actually.

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And this is the one of Anaxagoras; for his all things were together,Anaxagoras Fr. 1 (Diels). and the mixture of Empedocles and Anaximander and the doctrine of Democritus would be better expressed as all things were together potentially, but not actually. In this passage I follow Ross’s punctuation and interpretation, which seem to me to be certainly right. Anaxagoras’s undifferentiated infinity of homoeomerous particles (although contrasted with the unifying principle of Mind, cf. Aristot. Met. 1.8.14) can be regarded as in a sense a unity. Again, μῖγμα(as Ross points out) in its Aristotelian sense of complete fusion is a fair description of Anaximander’s indeterminate. The general meaning of the passage is that in each of the systems referred to the material principle in its elemental state should have been described as existing only potentially.

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Hence these thinkers must have had some conception of matter. All things which change have matter, but different things have different kinds; and of eternal things such as are not generable but are movable by locomotion have matter; matter, however, which admits not of generation, but of motion from one place to another.Cf. Aristot. Met. 12.1.3, Aristot. Met. 8.1.7, 8.

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One might raise the question from what sort of not-being generation takes place; for not-being has three senses.(1) the negation of a category, (2) falsity, (3) unrealized potentiality. Cf. Aristot. Met. 14.2.10. If a thing exists through a potentiality, nevertheless it is not through a potentiality for any chance thing; different things are derived from different things.

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Nor is it satisfactory to say that all things were together, for they differ in their matter, since otherwise why did they become an infinity and not one? For Mind is one; so that if matter is also one, only that could have come to be in actuality whose matter existed potentially. The causes and principles, then, are three; two being the pair of contraries, of which one is the formula or form and the other the privation, and the third being the matter.This classification is found in Aristot. Physics 1.6, 7, but is foreign to the main treatise of the Metaphysics. See Introduction.

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We must next observeSee Introduction. that neither matter nor form (I mean in the proximate sense) is generated. All change is of some subject by some agent into some object. The agent is the immediate mover; the subject is the matter; and the object is the form. Thus the process will go on to infinity if not only the bronze comes to be round, but also roundness or bronze comes to be; there must, then, be some stopping-point.

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We must next observe that every substance is generated from something which has the same name (substances including not only natural but all other products). Things are generated either by art or by nature or by chance or spontaneously. Art is a generative principle in something else; nature is a generative principle in the subject itselfIn natural reproduction the generative principle is obviously in the parent. But the offspring is in a sense a part of the parent, and so Aristotle identifies the two.(for man begets man); the other causes are privations of these.Cf. Aristot. Met. 11.8.12 n.

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There are three kinds of substance: (1.) matter, which exists individually in virtue of being apparentAristotle is contrasting proximate with primary matter. Fire, the primary matter of a man, is a simple undifferentiated element which cannot be perceived as such, and has no individuality. The head, and the other parts of the body, considered merely as in contact and not as forming an organic unity, are the proximate matter of a man; they are perceptible and individual. Flesh (in general) represents the matter in an intermediate stage.(for everything which is characterized by contact and so not by coalescence is matter and substrate; e.g. fire, flesh and head; these are all matter, and the last is the matter of a substance in the strictest sense); (2.) the naturei.e., form.(existing individually)—i.e. a kind of positive state which is the terminus of motion; and (3.) the particular combination of these, e.g. Socrates or Callias. In some cases the individuality does not exist apart from the composite substance (e.g., the form of a house does not exist separately, except as the art of building;

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nor are these forms liable to generation and destruction; there is a distinct sense in which house and health and every artificial product, considered in the abstract, do or do not existi.e., in the mind of the architect or doctor.); if it does so at all, it does so in the case of natural objects. Hence Plato was not far wrong in sayingSee Introduction. that there are as many Forms as there are kinds of natural objects; that is if there are Forms distinct from the things of our world.

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Moving causes are causes in the sense of pre-existent things, but formal causes coexist with their effects. For it is when the man becomes healthy that health exists, and the shape of the bronze sphere comes into being simultaneously with the bronze sphere.

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Whether any form remains also afterwards is another question. In some cases there is nothing to prevent this, e.g. the soul may be of this nature (not all of it, but the intelligent part; for presumably all of it cannot be). Clearly then there is no need on these grounds for the Ideas to exist; for man begets man, the individual begetting the particular person. And the same is true of the arts, for the art of medicine is the formula of health.

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In one sense the causes and principles are different for different things; but in another, if one speaks generally and analogically, they are the same for all. For the question might be raised whether the principles and elements of substances and of relations are the same or different; and similarly with respect to each of the other categories. But it is absurd that they should be the same for all; for then relations and substance would have the same constituents.

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What then can their common constituent be? For there is nothing common to and yet distinct from substance and the other predicable categories, yet the element is prior to that of which it is an element. Moreover substance is not an element of relations, nor is any of the latter an element of substance. Further, how can all the categories have the same elements?

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For no element can be the same as that which is composed of elements; e.g., neither B nor A can be the same as BA (nor indeed can any of the intelligibles,Unity and Being are called intelligibles as being the most universal predicates and as contrasted with particulars, which are sensible. e.g. Unity or Being, be an element; for these apply in every case, even to composite things); hence no element can be either substance or relation. But it must be one or the other. Therefore the categories have not all the same elements.

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The truth is that, as we say, in one sense all things have the same elements and in another they have not. E.g., the elements of sensible bodies are, let us say, (1) as form, the hot, and in another sense the cold, which is the corresponding privation; as matter, that which directly and of its own nature is potentially hot or cold. And not only these are substances, but so are (2) the compoundsThis apparently refers to the elements; fire and air are hot matter, water and earth cold matter. of which they are principles, and (3) any unity which is generated from hot and cold, e.g. flesh or bone; for the product of hot and cold must be distinct from them.

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These things, then, have the same elements and principles, although specifically different things have specifically different elements; we cannot, however, say that all things have the same elements in this sense, but only by analogy: i.e., one might say that there are three principles, form, privation and matter.

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But each of these is different in respect of each class of things, e.g., in the case of color they are white, black, surface; or again there is light, darkness and air, of which day and night are composed. And since not only things which are inherent in an object are its causes, but also certain external things, e.g. the moving cause, clearly principle and element are not the same; but both are causes. Principles are divided into these two kinds, and that which moves a thing or brings it to rest is a kind of principle and substance.

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Thus analogically there are three elements and four causes or principles; but they are different in different cases, and the proximate moving cause is different in different cases. Health, disease, body; and the moving cause is the art of medicine. Form, a particular kind of disorder, bricks; and the moving cause is the art of building.

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And since in the sphere of natural objects the moving cause of man is man, while in the sphere of objects of thought the moving cause is the form or its contrary, in one sense there are three causes and in another four. For in a sense the art of medicine is health, and the art of building is the form of a house, and man begets man; but besides these there is that which as first of all things moves all things.For the first time the ultimate efficient cause is distinguished from the proximate. Aristotle is leading up to the description of the Prime Mover which occupies the latter half of the book.

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Now since some things can exist in separation and others cannot, it is the former that are substances. And therefore all things have the same causes, because without substance there can be no affections and motions. Next we shall seeSee Introduction. that these causes are probably soul and body, or mind, appetite and body.Aristotle is thinking of animals and human beings, which are substances in the truest sense. Again, there is another sense in which by analogy the principles are the same viz. actuality and potentiality; but these are different for different things, and apply to them in different ways.

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For in some cases the same thing exists now actually and now potentially; e.g. wine or flesh or man (actuality and potentiality also fall under the causes as already described; for the form exists actually if it is separable, and so does the compound of form and matter, and the privation, e.g. darkness or disease; and the matter exists potentially, for it is this which has the potentiality of becoming bothi.e., of acquiring either of the contrary qualities distinguished by the form and the privation;

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but the distinction in virtue of actuality and potentiality applies in a different sense to cases where the matter of cause and effect is not the same, in some of which the form is not the same but different. E.g., the cause of a man is (i) his elements: fire and earth as matter, and the particular form; (2) some external formal cause, viz. his father; and besides these (3) the sun and the ecliptic,The sun, moving in the ecliptic, approaches nearer to the earth in summer, causing generation, and recedes farther from the earth in winter, causing destruction. Cf. Aristot. Met. 12.6.10 n., Aristot. De Gen. et Corr. 336a 32. which are neither matter nor form nor privation nor identical in form with him, but cause motion.

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Further, we must observe that some causes can be stated universally, but others cannot.

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The proximate principles of all things are the proximate actual individual and another individual which exists potentially.i.e., the proximate efficient cause and proximate matter. Therefore the proximate principles are not universal. For it is the particular that is the principle of particulars; man in general is the principle of man in general, but there is no such person as man, whereas Peleus is the principle of Achilles and your father of you, and this particular B of this particular BA; but B in general is the principle of BA regarded absolutely.

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Again, even if the causes of substances are universal, still, as has been said,Aristot. Met. 12.4.6. different things, i.e. things which are not in the same genus, as colors, sounds, substances and quantity, have different causes and elements, except in an analogical sense; and the causes of things which are in the same species are different, not in species, but because the causes of individuals are different: your matter and form and moving cause being different from mine, although in their universal formula they are the same.

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As for the question what are the principles or elements of substances and relations and qualities, whether they are the same or different, it is evident that when the terms principle and element are used with several meanings they are the same for everything; but when the meanings are distinguished, they are not the same but different; except that in a certain sense they are the same for all. In a certain sense they are the same or analogous, because (a) everything has matter, form, privation and a moving cause; (b) the causes of substances may be regarded as the causes of all things, since if substances are destroyed everything is destroyed; and further (c) that which is first in complete realityi.e., the prime mover. is the cause of all things.

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In another sense, however, proximate causes are different; there are as many proximate causes as there are contraries which are predicated neither as genera nor with a variety of meaningsi.e., individual forms and privations of individual things.; and further the particular material causes are different. Thus we have stated what the principles of sensible things are, and how many they are, and in what sense they are the same and in what sense different.

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Since we have seenAristot. Met. 12.1.3, 4. that there are three kinds of substance, two of which are natural and one immutable, we must now discuss the last named and show that there must be some substance which is eternal and immutable. Substances are the primary reality, and if they are all perishable, everything is perishable. But motion cannot be either generated or destroyed, for it always existedCf. Aristot. Physics 8.1-3; nor can time, because there can be no priority or posteriority if there is no time.The argument seems to be: If we assume that time was generated, it follows that before that there was no time; but the very term before implies time. The same applies to the destruction of time.

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Hence as time is continuous, so too is motion; for time is either identical with motion or an affection of it.Cf. Aristot. Met. 11.12.1 n. But there is no continuous motion except that which is spatial, of spatial motion only that which is circular.These statements are proved inAristot. Physics 8.8, 9.

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But even if we are to suppose that there is something which is kinetic and productive although it does not actually move or produce, there will not necessarily be motion; for that which has a potentiality may not actualize it.

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Thus it will not help matters if we posit eternal substances, as do the exponents of the Forms, unless there is in them some principle which can cause change.As there is not, according to Aristotle; cf. Aristot. Met. 1.7.4. And even this is not enough, nor is it enough if there is another substance besides the Forms; for unless it actually functions there will not be motion.

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And it will still not be enough even if it does function, if its essence is potentiality; for there will not be eternal motion, since that which exists potentially may not exist. Therefore there must be a principle of this kind whose essence is actuality. Furthermore these substancesAristotle is now thinking not only of the prime mover (God or Mind) but also of the movers of the celestial spheres. Cf. Aristot. Met. 12.8.14. must be immaterial; for they must be eternal if anything is. Therefore they are actuality.

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There is a difficulty, however; for it seems that everything which actually functions has a potentiality, whereas not everything which has a potentiality actually functions; so that potentiality is prior. But if this is so, there need be no reality; for everything may be capable of existing, but not yet existent.

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Yet if we accept the statements of the cosmologists who generate everything from Night,Cf. Hes. WD 17, Hes. Th. 116ff. or the doctrine of the physicists that all things were together,Cf. Aristot. Met. 12.2.3. we have the same impossibility; for how can there be motion if there is no actual cause? Wood will not move itself—carpentry must act upon it; nor will the menses or the earth move themselves—the seeds must act upon the earth, and the semen on the menses.

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Hence some, e.g. LeucippusCf. Aristot. Met. 1.4.12, Aristot. De Caelo 300b 8, and see Burnet, E.G.P. 178. and Plato,Cf. Plat. Tim. 30a, and sect. 8 below. posit an eternal actuality, for they say that there is always motion; but why there is, and what it is, they do not say; nor, if it moves in this or that particular way, what the cause is. For nothing is moved at haphazard, but in every case there must be some reason present; as in point of fact things are moved in one way by nature, and in another by force or mind or some other agent. And further, what kind of motion is primary? For this is an extremely important point.

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Again, Plato at least cannot even explain what it is that he sometimes thinks to be the source of motion, i.e., that which moves itself; for according to him the soul is posterior to motion and coeval with the sensible universe.Aristotle refers to Plato’s rather inconsistent account in Plat. Tim. 30-34. Now to suppose that potentiality is prior to actuality is in one sense right and in another wrong; we have explainedThe reference is probably to 5 above, but cf. Aristot. Met. 9.8. the distinction.

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But that actuality is prior is testified by Anaxagoras (since mind is actuality), and by Empedocles with his theory of Love and Strife, and by those who hold that motion is eternal, e.g. Leucippus.

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Therefore Chaos or Night did not endure for an unlimited time, but the same things have always existed, either passing through a cycle or in accordance with some other principle—that is, if actuality is prior to potentiality.

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Now if there is a regular cycle, there must be somethingThe sphere of the fixed stars, Aristot. Met. 12.8.9; cf. Aristot. De Gen. et Corr. 336a 23ff. which remains always active in the same way; but if there is to be generation and destruction, there must be something elseThe sun, which has its own yearly orbit in the ecliptic, and a daily rotation round the earth, which is explained most economically with reference to the rotation of the sphere of the fixed stars. Cf. Aristot. Met. 12.5.3 n., Aristot. De Gen. et Corr. 336a 23ff. which is always active in two different ways. Therefore this must be active in one way independently, and in the other in virtue of something else, i.e. either of some third active principle or of the first.

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It must, then, be in virtue of the first; for this is in turn the cause both of the third and of the second. Therefore the first is preferable, since it was the cause of perpetual regular motion, and something else was the cause of variety; and obviously both together make up the cause of perpetual variety. Now this is just what actually characterizes motions; therefore why need we seek any further principles?

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Since (a) this is a possible explanation, and (b) if it is not true, we shall have to regard everything as coming from Night Aristot. Met. 12.6.6 and all things together and not-being,Aristot. Met. 12.2.2, 3. these difficulties may be considered to be solved. There is something which is eternally moved with an unceasing motion, and that circular motion. This is evident not merely in theory, but in fact. Therefore the ultimate heaven must be eternal. Then there is also something which moves it.

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And since that which is moved while it moves is intermediate, there is something which moves without being moved; something eternal which is both substance and actuality.

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Now it moves in the following manner. The object of desire and the object of thought move without being moved. The primary objects of desire and thought are the same. For it is the apparent good that is the object of appetite, and the real good that is the object of the rational will.This shows that desire in general (of which appetite and will are the irrational and rational aspects) has as its object the good. Desire is the result of opinion rather than opinion that of desire; it is the act of thinking that is the starting-point.

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Now thought is moved by the intelligible, and one of the series of contrariesAristotle himself recognizes two series, lists or columns of contraries, similar to those of the Pythagoreans (Aristot. Met. 1.5.6). One, the positive, contains being, unity, substance, etc.; the other is negative and contains not-being, plurality, non-substance, etc. The negative terms are intelligible only in reference to the positive. Cf. Aristot. Met. 4.2.21. is essentially intelligible. In this series substance stands first, and of substance that which is simple and exists actually. (The one and the simple are not the same; for one signifies a measure,Cf Aristot. Met. 5.6.17. whereas simple means that the subject itself is in a certain state.)

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But the Good, and that which is in itself desirable, are also in the same series; and that which is first in a class is always best or analogous to the best.

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That the final cause may apply to immovable things is shown by the distinction of its meanings. For the final cause is not only the good for something, but also the good which is the end of some action. In the latter sense it applies to immovable things, although in the former it does not; and it causes motion as being an object of love, whereas all other things cause motion because they are themselves in motion.

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Now if a thing is moved, it can be otherwise than it is. Therefore if the actuality of the heaven is primary locomotion, then in so far as the heaven is moved, in this respect at least it is possible for it to be otherwise; i.e. in respect of place, even if not of substantiality. But since there is something—X—which moves while being itself unmoved, existing actually, X cannot be otherwise in any respect.

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For the primary kind of change is locomotion,Proved in Aristot. Physics 8.7. and of locomotion circular locomotion Aristot. Physics 8.9 ; and this is the motion which X induces. Thus X is necessarily existent; and qua necessary it is good, and is in this sense a first principle.The argument is: X (the prime mover), since it imparts the primary motion, cannot be liable to motion (or change) of any kind. Therefore it exists of necessity, and must be good (cf. Aristot. Met. 5.5.6); and it is qua good, i.e., the object of desire, that X is a first principle. For the necessary has all these meanings: that which is by constraint because it is contrary to impulse; and that without which excellence is impossible; and that which cannot be otherwise, but is absolutely necessary.Cf. Aristot. Met. 5.5

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Such, then, is the first principle upon which depend the sensible universe and the world of nature.

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And its life is like the best which we temporarily enjoy. It must be in that state always (which for us is impossible), since its actuality is also pleasure.For the relation of pleasure to actuality or activity see Aristot. Nic. Eth. 10.4.(And for this reason waking, sensation and thinking are most pleasant, and hopes and memories are pleasant because of them.) Now thinking in itself is concerned with that which is in itself best, and thinking in the highest sense with that which is in the highest sense best.Since the prime mover is pure actuality, and has or rather is the highest form of life, Aristotle identifies it with the highest activity—pure thinking.

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And thought thinks itself through participation in the object of thought; for it becomes an object of thought by the act of apprehension and thinking, so that thought and the object of thought are the same, because that which is receptive of the object of thought, i.e. essence, is thought. And it actually functions when it possesses this object.In actualization the subject and object of thought (like those of perception, Aristot. De Anima 3.2.) are identical. Hence it is actuality rather than potentiality that is held to be the divine possession of rational thought, and its active contemplation is that which is most pleasant and best.

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If, then, the happiness which God always enjoys is as great as that which we enjoy sometimes, it is marvellous; and if it is greater, this is still more marvellous. Nevertheless it is so. Moreover, life belongs to God. For the actuality of thought is life, and God is that actuality; and the essential actuality of God is life most good and eternal. We hold, then, that God is a living being, eternal, most good; and therefore life and a continuous eternal existence belong to God; for that is what God is.

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Those who suppose, as do the Pythagoreans and Speusippus,The view is referred to again in Aristot. Met. 12.10.6, Aristot. Met. 14.4.2, 3, Aristot. Met. 14.5.1. that perfect beauty and goodness do

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not exist in the beginning (on the ground that whereas the first beginnings of plants and animals are causes, it is in the products of these that beauty and perfection are found) are mistaken in their views.

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For seed comes from prior creatures which are perfect, and that which is first is not the seed but the perfect creature. E.g., one might say that prior to the seed is the man—not he who is produced from the seed, but another man from whom the seed comes.Cf. Aristot. Met. 9.8.4, 5.

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Thus it is evident from the foregoing account that there is some substance which is eternal and immovable and separate from sensible things; and it has also been shown that this substance can have no magnitude, but is impartible and indivisible (for it causes motion for infinite time, and nothing finite has an infinite potentialityCf.Aristot. Physics 266a24-b6.; and therefore since every magnitude is either finite or infinite, it cannot have finite magnitude,

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and it cannot have infinite magnitude because there is no such thing at all); and moreover that it is impassive and unalterable; for all the other kinds of motion are posterior to spatial motion. Thus it is clear why this substance has these attributes.

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We must not disregard the question whether we should hold that there is one substance of this kind or more than one, and if more than one, how many; we must review the pronouncements of other thinkers and show that with regard to the number of the substances they have said nothing that can be clearly stated.

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The theory of the Ideas contains no peculiar treatment of the question; for the exponents of the theory call the Ideas numbers, and speak of the numbers now as though they were unlimited and now as though they were limited by the number 10Cf. Aristot. Met. 13.8.17, 20. This was a Pythagorean survival, cf. Vol. I. Introduction. xvi.; but as for why there should be just so many numbers, there is no explanation given with demonstrative accuracy.

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We, however, must discuss the question on the basis of the assumptions and distinctions which we have already made.

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The first principle and primary reality is immovable, both essentially and accidentally, but it excites the primary form of motion, which is one and eternal.

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Now since that which is moved must be moved by something, and the prime mover must be essentially immovable, and eternal motion must be excited by something eternal, and one motion by some one thing; and since we can see that besides the simple spatial motion of the universei.e., the (apparent) diurnal revolution of the heavens.(which we hold to be excited by the primary immovable substance) there are other spatial motions—those of the planets—which are eternal (because a body which moves in a circle is eternal and is never at rest—this has been proved in our physical treatisesAristot. Physics 8.8, 9, Aristot. De Caelo 1.2, 2.3-8.); then each of these spatial motions must also be excited by a substance which is essentially immovable and eternal.

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For the nature of the heavenly bodies is eternal, being a kind of substance; and that which moves is eternal and prior to the moved; and that which is prior to a substance must be a substance. It is therefore clear that there must be an equal number of substances, in nature eternal, essentially immovable, and without magnitude; for the reason already stated.Aristot. Met. 12.7.12, 13.

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Thus it is clear that the movers are substances, and that one of them is first and another second and so on in the same order as the spatial motions of the heavenly bodies.

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As regards the number of these motions, we have now reached a question which must be investigated by the aid of that branch of mathematical science which is most akin to philosophy, i.e. astronomy; for this has as its object a substance which is sensible but eternal, whereas the other mathematical sciences, e.g. arithmetic and geometry, do not deal with any substance. That there are more spatial motions than there are bodies which move in space is obvious to those who have even a moderate grasp of the subject, since each of the non-fixed stars has more than one spatial motion.

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As to how many these spatial motions actually are we shall now, to give some idea of the subject, quote what some of the mathematicians say, in order that there may be some definite number for the mind to grasp; but for the rest we must partly investigate for ourselves and partly learn from other investigators, and if those who apply themselves to these matters come to some conclusion which clashes with what we have just stated, we must appreciate both views, but follow the more accurate.

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EudoxusOf Cnidus (circa 408 -355 B.C.). He was a pupil of Plato, and a distinguished mathematician. held that the motion of the sun and moon involves in either case three spheres,For a full discussion of the theories of Eudoxus and Callipus see Dreyer, Planetary Systems 87-114; Heath,Aristarchus of <placeName key="perseus,Samos City">Samos</placeName>190-224. of which the outermost is that of the fixed stars,Not identical with that of the fixed stars, but having the same motion. the second revolves in the circle which bisects the zodiac,i.e., revolves with its equator in the ecliptic. and the third revolves in a circle which is inclined across the breadth of the zodiaci.e., has the plane of its equator inclined to the plane of the ecliptic. This sphere carries the sun (or moon) fixed to a point in its equator.; but the circle in which the moon moves is inclined at a greater angle than that in which the sun moves.

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And he held that the motion of the planets involved in each case four spheres; and that of these the first and second are the sameNot the same, but having the same motion. as before (for the sphere of the fixed stars is that which carries round all the other spheres, and the sphere next in order, which has its motion in the circle which bisects the zodiac, is common to all the planets); the third sphere of all the planets has its poles in the circle which bisects the zodiac; and the fourth sphere moves in the circle inclined to the equator of the third. In the case of the third sphere, while the other planets have their own peculiar poles, those of Venus and Mercury are the same.

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Callippusof Cyzicus (fl. 380 B.C.). Simplicius says (Simplicius 493.5-8) that he corrected and elaborated Eudoxus’s theory with Aristotle’s help while on a visit to him at Athens. assumed the same arrangement of the spheres as did Eudoxus (that is, with respect to the order of their intervals), but as regards their number, whereas he assigned to Jupiter and Saturn the same number of spheres as Eudoxus, he considered that two further spheres should be added both for the sun and for the moon, if the phenomena are to be accounted for, and one for each of the other planets.

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But if all the spheres in combination are to account for the phenomena, there must be for each of the other planets other spheres, one less in number than those already mentioned, which counteract these and restore to the same position the first sphere of the star which in each case is next in order below.Aristotle is trying to establish a mechanical relation between the spheres, which Eudoxus and Callipus did not attempt to do. In this way only can the combination of forces produce the motion of the planets.

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Therefore since the forces by which the planets themselves are moved are 8 for Jupiter and Saturn, and 25 for the others, and since of these the only ones which do not need to be counteracted are those by which the lowest planetThe moon. is moved, the counteracting spheres for the first two planets will be 6, and those of the remaining four will be 16; and the total number of spheres, both those which move the planets and those which counteract these, will be 55.

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If we do not invest the moon and the sun with the additional motions which we have mentioned,In sect. 11. there will be 47 (?)Either Aristotle has made a slip in his calculations, or we should read ἐννέα(Sosigenes) for ἑπτά; this would give 49, which appears to be the correct total. For alternative explanations of an error in calculation see Ross ad loc. spheres in all.

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This, then, may be taken to be the number of the spheres; and thus it is reasonable to suppose that there are as many immovable substances and principles,i.e., the movers of the spheres.—the statement of logical necessity may be left to more competent thinkers.

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If there can be no spatial motion which is not conducive to the motion of a star, and if moreover every entity and every substance which is impassive and has in itself attained to the highest good should be regarded as an end, then there can be no other entity besides these,See previous note. and the number of the substances must be as we have said. For if there are other substances, they must move something, since they are the end of spatial motion.

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But there can be no other spatial motions besides those already mentioned. This is a reasonable inference from a general consideration of spatial motion. For if everything which moves exists for the sake of that which is moved, and every motion for the sake of something which is moved, no motion can exist for the sake of itself or of some other motion, but all motions must exist for the sake of the stars.

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For if we are to suppose that one motion is for the sake of another, the latter too must be for the sake of something else; and since the series cannot be infinite, the end of every motion must be one of the divine bodies which are moved through the heavens.

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It is evident that there is only one heaven.This paragraph seems to belong to an earlier period of Aristotle’s thought. At any rate the argument that plurality involves matter is inconsistent with the view that there are 55 immaterial movers. For if there is to be a plurality of heavens (as there is of men), the principle of each must be one in kind but many in number.

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But all things which are many in number have matter (for one and the same definition applies to many individuals, e.g. that of man; but Socrates is oneThe definition or form is one and universal; it is the combination of form with matter that constitutes an individual. Thus a plurality of individuals is caused by the combination of the same form with different matter.), but the primary essence has no matter, because it is complete reality. Therefore the prime mover, which is immovable, is one both in formula and in number; and therefore so also is that which is eternally and continuously in motion. Therefore there is only one heaven.

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A tradition has been handed down by the ancient thinkers of very early times, and bequeathed to posterity in the form of a myth, to the effect that these heavenly bodies are gods,This statement is not literally true. The planets do not seem to have been associated with the gods of popular mythology until the fourth century B.C. (see Burnet, E.G.P. p. 23 n.). But Aristotle’s general meaning seems to be that the gods were identified with the primary natural forces; and this is substantially true. and that the Divine pervades the whole of nature.

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The rest of their tradition has been added later in a mythological form to influence the vulgar and as a constitutional and utilitarian expedientCf. Aristot. Met. 2.3.1.; they say that these gods are human in shape or are like certain other animals,e.g. the Egyptian deities. Zoomorphism in Greek religion is a doubtful quantity. and make other statements consequent upon and similar to those which we have mentioned.

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Now if we separate these statements and accept only the first, that they supposed the primary substances to be gods, we must regard it as an inspired saying and reflect that whereas every art and philosophy has probably been repeatedly developed to the utmost and has perished again, these beliefs of theirs have been preserved as a relic of former knowledge. To this extent only, then, are the views of our forefathers and of the earliest thinkers intelligible to us.

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The subject of Mind involves certain difficulties. Mind is held to be of all phenomena the most supernatural; but the question of how we must regard it if it is to be of this nature involves certain difficulties. If Mind thinks nothing, where is its dignity? It is in just the same state as a man who is asleep. If it thinks, but something else determines its thinking, then since that which is its essence is not thinking but potentiality,i.e., if its thinking is determined by something else, Mind is only a potentiality, and not (as described in Aristot. Met. 12.7.1-9) the highest actuality. it cannot be the best reality; because it derives its excellence from the act of thinking.

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Again, whether its essence is thought or thinking, what does it think? It must think either itself or something else; and if something else, then it must think either the same thing always, or different things at different times. Then does it make any difference, or not, whether it thinks that which is good or thinks at random?

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Surely it would be absurd for it to think about some subjects. Clearly, then, it thinks that which is most divine and estimable, and does not change; for the change would be for the worse, and anything of this kind would immediately imply some sort of motion. Therefore if Mind is not thinking but a potentiality, (a) it is reasonable to suppose that the continuity of its thinking is laboriousCf. Aristot. Met. 9.8.18.; (b) clearly there must be something else which is more excellent than Mind; i.e. the object of thought;

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for both thought and the act of thinking will belong even to the thinker of the worst thoughts.If Mind is a potentiality, since a potentiality is of contraries, Mind may think that which is worst. Therefore if this is to be avoided (as it is, since it is better not to see some things than to see them), thinking cannot be the supreme good. Therefore Mind thinks itself, if it is that which is best; and its thinking is a thinking of thinking.

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Yet it seems that knowledge and perception and opinion and understanding are always of something else, and only incidentally of themselves.

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And further, if to think is not the same as to be thought, in respect of which does goodness belong to thought? for the act of thinking and the object of thought have not the same essence. The answer is that in some cases the knowledge is the object. In the productive sciences, if we disregard the matter, the substance, i.e. the essence, is the object; but in the speculative sciences the formula or the act of thinking is the object. Therefore since thought and the object of thought are not different in the case of things which contain no matter, they will be the same, and the act of thinking will be one with the object of thought.

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There still remains the question whether the object of thought is composite; for if so, thought would change in passing from one part of the whole to another. The answer is that everything which contains no matter is indivisible. Just as the human mind, or rather the mind of composite beings,i.e., beings composed of matter as well as form. Such beings are contrasted with the divine Mind, which is pure form. is in a certain space of timeThe meaning of this sentence is shown by the definition of Happiness in Aristot. Nic. Eth. 1098a 16-20. It takes the human mind a lifetime of the highest intellectual activity of which it is capable to attain to happiness; but the divine Mind is always happy. Cf. Aristot. Met. 12.7.9.(for it does not possess the good at this or at that moment, but in the course of a certain whole period it attains to the supreme good, which is other than itself), so is absolute self-thought throughout all eternity.

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We must also consider in which sense the nature of the universe contains the good or the supreme good; whether as something separate and independent, or as the orderly arrangement of its parts.

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Probably in both senses, as an army does; for the efficiency of an army consists partly in the order and partly in the general; but chiefly in the latter, because he does not depend upon the order, but the order depends upon him. All things, both fishes and birds and plants, are ordered together in some way, but not in the same way; and the system is not such that there is no relation between one thing and another; there is a definite connection.

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Everything is ordered together to one end; but the arrangement is like that in a household, where the free persons have the least liberty to act at random, and have all or most of their actions preordained for them, whereas the slaves and animals have little common responsibility and act for the most part at random; for the nature of each class is a principle such as we have described.The free persons correspond to the heavenly bodies, whose movements are fixed by necessity; the servile class to human beings. Each class acts in accordance with its nature, a principle which produces obedience to duty in the higher creatures, caprice in the lower ( Ross).

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I mean, for example, that everything must at least come to dissolution; and similarly there are other respects in which everything contributes to the good of the whole.

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We must not fail to observe how many impossibilities and absurdities are involved by other theories, and what views the more enlightened thinkers hold, and what views entail the fewest difficulties.

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All thinkers maintain that all things come from contraries; but they are wrong both in saying all thingsBecause there is an eternal substance, which is not derived from contraries (Aristot. Met. 12.6.1). and in saying that they come from contraries,Things are derived from a substrate as well (Aristot. Met. 12.2.1). nor do they explain how things in which the contraries really are present come from the contraries; for the contraries cannot act upon each other. For us, however, this problem is satisfactorily solved by the fact that there is a third factor. Other thinkers make one of the two contraries matter; e.g., this is done by thoseSee on Aristot. Met. 14.1.4. who make the Unequal matter for the Equal, or the Many matter for the One.

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But this also is disposed of in the same way; for the one matter of two contraries is contrary to nothing. Further, on their view everything except Unity itself will partake of evil; for the BadThe Bad was identified with the unequal; cf. Aristot. Met. 1.6.10. is itself one of the elements. The other schoolSee Aristot. Met. 12.7.10 does not even regard the Good and the Bad as principles; yet the Good is in the truest sense a principle in all things. The former school is right in holding that the Good is a principle, but they do not explain how it is a principle— whether as an end or as a moving cause or as form.

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Empedocles theory is also absurd, for he identifies the Good with Love.Cf. Aristot. Met. 1.4.3. This is a principle both as causing motion (since it combines) and as matter (since it is part of the mixture).Empedocles Fr. 17 (Diels), 18-20. Now even if it so happens that the same thing is a principle both as matter and as causing motion, still the essence of the two principles is not the same. In which respect, then, is Love a principle? And it is also absurd that Strife should be imperishable; strife is the very essence of evil.Cf. Aristot. Met. 9.9.3.

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Anaxagoras makes the Good a principle as causing motion; for Mind moves things, but moves them for some end, and therefore there must be some other GoodMotion presupposes a final cause, which was not what Anaxagoras meant by Mind. Cf. Aristot. Met. 1.7.5.—unless it is as we say; for on our view the art of medicine is in a sense health.Aristotle identifies the efficient cause, in a sense, with the final cause. Cf. Aristot. Met. 7.9.3. It is absurd also not to provide a contrary for the Good, i.e. for Mind.In Aristot. Met. 1.6.10 Aristotle describes Anaxagoras as a recognizing contrary principles of good and evil. Moreover, on Aristotle’s own showing, evil cannot be a principle (Aristot. Met. 9.9.3). But all those who recognize the contraries fail to make use of the contraries, unless we systematize their theories.

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And none of them explains why some things are perishable and others imperishable; for they make all existing things come from the same first principles.Cf. Aristot. Met. 3.4.11-20. Again, someCf. Aristot. Met. 12.2.2, 3. make existing things come from not-being, while others,The Eleatics. Cf. Aristot. Met. 1.5.10-13. to avoid this necessity, make all things one. Again, no one explains why there must always be generation, and what the cause of generation is.

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Moreover, those who posit two principles must admit another superior principle,i.e., an efficient cause. and so must the exponents of the Forms; for what made or makes particulars participate in the Forms? And on all other views it follows necessarily that there must be something which is contrary to Wisdom or supreme knowledge, but on ours it does not. For there is no contrary to that which is primary,

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since all contraries involve matter, and that which has matter exists potentially; and the ignorance which is contrary to Wisdom would tend towards the contrary of the object of Wisdom; but that which is primary has no contrary.

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Further, if there is to be nothing else besides sensible things, there will be no first principle, no order, no generation, and no celestial motions, but every principle will be based upon another,If there is nothing but what is sensible or potential, there can be no prime mover (which is actuality) to excite motion in the universe, and no teleology in causation. For the cosmologists on causation see Aristot. Met. 3.3.11-13. as in the accounts of all the cosmologists and physicists.

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And if the Forms or numbers are to exist, they will be causes of nothing; or if not of nothing, at least not of motion.

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Further, how can extension, i.e. a continuum, be produced from that which is unextended? Number cannot, either as a moving or as a formal cause, produce a continuum. Moreover, no contrary can be essentially productive and kinetic, for then it would be possible for it not to exist;

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and further, the act of production would in any case be posterior to the potentiality. Therefore the world of reality is not eternal. But there are real objects which are eternal. Therefore one of these premisses must be rejected. We have described how this may be done.By assuming an eternal actual mover (Aristot. Met. 12.6.4).

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Further, in virtue of what the numbers, or soul and body, or in general the form and the object, are one, no one attempts to explain; nor is it possible to do so except on our theory, that it is the moving cause that makes them one.Cf.Aristot. Met. 8.6.

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As for thoseSpeusippus and his followers; cf. Aristot. Met. 7.2.4, Aristot. Met. 14.3.8. who maintain that mathematical number is the primary reality, and so go on generating one substance after another and finding different principles for each one, they make the substance of the universe incoherent (for one substance in no way affects another by its existence or non-existence) and give us a great many governing principles. But the world must not be governed badly:

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The rule of many is not good; let one be the ruler.Hom. Il.2.204.

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We have already explained what the substance of sensible things is, dealing in our treatise on physicsThe reference is presumably to Aristot. Physics 1. with the material substrate, and subsequently with substance as actuality.In Books 7-9.

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Now since we are inquiring whether there is or is not some immutable and eternal substance besides sensible substances, and if there is, what it is, we must first examine the statements of other thinkers, so that if they have been mistaken in any respect, we may not be liable to the same mistakes; and if there is any view which is common to them and us, we may not feel any private self-irritation on this score. For we must be content if we state some points better than they have done, and others no worse.

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There are two views on this subject. Some say that mathematical objects, i.e. numbers and lines, are substances; and others again that the Ideas are substances.

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Now since someThis was the orthodox Platonist view; cf. Aristot. Met. 1.6.4. recognize these as two classes— the Ideas and the mathematical numbers—and othersXenocrates and his followers. regard both as having one nature, and yet othersThe Pythagoreans and Speusippus. hold that only the mathematical substances are substances, we must first consider the mathematical objects, without imputing to them any other characteristic—e.g. by asking whether they are really Ideas or not, or whether they are principles and substances of existing things or not—and merely inquire whether as mathematical objects they exist or not, and if they do, in what sense; then after this we must separately consider the Ideas themselves, simply and in so far as the accepted procedure requires; for most of the arguments have been made familiar already by the criticisms of other thinkers.

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And further, the greater part of our discussion must bear directly upon this second question—viz. when we are considering whether the substances and first principles of existing things are numbers and Ideas; for after we have dealt with the Ideas there remains this third question.

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Now if the objects of mathematics exist, they must be either in sensible things, as some hold; or separate from them (there are some also who hold this view); or if they are neither the one nor the other, either they do not exist at all, or they exist in some other way. Thus the point which we shall have to discuss is concerned not with their existence, but with the mode of their existence.

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That the objects of mathematics cannot be in sensible things, and that moreover the theory that they are is a fabrication, has been observed already in our discussion of difficultiesCf. Aristot. Met. 3.2.23-30. —the reasons being (a) that two solids cannot occupy the same space, and (b) that on this same theory all other potentialities and characteristics would exist in sensible things, and none of them would exist separately. This, then, has been already stated;

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but in addition to this it is clearly impossible on this theory for any body to be divided. For it must be divided in a plane, and the plane in a line, and the line at a point; and therefore if the point is indivisible, so is the line, and so on.

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For what difference does it make whether entities of this kind are sensible objects, or while not being the objects themselves, are yet present in them? the consequence will be the same, for either they must be divided when the sensible objects are divided, or else not even the sensible objects can be divided.

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Nor again can entities of this kind exist separately.

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For if besides sensible solids there are to be other solids which are separate from them and prior to sensible solids, clearly besides sensible planes there must be other separate planes, and so too with points and lines; for the same argument applies. And if these exist, again besides the planes, lines and points of the mathematical solid, there must be others which are separate;

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for the incomposite is prior to the composite, and if prior to sensible bodies there are other non-sensible bodies, then by the same argument the planes which exist independently must be prior to those which are present in the immovable solids. Therefore there will be planes and lines distinct from those which coexist with the separately-existent solids; for the latter coexist with the mathematical solids, but the former are prior to the mathematical solids.

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Again, in these planes there will be lines, and by the same argument there must be other lines prior to these; and prior to the points which are in the prior lines there must be other points, although there will be no other points prior to these.

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Now the accumulation becomes absurd; because whereas we get only one class of solids besides sensible solids, we get three classes of planes besides sensible planes—those which exist separately from sensible planes, those which exist in the mathematical solids, and those which exist separately from those in the mathematical solids—four classes of lines, and five of points;

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with which of these, then, will the mathematical sciences deal? Not, surely, with the planes, lines and points in the immovable solid; for knowledge is always concerned with that which is prior. And the same argument applies to numbers; for there will be other units besides each class of points, and besides each class of existing things, first the sensible and then the intelligible; so that there will be an infinite number of kinds of mathematical numbers.

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Again, there are the problems which we enumerated in our discussion of difficultiesAristot. Met. 3.2.23-27.: how can they be solved? For the objects of astronomy will similarly be distinct from sensible things, and so will those of geometry; but how can a heaven and its parts (or anything else which has motion) exist apart from the sensible heaven? And similarly the objects of optics and of harmonics will be distinct, for there will be sound and sight apart from the sensible and particular objects.

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Hence clearly the other senses and objects of sense will exist separately; for why should one class of objects do so rather than another? And if this is so, animals too will exist separately, inasmuch as the senses will.

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Again, there are certain general mathematical theorems which are not restricted to these substances.

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Here, then, we shall have yet another kind of substance intermediate between and distinct from the Ideas and the intermediates, which is neither number nor points nor spatial magnitude nor time. And if this is impossible, clearly it is also impossible that the aforesaid substances should exist separately from sensible objects.

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In general, consequences result which are contrary both to the truth and to received opinion if we thus posit the objects of mathematics as definite separately-existent entities. For if they exist in this way, they must be prior to sensible spatial magnitudes, whereas in truth they must be posterior to them; for the incomplete spatial magnitude is in point of generation prior, but in point of substantiality posterior, as the inanimate is to the animate.

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Again, in virtue of what can we possibly regard mathematical magnitudes as one? Things in this world of ours may be reasonably supposed to be one in virtue of soul or part of the soul, or some other influence; apart from this they are a plurality and are disintegrated. But inasmuch as the former are divisible and quantitative, what is the cause of their unity and cohesion?

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Again, the ways in which the objects of mathematics are generated prove our point;

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for they are generated first in the dimension of length, then in that of breadth, and finally in that of depth, whereupon the process is complete. Thus if that which is posterior in generationi.e., in the natural order of development. Thus generation (γένεσις) is used in two different senses in this argument, which therefore becomes invalid (Bonitz). is prior in substantiality, body will be prior to plane and line, and in this sense it will also be more truly complete and whole, because it can become animate; whereas how could a line or plane be animate? The supposition is beyond our powers of apprehension.

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Further, body is a kind of substance, since it already in some sense possesses completeness; but in what sense are lines substances? Neither as being a kind of form or shape, as perhaps the soul is, nor as being matter, like the body; for it does not appear that anything can be composed either of lines or of planes or of points,

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whereas if they were a kind of material substance it would be apparent that things can be so composed. Let it be granted that they are prior in formula; yet not everything which is prior in formula is also prior in substantiality. Things are prior in substantiality which when separated have a superior power of existence; things are prior in formula from whose formulae the formulae of other things are compounded. And these characteristics are not indissociable.

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For if attributes, such as moving or white, do not exist apart from their substances, white will be prior in formula to white man, but not in substantiality; for it cannot exist in separation, but always exists conjointly with the concrete whole—by which I mean white man.

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Thus it is obvious that neither is the result of abstraction prior, nor the result of adding a determinant posterior—for the expression white man is the result of adding a determinant to white.

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Thus we have sufficiently shown (a) that the objects of mathematics are not more substantial than corporeal objects; (b) that they are not prior in point of existence to sensible things, but only in formula; and (c) that they cannot in any way exist in separation.

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And since we have seensect. 1-3 above. that they cannot exist in sensible things, it is clear that either they do not exist at all, or they exist only in a certain way, and therefore not absolutely; for exist has several senses.

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The general propositions in mathematics are not concerned with objects which exist separately apart from magnitudes and numbers; they are concerned with magnitudes and numbers, but not with them as possessing magnitude or being divisible. It is clearly possible that in the same way propositions and logical proofs may apply to sensible magnitudes; not qua sensible, but qua having certain characteristics.

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For just as there can be many propositions about things merely qua movable, without any reference to the essential nature of each one or to their attributes, and it does not necessarily follow from this either that there is something movable which exists in separation from sensible things or that there is a distinct movable nature in sensible things; so too there will be propositions and sciences which apply to movable things, not qua movable but qua corporeal only; and again qua planes only and qua lines only, and qua divisible, and qua indivisible but having position, and qua indivisible only.

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Therefore since it is true to say in a general sense not only that things which are separable but that things which are inseparable exist, e.g., that movable things exist, it is also true to say in a general sense that mathematical objects exist, and in such a form as mathematicians describe them.

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And just as it is true to say generally of the other sciences that they deal with a particular subject—not with that which is accidental to it (e.g. not with white if the healthy is white, and the subject of the science is the healthy), but with that which is the subject of the particular science; with the healthy if it treats of things qua healthy, and with man if qua man—so this is also true of geometry. If the things of which it treats are accidentally sensible although it does not treat of them qua sensible, it does not follow that the mathematical sciences treat of sensible things—nor, on the other hand, that they treat of other things which exist independently apart from these.

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Many attributes are essential properties of things as possessing a particular characteristic; e.g., there are attributes peculiar to an animal qua female or qua male, although there is no such thing as female or male in separation from animals. Hence there are also attributes which are peculiar to things merely qua lines or planes.

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And in proportion as the things which we are considering are prior in formula and simpler, they admit of greater exactness; for simplicity implies exactness. Hence we find greater exactness where there is no magnitude, and the greatest exactness where there is no motion; or if motion is involved, where it is primary, because this is the simplest kind; and the simplest kind of primary motion is uniform motion.Aristot. Met. 12.7.6.

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The same principle applies to both harmonics and optics, for neither of these sciences studies objects qua sight or qua sound, but qua lines and numbersOptics studies lines and harmonics numbers because these sciences are subordinate to geometry and arithmetic (Aristot. An. Post. 75b 15).; yet the latter are affections peculiar to the former. The same is also true of mechanics.

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Thus if we regard objects independently of their attributes and investigate any aspect of them as so regarded, we shall not be guilty of any error on this account, any more than when we draw a diagram on the ground and say that a line is a foot long when it is not; because the error is not in the premisses.Cf. Aristot. Met. 14.2.9, 10. The best way to conduct an investigation in every case is to take that which does not exist in separation and consider it separately; which is just what the arithmetician or the geometrician does.

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For man, qua man, is one indivisible thing; and the arithmetician assumes man to be one indivisible thing, and then considers whether there is any attribute of man qua indivisible. And the geometrician considers man neither qua man nor qua indivisible, but qua something solid. For clearly the attributes which would have belonged to man even if man were somehow not indivisible can belong to man irrespectively of his humanity or indivisibility.

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Hence for this reason the geometricians are right in what they maintain, and treat of what really exists; i.e., the objects of geometry really exist. For things can exist in two ways, either in complete reality or as matter.i.e., potentially.

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And since goodness is distinct from beauty (for it is always in actions that goodness is present, whereas beauty is also in immovable things), theyCf. Aristot. Met. 3.2.4. are in error who assert that the mathematical sciences tell us nothing about beauty or goodness;

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for they describe and manifest these qualities in the highest degree, since it does not follow, because they manifest the effects and principles of beauty and goodness without naming them, that they do not treat of these qualities. The main species of beauty are orderly arrangement, proportion, and definiteness; and these are especially manifested by the mathematical sciences.

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And inasmuch as it is evident that these (I mean, e.g., orderly arrangement and definiteness) are causes of many things, obviously they must also to some extent treat of the cause in this sense, i.e. the cause in the sense of the Beautiful. But we shall deal with this subject more explicitly elsewhere.There is no obvious fulfilment of this promise.

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As regards the objects of mathematics, then, the foregoing account may be taken as sufficient to show that they exist, and in what sense they exist, and in what sense they are prior and in what they are not. But as regards the Ideas we must first consider the actual theory in relation to the Idea, without connecting it in any way with the nature of numbers, but approaching it in the form in which it was originally propounded by the first exponentsIt seems quite obvious that Aristotle intends this vague phrase to refer to Plato. Cf. Aristot. Met. 1.6.1-3, with which the following sections 2-5 should be compared. On the whole subject see Introduction. of the Ideas.

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The theory of Forms occurred to those who enunciated it because they were convinced as to the true nature of reality by the doctrine of Heraclitus, that all sensible things are always in a state of flux; so that if there is to be any knowledge or thought about anything, there must be certain other entities, besides sensible ones, which persist. For there can be no knowledge of that which is in flux.

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Now Socrates devoted his attention to the moral virtues, and was the first to seek a general definition of these (for of the Physicists Democritus gained only a superficial grasp of the subjectCf. Aristot. Phys. 194a 20, Aristot. De Part. Anim. 642a 24. and defined, after a fashion, the hot and the cold; while the PythagoreansCf. Aristot. Met. 1.5.2, 16. at an earlier date had arrived at definitions of some few things—whose formulae they connected with numbers—e.g., what opportunity is, or justice or marriage); and he naturally inquired into the essence of things;

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for he was trying to reason logically, and the starting-point of all logical reasoning is the essence. At that time there was as yet no such proficiency in Dialectic that men could study contraries independently of the essence, and consider whether both contraries come under the same science.

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There are two innovationsThis is perhaps too strong a word. What Aristotle means is that Socrates was the first thinker who attached importance to general definitions and systematically used arguments from analogy in order to arrive at them. The Greeks as a whole were only too readily impressed by analogy; Socrates merely developed an already prevalent tendency. For an example of his method see the reference at Aristot. Met. 5.29.5 n. which, may fairly be ascribed to Socrates: inductive reasoning and general definition. Both of these are associated with the starting-point of scientific knowledge.

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But whereas Socrates regarded neither universals nor definitions as existing in separation, the Idealists gave them a separate existence, and to these universals and definitions of existing things they gave the name of Ideas.Cf. Introduction.

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Hence on their view it followed by virtually the same argument that there are Ideas of all terms which are predicated universallyWith sect. 6-13 cf. Aristot. Met. 1.9.1-8, which are almost verbally the same. See Introduction.; and the result was very nearly the same as if a man who wishes to count a number of things were to suppose that he could not do so when they are few, and yet were to try to count them when he has added to them. For it is hardly an exaggeration to say that there are more Forms than there are particular sensible things (in seeking for whose causes these thinkers were led on from particulars to Ideas); because corresponding to each thing there is a synonymous entity, apart from the substances (and in the case of non-substantial things there is a One over the Many) both in our everyday world and in the realm of eternal entities.

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Again, not one of the ways in which it is attempted to prove that the Forms exist demonstrates their point; from some of them no necessary conclusion follows, and from others it follows that there are Form of things of which they hold that there are no Forms.

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For according to the arguments from the sciences, there will be Forms of all things of which there are sciences; and according to the One-over-Many argument, of negations too; and according to the argument that we have some conception of what has perished there will be Forms of perishable things, because we have a mental picture of these things. Further, of the most exact arguments some establish Ideas of relations, of which the Idealists deny that there is a separate genus, and others state the Third Man.

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And in general the arguments for the Forms do away with things which are more important to the exponents of the Forms than the existence of the Ideas; for they imply that it is not the Dyad that is primary, but Number; and that the relative is prior to number, and therefore to the absolute; and all the other conclusions in respect of which certain persons by following up the views held about the Forms have gone against the principles of the theory.

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Again, according to the assumption by which they hold that the Ideas exist, there will be Forms not only of substances but of many other things (since the concept is one not only in the case of substances but in the case of non-substantial things as well; and there can be sciences not only of substances but also of other things; and there are a thousand other similar consequences);

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but it follows necessarily from the views generally held about them that if the Forms are participated in, there can only be Ideas of substances, because they are not participated in accidentally; things can only participate in a Form in so far as it is not predicated of a subject.

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I mean, e.g., that if a thing participates in absolute doubleness, it participates also in something eternal, but only accidentally; because it is an accident of doubleness to be eternal. Thus the Ideas will be substance. But the same terms denote substance in the sensible as in the Ideal world; otherwise what meaning will there be in saying that something exists besides the particulars, i.e. the unity comprising their multiplicity?

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If the form of the Ideas and of the things which participate in them is the same, they will have something in common (for why should duality mean one and the same thing in the case of perishable 2’s and the 2’s which are many but eternal, and not in the case of absolute duality and a particular 2?). But if the form is not the same, they will simply be homonyms; just as though one were to call both Callias and a piece of wood man, without remarking any property common to them.

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sect. 14, 15 have no counterpart in Book 1.And if we profess that in all other respects the common definitions apply to the Forms, e.g. that plane figure and the other parts of the definition apply to the Ideal circle, only that we must also state of what the Form is a Form, we must beware lest this is a quite meaningless statement.The suggestion is that the definition of an Ideal circle is the same as that of a particular circle, except that it must have added to it the statement of what particular the Idea is an Idea.

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For to what element of the definition must the addition be made? to center, or plane or all of them? For all the elements in the essence of an Idea are Ideas; e.g. animal and two-footed. sc. in the definition or essence of Ideal man. Further, it is obvious that being an Idea, just like plane, must be a definite characteristic which belongs as genus to all its species.i.e., being an idea will be a characteristic common to all ideas, and so must be itself an Idea.

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This chapter corresponds almost verbally to Aristot. Met. 1.9.9-15. Cf. note on Aristot. Met. 13.4.6.Above all we might examine the question what on earth the Ideas contribute to sensible things, whether eternal or subject to generation and decay; for they are not the cause of any motion or change in them.

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Moreover they are no help towards the knowledge of other things (for they are not the substance of particulars, otherwise they would be in particulars) or to their existence (since they are not present in the things which participate in them. If they were, they might perhaps seem to be causes, in the sense in which the admixture of white causes a thing to be white.

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But this theory, which was stated first by Anaxagoras and later by Eudoxus in his discussion of difficulties, and by others also, is very readily refuted; for it is easy to adduce plenty of impossibilities against such a view). Again, other things are not in any accepted sense derived from the Forms.

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To say that the Forms are patterns, and that other things participate in them, is to use empty phrases and poetical metaphors; for what is it that fashions things on the model of the Ideas? Besides, anything may both be and come to be without being imitated from something else; thus a man may become like Socrates whether Socrates exists or not,

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and even if Socrates were eternal, clearly the case would be the same. Also there will be several patterns (and therefore Forms) of the same thing; e.g., animal and two-footed will be patterns of man, and so too will the Idea of man.

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Further, the Forms will be patterns not only of sensible things but of Ideas; e.g. the genus will be the pattern of its species; hence the same thing will be pattern and copy. Further, it would seem impossible for the substance and that of which it is the substance to exist in separation; then how can the Ideas, if they are the substances of things, exist in separation from them?

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In thePhaedoPlat. Phaedo 100d. this statement is made: that the Forms are causes both of being and of generation. Yet assuming that the Forms exist, still there is no generation unless there is something to impart motion; and many other things are generated (e.g. house and ring) of which the Idealists say that there are no Forms.

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Thus it is clearly possible that those things of which they say that there are Ideas may also exist and be generated through the same kind of causes as those of the things which we have just mentioned, and not because of the Forms. Indeed, as regards the Ideas, we can collect against them plenty of evidence similar to that which we have now considered; not only by the foregoing methods, but by means of more abstract and exact reasoning.

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Now that we have dealt with the problems concerning the Ideas, we had better re-investigate the problems connected with numbers that follow from the theory that numbers are separate substances and primary causes of existing things. Now if number is a kind of entity, and has nothing else as its substance, but only number itself, as some maintain; then either (a) there must be some one part of number which is primary, and some other part next in succession, and so on, each part being specifically differentThis statement bears two meanings, which Aristotle confuses: (i) There must be more than one number-series, each series being different in kind from every other series; (2) All numbers are different in kind, and inaddible. Confusion (or textual inaccuracy) is further suggested by the fact that Aristotle offers no alternative statement of the nature of number in general, such as we should expect from his language. In any case the classification is arbitrary and incomplete.—

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and this applies directly to units, and any given unit is inaddible to any other given unit; or (b) theyThe units. are all directly successive, and any units can be added to any other units, as is held of mathematical number; for in mathematical number no one unit differs in any way from another.

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Or (c) some units must be addible and others not. E.g., 2 is first after 1, and then 3, and so on with the other numbers; and the units in each number are addible, e.g. the units in the firsti.e., Ideal or natural.2 are addible to one another, and those in the first 3 to one another, and so on in the case of the other numbers; but the units in the Ideal 2 are inaddible to those in the Ideal 3;

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and similarly in the case of the other successive numbers. Hence whereas mathematical number is counted thus: after 1, 2 (which consists of another 1 added to the former) and 3 (which consists of another 1 added to these two) and the other numbers in the same way, Ideal number is counted like this: after 1, a distinct 2 not including the original 1; and a 3 not including the 2, and the rest of the numbers similarly.

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Or (d) one kind of number must be such as we first described, and another or such as the mathematicians maintain, and that which we have last described must be a third kind.

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Again, these numbers must exist either in separation from things, or not in separation, but in sensible things (not, however, in the way which we first considered,In Aristot. Met. 13.2.1-3. but in the sense that sensible things are composed of numbers which are present in themThe Pythagorean number-atomist view; See Introduction.)—either some of them and not others, or all of them.i.e., either all numbers are material elements of things, or some are and others are not.

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These are of necessity the only ways in which the numbers can exist. Now of those who say that unity is the beginning and substance and element of all things, and that number is derived from it and something else, almost everyone has described number in one of these ways (except that no one has maintained that all units are inaddibleCf. sect. 2.);

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and this is natural enough, because there can be no other way apart from those which we have mentioned. Some hold that both kinds of number exist, that which involves priority and posteriority being identical with the Ideas, and mathematical number being distinct from Ideas and sensible things, and both kinds being separable from sensible thingsCf. Aristot. Met. 1.6.4.; others hold that mathematical number alone exists,Cf. Aristot. Met. 12.10.14. being the primary reality and separate from sensible things.

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The Pythagoreans also believe in one kind of number—the mathematical; only they maintain that it is not separate, but that sensible substances are composed of it. For they construct the whole universe of numbers, but not of numbers consisting of abstract units; they suppose the units to be extended—but as for how the first extended unit was formed they appear to be at a loss.Cf. Aristot. Met. 13.8.9, 10, Aristot. Met. 14.3.15, Aristot. Met. 14.5.7, and see Introduction.

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Another thinker holds that primary or Ideal number alone exists; and someCf. 10ff., Aristot. Met. 13.1.4. identify this with mathematical number.

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The same applies in the case of lines, planes and solids.

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SomePlato. distinguish mathematical objects from those which come after the Ideasi.e., the (semi-)Ideal lines, planes, etc. Cf. Aristot. Met. 1.9.30.; and of those who treat the subject in a different manner someSpeusippus; cf. sect. 7 above. speak of the mathematical objects and in a mathematical way—viz. those who do not regard the Ideas as numbers, nor indeed hold that the Ideas exist—and othersXenocrates. For his belief in indivisible lines see Ritter and Preller 362. Aristotle ascribes the doctrine to Plato in Aristot. Met. 1.9.25. speak of the mathematical objects, but not in a mathematical way; for they deny that every spatial magnitude is divisible into extended magnitudes, or that any two given units make 2.

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But all who hold that Unity is an element and principle of existing things regard numbers as consisting of abstract units, except the Pythagoreans; and they regard number as having spatial magnitude, as has been previously stated.sect. 8.

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It is clear from the foregoing account (1.) in how many ways it is possible to speak of numbers, and that all the ways have been described. They are all impossible, but doubtless somesc. the view of Xenocrates (cf. Aristot. Met. 13.8.8). are more so than others.

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First, then, we must inquire whether the limits are addible or inaddible; and if inaddible, in which of the two ways which we have distinguished.Aristot. Met. 13.6.2, 3. For it is possible either (a) that any one unit is inaddible to any other, or (b) that the units in the Ideal 2 are inaddible to those in the Ideal 3, and thus that the units in each Ideal number are inaddible to those in the other Ideal numbers.

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Now if all units are addible and do not differ in kind, we get one type of number only, the mathematical, and the Ideas cannot be the numbers thus produced;

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for how can we regard the Idea of Man or Animal, or any other Form, as a number? There is one Idea of each kind of thing: e.g. one of Humanity and another one of Animality; but the numbers which are similar and do not differ in kind are infinitely many, so that this is no more the Idea of Man than any other 3 is. But if the Ideas are not numbers, they cannot exist at all;

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for from what principles can the Ideas be derived? Number is derived from Unity and the indeterminate dyad, and the principles and elements are said to be the principles and elements of number, and the Ideas cannot be placed either as prior or as posterior to numbers.Since the only principles which Plato recognizes are Unity and the Dyad, which are numerical (Aristotle insists on regarding them as a kind of 1 and 2), and therefore clearly principles of number; and the Ideas can only be derived from these principles if they (the Ideas) are (a) numbers (which has been proved impossible) or (b) prior or posterior to numbers (i.e., causes or effects of numbers, which they cannot be if they are composed of a different kind of units); then the Ideas are not derived from any principle at all, and therefore do not exist.

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But if the units are inaddible in the sense that any one unit is inaddible to any other, the number so composed can be neither mathematical number (since mathematical number consists of units which do not differ, and the facts demonstrated of it fit in with this character) nor Ideal number. For on this view 2 will not be the first number generated from Unity and the indeterminate dyad, and then the other numbers in succession, as theyThe Platonists. say 2, 3, because the units in the primary 2 are generated at the same time,This was the orthodox Platonist view of the generation of ideal numbers; or at least Aristotle is intending to describe the orthodox view. Plato should not have regarded the Ideal numbers as composed of units at all, and there is no real reason to suppose that he did (see Introduction). But Aristotle infers from the fact that the Ideal 2 is the first number generated (and then the other Ideal numbers in the natural order) that the units of the Ideal 2 are generated simultaneously, and then goes on to show that this is incompatible with the theory of inaddible units. whether, as the originator of the theory held, from unequalsi.e., the Great-and-Small, which Aristotle wrongly understands as two unequal things. It is practically certain that Plato used the term (as he did that of Indeterminate Dyad) to describe indeterminate quantity. See Introduction.(coming into being when these were equalized), or otherwise—

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since if we regard the one unit as prior to the other,This is a necessary implication of the theory of inaddible units (cf. Aristot. Met. 13.6.1, 2). it will be prior also to the 2 which is composed of them; because whenever one thing is prior and another posterior, their compound will be prior to the latter and posterior to the former.So the order of generation will be: (i) Unity (ungenerated); (2) first unit in 2; (3) second unit in 2; and the Ideal 2 will come between (2) and (3).

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Further, since the Ideal 1 is first, and then comes a particular 1 which is first of the other 1’s but second after the Ideal 1, and then a third 1 which is next

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after the second but third after the first 1, it follows that the units will be prior to the numbers after which they are called; e.g., there will be a third unit in 2 before 3 exists, and a fourth and fifth in 3 before these numbers exist.This is a corollary to the previous argument, and depends upon an identification of ones (including the Ideal One or Unity) with units.

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It is true that nobody has represented the units of numbers as inaddible in this way; but according to the principles held by these thinkers even this view is quite reasonable, although in actual fact it is untenable.

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For assuming that there is a first unit or first 1,i.e., the Ideal One. it is reasonable that the units should be prior and posterior; and similarly in the case of 2’s, if there is a first 2. For it is reasonable and indeed necessary that after the first there should be a second; and if a second, a third; and so on with the rest in sequence.

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But the two statements, that there is after 1 a first and a second unit, and that there is a first 2, are incompatible. These thinkers, however, recognize a first unit and first 1, but not a second and third; and they recognize a first 2, but not a second and third.

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It is also evident that if all units are inaddible, there cannot be an Ideal 2 and 3, and similarly with the other numbers;

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for whether the units are indistinguishable or each is different in kind from every other, numbers must be produced by addition; e.g. 2 by adding 1 to another 1, and 3 by adding another 1 to the 2, and 4 similarly.This is of course not true of the natural numbers.

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This being so, numbers cannot be generated as these thinkers try to generate them, from Unity and the dyad; because 2 becomes a part of 3,i.e., 3 is produced by adding 1 to 2. and 3 of 4, and the same applies to the following numbers.

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But according to them 4 was generated from the first 2 and the indeterminate dyad, thus consisting of two 2’s apart from the Ideal 2.Cf. sect. 18. Otherwise 4 will consist of the Ideal 2 and another 2 added to it, and the Ideal 2 will consist of the Ideal 1 and another 1; and if this is so the other element cannot be the indeterminate dyad, because it produces one unit and not a definite 2.The general argument is: Numbers are produced by addition; but this is incompatible with the belief in the Indeterminate Dyad as a generative principle, because, being duplicative, it cannot produce single units.

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Again, how can there be other 3’s and 2’s besides the Ideal numbers 3 and 2, and in what way can they be composed of prior and posterior units? All these theories are absurd and fictitious, and there can be no primary 2 and Ideal 3. Yet there must be, if we are to regard Unity and the indeterminate dyad as elements.i.e., if numbers are not generated by addition, there must be Ideal (or natural) numbers.

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But if the consequences are impossible, the principles cannot be of this nature.

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If, then, any one unit differs in kind from any other, these and other similar consequences necessarily follow. If, on the other hand, while the units in different numbers are different, those which are in the same number are alone indistinguishable from one another, even so the consequences which follow are no less difficult.

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For example, in the Ideal number 10 there are ten units, and 10 is composed both of these and of two 5’s. Now since the Ideal 10 is not a chance number,I think Ross’s interpretation of this passage must be right. The Ideal 10 is a unique number, and the numbers contained in it must be ideal and unique; therefore the two 5’s must be specifically different, and so must their units—which contradicts the view under discussion. and is not composed of chance 5’s, any more than of chance units, the units in this number 10 must be different;

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for if they are not different, the 5’s of which the 10 is composed will not be different; but since these are different, the units must be different too. Now if the units are different, will there or will there not be other 5’s in this 10, and not only the two? If there are not, the thing is absurdi.e., it is only reasonable to suppose that other 5’s might be made up out of different combinations of the units.; whereas if there are, what sort of 10 will be composed of them? for there is no other 10 in 10 besides the 10 itself:

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Again, it must also be true that 4 is not composed of chance 2’s. For according to them the indeterminate dyad, receiving the determinate dyad, made two dyads; for it was capable of duplicating that which it received.Cf. Introduction.

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Again, how is it possible that 2 can be a definite entity existing besides the two units, and 3 besides the three units? Either by participation of the one in the other, as white man exists besides white and man, because it partakes of these concepts; or when the one is a differentia of the other, as man exists besides animal and two-footed.

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Again, some things are one by contact, others by mixture, and others by position; but none of these alternatives can possibly apply to the units of which 2 and 3 consist. Just as two men do not constitute any one thing distinct from both of them, so it must be with the units.

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The fact that the units are indivisible will make no difference; because points are indivisible also, but nevertheless a pair of points is not anything distinct from the two single points.

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Moreover we must not fail to realize this: that on this theory it follows that 2’s are prior and posterior, and the other numbers similarly.

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Let it be granted that the 2’s in 4 are contemporaneous; yet they are prior to those in 8, and just as the <determinate> 2 produced the 2’s in 4, soIn each case the other factor is the indeterminate dyad (cf. sect. 18). they produced the 4’s in 8. Hence if the original 2 is an Idea, these 2’s will also be Ideas of a sort.

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And the same argument applies to the units, because the units in the original 2 produce the four units in 4; and so all the units become Ideas, and an Idea will be composed of Ideas. Hence clearly those things also of which these things are Ideas will be composite; e.g., one might say that animals are composed of animals, if there are Ideas of animals.

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In general, to regard units as different in any way whatsoever is absurd and fictitious (by fictitious I mean dragged in to support a hypothesis). For we can see that one unit differs from another neither in quantity nor in quality; and a number must be either equal or unequal—this applies to all numbers, but especially to numbers consisting of abstract units.

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Thus if a number is neither more nor less, it is equal; and things which are equal and entirely without difference we assume, in the sphere of number, to be identical. Otherwise even the 2’s in the Ideal 10 will be different, although they are equal; for if anyone maintains that they are not different, what reason will he be able to allege?

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Again, if every unit plus another unit makes 2, a unit from the Ideal 2 plus one from the Ideal 3 will make 2—a 2 composed of different unitsWhich conflicts with the view under discussion.; will this be prior or posterior to 3? It rather seems that it must be prior, because one of the units is contemporaneous with 3, and the other with 2.The implication seems to be, as Ross says, that the Platonists will refuse to admit that there is a number between 2 and 3.

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We assume that in general 1 and 1, whether the things are equal or unequal, make 2; e.g. good and bad, or man and horse; but the supporters of this theory say that not even two units make 2.

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If the number of the Ideal 3 is not greater than that of the Ideal 2, it is strange; and if it is greater, then clearly there is a number in it equal to the 2, so that this number is not different from the Ideal 2.

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But this is impossible, if there is a first and second number.i.e., if numbers are specifically different. Cf. Aristot. Met. 13.6.1. Nor will the Ideas be numbers. For on this particular point they are right who claim that the units must be different if there are to be Ideas, as has been already stated.sect. 2-4 above. For the form is unique; but if the units are undifferentiated, the 2’s and 3’s will be undifferentiated.

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Hence they have to say that when we count like this, l, 2, we do not add to the already existing number; for if we do, (a) number will not be generated from the indeterminate dyad, and (b) a number cannot be an Idea; because one Idea will pre-exist in another, and all the Forms will be parts of one Form.i.e., the biggest number.

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Thus in relation to their hypothesis they are right, but absolutely they are wrong, for their view is very destructive, inasmuch as they will say that this point presents a difficulty: whether, when we count and say 1, 2, 3, we count by addition or by enumerating distinct portions.This is Apelt’s interpretation of κατὰ μερίδας. For this sense of the word he quotes Plut. Mor. 644c. The meaning then is: If you count by addition, you regard number as exhibited only in concrete instances; if you treat each number as a distinct portion (i.e. generated separately), you admit another kind of number besides the mathematical. Aristotle says that number can be regarded in both ways. But we do both; and therefore it is ridiculous to refer this point to so great a difference in essence.

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First of all it would be well to define the differentia of a number; and of a unit, if it has a differentia. Now units must differ either in quantity or in quality; and clearly neither of these alternatives can be true. But units may differ, as number does, in quantity. But if units also differed in quantity, number would differ from number, although equal in number of units.

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Again, are the first units greater or smaller, and do the later units increase in size, or the opposite? All these suggestions are absurd. Nor can units differ in quality; for no modification can ever be applicable to them, because these thinkers hold that even in numbers quality is a later attribute than quantity.Numbers have quality as being prime or composite, plane or solid (i.e., products of two or three factors); but these qualities are clearly incidental to quantity. Cf. Aristot. Met. 5.14.2.

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Further, the units cannot derive quality either from unity or from the dyad; because unity has no quality, and the dyad produces quantity, because its nature causes things to be many. If, then, the units differ in some other way, they should most certainly state this at the outset, and explain, if possible, with regard to the differentia of the unit, why it must exist; or failing this, what differentia they mean.

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Clearly, then, if the Ideas are numbers, the units cannot all be addible, nor can they all be inaddible in either sense. Nor again is the theory sound which certain other thinkersCf. Aristot. Met. 13.1.4. hold concerning numbers.

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These are they who do not believe in Ideas, either absolutely or as being a kind of numbers, but believe that the objects of mathematics exist, and that the numbers are the first of existing things, and that their principle is Unity itself. For it is absurd that if, as they say, there is a 1 which is first of the 1’s,i.e., Speusippus recognized unity or the One as a formal principle, but admitted no other ideal numbers. Aristotle argues that this is inconsistent. there should not be a 2 first of the 2’s, nor a 3 of the 3’s; for the same principle applies to all cases.

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Now if this is the truth with regard to number, and we posit only mathematical number as existing, Unity is not a principle. For the Unity which is of this nature must differ from the other units; and if so, then there must be some 2 which is first of the 2’s; and similarly with the other numbers in succession.

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But if Unity is a principle, then the truth about numbers must rather be as Plato used to maintain; there must be a first 2 and first 3, and the numbers cannot be addible to each other. But then again, if we assume this, many impossibilities result, as has been already stated.Aristot. Met. 13.7.1-8.3. Moreover, the truth must lie one way or the other; so that if neither view is sound, number cannot have a separate abstract existence.

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From these considerations it is also clear that the third alternativeCf. Aristot. Met. 13.6.7.—that Ideal number and mathematical number are the same—is the worst; for two errors have to be combined to make one theory. (1.) Mathematical number cannot be of this nature, but the propounder of this view has to spin it out by making peculiar assumptions; (2.) his theory must admit all the difficulties which confront those who speak of Ideal number.

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The Pythagorean view in one way contains fewer difficulties than the view described above, but in another way it contains further difficulties peculiar to itself. By not regarding number as separable, it disposes of many of the impossibilities; but that bodies should be composed of numbers, and that these numbers should be mathematical, is impossible.See Introduction.

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For (a) it is not true to speak of indivisible magnitudesThis is proved in Aristot. De Gen. et. Corr. 315b 24-317a 17.; (b) assuming that this view is perfectly true, still units at any rate have no magnitude; and how can a magnitude be composed of indivisible parts? Moreover arithmetical number consists of abstract units. But the Pythagoreans identify number with existing things; at least they apply mathematical propositions to bodies as though they consisted of those numbers.See Introduction.

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Thus if number, if it is a self-subsistent reality, must be regarded in one of the ways described above, and if it cannot be regarded in any of these ways, clearly number has no such nature as is invented for it by those who treat it as separable.

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Again, does each unit come from the Great and the Small, when they are equalizedCf. Aristot. Met. 13.7.5 n. Aristotle is obviously referring to the two units in the Ideal 2.; or does one come from the Small and another from the Great? If the latter, each thing is not composed of all the elements, nor are the units undifferentiated; for one contains the Great, and the other the Small, which is by nature contrary to the Great.

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Again, what of the units in the Ideal 3? because there is one over. But no doubt it is for this reason that in an odd number they make the Ideal One the middle unit.Cf. DieIs, Vorsokratiker 270. 18. If on the other hand each of the units comes from both Great and Small, when they are equalized, how can the Ideal 2 be a single entity composed of the Great and Small? How will it differ from one of its units? Again, the unit is prior to the 2; because when the unit disappears the 2 disappears.

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Therefore the unit must be the Idea of an Idea, since it is prior to an Idea, and must have been generated before it. From what, then? for the indeterminate dyad, as we have seen,Aristot. Met. 13.7.18. causes duality.

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Again, number must be either infinite or finite (for they make number separable, so that one of these alternatives must be true).The point seems to be that if number is self-subsistent it must be actually finite or infinite. Aristotle himself holds that number is infinite only potentially; i.e., however high you can count, you can always count higher.

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Now it is obvious that it cannot be infinite, because infinite number is neither odd nor even, and numbers are always generated either from odd or from even number. By one process, when 1 is added to an even number, we get an odd number; by another, when 1 is multiplied by 2, we get ascending powers of 2; and by another, when powers of 2 are multiplied by odd numbers, we get the remaining even numbers.

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Again, if every Idea is an Idea of something, and the numbers are Ideas, infinite number will also be an Idea of something, either sensible or otherwise. This, however, is impossible, both logicallyi.e., as implying an actual infinite. and on their own assumption,i.e., as inconsistent with the conception of an Idea as a determining principle. since they regard the Ideas as they do.

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If, on the other hand, number is finite, what is its limit? In reply to this we must not only assert the fact, but give the reason.

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Now if number only goes up to 10, as some hold,Cf. Aristot. Met. 12.8.2. The Platonists derived this view from the Pythagoreans; see Introduction. in the first place the Forms will soon run short. For example, if 3 is the Idea of Man, what number will be the Idea of Horse? Each number up to 10 is an Idea; the Idea of Horse, then, must be one of the numbers in this series, for they are substances or Ideas.

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But the fact remains that they will run short, because the different types of animals will outnumber them. At the same time it is clear that if in this way the Ideal 3 is the Idea of Man, so will the other 3’s be also (for the 3’s in the same numbersRobin is probably right in taking this to mean that the 3 which is in the ideal 4 is like the 3 which is in the 4 which is in a higher ideal number, and so on (La Theorie platonicienne des Idees et des Nombres d’apres Aristote, p. 352). are similar), so that there will be an infinite number of men; and if each 3 is an Idea, each man will be an Idea of Man; or if not, they will still be men.

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And if the smaller number is part of the greater, when it is composed of the addible units contained in the same number, then if the Ideal 4 is the Idea of something, e.g. horse or white, then man will be part of horse, if man is 2. It is absurd also that there should be an Idea of 10 and not of 11, nor of the following numbers.

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Again, some things exist and come into being of which there are no FormsCf. Aristot. Met. 13.4.7, 8; Aristot. Met. 1.9.2, 3.; why, then, are there not Forms of these too? It follows that the Forms are not the causes of things.

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Again, it is absurd that number up to 10 should be more really existent, and a Form, than 10 itself; although the former is not generated as a unity, whereas the latter is. However, they try to make out that the series up to 10 is a complete number;

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at least they generate the derivatives, e.g. the void, proportion, the odd, etc., from within the decad. Some, such as motion, rest, good and evil, they assign to the first principles; the rest to numbers.From the Dyad were derived void (Theophrastus, Met. 312.18-313.3) and motion (cf. Aristot. Met. 1.9.29, Aristot. Met. 11.9.8). Rest would naturally be derived from unity. For good and evil see Aristot. Met. 1.6.10. Proportion alone of the derivatives here mentioned appears to be derived from number. As Syrianus says, the three types of proportion can be illustrated by numbers from within the decad—arithmetical 1. 2. 3, geometrical 1. 2. 4, harmonic 2. 3. 6.

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Hence they identify the odd with Unity; because if oddness depended on 3, how could 5 be odd?sc. because (on their theory) 3 is not contained in 5. Thus oddness had to be referred to not a number but a principle—unity.

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Again, they hold that spatial magnitudes and the like have a certain limit; e.g. the first or indivisible line, then the 2, and so on; these too extending up to 10.The indivisible line or point was connected with 1, the line with 2, the plane with 3 and the solid with 4 (Aristot. Met. 14.3.9); and 1+2+3+4=10.

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Again, if number is separable, the question might be raised whether Unity is prior, or 3 or 2.

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Now if we regard number as composite, Unity is prior; but if we regard the universal or form as prior, number is prior, because each unit is a material part of number, while number is the form of the units. And there is a sense in which the right angle is prior to the acute angle—since it is definite and is involved in the definition of the acute angle—and another sense in which the acute angle is prior, because it is a part of the other, i.e., the right angle is divided into acute angles.

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Thus regarded as matter the acute angle and element and unit are prior; but with respect to form and substance in the sense of formula, the right angle, and the whole composed of matter and form, is prior. For the concrete whole is nearer to the form or subject of the definition, although in generation it is posterior.Cf. Aristot. Met. 7.10, 11.

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In what sense, then, is the One a first principle? Because, they say, it is indivisible.

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But the universal and the part or element are also indivisible. Yes, but they are prior in a different sense; the one in formula and the other in time. In which sense, then, is the One a first principle? for, as we have just said, both the right angle seems to be prior to the acute angle, and the latter prior to the former; and each of them is one.

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Accordingly the Platonists make the One a first principle in both senses. But this is impossible; for in one sense it is the One qua form or essence, and in the other the One qua part or matter, that is primary. There is a sense in which both number and unit are one; they are so in truth potentially—that is, if a number is not an aggregate but a unity consisting of units distinct from those of other numbers, as the Platonists hold—

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but each of the twoAristotle takes the number two as an example, but the principle is of course universal. In a sense both number and unit are one; but if the number exists as an actual unity, the unit can only exist potentially. units is not one in complete reality. The cause of the error which befell the Platonists was that they were pursuing their inquiry from two points of view—that of mathematics and that of general definition—at the same time. Hence as a result of the former they conceived of the One or first principle as a point, for the unit is a point without position. (Thus they too, just like certain others,

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represented existing things as composed of that which is smallest.)Perhaps the Atomists; but cf. Aristot. Met. 1.8.3, 4. We get, then, that the unit is the material element of numbers, and at the same time is prior to the number 2; and again we get that it is posterior to 2 regarded as a whole or unity or form. On the other hand, through looking for the universal, they were led to speak of the unity predicated of a given number as a part in the formal sense also. But these two characteristics cannot belong simultaneously to the same thing.

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And if Unity itself must only be without positionIf the text is sound (and no convincing emendation has been suggested), it seems best to understand ἄθετον in a rather wider sense than the semi-technical one put forward by Ross. Without position = not localized, i.e. abstract. Unity as a principle has no concrete instance.(for it differs only in that it is a principle) and 2 is divisible whereas the unit is not, the unit will be more nearly akin to Unity itself; and if this is so, Unity itself will also be more nearly akin to the unit than to 2. Hence each of the units in 2 will be prior to 2. But this they deny; at least they make out that 2 is generated first.Cf. Aristot. Met. 13.7.5. Further, if 2 itself and 3 itself are each one thing, both together make 2. From what, then, does this 2 come?

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Since there is no contact in numbers, but units which have nothing between them—e.g. those in 2 or 3—are successive, the question might be raised whether or not they are successive to Unity itself, and whether of the numbers which succeed it 2 or one of the units in 2 is prior.

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We find similar difficulties in the case of the genera posterior to numberCf. Aristot. Met. 13.6.10.—the line, plane and solid. Some derive these from the species of the Great and Small; viz. lines from the Long and Short, planes from the Broad and Narrow, and solids from the Deep and Shallow. These are species of the Great and Small.

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As for the geometrical first principle which corresponds to the arithmetical One, different Platonists propound different views.Cf. Aristot. Met. 3.4.34, Aristot. Met. 14.3.9. In these too we can see innumerable impossibilities, fictions and contradictions of all reasonable probability. For (a) we get that the geometrical forms are unconnected with each other, unless their principles also are so associated that the Broad and Narrow is also Long and Short; and if this is so, the plane will be a line and the solid a plane.

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Moreover, how can angles and figures, etc., be explained? And (b) the same result follows as in the case of number; for these concepts are modifications of magnitude, but magnitude is not generated from them, any more than a line is generated from the Straight and Crooked, or solids from the Smooth and Rough.

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Common to all these Platonic theories is the same problem which presents itself in the case of species of a genus when we posit universals—viz. whether it is the Ideal animal that is present in the particular animal, or some other animal distinct from the Ideal animal. This question will cause no difficulty if the universal is not separable; but if, as the Platonists say, Unity and the numbers exist separately, then it is not easy to solve (if we should apply the phrase not easy to what is impossible).

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For when we think of the one in 2, or in number generally, are we thinking of an Idea or of something else?

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These thinkers, then, generate geometrical magnitudes from this sort of material principle, but othersThe reference is probably to Speusippus; Plato and Xenocrates did not believe in points (Aristot. Met. 1.9.25, Aristot. Met. 13.5.10 n). generate them from the point (they regard the point not as a unity but as similar to Unity) and another material principle which is not plurality but is similar to it; yet in the case of these principles none the less we get the same difficulties.

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For if the matter is one, line, plane and solid will be the same; because the product of the same elements must be one and the same. If on the other hand there is more than one kind of matter—one of the line, another of the plane, and another of the solid—either the kinds are associated with each other, or they are not. Thus the same result will follow in this case also; for either the plane will not contain a line, or it will be a line.

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Further, no attempt is made to explain how number can be generated from unity and plurality; but howsoever they account for this, they have to meet the same difficulties as those who generate number from unity and the indeterminate dyad. The one school generates number not from a particular plurality but from that which is universally predicated; the other from a particular plurality, but the first; for they hold that the dyad is the first plurality.Aristotle again identifies the indeterminate dyad with the number 2.

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Thus there is practically no difference between the two views; the same difficulties will be involved with regard to mixture, position, blending, generation and the other similar modes of combination.sc. of the elements of number.

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We might very well ask the further question: if each unit is one, of what it is composed; for clearly each unit is not absolute unity. It must be generated from absolute unity and either plurality or a part of plurality.

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Now we cannot hold that the unit is a plurality, because the unit is indivisible; but the view that it is derived from a part of plurality involves many further difficulties, because (a) each part must be indivisible; otherwise it will be a plurality and the unit will be divisible, and unity and plurality will not be its elements, because each unit will not be generated from pluralitysc. but from an indivisible part of plurality—which is not a plurality but a unity. and unity.

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(b) The exponent of this theory merely introduces another number; because plurality is a number of indivisible parts.i.e., to say that number is derived from plurality is to say that number is derived from number—which explains nothing.

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Again, we must inquire from the exponent of this theory whether the numbersc. which plurality has been shown to be. is infinite or finite.

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There was, it appears, a finite plurality from which, in combination with Unity, the finite units were generated; and absolute plurality is different from finite plurality. What sort of plurality is it, then, that is, in combination with unity, an element of number?

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We might ask a similar question with regard to the point, i.e. the element out of which they create spatial magnitudes.

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This is surely not the one and only point. At least we may ask from what each of the other points comes; it is not, certainly, from some interval and the Ideal point. Moreover, the parts of the interval cannot be indivisible parts, any more than the parts of the plurality of which the units are composed; because although number is composed of indivisible parts, spatial magnitudes are not.

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All these and other similar considerations make it clear that number and spatial magnitudes cannot exist separately. Further, the fact that the leading authoritiesAlexander preferred the reading πρώτους, interpreting it in this sense; and I do not see why he should not be followed. Ross objects that πρῶτος is used in the chronological sense in 16., but this is really no argument. For a much more serious (although different) inconsistency in the use of terms cf. Aristot. Met. 12.3.1. disagree about numbers indicates that it is the misrepresentation of the facts themselves that produces this confusion in their views.

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ThoseSpeusippus and his followers. who recognize only the objects of mathematics as existing besides sensible things, abandoned Ideal number and posited mathematical number because they perceived the difficulty and artificiality of the Ideal theory. Others,Xenocrates and his followers. wishing to maintain both Forms and numbers, but not seeing how, if one posits theseUnity and the indeterminate dyad; for the difficulty see Aristot. Met. 13.7.3, 4. as first principles, mathematical number can exist besides Ideal number, identified Ideal with mathematical number,—but only in theory, since actually mathematical number is done away with, because the hypotheses which they state are peculiar to them and not mathematical.Cf. Aristot. Met. 13.6.10.

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And hePlato. who first assumed that there are Ideas, and that the Ideas are numbers, and that the objects of mathematics exist, naturally separated them. Thus it happens that all are right in some respect, but not altogether right; even they themselves admit as much by not agreeing but contradicting each other. The reason of this is that their assumptions and first principles are wrong;

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and it is difficult to propound a correct theory from faulty premisses: as Epicharmus says, no sooner is it said than it is seen to be wrong. Epicharmus, Fr. 14, Diels.

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We have now examined and analyzed the questions concerning numbers to a sufficient extent; for although one who is already convinced might be still more convinced by a fuller treatment, he who is not convinced would be brought no nearer to conviction.

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As for the first principles and causes and elements, the views expressed by those who discuss only sensible substance either have been described in the PhysicsAristot. Physics 1.4-6. or have no place in our present inquiry; but the views of those who assert that there are other substances besides sensible ones call for investigation next after those which we have just discussed.

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Since, then, some thinkers hold that the Ideas and numbers are such substances, and that their elements are the elements and principles of reality, we must inquire what it is that they hold, and in what sense they hold it.

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ThoseThe Pythagoreans and Speusippus. who posit only numbers, and mathematical numbers at that, may be considered laterAristot. Met. 14.2.21, Aristot. Met. 14.3.2-8, 15, 16.; but as for those who speak of the Ideas, we can observe at the same time their way of thinking and the difficulties which befall them. For they not only treat the Ideas as universal substances, but also as separable and particular.

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(That this is impossible has been already shownAristot. Met. 3.6.7-9. by a consideration of the difficulties involved.) The reason why those who hold substances to be universal combined these two views was that they did not identify substances with sensible things. They considered that the particulars in the sensible world are in a state of flux, and that none of them persists, but that the universal exists besides them and is something distinct from them.

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This theory, as we have said in an earlier passage,Aristot. Met. 13.4, and cf. Aristot. Met. 1.6. was initiated by Socrates as a result of his definitions, but he did not separate universals from particulars; and he was right in not separating them. This is evident from the facts; for without the universal we cannot acquire knowledge, and the separation of the universal is the cause of the difficulties which we find in the Ideal theory.

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Others,The Platonists. regarding it as necessary, if there are to be any substances besides those which are sensible and transitory, that they should be separable, and having no other substances, assigned separate existence to those which are universally predicated; thus it followed that universals and particulars are practically the same kind of thing. This in itself would be one difficulty in the view which we have just described.See Introduction.

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Let us now mention a point which presents some difficulty both to those who hold the Ideal theory and to those who do not. It has been stated already, at the beginning of our treatise, among the problems.Cf. Aristot. Met. 3.4.8-10, Aristot. Met. 3.6.7-9. If we do not suppose substances to be separate, that is in the way in which particular things are said to be separate, we shall do away with substance in the sense in which we wish to maintain it; but if we suppose substances to be separable, how are we to regard their elements and principles?

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If they are particular and not universal, there will be as many real things as there are elements, and the elements will not be knowable. For let us suppose that the syllables in speech are substances, and that their letters are the elements of substances. Then there must be only one BA, and only one of each of the other syllables; that is, if they are not universal and identical in form, but each is numerically one and an individual, and not a member of a class bearing a common name.

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(Moreover, the Platonists assume that each Ideal entity is unique.) Now if this is true of the syllables, it is also true of their letters. Hence there will not be more than one A, nor more than one of any of the other letters,This is, as a matter of fact, the assumption upon which the whole argument rests; Aristotle is arguing in a circle. on the same argument by which in the case of the syllable there cannot be more than one instance of the same syllable. But if this is so, there will be no other things besides the letters, but only the letters.

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Nor again will the elements be knowable; for they will not be universal, and knowledge is of the universal. This can be seen by reference to proofs and definitions; for there is no logical conclusion that a given triangle has its angles equal to two right angles unless every triangle has its angles equal to two right angles, or that a given man is an animal unless every man is an animal.

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On the other hand, if the first principles are universal, either the substances composed of them will be universal too, or there will be a non-substance prior to substance; because the universal is not substance, and the element or first principle is universal; and the element or first principle is prior to that of which it is an element or first principle.

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All this naturally follows when they compose the Ideas of elements and assert that besides the substances which have the same form there are also Ideas each of which is a separate entity.

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But if, as in the case of the phonetic elements, there is no reason why there should not be many A’s and B’s, and no A itself or B itself apart from these many, then on this basis there may be any number of similar syllables.

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The doctrine that all knowledge is of the universal, and hence that the principles of existing things must also be universal and not separate substances, presents the greatest difficulty of all that we have discussed; there is, however, a sense in which this statement is true, although there is another in which it is not true.

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Knowledge, like the verb to know, has two senses, of which one is potential and the other actual. The potentiality being, as matter, universal and indefinite, has a universal and indefinite object; but the actuality is definite and has a definite object, because it is particular and deals with the particular.

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It is only accidentally that sight sees universal color, because the particular color which it sees is color; and the particular A which the grammarian studies is an A. For if the first principles must be universal, that which is derived from them must also be universal, as in the case of logical proofsBecause ἀπόδειξις (logical or syllogistic proof) must be in the first figure (Aristot. An. Post. 1.14), and in that figure universal premises always give a universal conclusion. (Ross.); and if this is so there will be nothing which has a separate existence; i.e. no substance. But it is clear that although in one sense knowledge is universal, in another it is not.

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With regard to this kind of substance,i.e., the Platonic Ideas or numbers, which they regarded as unchangeable substances. There is, however, no definite transition to a fresh subject at this point. The criticisms of the Ideas or numbers as substances, and of the Platonic first principles, have not been grouped systematically in Books 13 and 14. Indeed there is so little distinction in subject matter between the two books that in some Mss. 14 was made to begin at 13.9.10. (Syrianus ad loc.). See Introduction. then, let the foregoing account suffice. All thinkers make the first principles contraries; as in the realm of natural objects, so too in respect of the unchangeable substances.

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Now if nothing can be prior to the first principle of all things, that first principle cannot be first principle if it is an attribute of something else. This would be as absurd as to say that white is the first principle, not qua anything else but qua white, and yet that it is predicable of a subject, and is white because it is an attribute of something else; because the latter will be prior to it.

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Moreover, all things are generated from contraries as from a substrate, and therefore contraries must most certainly have a substrate. Therefore all contraries are predicated of a subject, and none of them exists separately. But there is no contrary to substance; not only is this apparent, but it is borne out by reasoned consideration.Cf. Aristot. Categories 3b 24-27 Thus none of the contraries is strictly a first principle; the first principle is something different.

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But the Platonists treat one of the contraries as matter, some opposing the unequal to Unity (on the ground that the former is of the nature of plurality) and others plurality.

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For according to some,Plato; cf. Aristot. Met. 13.7.5. numbers are generated from the unequal dyad of the Great and Small; and according to another,Probably Speusippus. from plurality; but in both cases they are generated by the essence of unity. For he who speaks of the unequal and Unity as elements, and describes the unequal as a dyad composed of Great and Small, speaks of the unequal, i.e. the Great and Small, as being one; and does not draw the distinction that they are one in formula but not in number.This shows clearly that by the Great-and Small Plato meant a single principle, i.e., indeterminate quantity. Aristotle admits this here because he is contrasting the Great-and Small with the One; but elsewhere he prefers to regard the Platonic material principle as a duality. See Introduction.

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Again, they state the first principles, which they call elements, badly; some say that the Great and the Small, together with Unity (making 3Cf. previous note. in all), are the elements of numbers; the two former as matter, and Unity as form. Others speak of the Many and Few, because the Great and the Small are in their nature more suited to be the principles of magnitude; and others use the more general term which covers these—the exceeding and the exceeded.

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But none of these variations makes any appreciable difference with respect to some of the consequences of the theory; they only affect the abstract difficulties, which these thinkers escape because the proofs which they themselves employ are abstract.

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There is, however, this exception: if the exceeding and the exceeded are the first principles, and not the Great and the Small, on the same principle number should be derived from the elements before 2 is derived; for as the exceeding and the exceeded is more universal than the Great and Small, so number is more universal than 2. But in point of fact they assert the one and not the other.

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Others oppose the different or other to Unity; and others contrast Plurality and Unity.

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Now if, as they maintain, existing things are derived from contraries, and if there is either no contrary to unity, or if there is to be any contrary it is plurality; and if the unequal is contrary to the equal, and the different to the same, and the other to the thing itself then those who oppose unity to plurality have the best claim to credibility—but even their theory is inadequate, because then unity will be few. For plurality is opposed to paucity, and many to few.

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That unity denotes a measureCf. Aristot. Met. 5.6.17, 18, Aristot. Met. 10.1.8, 21. is obvious. And in every case there is something else which underlies it; e.g., in the scale there is the quarter-tone; in spatial magnitude the inch or foot or some similar thing; and in rhythms the foot or syllable. Similarly in the case of gravity there is some definite weight. Unity is predicated of all things in the same way; of qualities as a quality, and of quantities as a quantity.

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(The measure is indivisible, in the former case in kind, and in the latter to our senses.) This shows that unity is not any independent substance. And this is reasonable; because unity denotes a measure of some plurality, and number denotes a measured plurality and a plurality of measures. (Hence too it stands to reason that unity is not a number; for the measure is not measures, but the measure and unity are starting-points.)

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The measure must always be something which applies to all alike; e.g., if the things are horses, the measure is a horse; if they are men, the measure is a man; and if they are man, horse and god, the measure will presumably be an animate being, and the number of them animate beings.

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If the things are man, white and walking, there will scarcely be a number of them, because they all belong to a subject which is one and the same in number; however, their number will be a number of genera, or some other such appellation.

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ThoseCf. sect. 5. who regard the unequal as a unity, and the dyad as an indeterminate compound of great and small, hold theories which are very far from being probable or possible. For these terms represent affections and attributes, rather than substrates, of numbers and magnitudes—many and few applying to number, and great and small to magnitude— just as odd and even, smooth and rough, straight and crooked, are attributes.

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Further, in addition to this error, great and small and all other such terms must be relative. And the relative is of all the categories in the least degree a definite entity or substance; it is posterior to quality and quantity. The relative is an affection of quantity, as we have said, and not its matter; since there is something else distinct which is the matter both of the relative in general and of its parts and kinds.

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There is nothing great or small, many or few, or in general relative, which is many or few, great or small, or relative to something else without having a distinct nature of its own. That the relative is in the lowest degree a substance and a real thing is shown by the fact that of it aloneCf. Aristot. Met. 11.12.1. There Aristotle refers to seven categories, but here he omits activity and passivity as being virtually identical with motion. there is neither generation nor destruction nor change in the sense that in respect of quantity there is increase and decrease, in respect of quality, alteration, in respect of place, locomotion, and in respect of substance, absolute generation and destruction.

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There is no real change in respect of the relative; for without any change in itself, one term will be now greater, now smaller or equal, as the other term undergoes quantitative change. Moreover, the matter of every thing, and therefore of substance, must be that which is potentially of that nature; but the relative is neither potentially substance nor actually.

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It is absurd, then, or rather impossible, to represent non-substance as an element of substance and prior to it; for all the other categories are posterior to substance. And further, the elements are not predicated of those things of which they are elements; yet many and few are predicated, both separately and together, of number; and long and short are predicated of the line, and the Plane is both broad and narrow.

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If, then, there is a plurality of which one term, viz. few, is always predicable, e.g. 2 (for if 2 is many, 1 will be fewCf. Aristot. Met. 10.6.1-3.), then there will be an absolute many; e.g., 10 will be many (if there is nothing more than 10Cf. Aristot. Met. 13.8.17.), or 10,000. How, then, in this light, can number be derived from Few and Many? Either both ought to be predicated of it, or neither; but according to this view only one or the other is predicated.

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But we must inquire in general whether eternal things can be composed of elements. If so, they will have matter; for everything which consists of elements is composite.

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Assuming, then, that that which consists of anything, whether it has always existed or it came into being, must come into being <if at all> out of that of which it consists; and that everything comes to be that which it comes to be out of that which is it potentially (for it could not have come to be out of that which was not potentially such, nor could it have consisted of it); and that the potential can either be actualized or not; then however everlasting number or anything else which has matter may be, it would be possible for it not to exist, just as that which is any number of years old is as capable of not existing as that which is one day old. And if this is so, that which has existed for so long a time that there is no limit to it may also not exist.

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Therefore things which contain matter cannot be eternal, that is, if that which is capable of not existing is not eternal, as we have had occasion to say elsewhere.Aristot. Met. 9.8.15-17, Aristot. De Caelo 1.12. Now if what we have just been saying—that no substance is eternal unless it is actuality—is true universally, and the elements are the matter of substance, an eternal substance can have no elements of which, as inherent in it, it consists.

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There are some who, while making the element which acts conjointly with unity the indeterminate dyad, object to the unequal, quite reasonably, on the score of the difficulties which it involves. But they are rid only of those difficultiesCf. Aristot. Met. 14.1.14-17. which necessarily attend the theory of those who make the unequal, i.e. the relative, an element; all the difficulties which are independent of this view must apply to their theories also, whether it is Ideal or mathematical number that they construct out of these elements.

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There are many causes for their resorting to these explanations, the chief being that they visualized the problem in an archaic form. They supposed that all existing things would be one, absolute Being, unless they encountered and refuted Parmenides’ dictum:

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It will ne’er be proved that things which are not, are,Parmenides Fr. 7 (Diels).

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i.e., that they must show that that which is not, is; for only so—of that which is, and of something else—could existing things be composed, if they are more than one.Cf. Plat. Soph. 237a, 241d, 256e.

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However, (i) in the first place, if being has several meanings (for sometimes it means substance, sometimes quality, sometimes quantity, and so on with the other categories), what sort of unity will all the things that are constitute, if not-being is not to be? Will it be the substances that are one, or the affections (and similarly with the other categories), or all the categories together? in which case the this and the such and the so great, and all the other categories which denote some sense of Being, will be one.

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But it is absurd, or rather impossible, that the introduction of one thing should account for the fact that what is sometimes means so-and-so, sometimes such-and-such, sometimes of such-and-such a size, sometimes in such-and-such a place.

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(2) Of what sort of not-being and Being do real things consist? Not-being, too, has several senses, inasmuch as Being has; and not-man means not so-and-so, whereas not straight means not such-and-such, and not five feet long means not of such-and-such a size. What sort of Being and not-being, then, make existing things a plurality?

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This thinker means by the not-being which together with Being makes existing things a plurality, falsity and everything of this naturePlat. Soph. 237a, 240; but Aristotle’s statement assumes too much.; and for this reason also it was saidPresumably by some Platonist. that we must assume something which is false, just as geometricians assume that a line is a foot long when it is not.

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But this cannot be so; for (a) the geometricians do not assume anything that is false (since the proposition is not part of the logical inferencei.e., the validity of a geometrical proof does not depend upon the accuracy of the figure.), and (b) existing things are not generated from or resolved into not-being in this sense. But not only has not-being in its various cases as many meanings as there are categories, but moreover the false and the potential are called not-being; and it is from the latter that generation takes place—man comes to be from that which is not man but is potentially man, and white from that which is not white but is potentially white; no matter whether one thing is generated or many.

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Clearly the point at issue is how being in the sense of the substances is many; for the things that are generated are numbers and lines and bodies. It is absurd to inquire how Being as substance is many, and not how qualities or quantities are many.

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Surely the indeterminate dyad or the Great and Small is no reason why there should be two whites or many colors or flavors or shapes; for then these too would be numbers and units. But if the Platonists had pursued this inquiry, they would have perceived the cause of plurality in substances as well; for the causeMatter, according to Aristotle; and there is matter, or something analogous to it, in every category. Cf. Aristot. Met. 12.5. is the same, or analogous.

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This deviation of theirs was the reason why in seeking the opposite of Being and unity, from which in combination with Being and unity existing things are derived, they posited the relative (i.e. the unequal), which is neither the contrary nor the negation of Being and unity, but is a single characteristic of existing things, just like substance or quality. They should have investigated this question also; how it is that relations are many, and not one.

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As it is, they inquire how it is that there are many units besides the primary unity, but not how there are many unequal things besides the Unequal. Yet they employ in their arguments and speak of Great and Small, Many and Few (of which numbers are composed), Long and Short (of which the line is composed), Broad and Narrow (of which the plane is composed), Deep and Shallow (of which solids are composed); and they mention still further kinds of relation.Cf. Aristot. Met. 14.1.6, 18, Aristot. Met. 1.9.23. Now what is the cause of plurality in these relations?

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We must, then, as I say, presuppose in the case of each thing that which is it potentially. The authorPlato. of this theory further explained what it is that is potentially a particular thing or substance, but is not per se existent—that it is the relative (he might as well have said quality); which is neither potentially unity or Being, nor a negation of unity or Being, but just a particular kind of Being.

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And it was still more necessary, as we have said,sect. 11. that, if he was inquiring how it is that things are many, he should not confine his inquiry to things in the same category, and ask how it is that substances or qualities are many, but that he should ask how it is that things in general are many; for some things are substances, some affections, and some relations.

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Now in the case of the other categories there is an additional difficulty in discovering how they are many. For it may be said that since they are not separable, it is because the substrate becomes or is many that qualities and quantities are many; yet there must be some matter for each class of entities, only it cannot be separable from substances.

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In the case of particular substances, however, it is explicable how the particular thing can be many, if we do not regard a thing both as a particular substance and as a certain characteristic.This, according to Aristotle, is how the Platonists regard the Ideas. See Introduction. The real difficulty which arises from these considerations is how substances are actually many and not one.

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Again, even if a particular thing and a quantity are not the same, it is not explained how and why existing things are many, but only how quantities are many;

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for all number denotes quantity, and the unit, if it does not mean a measure, means that which is quantitatively indivisible. If, then, quantity and substance are different, it is not explained whence or how substance is many; but if they are the same, he who holds this has to face many logical contradictions.

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One might fasten also upon the question with respect to numbers, whence we should derive the belief that they exist.

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For onePlato and his orthodox followers. who posits Ideas, numbers supply a kind of cause for existing things; that is if each of the numbers is a kind of Idea, and the Idea is, in some way or other, the cause of existence for other things; for let us grant them this assumption.

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But as for himSpeusippus. who does not hold this belief, because he can see the difficulties inherent in the Ideal theory (and so has not this reason for positing numbers), and yet posits mathematical number, what grounds have we for believing his statement that there is a number of this kind, and what good is this number to other things? He who maintains its existence does not claim that it is the cause of anything, but regards it as an independent entity; nor can we observe it to be the cause of anything; for the theorems of the arithmeticians will all apply equally well to sensible things, as we have said.Aristot. Met. 13.3.1.

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Those, then, who posit the Ideas and identify them with numbers, by their assumption (in accordance with their method of abstracting each general term from its several concrete examples) that every general term is a unity, make some attempt to explain why number exists.I have followed Ross’s text and interpretation of this sentence. For the meaning cf. Aristot. Met. 14.2.20. Since, however, their arguments are neither necessarily true nor indeed possible, there is no justification on this ground for maintaining the existence of number.

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The Pythagoreans, on the other hand, observing that many attributes of numbers apply to sensible bodies, assumed that real things are numbers; not that numbers exist separately, but that real things are composed of numbers.See Introduction. But why? Because the attributes of numbers are to be found in a musical scale, in the heavens, and in many other connections.Cf. Aristot. Met. 14.6.5.

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As for those who hold that mathematical number alone exists,Cf. Aristot. Met. 14.2.21. they cannot allege anything of this kindi.e., that things are composed of numbers. consistently with their hypotheses; what they did say was that the sciences could not have sensible things as their objects. But we maintain that they can; as we have said before. And clearly the objects of mathematics do not exist in separation; for if they did their attributes would not be present in corporeal things.

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Thus in this respect the Pythagoreans are immune from criticism; but in so far as they construct natural bodies, which have lightness and weight, out of numbers which have no weight or lightness, they appear to be treating of another universe and other bodies, not of sensible ones.See Introduction.

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But those who treat number as separable assume that it exists and is separable because the axioms will not apply to sensible objects; whereas the statements of mathematics are true and appeal to the soul.The statements of mathematics appeal so strongly to our intelligence that they must be true; therefore if they are not true of sensible things, there must be some class of objects of which they are true. The same applies to mathematical extended magnitudes.

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It is clear, then, both that the contrary theoryThe Pythagorean theory, which maintains that numbers not only are present in sensible things but actually compose them, is in itself an argument against the Speusippean view, which in separating numbers from sensible things has to face the question why sensible things exhibit numerical attributes. can make out a case for the contrary view, and that those who hold this theory must find a solution for the difficulty which was recently raisedsect. 3.—why it is that while numbers are in no way present in sensible things, their attributes are present in sensible things.

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There are someProbably Pythagoreans. Cf. Aristot. Met. 7.2.2, Aristot. Met. 3.5.3. who think that, because the point is the limit and extreme of the line, and the line of the plane, and the plane of the solid, there must be entities of this kind.

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We must, then, examine this argument also, and see whether it is not exceptionally weak. For (1.) extremes are not substances; rather all such things are merely limits. Even walking, and motion in general, has some limit; so on the view which we are criticizing this will be an individual thing, and a kind of substance. But this is absurd. And moreover (2.) even if they are substances, they will all be substances of particular sensible things, since it was to these that the argument applied. Why, then, should they be separable?

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Again, we may, if we are not unduly acquiescent, further object with regard to all number and mathematical objects that they contribute nothing to each other, the prior to the posterior. For if number does not exist, none the less spatial magnitudes will exist for those who maintain that only the objects of mathematics exist; and if the latter do not exist, the soul and sensible bodies will exist.That the criticism is directed against Speusippus is clear from Aristot. Met. 7.2.4. Cf. Aristot. Met. 12.10.14.

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But it does not appear, to judge from the observed facts, that the natural system lacks cohesion, like a poorly constructed drama. ThoseXenocrates (that the reference is not to Plato is clear from sect. 11). who posit the Ideas escape this difficulty, because they construct spatial magnitudes out of matter and a number—2 in the case of lines, and 3, presumably, in that of planes, and 4 in that of solids; or out of other numbers, for it makes no difference.

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But are we to regard these magnitudes as Ideas, or what is their mode of existence? and what contribution do they make to reality? They contribute nothing; just as the objects of mathematics contribute nothing. Moreover, no mathematical theorem applies to them, unless one chooses to interfere with the principles of mathematics and invent peculiar theoriese.g. that of indivisible lines. of one’s own. But it is not difficult to take any chance hypotheses and enlarge upon them and draw out a long string of conclusions.

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These thinkers, then, are quite wrong in thus striving to connect the objects of mathematics with the Ideas. But those who first recognized two kinds of number, the Ideal and the mathematical as well, neither have explained nor can explain in any way how mathematical number will exist and of what it will be composed; for they make it intermediate between Ideal and sensible number.

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For if it is composed of the Great and Small, it will be the same as the former, i.e. Ideal, number. But of what other Great and Small can it be composed? for Plato makes spatial magnitudes out of a Great and Small.This interpretation (Ross’s second alternative, reading τίνος for τινος) seems to be the most satisfactory. For the objection cf. Aristot. Met. 3.4.34. And if he speaks of some other component, he will be maintaining too many elements; while if some one thing is the first principle of each kind of number, unity will be something common to these several kinds.

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We must inquire how it is that unity is these many things, when at the same time number, according to him, cannot be derived otherwise than from unity and an indeterminate dyad.The argument may be summarized thus. If mathematical number cannot be derived from the Great-and-Small or a species of the Great-and-Small, either it has a different material principle (which is not economical) or its formal principle is in some sense distinct from that of the Ideal numbers. But this implies that unity is a kind of plurality, and number or plurality can only be referred to the dyad or material principle.

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All these views are irrational; they conflict both with one another and with sound logic, and it seems that in them we have a case of Simonides’ long storyThe exact reference is uncertain, but Aristotle probably means Simonides of Ceos. Cf. Simonides Fr. 189 (Bergk).; for men have recourse to the long story, such as slaves tell, when they have nothing satisfactory to say.

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The very elements too, the Great and Small, seem to protest at being dragged in; for they cannot possibly generate numbers except rising powers of 2.Assuming that the Great-and-Small, or indeterminate dyad, is duplicative (Aristot. Met. 13.7.18).

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It is absurd also, or rather it is one of the impossibilities of this theory, to introduce generation of things which are eternal.

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There is no reason to doubt whether the Pythagoreans do or do not introduce it; for they clearly state that when the One had been constituted—whether out of planes or superficies or seed or out of something that they cannot explain—immediately the nearest part of the Infinite began to be drawn in and limited by the Limit.Cf. Aristot. Physics 3.4, Aristot. Physics 4.6, and Burnet, E.G.P. sect. 53.

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However, since they are here explaining the construction of the universe and meaning to speak in terms of physics, although we may somewhat criticize their physical theories, it is only fair to exempt them from the present inquiry; for it is the first principles in unchangeable things that we are investigating, and therefore we have to consider the generation of this kind of numbers.

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TheyThe Platonists. say that there is no generation of odd numbers,This statement was probably symbolical. They described the odd numbers as ungenerated because they likened them to the One, the principle of pure form (Ross ad loc.). which clearly implies that there is generation of even ones; and some hold that the even is constructed first out of unequals—the Great and Small—when they are equalized.Cf. Aristot. Met. 13.7.5. Therefore the inequality must apply to them before they are equalized. If they had always been equalized they would not have been unequal before; for there is nothing prior to that which has always been.

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Hence evidently it is not for the sake of a logical theory that they introduce the generation of numbers

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A difficulty, and a discredit to those who make light of the difficulty, arises out of the question how the elements and first principles are related to the the Good and the Beautiful. The difficulty is this: whether any of the elements is such as we mean when weAristotle speaks as a Platonist. See Introduction. speak of the Good or the Supreme Good, or whether on the contrary these are later in generation than the elements.

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It would seem that there is an agreement between the mythologists and some present-day thinkers,The Pythagoreans and Speusippus; cf. Aristot. Met. 12.7.10. who deny that there is such an element, and say that it was only after some evolution in the natural order of things that both the Good and the Beautiful appeared. They do this to avoid a real difficulty which confronts those who hold, as some do, that unity is a first principle.

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This difficulty arises not from ascribing goodness to the first principle as an attribute, but from treating unity as a principle, and a principle in the sense of an element, and then deriving number from unity. The early poets agree with this view in so far as they assert that it was not the original forces—such as Night, Heaven, Chaos or Ocean—but Zeus who was king and ruler.

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It was, however, on the ground of the changing of the rulers of the world that the poets were led to state these theories; because those of them who compromise by not describing everything in mythological language—e.g. PherecydesOf Syros (circa 600-525 B.C.). He made Zeus one of the three primary beings (Diels,Vorsokratiker201, 202). and certain others—make the primary generator the Supreme Good; and so do the Magi,The Zoroastrian priestly caste. and some of the later philosophers such as Empedocles and Anaxagoras: the one making Love an element,Cf. Aristot. Met. 3.1.13. and the other making Mind a first principle.Cf. Aristot. Met. 1.3.16.

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And of those who hold that unchangeable substances exist, somePlato; cf. Aristot. Met. 1.6.10. identify absolute unity with absolute goodness; but they considered that the essence of goodness was primarily unity.

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This, then, is the problem: which of these two views we should hold.

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Now it is remarkable if that which is primary and eternal and supremely self-sufficient does not possess this very quality, viz. self-sufficiency and immunity, in a primary degree and as something good. Moreover, it is imperishable and self-sufficient for no other reason than because it is good. Hence it is probably true to say that the first principle is of this nature.

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But to say that this principle is unity, or if not that, that it is an element, and an element of numbers, is impossible; for this involves a serious difficulty, to avoid which some thinkersSpeusippus and his followers; cf. sect. 3. have abandoned the theory (viz. those who agree that unity is a first principle and element, but of mathematical number). For on this view all units become identical with some good, and we get a great abundance of goods.If unity is goodness, and every unit is a kind of unity, every unit must be a kind of goodness—which is absurd.

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Further, if the Forms are numbers, all Forms become identical with some good. Again, let us assume that there are Ideas of anything that we choose. If there are Ideas only of goods, the Ideas will not be substancesBecause they are Ideas not of substances but of qualities.; and if there are Ideas of substances also, all animals and plants, and all things that participate in the Ideas, will be goods.Because the Ideas are goods.

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Not only do these absurdities follow, but it also follows that the contrary element, whether it is plurality or the unequal, i.e. the Great and Small, is absolute badness. Hence one thinkerSpeusippus. avoided associating the Good with unity, on the ground that since generation proceeds from contraries, the nature of plurality would then necessarily be bad.

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OthersPlato and Xenocrates. hold that inequality is the nature of the bad. It follows, then, that all things partake of the Bad except one—absolute unity; and that numbers partake of it in a more unmitigated form than do spatial magnitudesAs being more directly derived from the first principles. Cf. Aristot. Met. 1.9.23 n.; and that the Bad is the province for the activity of the Good, and partakes of and tends towards that which is destructive of the Good; for a contrary is destructive of its contrary.

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And if, as we said,Aristot. Met. 14.1.17. the matter of each thing is that which is it potentially—e.g., the matter of actual fire is that which is potentially fire—then the Bad will be simply the potentially Good.

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Thus all these objections follow because (1.) they make every principle an element; (2.) they make contraries principles; (3.) they make unity a principle; and (4.) they make numbers the primary substances, and separable, and Forms.

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If, then, it is impossible both not to include the Good among the first principles, and to include it in this way, it is clear that the first principles are not being rightly represented, nor are the primary substances. Nor is a certain thinkerEvidently Speusippus; cf. Aristot. Met. 14.4.3. right in his assumption when he likens the principles of the universe to that of animals and plants, on the ground that the more perfect forms are always produced from those which are indeterminate and imperfect, and is led by this to assert that this is true also of the ultimate principles; so that not even unity itself is a real thing.Speusippus argued that since all things are originally imperfect, unity, which is the first principle, must be imperfect, and therefore distinct from the good. Aristotle objects that the imperfect does not really exist, and so Speusippus deprives his first principle of reality.

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He is wrong; for even in the natural world the principles from which these things are derived are perfect and complete—for it is man that begets man; the seed does not come first.Cf. Aristot. Met. 9.8.5. It is absurd also to generate space simultaneously with the mathematical solids (for space is peculiar to particular things, which is why they are separable in space, whereas the objects of mathematics have no position) and to say that they must be somewhere, and yet not explain what their spatial position is.

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Those who assert that reality is derived from elements, and that numbers are the primary realities, ought to have first distinguished the senses in which one thing is derived from another, and then explained in what way number is derived from the first principles. Is it by mixture? But (a) not everything admits of mixturee.g. to admit of mixture a thing must first have a separate existence, and the Great-and-Small, which is an affection or quality of number (Aristot. Met. 14.1.14) cannot exist separately.; (b) the result of mixture is something different; and unity will not be separable,sc. when it has once been mixed. Cf. Aristot. De Gen. et Corr. 327b 21-26. nor will it be a distinct entity, as they intend it to be.

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Is it by composition, as we hold of the syllable? But (a) this necessarily implies position; (b) in thinking of unity and plurality we shall think of them separately. This, then, is what number will be—a unit plus plurality, or unity plus the Unequal.

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And since a thing is derived from elements either as inherent or as not inherent in it, in which way is number so derived? Derivation from inherent elements is only possible for things which admit of generation.And numbers are supposed to be eternal. Cf. Aristot. Met. 14.2.1-3. Is it derived as from seed?

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But nothing can be emitted from that which is indivisible.i.e., unity, being indivisible, cannot contribute the formal principle of generation in the way that the male parent contributes it. Is it derived from a contrary which does not persist? But all things which derive their being in this way derive it also from something else which does persist. Since, therefore, one thinkerSpeusippus: Plato. Cf. Aristot. Met. 14.1.5. regards unity as contrary to plurality, and another (treating it as the Equal) as contrary to the Unequal, number must be derived as from contraries.

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Hence there is something else which persists from which, together with one contrary, number is or has been derived.The objection is directed against the Platonist treatment of the principles as contraries (cf. Aristot. Met. 14.4.12), and may be illustrated by Aristot. Met. 12.1.5-2.2. Plurality, as the contrary of unity, is privation, not matter; the Platonists should have derived numbers from unity and some other principle which is truly material.

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Further, why on earth is it that whereas all other things which are derived from contraries or have contraries perish, even if the contrary is exhausted in producing them,Because it may be regarded as still potentially present. number does not perish? Of this no explanation is given; yet whether it is inherent or not, a contrary is destructive; e.g., Strife destroys the mixture.According to Empedocles Fr. 17 (Diels). It should not, however, do this; because the mixture is not its contrary.

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Nor is it in any way defined in which sense numbers are the causes of substances and of Being; whether as bounds,The theories criticized from this point onwards to Aristot. Met. 14.6.11 are primarily Pythagorean. See Introduction. e.g. as points are the bounds of spatial magnitudes,e.g. the line by 2 points, the triangle (the simplest plane figure) by 3, the tetrahedron (the simplest solid figure) by 4. and as EurytusDisciple of Philolaus; he flourished in the early fourth century B.C. determined which number belongs to which thing—e.g. this number to man, and this to horse—by using pebbles to copy the shape of natural objects, like those who arrange numbers in the form of geometrical figures, the triangle and the square.cf. Burnet, E.G.P. sect. 47.

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Or is it because harmony is a ratio of numbers, and so too is man and everything else? But in what sense are attributes—white, and sweet, and hot—numbers?This is an objection to the view that numbers are causes as bounds. And clearly numbers are not the essence of things, nor are they causes of the form; for the ratioOr formula. is the essence, and numberIn the sense of a number of material particles. is matter.

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E.g. the essence of flesh or bone is number only in the sense that it is three parts of fire and two of earth.Cf. Empedocles Fr. 96 (Diels). And the number, whatever it is, is always a number of something; of particles of fire or earth, or of units. But the essence is the proportion of one quantity to another in the mixture; i.e. no longer a number, but a ratio of the mixture of numbers, either of corporeal particles or of any other kind. Thus number is not an efficient cause—neither number in general, nor that which consists of abstract units—nor is it the matter, nor the formula or form of things. Nor again is it a final cause.

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The question might also be raised as to what the good is which things derive from numbers because their mixture can be expressed by a number, either one which is easily calculable,i.e., a simple ratio. or an odd number.It is hard to see exactly what this means. If the terms of a ratio are rational, one of them must be odd. Alexander says a ratio like 1 : 3 is meant. Oddness was associated with goodness (cf. Aristot. Met. 1.5.6). For in point of fact honey-water is no more wholesome if it is mixed in the proportion three times threeApparently the Pythagoreans meant by this three parts of water to three of honey. Aristotle goes on to criticize this way of expressing ratios.; it would be more beneficial mixed in no particular proportion, provided that it be diluted, than mixed in an arithmetical proportion, but strong.

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Again, the ratios of mixtures are expressed by the relation of numbers, and not simply by numbers; e.g., it is 3 : 2, not 3 X 2Cf. previous note.; for in products of multiplication the units must belong to the same genus. Thus the product of 1 x 2 x 3 must be measurable by 1, and the product of 4 X 5 x 7 by 4. Therefore all products which contain the same factor must be measurable by that factor. Hence the number of fire cannot be 2 X 5 X 3 X 7 if the number of water is 2 x 3.sc. because if so, a particle of fire would simply equal 35 particles of water.

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If all things must share in number, it must follow that many things are the same; i.e., that the same number belongs both to this thing and to something else. Is number, then, a cause; i.e., is it because of number that the object exists? Or is this not conclusive? E.g., there is a certain number of the sun’s motions, and again of the moon’s,5 in each case, according to Aristotle; cf. Aristot. Met. 12.7.9, 11. and indeed of the life and maturity of every animate thing. What reason, then, is there why some of these numbers should not be squares and others cubes, some equal and others double?

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There is no reason; all things must fall within this range of numbers if, as was assumed, all things share in number, and different things may fall under the same number. Hence if certain things happened to have the same number, on the Pythagorean view they would be the same as one another, because they would have the same form of number; e.g., sun and moon would be the same.Cf. previous note.

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But why are these numbers causes? There are seven vowels,In the Greek alphabet. seven strings to the scale,In the old heptachord; cf. note on Aristot. Met. 5.11.4. seven Pleiads; most animals (though not allCf. Aristot. Hist. An. 576a 6.) lose their teeth in the seventh year; and there were seven heroes who attacked Thebes. Is it, then, because the number 7 is such as it is that there were seven heroes, or that the Pleiads consist of seven stars? Surely there were seven heroes because of the seven gates, or for some other reason, and the Pleiads are seven because we count them so; just as we count the Bear as 12, whereas others count more stars in both.

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Indeed, they assert also that Ξ, Ψ and Ζ are concords,According to Alexander ζ was connected with the fourth, ξ with the fifth, and ψ with the octave. and that because there are three concords, there are three double consonants. They ignore the fact that there might be thousands of double consonants—because there might be one symbol for ΓΡ. But if they say that each of these letters is double any of the others, whereas no other is,θ, φ , and χ are aspirated, not double, consonants. and that the reason is that there are three regionsPalate, lips, and teeth. of the mouth, and that one consonant is combined with σ in each region, it is for this reason that there are only three double consonants, and not because there are three concords—because there are really more than three; but there cannot be more than three double consonants.

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Thus these thinkers are like the ancient Homeric scholars, who see minor similarities but overlook important ones.

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Some say that there are many correspondences of this kind; e.g., the middle notesi.e., the μέση(fourth) and παραμέση(fifth), whose ratios can be expressed as 8 : 6, 9 : 6. of the octave are respectively 8 and 9, and the epic hexameter has seventeen syllables, which equals the sum of these two; and the line scans in the first half with nine syllables, and in the second with eight.i.e., a dactylic hexameter whose sixth foot is always a spondee or trochee has nine syllables in the first three feet and eight in the last three. For τὸ δεξιόν meaning the first part of a metrical system see Bassett,Journal of Classical Philology 11.458-460.

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And they point out that the interval from α to ω in the alphabet is equal to that from the lowest note of a flute to the highest, whose number is equal to that of the whole system of the universe.Alexander suggests that the number 24 may have been made up of the 12 signs of the zodiac, the 8 spheres (fixed stars, five planets, sun and moon) and 4 elements. We must realize that no one would find any difficulty either in discovering or in stating such correspondences as these in the realm of eternal things, since they occur even among perishable things.

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As for the celebrated characteristics of number, and their contraries, and in general the mathematical properties, in the sense that some describe them and make them out to be causes of the natural world, it would seem that if we examine them along these lines, they disappear; for not one of them is a cause in any of the senses which we distinguished with until respect to the first Principles.Cf. Aristot. Met. 1.3.1, Aristot. Met. 5.1, 2.

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There is a sense, however, in which these thinkers make it clear that goodness is predicable of numbers, and that the odd, the straight, the equal-by-equal,i.e., square. and the powersProbably their power of being represented as regular figures; e.g. the triangularity of 3 or 6. of certain numbers, belong to the series of the Beautiful.Cf. Aristot. Met. 1.5.6. For the seasons are connected with a certain kind of numberi.e., 4.; and the other examples which they adduce from mathematical theorems all have the same force.

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Hence they would seem to be mere coincidences, for they are accidental; but all the examples are appropriate to each other, and they are one by analogy. For there is analogy between all the categories of Being—as straight is in length, so is level in breadth, perhaps odd in number, and white in color.

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Again, it is not the Ideal numbers that are the causes of harmonic relations, etc. (for Ideal numbers, even when they are equal, differ in kind, since their units also differ in kind)Aristotle has argued (Aristot. Met. 13.6-8.) that if the Ideal numbers differ in kind, their units must differ in kind. Hence even equal numbers, being composed of different units, must be different in kind. In point of fact, since each ideal number is unique, no two of them could be equal.; so on this ground at least we need not posit Forms.

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Such, then, are the consequences of the theory, and even more might be adduced. But the mere fact that the Platonists find so much trouble with regard to the generation of Ideal numbers, and can in no way build up a system, would seem to be a proof that the objects of mathematics are not separable from sensible things, as some maintain, and that the first principles are not those which these thinkers assume.

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+ + + From 6f815c84eb40cc37dd9abfdf641b30a28a1905ad Mon Sep 17 00:00:00 2001 From: lcerrato Date: Wed, 8 May 2024 20:46:30 -0400 Subject: [PATCH 2/6] (grc_conversion) tlg0086 translation conversion continues #1399 --- .../tlg025/tlg0086.tlg025.perseus-eng2.xml | 44 +- data/tlg0086/tlg029/__cts__.xml | 6 + .../tlg029/tlg0086.tlg029.perseus-eng1.xml | 1206 ++++------------- .../tlg029/tlg0086.tlg029.perseus-eng2.xml | 304 +++++ .../tlg029/tlg0086.tlg029.perseus-grc2.xml | 176 +-- 5 files changed, 714 insertions(+), 1022 deletions(-) create mode 100644 data/tlg0086/tlg029/tlg0086.tlg029.perseus-eng2.xml diff --git a/data/tlg0086/tlg025/tlg0086.tlg025.perseus-eng2.xml b/data/tlg0086/tlg025/tlg0086.tlg025.perseus-eng2.xml index ea3dd4e53..6c81df1d9 100644 --- a/data/tlg0086/tlg025/tlg0086.tlg025.perseus-eng2.xml +++ b/data/tlg0086/tlg025/tlg0086.tlg025.perseus-eng2.xml @@ -33,7 +33,7 @@ -The Metaphysics + The Metaphysics Aristotle Hugh Tredennick @@ -288,7 +288,7 @@

As to what this participation or imitation may be, they left this an open question.)

Further, he states that besides sensible things and the Forms there exists an intermediate class, the objects of mathematics,i.e. arithmetical numbers and geometrical figures. which differ from sensible things in being eternal and immutable, and from the Forms in that there are many similar objects of mathematics, whereas each Form is itself unique.

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Now since the Forms are the causes of everything else, he supposed that their elements are the elements of all things. Accordingly the material principle is the Great and Small, and the essence <or formal principle> is the One, since the numbers are derived from the Great and Small by participation in the the One.

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Now since the Forms are the causes of everything else, he supposed that their elements are the elements of all things. Accordingly the material principle is the Great and Small, and the essence 〈or formal principle〉 is the One, since the numbers are derived from the Great and Small by participation in the the One.

In treating the One as a substance instead of a predicate of some other entity, his teaching resembles that of the Pythagoreans, and also agrees with it in stating that the numbers are the causes of Being in everything else; but it is peculiar to him to posit a duality instead of the single Unlimited, and to make the Unlimited consist of the Great and Small. He is also peculiar in regarding the numbers as distinct from sensible things, whereas they hold that things themselves are numbers, nor do they posit an intermediate class of mathematical objects.

@@ -407,7 +407,7 @@

Further, it becomes necessary to set up another kind of number (with which calculation deals), and all the objects which are called intermediate by some thinkers.Cf. vi. 4. But how or from what principles can these be derived? or on what grounds are they to be considered intermediate between things here and Ideal numbers? Further, each of the units in the number 2 comes from a prior 2; but this is impossible.i.e., if 2 is derived from a prior 2 (the Indeterminate Dyad; Aristotle always regards this as a number 2), and at the same time consists of two units or 1s, 2 will be prior both to itself and to 1.

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Further, why should a number <of units>, taken together, be one thing? And further, in addition to the above objections, if the units are unlike, they should be treated as the thinkers who assume two or four elements treat those elements; for not one of them applies the term element to the common substrate, e.g. body, but to fire and earth—whether there is a common substrate (i.e. body) or not.In the Aristot. De Gen. et Corr. 320b 23Aristotle says that there is not.

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Further, why should a number 〈of units〉, taken together, be one thing? And further, in addition to the above objections, if the units are unlike, they should be treated as the thinkers who assume two or four elements treat those elements; for not one of them applies the term element to the common substrate, e.g. body, but to fire and earth—whether there is a common substrate (i.e. body) or not.In the Aristot. De Gen. et Corr. 320b 23Aristotle says that there is not.

As it is, the One is spoken of as though it were homogeneous, like fire or water. But if this is so, the numbers will not be substances. And if there is an absolute One which is a principle, clearly the term one is ambiguous; otherwise this is impossible.This last sentence shows that in what goes before A. has been regarding the Platonic One as a unit. If this is so, he says, substance cannot be composed of it. If on the other hand the One is something different from the unit, they ought to make this clear.

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Yet how is this possible? for then there would be a class of healthy things apart from those which are sensible and from the Ideally healthy. Nor, at the same time, is it true that mensuration is concerned with sensible and perishable magnitudes; for then it would perish as they do. Nor, again, can astronomy be concerned with sensible magnitudes or with this heaven of ours;

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for as sensible lines are not like those of which the geometrician speaks (since there is nothing sensible which is straight or curved in that sense; the circlei.e., the visible circle which we draw. Like the ruler, it is geometrically imperfect; thus they touch at more than one point. touches the ruler not at a point, but <along a line> as Protagoras used to say in refuting the geometricians), so the paths and orbits of our heaven are not like those which astronomy discusses, nor have the symbols of the astronomer the same nature as the stars.

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for as sensible lines are not like those of which the geometrician speaks (since there is nothing sensible which is straight or curved in that sense; the circlei.e., the visible circle which we draw. Like the ruler, it is geometrically imperfect; thus they touch at more than one point. touches the ruler not at a point, but 〈along a line〉 as Protagoras used to say in refuting the geometricians), so the paths and orbits of our heaven are not like those which astronomy discusses, nor have the symbols of the astronomer the same nature as the stars.

Some, however, say that these so-called Intermediates between Forms and sensibles do exist: not indeed separately from the sensibles, but in them. It would take too long to consider in detail all the impossible consequences of this theory, but it will be sufficient to observe the following.

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On the other hand if they are numerically one, and each of the principles is one, and not, as in the case of sensible things, different in different instances (e.g. since a given syllable is always the same in kind, its first principles are always the same in kind, but only in kind, since they are essentially different in number)—if the first principles are one, not in this sense, but numerically, there will be nothing else apart from the elements; for numerically one and individual are identical in meaning. This is what we mean by individual: the numerically one; but by universal we mean what is predicable of individuals.

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Hence just as, if the elements of languageOr letters of the alphabet. Cf. Aristot. Met. 1.9.36n. were limited in number, the whole of literature would be no more than those elements—that is, if there were not two nor more than two of the same <so it would be in the case of existing things and their principles>.For the answer to the problem see Aristot. Met. 12.4-5, Aristot. Met. 13.10.

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Hence just as, if the elements of languageOr letters of the alphabet. Cf. Aristot. Met. 1.9.36n. were limited in number, the whole of literature would be no more than those elements—that is, if there were not two nor more than two of the same 〈so it would be in the case of existing things and their principles〉.For the answer to the problem see Aristot. Met. 12.4-5, Aristot. Met. 13.10.

(ix.) There is a difficulty, as serious as any, which has been left out of account both by present thinkers and by their predecessors: whether the first principles of perishable and imperishable things are the same or different. For if they are the same, how is it that some things are perishable and others imperishable, and for what cause?

@@ -1037,7 +1037,7 @@

Again, there will be an infinite progression, and existing things will be not only half as many again, but even more.

For again it will be possible to deny the intermediate in reference both to its assertion and to its negation, and the result will be somethingIf besides A and not-A there is an intermediate B, besides B and not-B there will be an intermediate C which is neither B nor not-B; and so on.; for its essence is something distinct.

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Again, when a man is asked whether a thing is white and says no, he has denied nothing except that it is <white>, and its not-being <white> is a negation.

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Again, when a man is asked whether a thing is white and says no, he has denied nothing except that it is 〈white〉, and its not-being 〈white〉 is a negation.

Now this view has occurred to certain people in just the same way as other paradoxes have also occurred; for when they cannot find a way out from eristic arguments, they submit to the argument and admit that the conclusion is true. Some, then, hold the theory for this kind of reason, and others because they require an explanation for everything. In dealing with all such persons the starting-point is from definition;

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Sometimes these things are said to be one in this sense, and sometimes their higher genus is said to be one and the same (if they are final species of their genus)—the genus, that is, which is above the genera of which their proximate genus is one; e.g., the isosceles and equilateral triangles are one and the same figure (because they are both triangles), but not the same triangles.

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(d) Again, things are said to be one when the definition stating the essence of one is indistinguishable from a definition explaining the other; for in itself every definition is distinguishable <into genus and differentiae>. In this way that which increases and decreases is one, because its definition is one; just as in the case of planes the definition of the form is one.

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(d) Again, things are said to be one when the definition stating the essence of one is indistinguishable from a definition explaining the other; for in itself every definition is distinguishable 〈into genus and differentiae〉. In this way that which increases and decreases is one, because its definition is one; just as in the case of planes the definition of the form is one.

And in general those things whose concept, which conceives the essence, is indistinguishable and cannot be separated either in time or in place or in definition, are in the truest sense one; and of these such as are substances are most truly one. For universally such things as do not admit of distinction are called one in so far as they do not admit of it; e.g., if man qua man does not admit of distinction, he is one man; and similarly if qua animal, he is one animal; and if qua magnitude, he is one magnitude.

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There is no difference between the man is recovering and the man recovers; or between the man is walking or cutting and the man walks or cuts; and similarly in the other cases.

(3.) Again, to be and is mean that a thing is true, and not to be that it is false.

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Similarly too in affirmation and negation; e.g., in Socrates is cultured is means that this is true; or in Socrates is not-white that this is true; but in the diagonal is not commensurableCf. Aristot. Met. 1.2.15.is not means that the statement is false. (4.) Again, to be <or is> means that some of these statements can be made in virtue of a potentiality and others in virtue of an actuality.

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Similarly too in affirmation and negation; e.g., in Socrates is cultured is means that this is true; or in Socrates is not-white that this is true; but in the diagonal is not commensurableCf. Aristot. Met. 1.2.15.is not means that the statement is false. (4.) Again, to be 〈or is〉 means that some of these statements can be made in virtue of a potentiality and others in virtue of an actuality.

For we say that both that which sees potentially and that which sees actually is a seeing thing. And in the same way we call understanding both that which can use the understanding, and that which does ; and we call tranquil both that in which tranquillity is already present, and that which is potentially tranquil.

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Further, there are the properties in virtue of which the things which possess them are called relative; e.g., equality is relative because the equal is relative, and similarity because the similar is relative. Other things are accidentally relative; e.g., a man is relative because he happens to be double something else, and double is a relative term; or white is relative if the same thing happens to be white as well as double.

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Perfect <or complete> means: (a) That outside which it is impossible to find even a single one of its parts; e.g., the complete time of each thing is that outside which it is impossible to find any time which is a part of it. (b) That which, in respect of goodness or excellence, cannot be surpassed in its kind; e.g., a doctor and a musician are perfect when they have no deficiency in respect of the form of their peculiar excellence.

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Perfect 〈or complete〉 means: (a) That outside which it is impossible to find even a single one of its parts; e.g., the complete time of each thing is that outside which it is impossible to find any time which is a part of it. (b) That which, in respect of goodness or excellence, cannot be surpassed in its kind; e.g., a doctor and a musician are perfect when they have no deficiency in respect of the form of their peculiar excellence.

And thus by an extension of the meaning we use the term in a bad connection, and speak of a perfect humbug and a perfect thief; since indeed we call them good— e.g. a good thief and a good humbug.

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Again, a negative affix may mean having something in a small degree—e.g. stoneless— that is, having it in some rudimentary manner. Again, it may mean having it not easily or not well; e.g., uncutable means not only that which cannot be cut, but that which cannot be cut easily or well. And again, it may mean not having a thing at all; for it is not the one-eyed man, but the man who lacks sight in both eyes, who is called blind. Hence not every man is good or bad, moral or immoral; there is also the intermediate state.

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To have <or possess> is used in various senses. (a) To direct in accordance with one’s own nature or impulse; whence we say that fever possesses a man, and despots possess cities, and people who wear clothes possess them. (b) We speak of anything as having in which, as receptive material, something is present. E.g., the bronze has the shape of the statue, and the body has the disease.

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To have 〈or possess〉 is used in various senses. (a) To direct in accordance with one’s own nature or impulse; whence we say that fever possesses a man, and despots possess cities, and people who wear clothes possess them. (b) We speak of anything as having in which, as receptive material, something is present. E.g., the bronze has the shape of the statue, and the body has the disease.

(c) In the sense that the container holds the contained; for when A is contained in B, we say that A is held by B. E.g., we say that the vessel holds the liquid, and the city holds men, and the ship holds sailors, and so too that the whole holds the parts.

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(d) The same term is applied to that which prevents anything from moving or acting in accordance with its own impulse; as pillars hold <up> the weights which are imposed upon them, and as the poets make AtlasCf. Hes. Th. 517. hold up the heaven, because otherwise it would fall upon the earth (as some of the physicistse.g., Empedocles held that the heavens were kept in place by the velocity of their rotation;Aristot. De Caelo 284a 24, 295a 16 (Ritter and Preller, 170 b). maintain also).

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(d) The same term is applied to that which prevents anything from moving or acting in accordance with its own impulse; as pillars hold 〈up〉 the weights which are imposed upon them, and as the poets make AtlasCf. Hes. Th. 517. hold up the heaven, because otherwise it would fall upon the earth (as some of the physicistse.g., Empedocles held that the heavens were kept in place by the velocity of their rotation;Aristot. De Caelo 284a 24, 295a 16 (Ritter and Preller, 170 b). maintain also).

It is in this sense that we say that that which holds together holds what it holds together; because otherwise the latter would disperse, each part in accordance with its own impulse.

To be in a thing is used similarly in senses corresponding to those of to have.

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(d) In the sense that the form is made out of the part of its definition; as, e.g., man is made out of two-footed and the syllable out of its elementIn the sense that στοιχεῖον(letter) forms part of the definition of syllable. (this is a different way from that in which the statue is made out of the bronze; for the composite entity is made out of perceptible material, but the form is also made out of the material of the form).

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These, then, are some of the meanings of from <or out of>, but (e) sometimes one of these senses only partially applies; e.g., the child comes from the father and mother, and plants from the earth, because they come from some part of those things. (f) It means after in time; e.g., we say that night comes from day, and storm from fine weather, because one comes after the other.

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These, then, are some of the meanings of from 〈or out of〉, but (e) sometimes one of these senses only partially applies; e.g., the child comes from the father and mother, and plants from the earth, because they come from some part of those things. (f) It means after in time; e.g., we say that night comes from day, and storm from fine weather, because one comes after the other.

And we speak thus of some of these things in view of their alternation with each other, as in the examples just mentioned, and of others in view merely of their succession in time; e.g., the voyage was made from the equinox, meaning that it was made after it; and the Thargelia are from the Dionysia, meaning after the Dionysia.The (city) Dionysia were celebrated in March; the Thargelia (a festival in honor of Apollo and Artemis) at the end of May.

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and a man is not mutilated if he loses flesh or his spleen, but if he loses some extremity; and not every extremity, but only such as cannot grow again when completely removed. Hence bald people are not mutilated.

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The term genus <or race> is used: (a) When there is a continuous generation of things of the same type; e.g., as long as the human race exists means as long as the generation of human beings is continuous. (b) Of anything from which things derive their being as the prime mover of them into being. Thus some are called Hellenes by race, and others Ionians, because some have Hellen and others Ion as their first ancestor.

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The term genus 〈or race〉 is used: (a) When there is a continuous generation of things of the same type; e.g., as long as the human race exists means as long as the generation of human beings is continuous. (b) Of anything from which things derive their being as the prime mover of them into being. Thus some are called Hellenes by race, and others Ionians, because some have Hellen and others Ion as their first ancestor.

(Races are called after the male ancestor rather than after the material.Aristotle regards the mother as providing the material, and the father the formal element of the child. Cf. Aristot. Met. 1.6.8, Aristot. Met. 8.4.5. Some derive their race from the female as well; e.g. the descendants of PyrrhaWife of Deucalion, the Greek Noah.. ) (c) In the sense that the plane is the genus of plane figures, and the solid of solids (for each one of the figures is either a particular plane or a particular solid); i.e., that which underlies the differentiae.

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for it assumes (a) that the false man is he who is able to deceive, i.e. the man who knows and is intelligent; (b) that the man who is willingly bad is better. This false assumption is due to the induction; for when he says that the man who limps willingly is better than he who does so unwillingly, he means by limping pretending to limp. For if he is willingly lame, he is presumably worse in this case just as he is in the case of moral character.

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Accident <or attribute> means that which applies to something and is truly stated, but neither necessarily nor usually; as if, for example, while digging a hole for a plant one found a treasure. Then the finding of treasure is an accident to the man who is digging the hole; for the one thing is not a necessary consequence or sequel of the other, nor does one usually find treasure while planting.

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Accident 〈or attribute〉 means that which applies to something and is truly stated, but neither necessarily nor usually; as if, for example, while digging a hole for a plant one found a treasure. Then the finding of treasure is an accident to the man who is digging the hole; for the one thing is not a necessary consequence or sequel of the other, nor does one usually find treasure while planting.

And a cultured man might be white; but since this does not happen necessarily or usually, we call it an accident. Thus since there are attributes and subjects, and some attributes apply to their subjects only at a certain place and time, any attribute which applies to a subject, but not because it was a particular subject or time or place, will be an accident.

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But as for the accidental term, e.g. cultured or white, since it has two meanings, it is not true to say that the term itself is the same as its essence; for both the accidental term and that of which it is an accident are white, so that in one sense the essence and the term itself are the same, and in another they are not, because the essence is not the same as the man or the white man, but it is the same as the affection.

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The absurdity <of separating a thing from its essence> will be apparent also if one supplies a name for each essence; for then there will be another essence besides the original one, e.g. the essence of horse will have a further essence. Yet why should not some things be identified with their essence from the outset,i.e. to avoid the infinite series implied in the last sentence. if essence is substance? Indeed not only are the thing and its essence one, but their formula is the same, as is clear from what we have just stated; for it is not by accident that the essence of one, and the one, are one.

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The absurdity 〈of separating a thing from its essence〉 will be apparent also if one supplies a name for each essence; for then there will be another essence besides the original one, e.g. the essence of horse will have a further essence. Yet why should not some things be identified with their essence from the outset,i.e. to avoid the infinite series implied in the last sentence. if essence is substance? Indeed not only are the thing and its essence one, but their formula is the same, as is clear from what we have just stated; for it is not by accident that the essence of one, and the one, are one.

Moreover, if they are different, there will be an infinite series; for the essence of one and the one will both exist; so that in that case too the same principle will apply.i.e. since there is a distinct term essence of one besides one, there will be a third distinct term essence of essence of one; and so on as in the case of horse above. Clearly, then, in the case of primary and self-subsistent terms, the individual thing and its essence are one and the same.

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Since substance in the sense of substrate or matter is admittedly substance, and this is potential substance, it remains to explain the nature of the actual substance of sensible things. Now DemocritusCf. Aristot. Met. 1.4.11. apparently assumes three differences in substance; for he says that the underlying body is one and the same in material, but differs in figure, i.e. shape; or inclination, i.e. position; or intercontact, i.e. arrangement.

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But evidently there are many differences; e.g. some things are defined by the way in which their materials are combined, as, for example, things which are unified by mixture, as honey-water; or by ligature, as a faggot; or by glue, as a book; or by clamping, as a chest; or by more than one of these methods. Other things are defined by their position, e.g. threshold and lintel (for these differ in being situated in a particular way); and others by place <or direction>, e.g. the winds; others by time, e.g. dinner and breakfast; and others by the attributes peculiar to sensible things, e.g. hardness and softness, density and rarity, dryness and humidity. Some are distinguished by some of these differences, and others by all of them; and in general some by excess and some by defect.

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But evidently there are many differences; e.g. some things are defined by the way in which their materials are combined, as, for example, things which are unified by mixture, as honey-water; or by ligature, as a faggot; or by glue, as a book; or by clamping, as a chest; or by more than one of these methods. Other things are defined by their position, e.g. threshold and lintel (for these differ in being situated in a particular way); and others by place 〈or direction〉, e.g. the winds; others by time, e.g. dinner and breakfast; and others by the attributes peculiar to sensible things, e.g. hardness and softness, density and rarity, dryness and humidity. Some are distinguished by some of these differences, and others by all of them; and in general some by excess and some by defect.

Hence it is clear that is has the same number of senses; for a thing is a threshold because it is situated in a particular way, and to be a threshold means to be situated in this particular way, and to be ice means to be condensed in this particular way. Some things have their being defined in all these ways: by being partly mixed, partly blended, partly bound, partly condensed, and partly subjected to all the other different processes; as, for example, a hand or a foot.

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Moreover, things which exist by nature but are not substances have no matter; their substrate is their substance. E.g., what is the cause of an eclipse; what is its matter? It has none; it is the moon which is affected. What is the moving cause which destroys the light? The earth. There is probably no final cause. The formal cause is the formula; but this is obscure unless it includes the efficient cause.

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E.g., what is an eclipse? A privation of light; and if we add caused by the earth’s intervention, this is the definition which includes the <efficient> cause. In the case of sleep it is not clear what it is that is proximately affected. Is it the animal? Yes; but in respect of what, and of what proximately? The heart, or some other part. Again, by what is it affected? Again, what is the affection which affects that part, and not the whole animal? A particular kind of immobility? Yes; but in virtue of what affection of the proximate subject is it this?

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E.g., what is an eclipse? A privation of light; and if we add caused by the earth’s intervention, this is the definition which includes the 〈efficient〉 cause. In the case of sleep it is not clear what it is that is proximately affected. Is it the animal? Yes; but in respect of what, and of what proximately? The heart, or some other part. Again, by what is it affected? Again, what is the affection which affects that part, and not the whole animal? A particular kind of immobility? Yes; but in virtue of what affection of the proximate subject is it this?

Since some things both are and are not, without being liable to generation and destructionCf. Aristot. Met. 6.3.1, Aristot. Met. 7.8.3.—e.g. points,Cf. Aristot. Met. 3.5.8, 9. if they exist at all; and in general the forms and shapes of things (because white does not come to be, but the wood becomes white, since everything which comes into being comes from something and becomes something)—not all the contrariesi.e., we must distinguish contraries in the sense of contrary qualities from contraries in the sense of things characterized by contrary qualities. can be generated from each other. White is not generated from black in the same way as a white man is generated from a black man; nor does everything contain matter, but only such things as admit of generation and transformation into each other.

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Also in the case of evils the end or actuality must be worse than the potentiality; for that which is capable is capable alike of both contraries.

Clearly, then, evil does not exist apart from things ; for evil is by nature posterior to potentiality.The argument is presumably as follows (the fallacy, as pointed out by Bonitz, is indicated in parenthesis): That which has a separate substantial existence is actuality. Actuality is prior (substantially) to potentiality. Potentiality is prior to evil (in the moral scale. But since by evil Aristotle means the actualization of a potentiality for evil, potentiality is substantially posterior to evil). Therefore that which has a separate substantial existence is prior to evil; i.e., evil does not exist apart from particular instances of evil. The argument is directed against the Platonic Idea of evil (Plat. Rep. 476a); and the corollary which follows against the identification of Evil with one of the principles of the universe (Aristot. Met. 1.6.10, Aristot. Met. 12.10.6, Aristot. Met. 14.4.10, 11; cf. Plat. Laws 896e, Plat. Laws 898c). Nor is there in things which are original and eternal any evil or error, or anything which has been destroyed—for destruction is an evil.

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Geometrical constructions, too, are discovered by an actualization, because it is by dividing that we discover them. If the division were already done, they would be obvious; but as it is the division is only there potentially. Why is the sum of the interior angles of a triangle equal to two right angles? Because the angles about one point <in a straight line> are equal to two right angles. If the line parallel to the side had been already drawn, the answer would have been obvious at sight.The figure, construction and proof are as follows: ***

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Geometrical constructions, too, are discovered by an actualization, because it is by dividing that we discover them. If the division were already done, they would be obvious; but as it is the division is only there potentially. Why is the sum of the interior angles of a triangle equal to two right angles? Because the angles about one point 〈in a straight line〉 are equal to two right angles. If the line parallel to the side had been already drawn, the answer would have been obvious at sight.The figure, construction and proof are as follows: ***

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Why is the angle in a semicircle always a right angle? If three lines are equal, the two forming the base, and the one set upright from the middle of the base, the answer is obvious to one who knows the former proposition.Aristotle implies a proof something after this fashion: FIGURE BAC is an angle in a semicircle. From D, the mid-point of the diameter BC, draw a perpendicular DE to meet the circumference at E. Join EB, EC.*** Thus it is evident that the potential constructions are discovered by being actualized. The reason for this is that the actualization is an act of thinking. Thus potentiality comes from actuality (and therefore it is by constructive action that we acquire knowledge). <But this is true only in the abstract>, for the individual actuality is posterior in generation to its potentiality.This whole passage (sects. 4, 5) should be compared with Aristot. Met. 9.8.3-7, where it logically belongs.

+

Why is the angle in a semicircle always a right angle? If three lines are equal, the two forming the base, and the one set upright from the middle of the base, the answer is obvious to one who knows the former proposition.Aristotle implies a proof something after this fashion: FIGURE BAC is an angle in a semicircle. From D, the mid-point of the diameter BC, draw a perpendicular DE to meet the circumference at E. Join EB, EC.*** Thus it is evident that the potential constructions are discovered by being actualized. The reason for this is that the actualization is an act of thinking. Thus potentiality comes from actuality (and therefore it is by constructive action that we acquire knowledge). 〈But this is true only in the abstract〉, for the individual actuality is posterior in generation to its potentiality.This whole passage (sects. 4, 5) should be compared with Aristot. Met. 9.8.3-7, where it logically belongs.

The terms being and not-being are used not only with reference to the types of predication, and to the potentiality or actuality, or non-potentiality and non-actuality, of these types, but also (in the strictest senseThis appears to contradict Aristot. Met. 6.4.3. But it is just possible to interpret κυριώτατα(with Jaeger) as in the commonest sense. ) to denote truth and falsity. This depends, in the case of the objects, upon their being united or divided; so that he who thinks that what is divided is divided, or that what is united is united, is right; while he whose thought is contrary to the real condition of the objects is in error. Then when do what we call truth and falsity exist or not exist? We must consider what we mean by these terms.

@@ -2696,7 +2696,7 @@

As for what is in the sense of what is true or what is accidental , the former depends upon a combination in thought, and is an affection of thought (hence we do not look for the principles of Being in this sense, but only for those of objective and separable Being) the latter is not necessary but indeterminate (I mean the accidental); and of such a thing the causes are indefinite and cannot be reduced to a system.

-

Teleology is found in events which come about in the course of nature or as a result of thought.This section is taken from Aristot. Physics 2.5, 6. It is chance <or luck> when one of these comes about by accident; for a thing may be a cause, just as it may exist, either per se or accidentally. Chance is an accidental cause of normally purposive teleological events.

+

Teleology is found in events which come about in the course of nature or as a result of thought.This section is taken from Aristot. Physics 2.5, 6. It is chance 〈or luck〉 when one of these comes about by accident; for a thing may be a cause, just as it may exist, either per se or accidentally. Chance is an accidental cause of normally purposive teleological events.

Hence chance and thought have the same sphere of action, for there is no purpose without thought. Causes from which chance results may come about are indeterminate; hence chance is inscrutable to human calculation, and is a cause only accidentally, but in the strictest sense is a cause of nothing.

@@ -3242,7 +3242,7 @@

The fact that the units are indivisible will make no difference; because points are indivisible also, but nevertheless a pair of points is not anything distinct from the two single points.

Moreover we must not fail to realize this: that on this theory it follows that 2’s are prior and posterior, and the other numbers similarly.

-

Let it be granted that the 2’s in 4 are contemporaneous; yet they are prior to those in 8, and just as the <determinate> 2 produced the 2’s in 4, soIn each case the other factor is the indeterminate dyad (cf. sect. 18). they produced the 4’s in 8. Hence if the original 2 is an Idea, these 2’s will also be Ideas of a sort.

+

Let it be granted that the 2’s in 4 are contemporaneous; yet they are prior to those in 8, and just as the 〈determinate〉 2 produced the 2’s in 4, soIn each case the other factor is the indeterminate dyad (cf. sect. 18). they produced the 4’s in 8. Hence if the original 2 is an Idea, these 2’s will also be Ideas of a sort.

And the same argument applies to the units, because the units in the original 2 produce the four units in 4; and so all the units become Ideas, and an Idea will be composed of Ideas. Hence clearly those things also of which these things are Ideas will be composite; e.g., one might say that animals are composed of animals, if there are Ideas of animals.

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But we must inquire in general whether eternal things can be composed of elements. If so, they will have matter; for everything which consists of elements is composite.

-

Assuming, then, that that which consists of anything, whether it has always existed or it came into being, must come into being <if at all> out of that of which it consists; and that everything comes to be that which it comes to be out of that which is it potentially (for it could not have come to be out of that which was not potentially such, nor could it have consisted of it); and that the potential can either be actualized or not; then however everlasting number or anything else which has matter may be, it would be possible for it not to exist, just as that which is any number of years old is as capable of not existing as that which is one day old. And if this is so, that which has existed for so long a time that there is no limit to it may also not exist.

+

Assuming, then, that that which consists of anything, whether it has always existed or it came into being, must come into being 〈if at all〉 out of that of which it consists; and that everything comes to be that which it comes to be out of that which is it potentially (for it could not have come to be out of that which was not potentially such, nor could it have consisted of it); and that the potential can either be actualized or not; then however everlasting number or anything else which has matter may be, it would be possible for it not to exist, just as that which is any number of years old is as capable of not existing as that which is one day old. And if this is so, that which has existed for so long a time that there is no limit to it may also not exist.

Therefore things which contain matter cannot be eternal, that is, if that which is capable of not existing is not eternal, as we have had occasion to say elsewhere.Aristot. Met. 9.8.15-17, Aristot. De Caelo 1.12. Now if what we have just been saying—that no substance is eternal unless it is actuality—is true universally, and the elements are the matter of substance, an eternal substance can have no elements of which, as inherent in it, it consists.

diff --git a/data/tlg0086/tlg029/__cts__.xml b/data/tlg0086/tlg029/__cts__.xml index 1fd9b8338..a4f3ab4cb 100644 --- a/data/tlg0086/tlg029/__cts__.xml +++ b/data/tlg0086/tlg029/__cts__.xml @@ -7,4 +7,10 @@ Οἰκονομικά Aristotle. Metaphysics; Oeconomica and Magna Moralia. Armstrong, George Cyril, editor. London: William Heinemann Ltd.; Cambridge, MA: Harvard University Press, 1935 (printing). + + + Economics + Aristotle. Metaphysics; Oeconomica and Magna Moralia. Armstrong, George Cyril, translator. London: William Heinemann Ltd.; Cambridge, MA: Harvard University Press, 1935 (printing). + + \ No newline at end of file diff --git a/data/tlg0086/tlg029/tlg0086.tlg029.perseus-eng1.xml b/data/tlg0086/tlg029/tlg0086.tlg029.perseus-eng1.xml index a88a1fcae..b446e5b8a 100644 --- a/data/tlg0086/tlg029/tlg0086.tlg029.perseus-eng1.xml +++ b/data/tlg0086/tlg029/tlg0086.tlg029.perseus-eng1.xml @@ -1,922 +1,304 @@ - - - -%PersProse; -]> - - - + + + + - - Economics (English). Machine readable text - Aristotle - - Perseus Project, Tufts University - Gregory Crane - - Prepared under the supervision of - Lisa Cerrato - William Merrill - Elli Mylonas - David Smith - - The Annenberg CPB/Project + + Economics + Aristotle + George Cyril Armstrong + Perseus Project, Tufts University + Gregory Crane + + Prepared under the supervision of + Lisa Cerrato + William Merrill + Elli Mylonas + David Smith + + The Annenberg CPB/Project - About 91Kb - - Trustees of Tufts University - Medford, MA - Perseus Project - - - Text was scanned at St. Olaf Spring, 1992. - - - - - Aristotle - Aristotle in 23 Volumes, Vol. 18, translated by G.C. Armstrong. - - - Cambridge, MA, Harvard University Press; London, William - Heinemann Ltd. - 1935 - - - - + + + Trustees of Tufts University + Medford, MA + Perseus Digital Library Project + Perseus 2.0 + tlg0086.tlg029.perseus-eng2.xml + + Available under a Creative Commons Attribution-ShareAlike 4.0 International License + + + + + + + The Metaphysics; The Oeconomica and The Magna Moralia + Aristotle + George Cyril Armstrong + + William Heinemann Ltd. + London + Harvard University Press + Cambridge, MA + 1935 + + + + Loeb Classical Library + + Internet Archive + + - - - - - - - - - English - Greek - - - - - June, 1993 - - wpm - (n/a) - - Tagged in conformance with Prose.e dtd. - - - 7/27, 1993 - - em - (n/a) - - Put Bekker line 1 milestone tags at the beginning of each section so that the - incoming list creator would work. Changed RREFDECL. - - - 5/27/09 - - RS - (n/a) - - - $Log: aristot.econ_eng.xml,v $ - Revision 1.2 2010-06-16 19:18:48 rsingh04 - cleaned up bad place tags in a few texts and cleaned up the document format - Revision 1.1 2009/10/09 19:49:17 rsingh04 - more reorganizing of texts module by collection + + + +

This pointer pattern extracts book and section and subsection.

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+ + + + - Revision 1.1 2009/10/08 19:12:41 rsingh04 - began reorganizing texts module by collection. created separate work directory in texts module to keep hopper files separate from in progress files + + + English + Greek + Latin + + - Revision 1.11 2009/07/15 17:52:35 student - edited entity tags CEH + + EpiDoc and CTS conversion and general header review. +cleaned up bad place tags in a few texts and cleaned up the document format + more reorganizing of texts module by collection + began reorganizing texts module by collection. created separate work directory in texts module to keep hopper files separate from in progress files + edited entity tags CEH + + added cvs log keyword + Put Bekker line 1 milestone tags at the beginning of each section so that the incoming list creator would work. Changed RREFDECL. + Tagged in conformance with Prose.e dtd. + Text was scanned at St. Olaf Spring, 1992. + + - Revision 1.10 2009/07/15 17:50:40 student - edited entity tags CEH + + + +
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Between Housecraft (the art of governing a Household or Home) and Statecraft - (the art of governing a Nation) there are differences corresponding to those - between the two kinds of community over which they severally preside. There is, - however, this further difference: that whereas the government of a nation is in - many hands, a household has but a single ruler.Now some arts are divided into two separate branches, one concerned with the - making of an object—for example a lyre or a flute—and the - other with its use when made. Statecraft on the other hand shows us how to build - up a nation from its beginning, as well as how to order rightly a nation that - already exists; from which we infer that Housecraft also tells us first how to - acquire a household and then how to conduct its affairs. By a Nation we - mean an assemblage of houses, lands, and property sufficient to enable the - inhabitants to lead a civilized life. This is proved by the fact that when such - a life is no longer possible for them, the tie itself which unites them is - dissolved. Moreover, it is with such a life in view that the association is - originally formed; and the object for which a thing exists and has come into - being is in fact the very essence of that particular thing.From this definition of a Nation, it is evident that the art of - Housecraft is older than that of Statecraft, since the Household, which it - creates, is older; being a component part of the Nation created by - Statecraft.Accordingly we must consider the - nature of Housecraft, and what the Household, which it creates, actually - is. The component parts of a household are (l) human beings, and (2) goods and - chattels. And as households are no exception to the rule that the nature of a - thing is first studied in its barest and simplest form,we will follow Hesiod and begin by postulating - "Homestead first, and a woman; a plough-ox hardy to furrow." For the steading - takes precedence among our physical necessities, and the woman among our free - associates. It is, therefore, one of the tasks of Homecraft to set in order the - relation between man and woman; in other words, to see that it is what it ought - to be. Of occupations attendant on our goods and chattels, those come first which - are natural. Among these precedence is given to the one which cultivates the - land; those like mining, which extract wealth from it, take the second place. - Agriculture is the most honest of all such occupations; seeing that the wealth - it brings is not derived from other men. Herein it is distinguished from trade - and the wage-earning employments, which acquire wealth from others by their - consent; and from war, which wrings it from them perforce. It is also a natural - occupation; since by Nature's appointment all creatures receive sustenance from - their mother,

and mankind like the rest from their common mother the - earth. And besides all this, agriculture contributes notably to - the making of a manly character; because, unlike the mechanical arts, it does - not cripple and weaken the bodies of those engaged in it, but inures them to - exposure and toil and invigorates them to face the perils of war. For the - farmer's possessions, unlike those of other men, lie outside the city's - defences. When we turn our attention to the human part of the - household, it is the woman who makes the first claim upon it; <for the - natural comes first, as we have said,> and nothing is more natural than - the tie between female and male. For we have elsewhere laid down the - premissCf. Aristot. Pol. 1.1. that Nature is intent on multiplying severally her types; - and this is true of every animal in particular. Neither the female, however, can - effect this without the male, nor the male without the female; whence the union - of the sexes has of necessity arisen. Now among the lower animals, this union is - irrational in character; it exists merely for the purpose of procreation, and - lasts only so long as the parents are occupied in producing their brood. In tame - animals, on the other hand, and those which possess a greater share of - intelligence, it has assumed a more complex form; for in their case we see more - examples of mutual help, goodwill, and co-operation. It is, however, in the human species that this complexity - is most marked; since the co-operation between woman and man aims not merely at - existence, but at a happy existence. - Nor do mankind beget children merely to pay the service they owe to Nature, but - also that they may themselves receive a benefit; for the toil they undergo while - they are strong and their offspring is still weak is repaid by that offspring - when it in turn is grown strong and the parents by reason of age are - weak. At the same time Nature, by this cycle of changes, - fulfills her purpose of perpetuating existence; preserving the type when she is - unable to preserve the individual.Cf. Aristot. De Gen. An. 731b. And so - with this purpose in view Divine Providence has fashioned the nature of man and - of woman for their partnership. For they are distinguished from each other by - the possession of faculties not adapted in every case to the same tasks, but in - some cases for opposite ones, though contributing to the same end. For - Providence made man stronger and woman weaker,

so that he in - virtue of his manly prowess may be more ready to defend the home, and she, by - reason of her timid nature, more ready to keep watch over it; and while he - brings in fresh supplies from without, she may keep safe what lies within. In - handicrafts again, woman was given a sedentary patience, though denied stamina - for endurance of exposure; while man, though inferior to her in quiet - employments, is endowed with vigor for every active occupation. In the - production of children both share alike; but each makes a different contribution - to their upbringing. It is the mother who nurtures, and the father who - educates. We begin then with the rules that should govern a man's - treatment of his wife. And the first of these forbids him to do her wrong; for - if he observes this, he is not likely himself to suffer wrong at her hands. As - the Pythagoreans declare, even the common rule or custom of mankind thus - ordains, forbidding all wrong to a wife as stringently as though she were a - suppliant whom one has raised from the hearthstone. And a man does wrong to his - wife when he associates with other women. As regards the intercourse of - marriage, wives should neither importune their husbands, nor be restless in - their absence; but a man should accustom his wife to be content whether he is at - home or away. Good also is the advice of Hesiod: - - Take thee a maiden to wife, and teach her ways of - discretion. - - Hes. WD 699 - For differences of ways and habits are little conducive to - affection. As regards adornment: it is not wellthat souls should approach one another in - borrowed plumes, nor is it well in the case of bodies. Intercourse which depends - <for its charm> upon outward adornment differs in no respect from - that of figures on the stage in their conventional attire. Of property, the - first and most indispensable kind is that which is also best and most amenable - to Housecraft; and this is the human chattel. Our first step therefore must be - to procure good slaves. Of slaves there are two kinds; those in positions of - trust, and the laborers. And since it is matter of experience that the character - of the young can be moulded by training, when we require to charge slaves with - tasks befitting the free, we have not only to procure the slaves, but to bring - them up <for the trust>. In our intercourse with slaves we must - neither suffer them to be insolent nor treat them with cruelty. A share of honor - should be given to those who are doing more of a freeman's work, and abundance - of food to those who are laboring with their hands. And whereas the use of wine - renders even free men insolent, so that in many countries they too refrain from - it—as, for instance, the Carthaginians do when they are on - campaign—it follows that we must either deny wine to slaves - altogether, or reserve it for rare occasions. We may apportion to our - slaves (1) work, (2) chastisement, and (3) food. If men are given food, but no - chastisement nor any work, they become insolent.

If they are made - to work, and are chastised, but stinted of their food, such treatment is - oppressive, and saps their strength. The remaining alternative, therefore, is to - give them work, and a sufficiency of food. Unless we pay men, we cannot control - them; and food is a slave's pay.Slaves, again, - are no exception to the rule that men become worse when better conduct is not - followed by better treatment, but virtue and vice remain alike unrewarded. - Accordingly we must keep watch - over our workers, suiting our dispensations and indulgences to their desert; - whether it be food or clothing, leisure or chastisement that we are - apportioning. Both in theory and in practice we must take for our model a - physician's freedom in prescribing his medicines; observing at the same time - that food differs from medicine in that it requires to be constantly - administered. The best laborers will be furnished by those races of - mankind which are neither wholly spiritless nor yet overbold. Each extreme has - its vice; the spiritless cannot endure hard labor, and the high-spirited will - not readily brook control. Every slave should have before his eyes a - definite goal or term of his labor. To set the prize of freedom before him is - both just and expedient; since having a prize to work for, and a time defined - for its attainment, he will put his heart into his labors. We should, moreover, - take hostages <for our slaves' fidelity> by allowing them to beget - children; and avoid the practice of purchasing many slaves of the same - nationality, as men avoid doing in towns. We should also keep festivals and give - treats, more on the slaves account than on that of the freemen;since the free have a fuller share in those - enjoyments for the sake of which these institutions exist. There are four - qualities which the head of a household must possess in dealing with his - property. Firstly, he must have the faculty of acquiring, and secondly that of - preserving what he has acquired; otherwise there is no more benefit in acquiring - than in baling with a colander, or in the proverbial wine-jar with a hole in the - bottom. Thirdly and fourthly, he must know how to improve his property, and how - to make use of it; since these are the ends for which the powers of acquisition - and of preservation are sought. Everything we possess should be duly classified ; - and the amount of our productive property exceed that of the unproductive. - Produce should be so employed that we do not risk all our possessions at once. - For the safe keeping of our property, we shall do well to adopt the Persian and - Laconian systems. Athenian housecraft has, however, some advantages. The - Athenian buys immediately with the produce of his sales, and the smaller - households keep no idle deposits in store. Under the Persian system, the - master himself undertook the entire disposition and supervision of the - household, following the practice which - Dion used to remark in Dionysius. No one, indeed, takes the same - care of another's property as of his own; so that, as far as is possible, -

each man ought to attend to his affairs in person. We may - commend also a pair of sayings, one attributed to a Persian and the other to a - Libyan. The former on being asked what best conditions a horse, replied "His - master's eye."Cf. Xen. Ec. - 12. The Libyan, when asked what kind of manure is best, - answered "The master's footprints." The master and mistress should, therefore, - give personal supervision, each to his or her special department of the - household work. In small households, an occasional inspection will suffice; in - estates managed through stewards, inspections must be frequent. For in - stewardship as in other matters there can be no good copy without a good - example; and if the master and mistress do not attend diligently to their - estate, their deputies will certainly not do so. Moreover, as such habits are - both commendable for moral reasons and also conducive to good management, the - master and mistress will do well to rise earlier than their servants and to - retire later; to treat their home as a city, and never leave it unguarded; nor - ever, by night or by day, to postpone a task which ought to be done. Rising - before daylight is also to be commended; it is a healthy habit, and gives more - time for the management of the household as well as for liberal - studies. We have remarked that on small holdings the Athenian - method of disposing of the produce is advantageous.On large estates, after the amount for the year's or the - month's outlay has been set apart, it should be handed to the overseers; and so - also with implements, whether for daily or for occasional use. In addition, an - inspection of implements and stores should be made periodically, so that - remainders and deficiencies may alike be noted. In constructing a homestead, - we have to provide for the stock which it is to shelter, and for its health and - well-being. Providing for the stock involves questions such as these: What type - of building is best for the storage of crops and of clothing? How are we to - store the dry crops, and how the moist ones? Of the other stock, how is the - living to be housed, and how the dead? and what accommodation are we to make for - slaves and free, for women and men, for foreigners and fellow-citizens? For - well-being and health, again, the homestead should be airy in summer, and sunny - in winter. A homestead possessing these qualities would be longer - than it is deep; and its main front would face the south. On large estates, - moreover, it seems worth while to instal as porter a man incapable of other - work, to keep his eye on what passes in and out.

That implements - may be ready for use, the Laconian practice should be followed. Each should be - kept in its own place; thus it will always be to hand, and not require - seeking. -

Right administration of a household demands in the first place familiarity - with the sphere of one's actionOr, "the - localities wherein we work."; in the second Place, good natural - endowments; and in the third, an uprights and industrious way of life. For the - lack of any one of these qualifications will involve many a failure in the task - one takes in hand.Of such administrations there - are four main types, under which all others may be classified. We have the - administration of a king; of the governors under him; of a free state; and of a - private citizen. Of these, that of a king is the most extensive, yet at - the same time the simplest. A governor's office is also very extensive, but - divided into a great variety of departments. The administration of a free state - is again very varied, but it is the easiest to conduct; while that, of a private - individual presents the like variety, but within limits which are narrowest of - all. For the most part, all four will of necessity cover the same ground; we - will, however, take them in turn, and see what is especially characteristic of - each.Taking first the royal administration, - we see that while theoretically its power is unlimited,it is in practice concerned with four departments, - namely currency, exports, imports, and expenditure. Taking these severally, I - assign to that of currency the seasonable regulation of prices; to imports and - exports, the profitable disposition, at any given time, of the dues received - from provincial governors; and to expenditure, the reduction of outgoings as - occasion may serve, and the question of meeting expenses by currency or by - commodities. The second kind of administration, that of the governor, - is concerned with six different classes of revenue; those, namely, arising from - agriculture, from the special products of the country, from markets, from taxes, - from cattle, and from other sources.Taking these - in turn, the first and most important of them is revenue from agriculture, which - some call tithe and some produce-tax.Boeckh - translates E)KFO/RION "Grundsteuer." But how - then does it differ from TW=N KATA\ GH=N - TELW=N below? The second is that from special products; in - one place gold, in another silver, in another copper, and so on. Third in - importance is revenue from markets,

and fourth that which arises - from taxes on land and on sales. In the fifth place we have revenue from cattle, - called tithe or first-fruits; and in the sixth, revenue from other sources, - which we term poll-tax, or tax on industry. Of our third kind of - administration, that of a free state, the most important revenue is that arising - from the special products of the country. Next follows revenue from markets and - occupations; and finally that from every-day transactions.Or (understanding LEITOURGIW=N) "regular public services." - - Fourthly and lastly, we must consider the administration of a private citizen. - It is difficult to reduce this to rules owing to the necessary variety of its - aims; yet it is the most limited of the four, because both revenues and expenses - are <comparatively> small. Taking its revenues in turn, the chief - are those from agriculture; next in importance, those from other every-day - occupations; while third comes interest on money. Apart from all these, there is - a matter common to all kinds of administration which is best considered at this - particular point, and deserves more than cursory attention. This is the - importance of keeping expenditure within the limits of revenue. Having thus - enumerated the divisions of our subject, we must next consider whether the - province or the free state with which we are concerned is able to produce all - the forms of revenue we have just detailedor at least the chief of them; <and this being - known> must make the best use of what we have. Next we must inquire what - kinds of revenue, at present wholly lacking, are yet potentially existent; what - kinds, though now small, may with care be increased, and how far certain items - of present expenditure may without prejudice to the commonwealth be - diminished. Having spoken thus of administrations and their various - departments, we have further proceeded to collect such instances as we deemed - noteworthy of the means adopted by certain statesmen in times past for the - replenishment of the treasury, and also of their skill in administration. These - anecdotes <which follow>, seemed to us by no means lacking in - utility; being capable from time to time of application by others to the - business they themselves have in hand. Cypselus of Corinth had made a vow that if he became - master of the city, he would offer to Zeus the entire property of the - Corinthians. Accordingly he commanded them to make a return of their - possessions;

which done, he took from each a tenth part, and told them to - employ the remainder in trading. A year later, he repeated the process. And so - in ten years' time it came to pass that Cypselus received the entire amount - which he had dedicated; while the Corinthians on their part had replaced all - that they had paid him. Lygdamis of Naxos, after driving into exile a party of the inhabitants, found - that no one would give him a fair price for their property. He therefore sold it - to the exiled owners. The exiles had left behind them a number of works of art - destined for temple offerings, which lay in certain workshops in an unfinished - condition. These Lygdamis proceeded to sell to the exiles and whoso else would - buy them; allowing each purchaser to have his name engraved on the - offering. The people of Byzantium, being in need of funds, sold such dedicated lands as - belonged to the State; those under crops, for a term of years, and those - uncultivated, in perpetuity. In like manner they sold lands appropriated to - religious celebrations or ancestral cults, not excepting those that were on - private estatesSee Lys. 7, - the seventh Speech of the Athenian orator Lysias.; for the owners of - the surrounding land were ready to give a high price for them. To the - dispossessed celebrants <they assigned> such other public lands - surrounding the gymnasium, the agora, or the harbor,as belonged to the State. Moreover they claimed as - public property all open spaces where anything was sold, together with the - sea-fisheries, the traffic in salt, and the trade of professional conjurors, - soothsayers, charm-sellers, and the like; exacting from all these one-third of - their gains. The right of changing money they sold to a single bank, whose - proprietor was given a monopoly of the sale and purchase of coin, protected - under penalty of confiscation.And whereas - previously the rights of citizenship were by law confined to those whose parents - were both citizens, lack of funds, induced them to offer citizenship to him who - had one citizen parent on payment of the sum of thirty minae.A mina of silver (1 lb. 5 oz. avoirdupois) was coined into - 100 drachmae, each being an artisan's ordinary daily wage. - On another occasion, when food and funds were - both scarce, they called home all vessels that were trading in the Pontus. On the merchants protesting, they were - at length allowed to trade on payment of a tithe of their profits. This tax of - 10 per cent was also extended to purchases of every kind.

It happened that certain aliens residing in the city had lent - money on the security of citizens' property. As these aliens did not possess the - right of holding such property, the people offered to recognize the title of - anyone who chose to pay into the treasury one third of the amount - secured. Hippias of Athens offered for sale upper stories that projected over the - public streets,Cf. Goethe,Warheit und - Dichtung, Book I. "In Frankfurt, as in several ancient cities, - those who had erected wooden buildings had sought to obtain more room by - allowing the first and higher floors to overhang in the street. . . . At - last a law was carried that in all entirely new houses the first floor alone - should project; above that, the wall should be perpendicular." The poet's - father, wishing to rebuild his house without sacrifice of floor-space, - underpinned the upper stories and renewed the building piecemeal from below. - Cf. also 14. together with flights of steps, railings, and doors that - opened outwards. The owners of the buildings bought them, and in this way a - large sum of money was collected.He also called - inLit. "rendered invalid." the - existing currency, promising to pay the holders at a fixed rate. But when they - came to receive the new mintage, he reissued the old coins.Those who were expecting to equip a war-vessel or preside over - a tribe or train a chorus or undertake the expense of some other public service - of the kind, he allowed, if they chose, to commute the service for a moderate - sum, and to be enrolled on the list of those who had performed it.Moreover, whenever a citizen died, the priestess of the - temple of Athena on the AcropolisThis was the - public treasury, like the Temple of Saturnus at Rome. was to receive one quart - measure of barley, one of wheat, and a silver obolus.1/6 of the drachma. See 3 above. And when a child was - born, the father paid the same dues. The Athenian colonists at Potidaea, being in need of funds for the war, - agreed that all should make a return of their property for assessment of - tax.But instead of each returning - the entire amount to his own parish, properties were to be assessed separately, - each in its own locality, so that the poor might propose a reduced assessment; - while those without any <landed> property were assessed at two - minae a head. On these assessments each man paid the State the full amount of - the war-tax. The city of Antissa had been accustomed to celebrate the festival of Dionysus - with great magnificence. Year by yearOr "All - through the year." great provision was made for the occasion, and - costly sacrifices were prepared. Now one year the city found itself in need of - funds; and shortly before the festival, on the proposal of a citizen named - Sosipolis, the people after vowing that they would next year offer to Dionysus a - double amount, collected all that had been provided and sold it. In this way - they realized a large sum of money to meet their necessity. On one occasion - the people of Lampsacus were expecting - to be attacked by a large fleet of triremes.War-ships, each propelled by some 174 rowers ranked in three tiers. - The price of barley meal being then four drachmae for a bushel and a half, they - instructed the retailers to sell it at six drachmae. Oil, which was at three - drachmae for six pints, was to be sold at four drachmae and a half, and wine and - other commodities at a proportionate increase. In this way the retailer got the - original price,

while the State took the addition and filled its - treasury. The people of Heraclea, being about to dispatch a fleet of forty ships against - the lords of Bosporus, were at a loss - for the necessary funds. They therefore bought up all the merchants' stock of - corn and oil and wine and other marketable commodities, agreeing to pay at a - future date. The merchants were well satisfied that they had disposed of their - cargoes without breaking bulk; and the people, advancing two months' pay to - their armament, sent along with it a fleet of merchant-vessels laden with the - commodities, every ship being in charge of a public official. When the - expedition reached its goal, the men purchased from these officials all they - needed. In this way, the money was collected before the leaders again paid their - men; so that the same payment sufficed until the expedition returned - home. When the Samians entreated the Lacedaemonians for money - to enable them to return to their country, the Lacedaemonians passed a - resolution that they and their servants and their beasts of burden should go - without food for one day; and that the expense each one thus saved should be - given to the Samians. The people - of Chalcedon had a large number - of mercenary troops in their city, to whom they could not pay the wages they - owed. Accordingly they made proclamation that anyone, either citizen or alien, - who had right of reprisal against any city or individual, and wished to exercise - it, should have his name entered on a list. A large number of names was - enrolled, and the people thus obtained a specious pretext for exercising - reprisal upon ships that were passing on their way to the Pontus. They accordingly arrested the ships - and fixed a period within which they would consider any claims that might be - made in respect of them. Having now a large fund in hand, they paid off the - mercenaries, and set up a tribunal to decide the claims; and those whose goods - had been unjustly seized were compensated out of the revenues of the - state. At Cyzicus, - civil strife broke out between the democratic and oligarchic parties. The former - proved victorious, and the rich citizens were placed under arrest. But as the - city owed money to its troops, a resolution was passed that the lives of those - under arrest should be spared, and that they should be allowed to depart into - exile on paying a sum of money to the state. At Chios there was a law that all debts should be - entered on a public register. Being in need of funds,

the people - resolved that debtors should pay their debts into the treasury, and that the - state should meet the creditors' interest out of its revenues until its former - prosperity returned. Mausolus lord of Caria received from the King of PersiaProbably Artaxerxes II. - who reigned 405-359 - B.C. a demand for tribute. Therefore he summoned the wealthiest men in - his dominion, and told them that the King was asking for the tribute, and he had - not the means of paying it. Men whom he had previously suborned at once came - forward and declared what each was ready to contribute. With this example before - them, they who were wealthier than these, partly in shame and partly in alarm, - promised and paid much larger sums than the others.Being again in lack of funds, Mausolus summoned a public meeting of the people - of Mylassa and told them that the King of Persia was preparing to attack him; and that Mylassa his capital - city was unfortified. He therefore bade the citizens contribute each as - liberally as he could, saying that what they now paid in would afford security - to the rest of their possessions. By these means he obtained large - contributions. But though he kept the money, he declared that heaven, for the - present, forbade the building of the walls. Condalus, who was a - lieutenant-governor under Mausolus, whenever on his progress through the country - he was presented with a sheep,a pig, - or a calf, had a record made of the donor's name and of the date. He then bade - the man take the beast home and keep it until he should again pass that way. - After what he considered a sufficient interval, he would demand the beast - together with such profits as he reckoned it had produced. All trees, too, which - projected over the king's highway, or fell thereon, he sold as profits accruing - to the State.When one of his soldiers died, he - charged a drachma for the right of passing the body through the gates. This was - not only a source of revenue, but a check on the commanders, who were thus - prevented from falsifying the date of the man's death.Noticing that the Lycians were fond of wearing their hair long, - Condalus proclaimed that a dispatch had arrived from the King ordering him to - send hair to make forelocks for his horses; and that Mausolus had therefore - instructed him to shave their heads. However, if they would pay him a fixed sum - per head, he would send to Greece for - hair. They were glad to comply with his demand, and a large sum was collected, - the number of those taxed being great. Aristoteles of Rhodes,Mentioned by Proclus in his commentary on the Timaeus of - Plato. A coin of Phocaea is extant - bearing the name. when governor of Phocaea, found himself in need of funds. Noticing that there - were at Phocaea two opposing parties, - he held a secret conference with one of them,

at which he - declared that the other party was offering him money if he would favor their - pretensions; that he, however, preferred to receive from those now before him, - and to entrust to them the administration of the city. On hearing this, they - immediately contributed the money he asked, and gave it him. Thereupon he told - the other party what he had received from them; and they in turn promised him at - least an equal amount. Having thus taken the money of both factions, he effected - a reconciliation between them.He also observed - that there were many law-suits pending between the citizens, and that they had - grave and long-standing plaints against one another which had arisen in course - of war. He therefore appointed a tribunal, and made proclamation that all who - failed to appear before it within a stated period should lose the right to a - legal decision of their outstanding claims. Then, by taking into his own hands - the court-fees for a number of suits, and also those appeal-cases which involved - penalties, and receiving [through others] money from both sides, he obtained - altogether a very considerable sum. The people of Clazomenae, suffering from - dearth of grain and scarcity of funds, passed a resolution that any private - citizens who had stores of oil should lend it to the State at - interest;this being a produce - which their land bears in abundance. The loan arranged, they hired vessels and - sent them to the depots whence they obtained their grain, <and bought a - consignment> on security of the value of the oil.The same people, owing their mercenaries twenty talents of pay - and being unable to find it, were giving the leaders of the troop four talents - of interest each year. But failing to reduce the capital debt, and committed to - this fruitless drain on their revenue, they struck an iron coinage of twenty - talents, bearing the face-value of the silver. This they distributed - proportionately among the wealthiest citizens, and received from them silver to - the same amount. Through this expedient, the private citizens possessed a - currency which was good for their daily needs, and the state was relieved of its - debt. Next, they proceeded to pay interest out of revenue to those who had - advanced the silver; and little by little distributed repayment among them, - recalling at the same time the currency of iron.Plut. Lycurgus speaks of an iron - currency at Sparta, and Seneca De beneficiis of a leather one. These, - not being exchangeable abroad, threw the nation upon its own resources and - prevented the import of luxuries. - The - people of Selybria had a law, passed in time of famine, which forbade the export - of grain. On one occasion, however, they were in need of funds; and as they - possessed large stores of grain, they passed a resolution that citizens should - deliver up their corn to the state at the regular fixed price,

each - retaining for himself a year's supply. They then granted right of export to any - who desired it, fixing what they deemed a suitable price. At Abydos civil strife had caused the land to - remain uncultivated; while the resident aliens, to whom the city was already - indebted, refused to make any further advances. A resolution was accordingly - passed that anyone who would might lend money to enable the farmers to cultivate - their land, on the understanding that the lender had the first claim on its - produce; others taking from what was then left. The people of Ephesus, being in need of funds, passed a law - forbidding their women to wear gold, and ordering them to lend the State what - gold they had in their possession.They also - offered to any citizen who was willing to pay a fixed sum the right of having - his name inscribed on a certain pillar of their templeThis temple, dedicated to Artemis, was restored with great - magnificence after its destruction by fire in 356 - B.C. For its fame see Acts 19. Portions of the - sculptured pillars are to be seen in the British Museum. as the donor - thereof. Dionysius of Syracuse, being desirous of collecting funds, called a public - assembly, and declared that Demeter had appeared to him, and bade him convey all - the women's ornaments into her temple. That he himself had done so with the - ornaments of his own household; and the others must now follow his example, and - thereby avoid any visitation of the goddess's anger. Anyone who failed to comply - would, he declared, be guilty of sacrilege.Through fear of the goddess as well as of the despot, all the - citizens brought in whatever they had. Then Dionysius, after sacrificing to the - goddess, removed the ornaments to his own treasury as a loan which he had - borrowed from her. As time went on, the women again appeared with precious - ornaments. Dionysius thereupon issued a decree that any woman who desired to - wear gold should make an offering of a fixed amount in the temple.Intending to build a fleet of triremes, Dionysius knew - that he should require funds for the purpose. He therefore called an assembly - and declared that a certain city was offered to him by traitors, and he needed - money to pay them. The citizens therefore must contribute two staters - apiece.The stater was a Persian gold coin - worth 20 drachmae. (See 3.) The money was paid; but after two or - three days, Dionysius, pretending that the plot had failed, thanked the citizens - and returned to each his contribution. In this way he won the confidence of the - citizens; so that when he again asked for money, they contributed in the - expectation that they would receive it back. But this time he kept it for - building the fleet.On another occasion being in - straits for silver he minted a coinage of tin, and summoning a public assembly, - spoke at length in its favor. The citizens perforce voted that everyone should - regard as silver, and not as tin, whatever he received.

Again being in need of funds, he requested the citizens to - contribute. On their declaring that they had not the wherewithal, he brought out - the furnishings of his palace and offered them for sale, pretending to be - compelled through lack of money. At the sale, he had a list made of the articles - and their purchasers; and when they had all paid, he commanded every one to - bring back the article he had bought.Finding that - because of his imposts the citizens were ceasing to rear sheep and cattle, he - made proclamation that he needed no more money until a certain - <date>; so that those who now became possessed of any stock would - not be liable to taxation. A large number of citizens lost no time in acquiring - a quantity of sheep and cattle, on the understanding that they would be free of - impost. But Dionysius, when he thought the fitting time was come, had them all - valued and imposed a tax. The citizens were angry at being thus deceived, and - proceeded to kill and sell their beasts. On Dionysius's making a decree that - only such beasts should be slain as were needed each day, the owners retorted by - offering their animals as sacrifices; whereupon the despot forbade the sacrifice - of female beasts.Once more funds were lacking, - and Dionysius ordered a list to be made for him of all houses whose heirs were - orphan. Having obtained a complete list, he made use of the orphans' property - until each should come of age.After the capture - of Rhegium, he summoned a meeting of - the citizens, and told them why he had a good right to sell them as - slaves.If, however, they would - pay him the expenses of the war and three minaeSee 3. a head besides, he would release them. The people of - Rhegium brought forth all their - hoards; the poor borrowed from the wealthier and from the foreigners resident in - the city; and so the amount demanded was paid. But though he received this money - from them, none the less he sold them all for slaves, having succeeded - <by his trick> in bringing to light the hoarded goods which they - had previously concealed.On another occasion he - had borrowed money from the citizens, promising to repay it. On their demanding - its return, he bade each bring him, under pain of death, whatever silver he - possessed. This silver when brought he coined into drachmae each bearing the - face value of two: with these he repaid the <previous> debt and - also what had just been brought in.He also made a - raid on Tyrrhenia with a hundred ships, and rifled the temple of Leucothea of a - large amount of gold and silver, besides a quantity of works of art. But being - aware that his sailors too had taken much plunder,

he made - proclamation that each should bring him, under pain of death, one-half of what - he had; the remainder of their takings they might keep. On the understanding - that if they brought in half their plunder they would retain the rest in - security, they obeyed. But when Dionysius had got the treasure into his hands, - he commanded them to bring him the other half as well. The people of - Mende used to meet the expenses of administration from harbor and other duties, - but refrained from collecting the imposts on land and on houses. They kept, - however, a register of the owners, and when the state was in need of funds, they - collected the arrears. Meanwhile the owners had the advantage of trafficking - with their whole property undiminished by any payment of percentages.The same city being at war with Olynthus and needing funds, passed a - resolution that all the slaves they possessed, with the exception of one male - and one female apiece, should be sold on behalf of the State, which was thus - enabled to raise a loan from private citizens.Or: "that citizens should sell to the state what slaves they possessed . . - . as the equivalent of a loan from private persons to the city <of - the slaves' value>." - - Callistratus, when in Macedonia, caused - the harbor-dues, which were usually sold for twenty talents, to produce twice as - much. For noticing that only the wealthier men were accustomed to buy them - because the sureties for the twenty talents were obliged to show talent for - talent,he issued a proclamation - that anyone might buy the dues on furnishing securities for one-third of the - amount, or as much more as could be procured in each case. Timotheus of - Athens during his campaign - against Olynthus was short of - silver, and issued to his men a copper coinage instead. On their complaining, he - told them that all the merchants and retailers would accept it in lieu of - silver. But the merchants he instructed to buy in turn with the copper they - received such produce of the land as was for sale, as well as any booty brought - to them; such copper as remained on their hands he would exchange for - silver.During the campaign of CorcyraApparently in 375 B.C. See the end of Xenophon's - fifth Book ofHellenicaXen. Hell. 5. - this same Timotheus was reduced to sore straits. His men demanded their pay; - refused to obey his orders; and declared they would desert to the enemy. - Accordingly he summoned a meeting and told them that the stormy weather was - delaying the arrival of the silver he expected; meanwhile, as he had on hand - such abundance of provisions, he would charge them nothing for the three months' - ration of grain already advanced.

The men, unable to believe that - Timotheus would have sacrificed so large a sum to them unless he was in truth - expecting the money, made no further claim for pay until he had completed his - dispositions.At the siege of Samos,In - 366 B.C. Timotheus sold the crops and - other country property to the besieged Samians themselves, and thus obtained - plenty of money to pay his men. But finding the camp was short of provisions - owing to the arrival of reinforcements, he forbade the sale of milled corn, or - of any measure less than 1 1/2 bushels of corn or 8 1/2 gallons of wine or oil. - Accordingly the officers bought supplies wholesale and issued them to their men; - the reinforcements thenceforth brought their own provisions, and sold any - surplus on their departure. In this way the needs of the soldiers were - satisfactorily met. Didales the Persian was able to provide for the daily - needs of his mercenaries from the enemy's country; but had no coined money to - give them. When their pay became due, and they demanded it, he had recourse to - the following trick.He called a - meeting, and told the men that he had plenty of money, but that it was stored in - a certain fortress, which he named. He then broke up his encampment and marched - in that direction. On reaching the neighborhood of the fortress, he himself went - on ahead, and entering the place seized all the silver vessels in the temples. - He then loaded his mules in such a way that this plate was exposed, thus - suggesting that silver formed the entire load; and so continued his march. The - soldiers, beholding the plate and supposing that they convoyed a full load of - silver, were cheered by the expectation of their pay. They were informed however - by Didales that they would have to take it to Amisus to be coined—a journey of many days, and in - the winter season. And during all this time, he continued to employ the army - without giving it more than its necessary rations.Moreover, all the craftsmen in the army, and the hucksters who traded with the - soldiers by barter, were under his personal control, and enjoyed a complete - monopoly. When Taos,Called Tachos (*TAXW/S) by Xenophon and Plutarch. Perhaps that form should be - restored here. (Bonitz and Susemihl.) The name recurs in 37. king of - Egypt, needed funds for an - expedition he was making, Chabrias of Athens advised him to inform the priests that to save expense it - was necessary to suppress some of the temples together with the majority of the - attendant priests.

On hearing this, each priesthood, being anxious to retain - their own temple, offered him money from their private possessions <as - well as from the temple funds>. When the king had thus received money - from them all, Chabrias bade him tell the priests to spend on the temple-service - and on their own maintenance one-tenth of what they formerly spent, and lend him - the remainder until he had made peace with the King <of Persia>.Moreover, each inhabitant was to contribute a stated proportion of his - household and personal possessions; and when grain was sold, buyer and seller - were each to contribute, apart from the price, one obol per artabeThe artabe was a Persian measure containing - nearly 50 quarts. The obol was 1/6 of a drachma of silver.; while a - tax of one tenth was to be imposed on profits arising from ships and workshops - and other sources of gain.Again, when Taos was on the point of setting out from - Egypt, Chabrias advised him to make - requisition of all uncoined gold and silver in the possession of the - inhabitants; and when most of them complied, he bade the king make use of the - bullion, and refer the lenders to the governors of his provinces for - compensation out of the taxes. Iphicrates of Athens provided Cotys with money for a force which he had - collected in the following manner.He - bade him order <each> of his subjects to sow for him a piece of - land bearing 4 1/2 bushels. A large quantity of grain was thus gathered, from - the price of which, when brought to the depots on the coast, the king obtained - as much money as he wanted. Cotys of Thrace asked the people of Peirinthus for a loan to enable him to - raise an army. On their refusing, he begged them at any rate to let him have - some of their citizens to garrison certain fortresses, and release for active - service the men who were there on duty. They readily complied, thinking thus to - obtain control of the fortresses. But Cotys placed in custody the men they sent, - and told the citizens that they might have them back when they had sent him the - amount of the loan he desired. Mentor of Rhodes, after taking Hermias prisoner and seizing his fortresses, - left in their various districts the officials appointed by him. By this means he - restored their confidence, so that they all took again to themselves the - property they had hidden or had sent secretly out of the country. Then Mentor - arrested them and stripped them of all they had.

Memnon of - Rhodes, on making himself master of - Lampsacus, found he was in need of - funds. He therefore assessed upon the wealthiest inhabitants a quantity of - silver, telling them that they should recover it from the other citizens. But - when the other citizens made their contributions, Memnon said they must lend him - this money also, fixing a certain date for its repayment.Again being in need of funds, he asked for a contribution, to - be recovered, as he said, from the city revenues. The citizens complied, - thinking that they would speedily reimburse themselves. But when the revenue - payments came in, he declared that he must have these also, and would repay the - lenders subsequently with interest.His mercenary - troops he requested to forgo six days' pay and rations each year, on the plea - that on those days they were neither on garrison duty nor on the march nor did - they incur any expense. (He referred to the days omitted from alternate - months.As the moon's cycle is completed in - 29 1/2 days, it was customary to alternate "hollow" months of 29 days with - the "full" months of 30 days. Memnon paid his men by the month, but deducted - a day's pay every "hollow" month.) Moreover, being accustomed previously to issue his men's rations of corn on - the second day of the month, in the first month he postponed the distribution - for three days, and in the second month for five; proceeding in this fashion - until at length it took place on the last day of the month. Charidemus of - Oreus, being in occupation of certain fortress-towns in Aeolis,and threatened with an attack by Artabazus,For the circumstances, and a (hostile) account of this - commander's adventures, see Demosthenes,Against - AristocratesDem. 23. was in need of - money to pay his troops. After their first contributions, the inhabitants - declared they had no more to give. Charidemus then issued a proclamation to the - town he deemed wealthiest, bidding the inhabitants send away to another fortress - all the coin and valuables they possessed, under convoy which he would provide. - He himself openly set the example with his own goods, and prevailed on them to - comply. But when he had conducted them a little way out of the town, he made an - inventory of their goods, took all he wanted, and led them home again.He had also issued a proclamation in the cities he - governed forbidding anyone to keep arms in his house, under pain of a stated - fine. At first, however, he took no care to enforce it, nor did he make any - inquisition; so that the people treated his proclamation as nugatory, and made - no attempt to get rid of what arms each possessed. Then Charidemus unexpectedly - ordered a search to be made from house to house, and exacted the penalty from - those who were found in possession of arms. A Macedonian named - Philoxenus, who was governor of Caria, - being in need of funds proclaimed that he intended to celebrate the festival of - Dionysus.

The wealthiest inhabitants were selected to provide the - choruses, and were informed what they were expected to furnish. Noticing their - disinclination, Philoxenus sent to them privately and asked what they would give - to be relieved of the duty. They told him they were prepared to pay a much - larger sum than they expected to spend <on the choruses> in order - to avoid the trouble and the interruption of their business. Philoxenus accepted - their offers, and proceeded to enrol a second levy. These also paid; and at last - he received what he desired from each company. Euaises the Syrian, when - governor of Egypt, received information - that the local governors were meditating rebellion. He therefore summoned them - to the palace and proceeded to hang them all, sending word to their relations - that they were in prison. These accordingly made offers, each on behalf of his - own kinsman, seeking by payment to secure their release. Euaises agreed to - accept a certain sum for each, and when it had been paid returned to the - relations the dead body. While Cleomenes of Alexandria was governor of Egypt,Cf. - Dem. 56: "Cleomenes . . . from the time that he - received the government, has done immense mischief to your state, and still - more to the rest of Greece, by - buying up corn for resale and keeping it at his own price" ( - Kennedy's translation). at a time - when there was some scarcity in the land, but elsewhere a grievous famine, he - forbade the export of grain. On the local governors representingthat if there were no export of grain they - would be unable to pay in their taxes, he allowed the export, but laid a heavy - duty on the corn. By this means he obtained a large amount of duty from a small - amount of export, and at the same time deprived the officials of their - excuse.When Cleomenes was making a progress - by water through the province where the crocodile is worshipped, one of his - servants was carried off. Accordingly, summoning the priests, he told them that - he intended to retaliate on the crocodiles for this unprovoked aggression; and - gave orders for a battue. The priests, to save the credit of their god, - collected all the gold they could, and succeeded in putting an end to the - pursuit.King Alexander had given Cleomenes - command to establish a town near the island of Pharus, and to transfer thither the market hitherto held at - Canopus. Sailing therefore to - Canopus he informed the priests and - the men of property there that he was come to remove them. The priests and - residents thereupon contributed money to induce him to leave their market where - it was. He took what they offered, and departed; but afterwards returned, when - all was ready to build the town,

and proceeded to demand an excessive sum; - which represented, he said, the difference the change of site would make to him. - They however declared themselves unable to pay it, and were accordingly - removed.On another occasion he sent an agent - to make a certain purchase for him. Learning that the agent had made a good - bargain, but intended to charge him a high price, he proceeded to inform the - man's associates that he had been told he had purchased the goods at an - excessive price, and that therefore he did not intend to recognize the - transaction; denouncing at the same time with feigned anger the fellow's - stupidity. They on hearing this asked him not to believe what was said against - the agent until he himself arrived and rendered his account. On the man's - arrival, his associates told him what Cleomenes had said. He, desirous of - winning their approval as well as that of Cleomenes, debited the latter with the - actual price he had given.At a time when the - price of grain in Egypt was ten - drachmae <a measure> ,If the - measure intended is the Attic medimnos , it is 1 1/2 bushels. The Persian - artabe may however be meant, which was equal to 1 medimnos and 1/16th. In - either case the price is very high compared with 3 drachmae per medimnos, - the price at Athens in 390 B.C. Yet Polybius - 9.44 says that at Rome - during the war with Hannibal (210) corn was sold for fifteen drachmae per - medimnos. As a contrast cf. what the same author says of the fertility of - Gallia Cisalpina, where in time of peace this same measure of wheat was sold - for four obols, and of barley for two. See note on 25. Cleomenes sent - for the growers and asked them at what price they would contract to supply him - with their produce. On their quoting a price lower than what they were charging - the merchants, he offered them the full price they were accustomed to receive - from others; and taking over the entire supply,sold it at a fixed rate of thirty-two drachmae <for the - same measure>.He also sent for the - priests, and told them that the expenditure on the temples was very unevenly - distributed in the country; and that some of these, together with the majority - of the attendant priests, must accordingly be suppressed. The priests, supposing - him to be in earnest, and wishing each to secure the continuance of his own - temple and office, gave him money individually from their private possessions as - well as collectively from the temple funds.Cf. - 25. - - Antimenes of Rhodes, who was appointed by Alexander superintendent of highways - in the province of Babylon, adopted the - following means of raising funds. An ancient law of the country imposed a tax of - one-tenth on all imports; but this had fallen into total abeyance. Antimenes - kept a watch for all governors and soldiers whose arrival was expected, and upon - the many ambassadors and craftsmen who were invited to the city, but brought - with them others who dwelt there unofficially; and also upon the multitude of - presents that were brought <to these persons> , on which he - exacted the legal tax of a tenth.Another - expedient was this. He invited the owners of any slaves in the camp to register - them at whatever value they desired, undertaking at the same time to pay him - eight drachmae a year. If the slave ran away, the owner was to recover the - registered value.

Many slaves were thus registered, and a large sum of - money was paid <in premiums>. And when a slave ran away, Antimenes - instructed the governor of the <province> where the camp lay - either to recover the man or to pay his master his value. Ophellas of - Olynthus appointed an officer - to superintend the revenues of the Province of Athribis. The local governors came to him, and told him they - were willing to pay a much larger amount in taxes; but asked him to remove the - present superintendent. Ophellas inquired if they were really able to pay what - they promised; and on their assuring him that they were, left the superintendent - in office and instructed him to demand from them the amount of tax which they - themselves had assessed. And so, without being chargeable either with - discountenancing the officer he had appointed, or with taxing the governors - beyond their own estimate, he obtained from the latter many times his previous - revenue. Pythocles the Athenian recommended his fellow-countrymen - that the State should take over from private citizens the lead obtained from the - mines of LauriumThese silver mines were state property; but mining rights - therein were let to private citizens. Lead and silver were found in the same - ore and had to be separated. The weight of the lead is not specified: it may - have been a talent of 80 lbs. See Boeckh, Staatshaushaltung der - Athener; and Xen. Ways. at the price - of two drachmae <per talent> which they were asking, and should - itself sell it at the fixed price of six drachmae. Chabrias had levied crews - fora hundred and twenty ships to - serve King Taos.See 25. Finding that - Taos needed only sixty ships, he gave the crews of the superfluous sixty their - choice between providing those who were to serve with two months' rations, and - themselves taking their place. Desiring to remain at their business, they gave - what he demanded. Antimenes bade the governors of the provinces replenish, - in accordance with the law of the country, the magazines along the royal - highways. Whenever an army passed through the country or any other body of men - unaccompanied by the king, he sent an officer to sell them the contents of the - magazines.

Cleomenes, as the beginning of the month approached when - his soldiers' allowance became due, deliberately sailed away down the river; and - not till the month was advanced did he return and distribute the allowance. For - the coming month, he omitted the distribution altogether until the following - month began. Thus the men were quieted by the recent distribution, and - Cleomenes, passing over a month each year, docked his troops of a month's - pay.SITARXI/A (corn allowance) and MISQO/S (pay) here seem to be identified; possibly because in a - land where grain was readily purchasable the former was given in money. Cf. - 23, 29. - - Stabelbius, king of the Mysians, lacking pay to give his troops, summoned a - meeting of the officers, and declared that he no longer needed the private - soldiers, but only the officers. When he required troops, he would entrust a sum - of money to each officer and send him to collect mercenaries; but that meanwhile - he preferred to give the officers the pay he would otherwise have to give the - men. Accordingly he bade each dismiss the men who were on his own muster-roll. - The officers, scenting a source of gain for themselves, dismissed their men, as - they were bidden. Shortly afterwards, Stabelbius called them together and - informed them that a conductor without his chorus and an officer without his men - were alike useless; wherefore let them depart from his country. When Dionysius was making a tour of the - temples, wherever he saw a gold or silver table set, he bade them fill a cup "in - honor of the good spirit,"Cf. Cic. De natura deorum 3.3.4 and Athenaeus Deipnosophistae 15.693. and then - had the table carried away. Wherever, again, he saw a precious bowl set before - one of the images, he would order its removal, with the words" I accept it." He - also stripped the images of their golden raiment and garlands, and declaring he - would give them lighter and more fragrant wear, arrayed them in robes of white - <linen> and garlands of white socks.

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Between Housecraft (the art of governing a Household or Home) and Statecraft (the art of governing a Nation) there are differences corresponding to those between the two kinds of community over which they severally preside. There is, however, this further difference: that whereas the government of a nation is in many hands, a household has but a single ruler.

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Now some arts are divided into two separate branches, one concerned with the making of an object—for example a lyre or a flute—and the other with its use when made. Statecraft on the other hand shows us how to build up a nation from its beginning, as well as how to order rightly a nation that already exists; from which we infer that Housecraft also tells us first how to acquire a household and then how to conduct its affairs.

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By a Nation we mean an assemblage of houses, lands, and property sufficient to enable the inhabitants to lead a civilized life. This is proved by the fact that when such a life is no longer possible for them, the tie itself which unites them is dissolved. Moreover, it is with such a life in view that the association is originally formed; and the object for which a thing exists and has come into being is in fact the very essence of that particular thing.

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From this definition of a Nation, it is evident that the art of Housecraft is older than that of Statecraft, since the Household, which it creates, is older; being a component part of the Nation created by Statecraft.

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Accordingly we must consider the nature of Housecraft, and what the Household, which it creates, actually is.

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The component parts of a household are (l) human beings, and (2) goods and chattels. And as households are no exception to the rule that the nature of a thing is first studied in its barest and simplest form, we will follow Hesiod and begin by postulatingHomestead first, and a woman; a plough-ox hardy to furrow. For the steading takes precedence among our physical necessities, and the woman among our free associates. It is, therefore, one of the tasks of Homecraft to set in order the relation between man and woman; in other words, to see that it is what it ought to be.

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Of occupations attendant on our goods and chattels, those come first which are natural. Among these precedence is given to the one which cultivates the land; those like mining, which extract wealth from it, take the second place. Agriculture is the most honest of all such occupations; seeing that the wealth it brings is not derived from other men. Herein it is distinguished from trade and the wage-earning employments, which acquire wealth from others by their consent; and from war, which wrings it from them perforce. It is also a natural occupation; since by Nature’s appointment all creatures receive sustenance from their mother, and mankind like the rest from their common mother the earth.

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And besides all this, agriculture contributes notably to the making of a manly character; because, unlike the mechanical arts, it does not cripple and weaken the bodies of those engaged in it, but inures them to exposure and toil and invigorates them to face the perils of war. For the farmer’s possessions, unlike those of other men, lie outside the city’s defences.

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When we turn our attention to the human part of the household, it is the woman who makes the first claim upon it; 〈for the natural comes first, as we have said,〉 and nothing is more natural than the tie between female and male. For we have elsewhere laid down the premissCf. Aristot. Pol. 1.1. that Nature is intent on multiplying severally her types; and this is true of every animal in particular. Neither the female, however, can effect this without the male, nor the male without the female; whence the union of the sexes has of necessity arisen.

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Now among the lower animals, this union is irrational in character; it exists merely for the purpose of procreation, and lasts only so long as the parents are occupied in producing their brood. In tame animals, on the other hand, and those which possess a greater share of intelligence, it has assumed a more complex form; for in their case we see more examples of mutual help, goodwill, and co-operation.

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It is, however, in the human species that this complexity is most marked; since the co-operation between woman and man aims not merely at existence, but at a happy existence. Nor do mankind beget children merely to pay the service they owe to Nature, but also that they may themselves receive a benefit; for the toil they undergo while they are strong and their offspring is still weak is repaid by that offspring when it in turn is grown strong and the parents by reason of age are weak.

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At the same time Nature, by this cycle of changes, fulfills her purpose of perpetuating existence; preserving the type when she is unable to preserve the individual.Cf. Aristot. De Gen. An. 731b. And so with this purpose in view Divine Providence has fashioned the nature of man and of woman for their partnership. For they are distinguished from each other by the possession of faculties not adapted in every case to the same tasks, but in some cases for opposite ones, though contributing to the same end. For Providence made man stronger and woman weaker, so that he in virtue of his manly prowess may be more ready to defend the home, and she, by reason of her timid nature, more ready to keep watch over it; and while he brings in fresh supplies from without, she may keep safe what lies within. In handicrafts again, woman was given a sedentary patience, though denied stamina for endurance of exposure; while man, though inferior to her in quiet employments, is endowed with vigor for every active occupation. In the production of children both share alike; but each makes a different contribution to their upbringing. It is the mother who nurtures, and the father who educates.

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We begin then with the rules that should govern a man’s treatment of his wife. And the first of these forbids him to do her wrong; for if he observes this, he is not likely himself to suffer wrong at her hands. As the Pythagoreans declare, even the common rule or custom of mankind thus ordains, forbidding all wrong to a wife as stringently as though she were a suppliant whom one has raised from the hearthstone. And a man does wrong to his wife when he associates with other women.

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As regards the intercourse of marriage, wives should neither importune their husbands, nor be restless in their absence; but a man should accustom his wife to be content whether he is at home or away. Good also is the advice of Hesiod: Take thee a maiden to wife, and teach her ways of discretion. Hes. WD 699 For differences of ways and habits are little conducive to affection.

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As regards adornment: it is not well that souls should approach one another in borrowed plumes, nor is it well in the case of bodies. Intercourse which depends 〈for its charm〉 upon outward adornment differs in no respect from that of figures on the stage in their conventional attire.

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Of property, the first and most indispensable kind is that which is also best and most amenable to Housecraft; and this is the human chattel. Our first step therefore must be to procure good slaves. Of slaves there are two kinds; those in positions of trust, and the laborers. And since it is matter of experience that the character of the young can be moulded by training, when we require to charge slaves with tasks befitting the free, we have not only to procure the slaves, but to bring them up 〈for the trust〉.

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In our intercourse with slaves we must neither suffer them to be insolent nor treat them with cruelty. A share of honor should be given to those who are doing more of a freeman’s work, and abundance of food to those who are laboring with their hands. And whereas the use of wine renders even free men insolent, so that in many countries they too refrain from it—as, for instance, the Carthaginians do when they are on campaign—it follows that we must either deny wine to slaves altogether, or reserve it for rare occasions.

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We may apportion to our slaves (1) work, (2) chastisement, and (3) food. If men are given food, but no chastisement nor any work, they become insolent. If they are made to work, and are chastised, but stinted of their food, such treatment is oppressive, and saps their strength. The remaining alternative, therefore, is to give them work, and a sufficiency of food. Unless we pay men, we cannot control them; and food is a slave’s pay.

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Slaves, again, are no exception to the rule that men become worse when better conduct is not followed by better treatment, but virtue and vice remain alike unrewarded.

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Accordingly we must keep watch over our workers, suiting our dispensations and indulgences to their desert; whether it be food or clothing, leisure or chastisement that we are apportioning. Both in theory and in practice we must take for our model a physician’s freedom in prescribing his medicines; observing at the same time that food differs from medicine in that it requires to be constantly administered.

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The best laborers will be furnished by those races of mankind which are neither wholly spiritless nor yet overbold. Each extreme has its vice; the spiritless cannot endure hard labor, and the high-spirited will not readily brook control.

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Every slave should have before his eyes a definite goal or term of his labor. To set the prize of freedom before him is both just and expedient; since having a prize to work for, and a time defined for its attainment, he will put his heart into his labors. We should, moreover, take hostages 〈for our slaves’ fidelity〉 by allowing them to beget children; and avoid the practice of purchasing many slaves of the same nationality, as men avoid doing in towns. We should also keep festivals and give treats, more on the slaves account than on that of the freemen; since the free have a fuller share in those enjoyments for the sake of which these institutions exist.

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There are four qualities which the head of a household must possess in dealing with his property. Firstly, he must have the faculty of acquiring, and secondly that of preserving what he has acquired; otherwise there is no more benefit in acquiring than in baling with a colander, or in the proverbial wine-jar with a hole in the bottom. Thirdly and fourthly, he must know how to improve his property, and how to make use of it; since these are the ends for which the powers of acquisition and of preservation are sought.

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Everything we possess should be duly classified ; and the amount of our productive property exceed that of the unproductive. Produce should be so employed that we do not risk all our possessions at once. For the safe keeping of our property, we shall do well to adopt the Persian and Laconian systems. Athenian housecraft has, however, some advantages. The Athenian buys immediately with the produce of his sales, and the smaller households keep no idle deposits in store.

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Under the Persian system, the master himself undertook the entire disposition and supervision of the household, following the practice which Dion used to remark in Dionysius. No one, indeed, takes the same care of another’s property as of his own; so that, as far as is possible, each man ought to attend to his affairs in person. We may commend also a pair of sayings, one attributed to a Persian and the other to a Libyan. The former on being asked what best conditions a horse, repliedHis master’s eye.Cf. Xen. Ec. 12. The Libyan, when asked what kind of manure is best, answeredThe master’s footprints.

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The master and mistress should, therefore, give personal supervision, each to his or her special department of the household work. In small households, an occasional inspection will suffice; in estates managed through stewards, inspections must be frequent. For in stewardship as in other matters there can be no good copy without a good example; and if the master and mistress do not attend diligently to their estate, their deputies will certainly not do so.

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Moreover, as such habits are both commendable for moral reasons and also conducive to good management, the master and mistress will do well to rise earlier than their servants and to retire later; to treat their home as a city, and never leave it unguarded; nor ever, by night or by day, to postpone a task which ought to be done. Rising before daylight is also to be commended; it is a healthy habit, and gives more time for the management of the household as well as for liberal studies.

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We have remarked that on small holdings the Athenian method of disposing of the produce is advantageous. On large estates, after the amount for the year’s or the month’s outlay has been set apart, it should be handed to the overseers; and so also with implements, whether for daily or for occasional use. In addition, an inspection of implements and stores should be made periodically, so that remainders and deficiencies may alike be noted.

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In constructing a homestead, we have to provide for the stock which it is to shelter, and for its health and well-being. Providing for the stock involves questions such as these: What type of building is best for the storage of crops and of clothing? How are we to store the dry crops, and how the moist ones? Of the other stock, how is the living to be housed, and how the dead? and what accommodation are we to make for slaves and free, for women and men, for foreigners and fellow-citizens? For well-being and health, again, the homestead should be airy in summer, and sunny in winter.

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A homestead possessing these qualities would be longer than it is deep; and its main front would face the south. On large estates, moreover, it seems worth while to instal as porter a man incapable of other work, to keep his eye on what passes in and out. That implements may be ready for use, the Laconian practice should be followed. Each should be kept in its own place; thus it will always be to hand, and not require seeking.

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Right administration of a household demands in the first place familiarity with the sphere of one’s actionOr,the localities wherein we work.; in the second Place, good natural endowments; and in the third, an uprights and industrious way of life. For the lack of any one of these qualifications will involve many a failure in the task one takes in hand.

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Of such administrations there are four main types, under which all others may be classified. We have the administration of a king; of the governors under him; of a free state; and of a private citizen.

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Of these, that of a king is the most extensive, yet at the same time the simplest. A governor’s office is also very extensive, but divided into a great variety of departments. The administration of a free state is again very varied, but it is the easiest to conduct; while that, of a private individual presents the like variety, but within limits which are narrowest of all. For the most part, all four will of necessity cover the same ground; we will, however, take them in turn, and see what is especially characteristic of each.

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Taking first the royal administration, we see that while theoretically its power is unlimited, it is in practice concerned with four departments, namely currency, exports, imports, and expenditure.

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Taking these severally, I assign to that of currency the seasonable regulation of prices; to imports and exports, the profitable disposition, at any given time, of the dues received from provincial governors; and to expenditure, the reduction of outgoings as occasion may serve, and the question of meeting expenses by currency or by commodities.

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The second kind of administration, that of the governor, is concerned with six different classes of revenue; those, namely, arising from agriculture, from the special products of the country, from markets, from taxes, from cattle, and from other sources.

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Taking these in turn, the first and most important of them is revenue from agriculture, which some call tithe and some produce-tax.Boeckh translates ἐκφόριονGrundsteuer. But how then does it differ from τῶν κατὰ γῆν τελῶν below? The second is that from special products; in one place gold, in another silver, in another copper, and so on. Third in importance is revenue from markets, and fourth that which arises from taxes on land and on sales. In the fifth place we have revenue from cattle, called tithe or first-fruits; and in the sixth, revenue from other sources, which we term poll-tax, or tax on industry.

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Of our third kind of administration, that of a free state, the most important revenue is that arising from the special products of the country. Next follows revenue from markets and occupations; and finally that from every-day transactions.Or (understanding λειτουργιῶν)regular public services.

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Fourthly and lastly, we must consider the administration of a private citizen. It is difficult to reduce this to rules owing to the necessary variety of its aims; yet it is the most limited of the four, because both revenues and expenses are 〈comparatively〉 small. Taking its revenues in turn, the chief are those from agriculture; next in importance, those from other every-day occupations; while third comes interest on money. Apart from all these, there is a matter common to all kinds of administration which is best considered at this particular point, and deserves more than cursory attention. This is the importance of keeping expenditure within the limits of revenue.

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Having thus enumerated the divisions of our subject, we must next consider whether the province or the free state with which we are concerned is able to produce all the forms of revenue we have just detailed or at least the chief of them; 〈and this being known〉 must make the best use of what we have. Next we must inquire what kinds of revenue, at present wholly lacking, are yet potentially existent; what kinds, though now small, may with care be increased, and how far certain items of present expenditure may without prejudice to the commonwealth be diminished.

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Having spoken thus of administrations and their various departments, we have further proceeded to collect such instances as we deemed noteworthy of the means adopted by certain statesmen in times past for the replenishment of the treasury, and also of their skill in administration. These anecdotes 〈which follow〉, seemed to us by no means lacking in utility; being capable from time to time of application by others to the business they themselves have in hand.

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Cypselus of Corinth had made a vow that if he became master of the city, he would offer to Zeus the entire property of the Corinthians. Accordingly he commanded them to make a return of their possessions; which done, he took from each a tenth part, and told them to employ the remainder in trading. A year later, he repeated the process. And so in ten years’ time it came to pass that Cypselus received the entire amount which he had dedicated; while the Corinthians on their part had replaced all that they had paid him.

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Lygdamis of Naxos, after driving into exile a party of the inhabitants, found that no one would give him a fair price for their property. He therefore sold it to the exiled owners. The exiles had left behind them a number of works of art destined for temple offerings, which lay in certain workshops in an unfinished condition. These Lygdamis proceeded to sell to the exiles and whoso else would buy them; allowing each purchaser to have his name engraved on the offering.

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The people of Byzantium, being in need of funds, sold such dedicated lands as belonged to the State; those under crops, for a term of years, and those uncultivated, in perpetuity. In like manner they sold lands appropriated to religious celebrations or ancestral cults, not excepting those that were on private estatesSee Lys. 7, the seventh Speech of the Athenian orator Lysias.; for the owners of the surrounding land were ready to give a high price for them. To the dispossessed celebrants 〈they assigned〉 such other public lands surrounding the gymnasium, the agora, or the harbor, as belonged to the State. Moreover they claimed as public property all open spaces where anything was sold, together with the sea-fisheries, the traffic in salt, and the trade of professional conjurors, soothsayers, charm-sellers, and the like; exacting from all these one-third of their gains. The right of changing money they sold to a single bank, whose proprietor was given a monopoly of the sale and purchase of coin, protected under penalty of confiscation.

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And whereas previously the rights of citizenship were by law confined to those whose parents were both citizens, lack of funds, induced them to offer citizenship to him who had one citizen parent on payment of the sum of thirty minae.A mina of silver (1 lb. 5 oz. avoirdupois) was coined into 100 drachmae, each being an artisan’s ordinary daily wage.

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On another occasion, when food and funds were both scarce, they called home all vessels that were trading in the Pontus. On the merchants protesting, they were at length allowed to trade on payment of a tithe of their profits. This tax of 10 per cent was also extended to purchases of every kind.

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It happened that certain aliens residing in the city had lent money on the security of citizens’ property. As these aliens did not possess the right of holding such property, the people offered to recognize the title of anyone who chose to pay into the treasury one third of the amount secured.

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Hippias of Athens offered for sale upper stories that projected over the public streets,Cf. Goethe,Warheit und Dichtung, Book I.In Frankfurt, as in several ancient cities, those who had erected wooden buildings had sought to obtain more room by allowing the first and higher floors to overhang in the street. . . . At last a law was carried that in all entirely new houses the first floor alone should project; above that, the wall should be perpendicular. The poet’s father, wishing to rebuild his house without sacrifice of floor-space, underpinned the upper stories and renewed the building piecemeal from below. Cf. also 14. together with flights of steps, railings, and doors that opened outwards. The owners of the buildings bought them, and in this way a large sum of money was collected.

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He also called inLit.rendered invalid. the existing currency, promising to pay the holders at a fixed rate. But when they came to receive the new mintage, he reissued the old coins.

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Those who were expecting to equip a war-vessel or preside over a tribe or train a chorus or undertake the expense of some other public service of the kind, he allowed, if they chose, to commute the service for a moderate sum, and to be enrolled on the list of those who had performed it.

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Moreover, whenever a citizen died, the priestess of the temple of Athena on the AcropolisThis was the public treasury, like the Temple of Saturnus at Rome. was to receive one quart measure of barley, one of wheat, and a silver obolus.1/6 of the drachma. See 3 above. And when a child was born, the father paid the same dues.

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The Athenian colonists at Potidaea, being in need of funds for the war, agreed that all should make a return of their property for assessment of tax. But instead of each returning the entire amount to his own parish, properties were to be assessed separately, each in its own locality, so that the poor might propose a reduced assessment; while those without any 〈landed〉 property were assessed at two minae a head. On these assessments each man paid the State the full amount of the war-tax.

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The city of Antissa had been accustomed to celebrate the festival of Dionysus with great magnificence. Year by yearOrAll through the year. great provision was made for the occasion, and costly sacrifices were prepared. Now one year the city found itself in need of funds; and shortly before the festival, on the proposal of a citizen named Sosipolis, the people after vowing that they would next year offer to Dionysus a double amount, collected all that had been provided and sold it. In this way they realized a large sum of money to meet their necessity.

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On one occasion the people of Lampsacus were expecting to be attacked by a large fleet of triremes.War-ships, each propelled by some 174 rowers ranked in three tiers. The price of barley meal being then four drachmae for a bushel and a half, they instructed the retailers to sell it at six drachmae. Oil, which was at three drachmae for six pints, was to be sold at four drachmae and a half, and wine and other commodities at a proportionate increase. In this way the retailer got the original price, while the State took the addition and filled its treasury.

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The people of Heraclea, being about to dispatch a fleet of forty ships against the lords of Bosporus, were at a loss for the necessary funds. They therefore bought up all the merchants’ stock of corn and oil and wine and other marketable commodities, agreeing to pay at a future date. The merchants were well satisfied that they had disposed of their cargoes without breaking bulk; and the people, advancing two months’ pay to their armament, sent along with it a fleet of merchant-vessels laden with the commodities, every ship being in charge of a public official. When the expedition reached its goal, the men purchased from these officials all they needed. In this way, the money was collected before the leaders again paid their men; so that the same payment sufficed until the expedition returned home.

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When the Samians entreated the Lacedaemonians for money to enable them to return to their country, the Lacedaemonians passed a resolution that they and their servants and their beasts of burden should go without food for one day; and that the expense each one thus saved should be given to the Samians.

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The people of Chalcedon had a large number of mercenary troops in their city, to whom they could not pay the wages they owed. Accordingly they made proclamation that anyone, either citizen or alien, who had right of reprisal against any city or individual, and wished to exercise it, should have his name entered on a list. A large number of names was enrolled, and the people thus obtained a specious pretext for exercising reprisal upon ships that were passing on their way to the Pontus. They accordingly arrested the ships and fixed a period within which they would consider any claims that might be made in respect of them. Having now a large fund in hand, they paid off the mercenaries, and set up a tribunal to decide the claims; and those whose goods had been unjustly seized were compensated out of the revenues of the state.

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At Cyzicus, civil strife broke out between the democratic and oligarchic parties. The former proved victorious, and the rich citizens were placed under arrest. But as the city owed money to its troops, a resolution was passed that the lives of those under arrest should be spared, and that they should be allowed to depart into exile on paying a sum of money to the state.

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At Chios there was a law that all debts should be entered on a public register. Being in need of funds, the people resolved that debtors should pay their debts into the treasury, and that the state should meet the creditors’ interest out of its revenues until its former prosperity returned.

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Mausolus lord of Caria received from the King of PersiaProbably Artaxerxes II. who reigned 405-359 B.C. a demand for tribute. Therefore he summoned the wealthiest men in his dominion, and told them that the King was asking for the tribute, and he had not the means of paying it. Men whom he had previously suborned at once came forward and declared what each was ready to contribute. With this example before them, they who were wealthier than these, partly in shame and partly in alarm, promised and paid much larger sums than the others.

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Being again in lack of funds, Mausolus summoned a public meeting of the people of Mylassa and told them that the King of Persia was preparing to attack him; and that Mylassa his capital city was unfortified. He therefore bade the citizens contribute each as liberally as he could, saying that what they now paid in would afford security to the rest of their possessions. By these means he obtained large contributions. But though he kept the money, he declared that heaven, for the present, forbade the building of the walls.

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Condalus, who was a lieutenant-governor under Mausolus, whenever on his progress through the country he was presented with a sheep, a pig, or a calf, had a record made of the donor’s name and of the date. He then bade the man take the beast home and keep it until he should again pass that way. After what he considered a sufficient interval, he would demand the beast together with such profits as he reckoned it had produced. All trees, too, which projected over the king’s highway, or fell thereon, he sold as profits accruing to the State.

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When one of his soldiers died, he charged a drachma for the right of passing the body through the gates. This was not only a source of revenue, but a check on the commanders, who were thus prevented from falsifying the date of the man’s death.

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Noticing that the Lycians were fond of wearing their hair long, Condalus proclaimed that a dispatch had arrived from the King ordering him to send hair to make forelocks for his horses; and that Mausolus had therefore instructed him to shave their heads. However, if they would pay him a fixed sum per head, he would send to Greece for hair. They were glad to comply with his demand, and a large sum was collected, the number of those taxed being great.

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Aristoteles of Rhodes,Mentioned by Proclus in his commentary on the Timaeus of Plato. A coin of Phocaea is extant bearing the name. when governor of Phocaea, found himself in need of funds. Noticing that there were at Phocaea two opposing parties, he held a secret conference with one of them, at which he declared that the other party was offering him money if he would favor their pretensions; that he, however, preferred to receive from those now before him, and to entrust to them the administration of the city. On hearing this, they immediately contributed the money he asked, and gave it him. Thereupon he told the other party what he had received from them; and they in turn promised him at least an equal amount. Having thus taken the money of both factions, he effected a reconciliation between them.

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He also observed that there were many law-suits pending between the citizens, and that they had grave and long-standing plaints against one another which had arisen in course of war. He therefore appointed a tribunal, and made proclamation that all who failed to appear before it within a stated period should lose the right to a legal decision of their outstanding claims. Then, by taking into his own hands the court-fees for a number of suits, and also those appeal-cases which involved penalties, and receiving [through others] money from both sides, he obtained altogether a very considerable sum.

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The people of Clazomenae, suffering from dearth of grain and scarcity of funds, passed a resolution that any private citizens who had stores of oil should lend it to the State at interest; this being a produce which their land bears in abundance. The loan arranged, they hired vessels and sent them to the depots whence they obtained their grain, 〈and bought a consignment〉 on security of the value of the oil.

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The same people, owing their mercenaries twenty talents of pay and being unable to find it, were giving the leaders of the troop four talents of interest each year. But failing to reduce the capital debt, and committed to this fruitless drain on their revenue, they struck an iron coinage of twenty talents, bearing the face-value of the silver. This they distributed proportionately among the wealthiest citizens, and received from them silver to the same amount. Through this expedient, the private citizens possessed a currency which was good for their daily needs, and the state was relieved of its debt. Next, they proceeded to pay interest out of revenue to those who had advanced the silver; and little by little distributed repayment among them, recalling at the same time the currency of iron.Plut. Lycurgus speaks of an iron currency at Sparta, and Seneca De beneficiis of a leather one. These, not being exchangeable abroad, threw the nation upon its own resources and prevented the import of luxuries.

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The people of Selybria had a law, passed in time of famine, which forbade the export of grain. On one occasion, however, they were in need of funds; and as they possessed large stores of grain, they passed a resolution that citizens should deliver up their corn to the state at the regular fixed price, each retaining for himself a year’s supply. They then granted right of export to any who desired it, fixing what they deemed a suitable price.

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At Abydos civil strife had caused the land to remain uncultivated; while the resident aliens, to whom the city was already indebted, refused to make any further advances. A resolution was accordingly passed that anyone who would might lend money to enable the farmers to cultivate their land, on the understanding that the lender had the first claim on its produce; others taking from what was then left.

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The people of Ephesus, being in need of funds, passed a law forbidding their women to wear gold, and ordering them to lend the State what gold they had in their possession.

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They also offered to any citizen who was willing to pay a fixed sum the right of having his name inscribed on a certain pillar of their templeThis temple, dedicated to Artemis, was restored with great magnificence after its destruction by fire in 356 B.C. For its fame see Acts 19. Portions of the sculptured pillars are to be seen in the British Museum. as the donor thereof.

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Dionysius of Syracuse, being desirous of collecting funds, called a public assembly, and declared that Demeter had appeared to him, and bade him convey all the women’s ornaments into her temple. That he himself had done so with the ornaments of his own household; and the others must now follow his example, and thereby avoid any visitation of the goddess’s anger. Anyone who failed to comply would, he declared, be guilty of sacrilege. Through fear of the goddess as well as of the despot, all the citizens brought in whatever they had. Then Dionysius, after sacrificing to the goddess, removed the ornaments to his own treasury as a loan which he had borrowed from her. As time went on, the women again appeared with precious ornaments. Dionysius thereupon issued a decree that any woman who desired to wear gold should make an offering of a fixed amount in the temple.

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Intending to build a fleet of triremes, Dionysius knew that he should require funds for the purpose. He therefore called an assembly and declared that a certain city was offered to him by traitors, and he needed money to pay them. The citizens therefore must contribute two staters apiece.The stater was a Persian gold coin worth 20 drachmae. (See 3.) The money was paid; but after two or three days, Dionysius, pretending that the plot had failed, thanked the citizens and returned to each his contribution. In this way he won the confidence of the citizens; so that when he again asked for money, they contributed in the expectation that they would receive it back. But this time he kept it for building the fleet.

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On another occasion being in straits for silver he minted a coinage of tin, and summoning a public assembly, spoke at length in its favor. The citizens perforce voted that everyone should regard as silver, and not as tin, whatever he received.

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Again being in need of funds, he requested the citizens to contribute. On their declaring that they had not the wherewithal, he brought out the furnishings of his palace and offered them for sale, pretending to be compelled through lack of money. At the sale, he had a list made of the articles and their purchasers; and when they had all paid, he commanded every one to bring back the article he had bought.

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Finding that because of his imposts the citizens were ceasing to rear sheep and cattle, he made proclamation that he needed no more money until a certain 〈date〉; so that those who now became possessed of any stock would not be liable to taxation. A large number of citizens lost no time in acquiring a quantity of sheep and cattle, on the understanding that they would be free of impost. But Dionysius, when he thought the fitting time was come, had them all valued and imposed a tax. The citizens were angry at being thus deceived, and proceeded to kill and sell their beasts. On Dionysius’s making a decree that only such beasts should be slain as were needed each day, the owners retorted by offering their animals as sacrifices; whereupon the despot forbade the sacrifice of female beasts.

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Once more funds were lacking, and Dionysius ordered a list to be made for him of all houses whose heirs were orphan. Having obtained a complete list, he made use of the orphans’ property until each should come of age.

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After the capture of Rhegium, he summoned a meeting of the citizens, and told them why he had a good right to sell them as slaves. If, however, they would pay him the expenses of the war and three minaeSee 3. a head besides, he would release them. The people of Rhegium brought forth all their hoards; the poor borrowed from the wealthier and from the foreigners resident in the city; and so the amount demanded was paid. But though he received this money from them, none the less he sold them all for slaves, having succeeded 〈by his trick〉 in bringing to light the hoarded goods which they had previously concealed.

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On another occasion he had borrowed money from the citizens, promising to repay it. On their demanding its return, he bade each bring him, under pain of death, whatever silver he possessed. This silver when brought he coined into drachmae each bearing the face value of two: with these he repaid the 〈previous〉 debt and also what had just been brought in.

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He also made a raid on Tyrrhenia with a hundred ships, and rifled the temple of Leucothea of a large amount of gold and silver, besides a quantity of works of art. But being aware that his sailors too had taken much plunder, he made proclamation that each should bring him, under pain of death, one-half of what he had; the remainder of their takings they might keep. On the understanding that if they brought in half their plunder they would retain the rest in security, they obeyed. But when Dionysius had got the treasure into his hands, he commanded them to bring him the other half as well.

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The people of Mende used to meet the expenses of administration from harbor and other duties, but refrained from collecting the imposts on land and on houses. They kept, however, a register of the owners, and when the state was in need of funds, they collected the arrears. Meanwhile the owners had the advantage of trafficking with their whole property undiminished by any payment of percentages.

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The same city being at war with Olynthus and needing funds, passed a resolution that all the slaves they possessed, with the exception of one male and one female apiece, should be sold on behalf of the State, which was thus enabled to raise a loan from private citizens.Or:that citizens should sell to the state what slaves they possessed . . . as the equivalent of a loan from private persons to the city 〈of the slaves’ value〉.

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Callistratus, when in Macedonia, caused the harbor-dues, which were usually sold for twenty talents, to produce twice as much. For noticing that only the wealthier men were accustomed to buy them because the sureties for the twenty talents were obliged to show talent for talent, he issued a proclamation that anyone might buy the dues on furnishing securities for one-third of the amount, or as much more as could be procured in each case.

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Timotheus of Athens during his campaign against Olynthus was short of silver, and issued to his men a copper coinage instead. On their complaining, he told them that all the merchants and retailers would accept it in lieu of silver. But the merchants he instructed to buy in turn with the copper they received such produce of the land as was for sale, as well as any booty brought to them; such copper as remained on their hands he would exchange for silver.

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During the campaign of CorcyraApparently in 375 B.C. See the end of Xenophon’s fifth Book ofHellenicaXen. Hell. 5. this same Timotheus was reduced to sore straits. His men demanded their pay; refused to obey his orders; and declared they would desert to the enemy. Accordingly he summoned a meeting and told them that the stormy weather was delaying the arrival of the silver he expected; meanwhile, as he had on hand such abundance of provisions, he would charge them nothing for the three months’ ration of grain already advanced. The men, unable to believe that Timotheus would have sacrificed so large a sum to them unless he was in truth expecting the money, made no further claim for pay until he had completed his dispositions.

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At the siege of Samos,In 366 B.C. Timotheus sold the crops and other country property to the besieged Samians themselves, and thus obtained plenty of money to pay his men. But finding the camp was short of provisions owing to the arrival of reinforcements, he forbade the sale of milled corn, or of any measure less than 1 1/2 bushels of corn or 8 1/2 gallons of wine or oil. Accordingly the officers bought supplies wholesale and issued them to their men; the reinforcements thenceforth brought their own provisions, and sold any surplus on their departure. In this way the needs of the soldiers were satisfactorily met.

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Didales the Persian was able to provide for the daily needs of his mercenaries from the enemy’s country; but had no coined money to give them. When their pay became due, and they demanded it, he had recourse to the following trick. He called a meeting, and told the men that he had plenty of money, but that it was stored in a certain fortress, which he named. He then broke up his encampment and marched in that direction. On reaching the neighborhood of the fortress, he himself went on ahead, and entering the place seized all the silver vessels in the temples. He then loaded his mules in such a way that this plate was exposed, thus suggesting that silver formed the entire load; and so continued his march. The soldiers, beholding the plate and supposing that they convoyed a full load of silver, were cheered by the expectation of their pay. They were informed however by Didales that they would have to take it to Amisus to be coined—a journey of many days, and in the winter season. And during all this time, he continued to employ the army without giving it more than its necessary rations.

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Moreover, all the craftsmen in the army, and the hucksters who traded with the soldiers by barter, were under his personal control, and enjoyed a complete monopoly.

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When Taos,Called Tachos (Ταχώς) by Xenophon and Plutarch. Perhaps that form should be restored here. (Bonitz and Susemihl.) The name recurs in 37. king of Egypt, needed funds for an expedition he was making, Chabrias of Athens advised him to inform the priests that to save expense it was necessary to suppress some of the temples together with the majority of the attendant priests. On hearing this, each priesthood, being anxious to retain their own temple, offered him money from their private possessions 〈as well as from the temple funds〉. When the king had thus received money from them all, Chabrias bade him tell the priests to spend on the temple-service and on their own maintenance one-tenth of what they formerly spent, and lend him the remainder until he had made peace with the King 〈of Persia〉.

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Moreover, each inhabitant was to contribute a stated proportion of his household and personal possessions; and when grain was sold, buyer and seller were each to contribute, apart from the price, one obol per artabeThe artabe was a Persian measure containing nearly 50 quarts. The obol was 1/6 of a drachma of silver.; while a tax of one tenth was to be imposed on profits arising from ships and workshops and other sources of gain.

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Again, when Taos was on the point of setting out from Egypt, Chabrias advised him to make requisition of all uncoined gold and silver in the possession of the inhabitants; and when most of them complied, he bade the king make use of the bullion, and refer the lenders to the governors of his provinces for compensation out of the taxes.

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Iphicrates of Athens provided Cotys with money for a force which he had collected in the following manner. He bade him order 〈each〉 of his subjects to sow for him a piece of land bearing 4 1/2 bushels. A large quantity of grain was thus gathered, from the price of which, when brought to the depots on the coast, the king obtained as much money as he wanted.

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Cotys of Thrace asked the people of Peirinthus for a loan to enable him to raise an army. On their refusing, he begged them at any rate to let him have some of their citizens to garrison certain fortresses, and release for active service the men who were there on duty. They readily complied, thinking thus to obtain control of the fortresses. But Cotys placed in custody the men they sent, and told the citizens that they might have them back when they had sent him the amount of the loan he desired.

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Mentor of Rhodes, after taking Hermias prisoner and seizing his fortresses, left in their various districts the officials appointed by him. By this means he restored their confidence, so that they all took again to themselves the property they had hidden or had sent secretly out of the country. Then Mentor arrested them and stripped them of all they had.

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Memnon of Rhodes, on making himself master of Lampsacus, found he was in need of funds. He therefore assessed upon the wealthiest inhabitants a quantity of silver, telling them that they should recover it from the other citizens. But when the other citizens made their contributions, Memnon said they must lend him this money also, fixing a certain date for its repayment.

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Again being in need of funds, he asked for a contribution, to be recovered, as he said, from the city revenues. The citizens complied, thinking that they would speedily reimburse themselves. But when the revenue payments came in, he declared that he must have these also, and would repay the lenders subsequently with interest.

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His mercenary troops he requested to forgo six days’ pay and rations each year, on the plea that on those days they were neither on garrison duty nor on the march nor did they incur any expense. (He referred to the days omitted from alternate months.As the moon’s cycle is completed in 29 1/2 days, it was customary to alternatehollow months of 29 days with thefull months of 30 days. Memnon paid his men by the month, but deducted a day’s pay everyhollow month.)

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Moreover, being accustomed previously to issue his men’s rations of corn on the second day of the month, in the first month he postponed the distribution for three days, and in the second month for five; proceeding in this fashion until at length it took place on the last day of the month.

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Charidemus of Oreus, being in occupation of certain fortress-towns in Aeolis, and threatened with an attack by Artabazus,For the circumstances, and a (hostile) account of this commander’s adventures, see Demosthenes,Against AristocratesDem. 23. was in need of money to pay his troops. After their first contributions, the inhabitants declared they had no more to give. Charidemus then issued a proclamation to the town he deemed wealthiest, bidding the inhabitants send away to another fortress all the coin and valuables they possessed, under convoy which he would provide. He himself openly set the example with his own goods, and prevailed on them to comply. But when he had conducted them a little way out of the town, he made an inventory of their goods, took all he wanted, and led them home again.

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He had also issued a proclamation in the cities he governed forbidding anyone to keep arms in his house, under pain of a stated fine. At first, however, he took no care to enforce it, nor did he make any inquisition; so that the people treated his proclamation as nugatory, and made no attempt to get rid of what arms each possessed. Then Charidemus unexpectedly ordered a search to be made from house to house, and exacted the penalty from those who were found in possession of arms.

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A Macedonian named Philoxenus, who was governor of Caria, being in need of funds proclaimed that he intended to celebrate the festival of Dionysus. The wealthiest inhabitants were selected to provide the choruses, and were informed what they were expected to furnish. Noticing their disinclination, Philoxenus sent to them privately and asked what they would give to be relieved of the duty. They told him they were prepared to pay a much larger sum than they expected to spend 〈on the choruses〉 in order to avoid the trouble and the interruption of their business. Philoxenus accepted their offers, and proceeded to enrol a second levy. These also paid; and at last he received what he desired from each company.

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Euaises the Syrian, when governor of Egypt, received information that the local governors were meditating rebellion. He therefore summoned them to the palace and proceeded to hang them all, sending word to their relations that they were in prison. These accordingly made offers, each on behalf of his own kinsman, seeking by payment to secure their release. Euaises agreed to accept a certain sum for each, and when it had been paid returned to the relations the dead body.

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While Cleomenes of Alexandria was governor of Egypt,Cf. Dem. 56:Cleomenes . . . from the time that he received the government, has done immense mischief to your state, and still more to the rest of Greece, by buying up corn for resale and keeping it at his own price ( Kennedy’s translation). at a time when there was some scarcity in the land, but elsewhere a grievous famine, he forbade the export of grain. On the local governors representing that if there were no export of grain they would be unable to pay in their taxes, he allowed the export, but laid a heavy duty on the corn. By this means he obtained a large amount of duty from a small amount of export, and at the same time deprived the officials of their excuse.

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When Cleomenes was making a progress by water through the province where the crocodile is worshipped, one of his servants was carried off. Accordingly, summoning the priests, he told them that he intended to retaliate on the crocodiles for this unprovoked aggression; and gave orders for a battue. The priests, to save the credit of their god, collected all the gold they could, and succeeded in putting an end to the pursuit.

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King Alexander had given Cleomenes command to establish a town near the island of Pharus, and to transfer thither the market hitherto held at Canopus. Sailing therefore to Canopus he informed the priests and the men of property there that he was come to remove them. The priests and residents thereupon contributed money to induce him to leave their market where it was. He took what they offered, and departed; but afterwards returned, when all was ready to build the town, and proceeded to demand an excessive sum; which represented, he said, the difference the change of site would make to him. They however declared themselves unable to pay it, and were accordingly removed.

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On another occasion he sent an agent to make a certain purchase for him. Learning that the agent had made a good bargain, but intended to charge him a high price, he proceeded to inform the man’s associates that he had been told he had purchased the goods at an excessive price, and that therefore he did not intend to recognize the transaction; denouncing at the same time with feigned anger the fellow’s stupidity. They on hearing this asked him not to believe what was said against the agent until he himself arrived and rendered his account. On the man’s arrival, his associates told him what Cleomenes had said. He, desirous of winning their approval as well as that of Cleomenes, debited the latter with the actual price he had given.

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At a time when the price of grain in Egypt was ten drachmae 〈a measure〉 ,If the measure intended is the Attic medimnos , it is 1 1/2 bushels. The Persian artabe may however be meant, which was equal to 1 medimnos and 1/16th. In either case the price is very high compared with 3 drachmae per medimnos, the price at Athens in 390 B.C. Yet Polybius 9.44 says that at Rome during the war with Hannibal (210) corn was sold for fifteen drachmae per medimnos. As a contrast cf. what the same author says of the fertility of Gallia Cisalpina, where in time of peace this same measure of wheat was sold for four obols, and of barley for two. See note on 25. Cleomenes sent for the growers and asked them at what price they would contract to supply him with their produce. On their quoting a price lower than what they were charging the merchants, he offered them the full price they were accustomed to receive from others; and taking over the entire supply, sold it at a fixed rate of thirty-two drachmae 〈for the same measure〉.

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He also sent for the priests, and told them that the expenditure on the temples was very unevenly distributed in the country; and that some of these, together with the majority of the attendant priests, must accordingly be suppressed. The priests, supposing him to be in earnest, and wishing each to secure the continuance of his own temple and office, gave him money individually from their private possessions as well as collectively from the temple funds.Cf. 25.

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Antimenes of Rhodes, who was appointed by Alexander superintendent of highways in the province of Babylon, adopted the following means of raising funds. An ancient law of the country imposed a tax of one-tenth on all imports; but this had fallen into total abeyance. Antimenes kept a watch for all governors and soldiers whose arrival was expected, and upon the many ambassadors and craftsmen who were invited to the city, but brought with them others who dwelt there unofficially; and also upon the multitude of presents that were brought 〈to these persons〉 , on which he exacted the legal tax of a tenth.

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Another expedient was this. He invited the owners of any slaves in the camp to register them at whatever value they desired, undertaking at the same time to pay him eight drachmae a year. If the slave ran away, the owner was to recover the registered value. Many slaves were thus registered, and a large sum of money was paid 〈in premiums〉. And when a slave ran away, Antimenes instructed the governor of the 〈province〉 where the camp lay either to recover the man or to pay his master his value.

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Ophellas of Olynthus appointed an officer to superintend the revenues of the Province of Athribis. The local governors came to him, and told him they were willing to pay a much larger amount in taxes; but asked him to remove the present superintendent. Ophellas inquired if they were really able to pay what they promised; and on their assuring him that they were, left the superintendent in office and instructed him to demand from them the amount of tax which they themselves had assessed. And so, without being chargeable either with discountenancing the officer he had appointed, or with taxing the governors beyond their own estimate, he obtained from the latter many times his previous revenue.

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Pythocles the Athenian recommended his fellow-countrymen that the State should take over from private citizens the lead obtained from the mines of LauriumThese silver mines were state property; but mining rights therein were let to private citizens. Lead and silver were found in the same ore and had to be separated. The weight of the lead is not specified: it may have been a talent of 80 lbs. See Boeckh, Staatshaushaltung der Athener; and Xen. Ways. at the price of two drachmae 〈per talent〉 which they were asking, and should itself sell it at the fixed price of six drachmae.

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Chabrias had levied crews for a hundred and twenty ships to serve King Taos.See 25. Finding that Taos needed only sixty ships, he gave the crews of the superfluous sixty their choice between providing those who were to serve with two months’ rations, and themselves taking their place. Desiring to remain at their business, they gave what he demanded.

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Antimenes bade the governors of the provinces replenish, in accordance with the law of the country, the magazines along the royal highways. Whenever an army passed through the country or any other body of men unaccompanied by the king, he sent an officer to sell them the contents of the magazines.

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Cleomenes, as the beginning of the month approached when his soldiers’ allowance became due, deliberately sailed away down the river; and not till the month was advanced did he return and distribute the allowance. For the coming month, he omitted the distribution altogether until the following month began. Thus the men were quieted by the recent distribution, and Cleomenes, passing over a month each year, docked his troops of a month’s pay.σιταρχία (corn allowance) and μισθός (pay) here seem to be identified; possibly because in a land where grain was readily purchasable the former was given in money. Cf. 23, 29.

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Stabelbius, king of the Mysians, lacking pay to give his troops, summoned a meeting of the officers, and declared that he no longer needed the private soldiers, but only the officers. When he required troops, he would entrust a sum of money to each officer and send him to collect mercenaries; but that meanwhile he preferred to give the officers the pay he would otherwise have to give the men. Accordingly he bade each dismiss the men who were on his own muster-roll. The officers, scenting a source of gain for themselves, dismissed their men, as they were bidden. Shortly afterwards, Stabelbius called them together and informed them that a conductor without his chorus and an officer without his men were alike useless; wherefore let them depart from his country.

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When Dionysius was making a tour of the temples, wherever he saw a gold or silver table set, he bade them fill a cupin honor of the good spirit,Cf. Cic. De natura deorum 3.3.4 and Athenaeus Deipnosophistae 15.693. and then had the table carried away. Wherever, again, he saw a precious bowl set before one of the images, he would order its removal, with the words I accept it. He also stripped the images of their golden raiment and garlands, and declaring he would give them lighter and more fragrant wear, arrayed them in robes of white 〈linen〉 and garlands of white socks.

 - + diff --git a/data/tlg0086/tlg029/tlg0086.tlg029.perseus-eng2.xml b/data/tlg0086/tlg029/tlg0086.tlg029.perseus-eng2.xml new file mode 100644 index 000000000..b446e5b8a --- /dev/null +++ b/data/tlg0086/tlg029/tlg0086.tlg029.perseus-eng2.xml @@ -0,0 +1,304 @@ + + + + + + + Economics + Aristotle + George Cyril Armstrong + Perseus Project, Tufts University + Gregory Crane + + Prepared under the supervision of + Lisa Cerrato + William Merrill + Elli Mylonas + David Smith + + The Annenberg CPB/Project + + + + Trustees of Tufts University + Medford, MA + Perseus Digital Library Project + Perseus 2.0 + tlg0086.tlg029.perseus-eng2.xml + + Available under a Creative Commons Attribution-ShareAlike 4.0 International License + + + + + + + The Metaphysics; The Oeconomica and The Magna Moralia + Aristotle + George Cyril Armstrong + + William Heinemann Ltd. + London + Harvard University Press + Cambridge, MA + 1935 + + + + Loeb Classical Library + + Internet Archive + + + + + + + +

This pointer pattern extracts book and section and subsection.

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This pointer pattern extracts book and section.

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This pointer pattern extracts book.

+ + + + + + + + English + Greek + Latin + + + + + EpiDoc and CTS conversion and general header review. +cleaned up bad place tags in a few texts and cleaned up the document format + more reorganizing of texts module by collection + began reorganizing texts module by collection. created separate work directory in texts module to keep hopper files separate from in progress files + edited entity tags CEH + + added cvs log keyword + Put Bekker line 1 milestone tags at the beginning of each section so that the incoming list creator would work. Changed RREFDECL. + Tagged in conformance with Prose.e dtd. + Text was scanned at St. Olaf Spring, 1992. + + + + + + +
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Between Housecraft (the art of governing a Household or Home) and Statecraft (the art of governing a Nation) there are differences corresponding to those between the two kinds of community over which they severally preside. There is, however, this further difference: that whereas the government of a nation is in many hands, a household has but a single ruler.

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Now some arts are divided into two separate branches, one concerned with the making of an object—for example a lyre or a flute—and the other with its use when made. Statecraft on the other hand shows us how to build up a nation from its beginning, as well as how to order rightly a nation that already exists; from which we infer that Housecraft also tells us first how to acquire a household and then how to conduct its affairs.

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By a Nation we mean an assemblage of houses, lands, and property sufficient to enable the inhabitants to lead a civilized life. This is proved by the fact that when such a life is no longer possible for them, the tie itself which unites them is dissolved. Moreover, it is with such a life in view that the association is originally formed; and the object for which a thing exists and has come into being is in fact the very essence of that particular thing.

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From this definition of a Nation, it is evident that the art of Housecraft is older than that of Statecraft, since the Household, which it creates, is older; being a component part of the Nation created by Statecraft.

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Accordingly we must consider the nature of Housecraft, and what the Household, which it creates, actually is.

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The component parts of a household are (l) human beings, and (2) goods and chattels. And as households are no exception to the rule that the nature of a thing is first studied in its barest and simplest form, we will follow Hesiod and begin by postulatingHomestead first, and a woman; a plough-ox hardy to furrow. For the steading takes precedence among our physical necessities, and the woman among our free associates. It is, therefore, one of the tasks of Homecraft to set in order the relation between man and woman; in other words, to see that it is what it ought to be.

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Of occupations attendant on our goods and chattels, those come first which are natural. Among these precedence is given to the one which cultivates the land; those like mining, which extract wealth from it, take the second place. Agriculture is the most honest of all such occupations; seeing that the wealth it brings is not derived from other men. Herein it is distinguished from trade and the wage-earning employments, which acquire wealth from others by their consent; and from war, which wrings it from them perforce. It is also a natural occupation; since by Nature’s appointment all creatures receive sustenance from their mother, and mankind like the rest from their common mother the earth.

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And besides all this, agriculture contributes notably to the making of a manly character; because, unlike the mechanical arts, it does not cripple and weaken the bodies of those engaged in it, but inures them to exposure and toil and invigorates them to face the perils of war. For the farmer’s possessions, unlike those of other men, lie outside the city’s defences.

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When we turn our attention to the human part of the household, it is the woman who makes the first claim upon it; 〈for the natural comes first, as we have said,〉 and nothing is more natural than the tie between female and male. For we have elsewhere laid down the premissCf. Aristot. Pol. 1.1. that Nature is intent on multiplying severally her types; and this is true of every animal in particular. Neither the female, however, can effect this without the male, nor the male without the female; whence the union of the sexes has of necessity arisen.

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Now among the lower animals, this union is irrational in character; it exists merely for the purpose of procreation, and lasts only so long as the parents are occupied in producing their brood. In tame animals, on the other hand, and those which possess a greater share of intelligence, it has assumed a more complex form; for in their case we see more examples of mutual help, goodwill, and co-operation.

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It is, however, in the human species that this complexity is most marked; since the co-operation between woman and man aims not merely at existence, but at a happy existence. Nor do mankind beget children merely to pay the service they owe to Nature, but also that they may themselves receive a benefit; for the toil they undergo while they are strong and their offspring is still weak is repaid by that offspring when it in turn is grown strong and the parents by reason of age are weak.

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At the same time Nature, by this cycle of changes, fulfills her purpose of perpetuating existence; preserving the type when she is unable to preserve the individual.Cf. Aristot. De Gen. An. 731b. And so with this purpose in view Divine Providence has fashioned the nature of man and of woman for their partnership. For they are distinguished from each other by the possession of faculties not adapted in every case to the same tasks, but in some cases for opposite ones, though contributing to the same end. For Providence made man stronger and woman weaker, so that he in virtue of his manly prowess may be more ready to defend the home, and she, by reason of her timid nature, more ready to keep watch over it; and while he brings in fresh supplies from without, she may keep safe what lies within. In handicrafts again, woman was given a sedentary patience, though denied stamina for endurance of exposure; while man, though inferior to her in quiet employments, is endowed with vigor for every active occupation. In the production of children both share alike; but each makes a different contribution to their upbringing. It is the mother who nurtures, and the father who educates.

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We begin then with the rules that should govern a man’s treatment of his wife. And the first of these forbids him to do her wrong; for if he observes this, he is not likely himself to suffer wrong at her hands. As the Pythagoreans declare, even the common rule or custom of mankind thus ordains, forbidding all wrong to a wife as stringently as though she were a suppliant whom one has raised from the hearthstone. And a man does wrong to his wife when he associates with other women.

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As regards the intercourse of marriage, wives should neither importune their husbands, nor be restless in their absence; but a man should accustom his wife to be content whether he is at home or away. Good also is the advice of Hesiod: Take thee a maiden to wife, and teach her ways of discretion. Hes. WD 699 For differences of ways and habits are little conducive to affection.

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As regards adornment: it is not well that souls should approach one another in borrowed plumes, nor is it well in the case of bodies. Intercourse which depends 〈for its charm〉 upon outward adornment differs in no respect from that of figures on the stage in their conventional attire.

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Of property, the first and most indispensable kind is that which is also best and most amenable to Housecraft; and this is the human chattel. Our first step therefore must be to procure good slaves. Of slaves there are two kinds; those in positions of trust, and the laborers. And since it is matter of experience that the character of the young can be moulded by training, when we require to charge slaves with tasks befitting the free, we have not only to procure the slaves, but to bring them up 〈for the trust〉.

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In our intercourse with slaves we must neither suffer them to be insolent nor treat them with cruelty. A share of honor should be given to those who are doing more of a freeman’s work, and abundance of food to those who are laboring with their hands. And whereas the use of wine renders even free men insolent, so that in many countries they too refrain from it—as, for instance, the Carthaginians do when they are on campaign—it follows that we must either deny wine to slaves altogether, or reserve it for rare occasions.

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We may apportion to our slaves (1) work, (2) chastisement, and (3) food. If men are given food, but no chastisement nor any work, they become insolent. If they are made to work, and are chastised, but stinted of their food, such treatment is oppressive, and saps their strength. The remaining alternative, therefore, is to give them work, and a sufficiency of food. Unless we pay men, we cannot control them; and food is a slave’s pay.

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Slaves, again, are no exception to the rule that men become worse when better conduct is not followed by better treatment, but virtue and vice remain alike unrewarded.

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Accordingly we must keep watch over our workers, suiting our dispensations and indulgences to their desert; whether it be food or clothing, leisure or chastisement that we are apportioning. Both in theory and in practice we must take for our model a physician’s freedom in prescribing his medicines; observing at the same time that food differs from medicine in that it requires to be constantly administered.

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The best laborers will be furnished by those races of mankind which are neither wholly spiritless nor yet overbold. Each extreme has its vice; the spiritless cannot endure hard labor, and the high-spirited will not readily brook control.

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Every slave should have before his eyes a definite goal or term of his labor. To set the prize of freedom before him is both just and expedient; since having a prize to work for, and a time defined for its attainment, he will put his heart into his labors. We should, moreover, take hostages 〈for our slaves’ fidelity〉 by allowing them to beget children; and avoid the practice of purchasing many slaves of the same nationality, as men avoid doing in towns. We should also keep festivals and give treats, more on the slaves account than on that of the freemen; since the free have a fuller share in those enjoyments for the sake of which these institutions exist.

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There are four qualities which the head of a household must possess in dealing with his property. Firstly, he must have the faculty of acquiring, and secondly that of preserving what he has acquired; otherwise there is no more benefit in acquiring than in baling with a colander, or in the proverbial wine-jar with a hole in the bottom. Thirdly and fourthly, he must know how to improve his property, and how to make use of it; since these are the ends for which the powers of acquisition and of preservation are sought.

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Everything we possess should be duly classified ; and the amount of our productive property exceed that of the unproductive. Produce should be so employed that we do not risk all our possessions at once. For the safe keeping of our property, we shall do well to adopt the Persian and Laconian systems. Athenian housecraft has, however, some advantages. The Athenian buys immediately with the produce of his sales, and the smaller households keep no idle deposits in store.

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Under the Persian system, the master himself undertook the entire disposition and supervision of the household, following the practice which Dion used to remark in Dionysius. No one, indeed, takes the same care of another’s property as of his own; so that, as far as is possible, each man ought to attend to his affairs in person. We may commend also a pair of sayings, one attributed to a Persian and the other to a Libyan. The former on being asked what best conditions a horse, repliedHis master’s eye.Cf. Xen. Ec. 12. The Libyan, when asked what kind of manure is best, answeredThe master’s footprints.

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The master and mistress should, therefore, give personal supervision, each to his or her special department of the household work. In small households, an occasional inspection will suffice; in estates managed through stewards, inspections must be frequent. For in stewardship as in other matters there can be no good copy without a good example; and if the master and mistress do not attend diligently to their estate, their deputies will certainly not do so.

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Moreover, as such habits are both commendable for moral reasons and also conducive to good management, the master and mistress will do well to rise earlier than their servants and to retire later; to treat their home as a city, and never leave it unguarded; nor ever, by night or by day, to postpone a task which ought to be done. Rising before daylight is also to be commended; it is a healthy habit, and gives more time for the management of the household as well as for liberal studies.

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We have remarked that on small holdings the Athenian method of disposing of the produce is advantageous. On large estates, after the amount for the year’s or the month’s outlay has been set apart, it should be handed to the overseers; and so also with implements, whether for daily or for occasional use. In addition, an inspection of implements and stores should be made periodically, so that remainders and deficiencies may alike be noted.

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In constructing a homestead, we have to provide for the stock which it is to shelter, and for its health and well-being. Providing for the stock involves questions such as these: What type of building is best for the storage of crops and of clothing? How are we to store the dry crops, and how the moist ones? Of the other stock, how is the living to be housed, and how the dead? and what accommodation are we to make for slaves and free, for women and men, for foreigners and fellow-citizens? For well-being and health, again, the homestead should be airy in summer, and sunny in winter.

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A homestead possessing these qualities would be longer than it is deep; and its main front would face the south. On large estates, moreover, it seems worth while to instal as porter a man incapable of other work, to keep his eye on what passes in and out. That implements may be ready for use, the Laconian practice should be followed. Each should be kept in its own place; thus it will always be to hand, and not require seeking.

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Right administration of a household demands in the first place familiarity with the sphere of one’s actionOr,the localities wherein we work.; in the second Place, good natural endowments; and in the third, an uprights and industrious way of life. For the lack of any one of these qualifications will involve many a failure in the task one takes in hand.

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Of such administrations there are four main types, under which all others may be classified. We have the administration of a king; of the governors under him; of a free state; and of a private citizen.

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Of these, that of a king is the most extensive, yet at the same time the simplest. A governor’s office is also very extensive, but divided into a great variety of departments. The administration of a free state is again very varied, but it is the easiest to conduct; while that, of a private individual presents the like variety, but within limits which are narrowest of all. For the most part, all four will of necessity cover the same ground; we will, however, take them in turn, and see what is especially characteristic of each.

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Taking first the royal administration, we see that while theoretically its power is unlimited, it is in practice concerned with four departments, namely currency, exports, imports, and expenditure.

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Taking these severally, I assign to that of currency the seasonable regulation of prices; to imports and exports, the profitable disposition, at any given time, of the dues received from provincial governors; and to expenditure, the reduction of outgoings as occasion may serve, and the question of meeting expenses by currency or by commodities.

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The second kind of administration, that of the governor, is concerned with six different classes of revenue; those, namely, arising from agriculture, from the special products of the country, from markets, from taxes, from cattle, and from other sources.

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Taking these in turn, the first and most important of them is revenue from agriculture, which some call tithe and some produce-tax.Boeckh translates ἐκφόριονGrundsteuer. But how then does it differ from τῶν κατὰ γῆν τελῶν below? The second is that from special products; in one place gold, in another silver, in another copper, and so on. Third in importance is revenue from markets, and fourth that which arises from taxes on land and on sales. In the fifth place we have revenue from cattle, called tithe or first-fruits; and in the sixth, revenue from other sources, which we term poll-tax, or tax on industry.

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Of our third kind of administration, that of a free state, the most important revenue is that arising from the special products of the country. Next follows revenue from markets and occupations; and finally that from every-day transactions.Or (understanding λειτουργιῶν)regular public services.

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Fourthly and lastly, we must consider the administration of a private citizen. It is difficult to reduce this to rules owing to the necessary variety of its aims; yet it is the most limited of the four, because both revenues and expenses are 〈comparatively〉 small. Taking its revenues in turn, the chief are those from agriculture; next in importance, those from other every-day occupations; while third comes interest on money. Apart from all these, there is a matter common to all kinds of administration which is best considered at this particular point, and deserves more than cursory attention. This is the importance of keeping expenditure within the limits of revenue.

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Having thus enumerated the divisions of our subject, we must next consider whether the province or the free state with which we are concerned is able to produce all the forms of revenue we have just detailed or at least the chief of them; 〈and this being known〉 must make the best use of what we have. Next we must inquire what kinds of revenue, at present wholly lacking, are yet potentially existent; what kinds, though now small, may with care be increased, and how far certain items of present expenditure may without prejudice to the commonwealth be diminished.

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Having spoken thus of administrations and their various departments, we have further proceeded to collect such instances as we deemed noteworthy of the means adopted by certain statesmen in times past for the replenishment of the treasury, and also of their skill in administration. These anecdotes 〈which follow〉, seemed to us by no means lacking in utility; being capable from time to time of application by others to the business they themselves have in hand.

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Cypselus of Corinth had made a vow that if he became master of the city, he would offer to Zeus the entire property of the Corinthians. Accordingly he commanded them to make a return of their possessions; which done, he took from each a tenth part, and told them to employ the remainder in trading. A year later, he repeated the process. And so in ten years’ time it came to pass that Cypselus received the entire amount which he had dedicated; while the Corinthians on their part had replaced all that they had paid him.

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Lygdamis of Naxos, after driving into exile a party of the inhabitants, found that no one would give him a fair price for their property. He therefore sold it to the exiled owners. The exiles had left behind them a number of works of art destined for temple offerings, which lay in certain workshops in an unfinished condition. These Lygdamis proceeded to sell to the exiles and whoso else would buy them; allowing each purchaser to have his name engraved on the offering.

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The people of Byzantium, being in need of funds, sold such dedicated lands as belonged to the State; those under crops, for a term of years, and those uncultivated, in perpetuity. In like manner they sold lands appropriated to religious celebrations or ancestral cults, not excepting those that were on private estatesSee Lys. 7, the seventh Speech of the Athenian orator Lysias.; for the owners of the surrounding land were ready to give a high price for them. To the dispossessed celebrants 〈they assigned〉 such other public lands surrounding the gymnasium, the agora, or the harbor, as belonged to the State. Moreover they claimed as public property all open spaces where anything was sold, together with the sea-fisheries, the traffic in salt, and the trade of professional conjurors, soothsayers, charm-sellers, and the like; exacting from all these one-third of their gains. The right of changing money they sold to a single bank, whose proprietor was given a monopoly of the sale and purchase of coin, protected under penalty of confiscation.

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And whereas previously the rights of citizenship were by law confined to those whose parents were both citizens, lack of funds, induced them to offer citizenship to him who had one citizen parent on payment of the sum of thirty minae.A mina of silver (1 lb. 5 oz. avoirdupois) was coined into 100 drachmae, each being an artisan’s ordinary daily wage.

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On another occasion, when food and funds were both scarce, they called home all vessels that were trading in the Pontus. On the merchants protesting, they were at length allowed to trade on payment of a tithe of their profits. This tax of 10 per cent was also extended to purchases of every kind.

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It happened that certain aliens residing in the city had lent money on the security of citizens’ property. As these aliens did not possess the right of holding such property, the people offered to recognize the title of anyone who chose to pay into the treasury one third of the amount secured.

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Hippias of Athens offered for sale upper stories that projected over the public streets,Cf. Goethe,Warheit und Dichtung, Book I.In Frankfurt, as in several ancient cities, those who had erected wooden buildings had sought to obtain more room by allowing the first and higher floors to overhang in the street. . . . At last a law was carried that in all entirely new houses the first floor alone should project; above that, the wall should be perpendicular. The poet’s father, wishing to rebuild his house without sacrifice of floor-space, underpinned the upper stories and renewed the building piecemeal from below. Cf. also 14. together with flights of steps, railings, and doors that opened outwards. The owners of the buildings bought them, and in this way a large sum of money was collected.

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He also called inLit.rendered invalid. the existing currency, promising to pay the holders at a fixed rate. But when they came to receive the new mintage, he reissued the old coins.

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Those who were expecting to equip a war-vessel or preside over a tribe or train a chorus or undertake the expense of some other public service of the kind, he allowed, if they chose, to commute the service for a moderate sum, and to be enrolled on the list of those who had performed it.

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Moreover, whenever a citizen died, the priestess of the temple of Athena on the AcropolisThis was the public treasury, like the Temple of Saturnus at Rome. was to receive one quart measure of barley, one of wheat, and a silver obolus.1/6 of the drachma. See 3 above. And when a child was born, the father paid the same dues.

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The Athenian colonists at Potidaea, being in need of funds for the war, agreed that all should make a return of their property for assessment of tax. But instead of each returning the entire amount to his own parish, properties were to be assessed separately, each in its own locality, so that the poor might propose a reduced assessment; while those without any 〈landed〉 property were assessed at two minae a head. On these assessments each man paid the State the full amount of the war-tax.

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The city of Antissa had been accustomed to celebrate the festival of Dionysus with great magnificence. Year by yearOrAll through the year. great provision was made for the occasion, and costly sacrifices were prepared. Now one year the city found itself in need of funds; and shortly before the festival, on the proposal of a citizen named Sosipolis, the people after vowing that they would next year offer to Dionysus a double amount, collected all that had been provided and sold it. In this way they realized a large sum of money to meet their necessity.

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On one occasion the people of Lampsacus were expecting to be attacked by a large fleet of triremes.War-ships, each propelled by some 174 rowers ranked in three tiers. The price of barley meal being then four drachmae for a bushel and a half, they instructed the retailers to sell it at six drachmae. Oil, which was at three drachmae for six pints, was to be sold at four drachmae and a half, and wine and other commodities at a proportionate increase. In this way the retailer got the original price, while the State took the addition and filled its treasury.

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The people of Heraclea, being about to dispatch a fleet of forty ships against the lords of Bosporus, were at a loss for the necessary funds. They therefore bought up all the merchants’ stock of corn and oil and wine and other marketable commodities, agreeing to pay at a future date. The merchants were well satisfied that they had disposed of their cargoes without breaking bulk; and the people, advancing two months’ pay to their armament, sent along with it a fleet of merchant-vessels laden with the commodities, every ship being in charge of a public official. When the expedition reached its goal, the men purchased from these officials all they needed. In this way, the money was collected before the leaders again paid their men; so that the same payment sufficed until the expedition returned home.

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When the Samians entreated the Lacedaemonians for money to enable them to return to their country, the Lacedaemonians passed a resolution that they and their servants and their beasts of burden should go without food for one day; and that the expense each one thus saved should be given to the Samians.

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The people of Chalcedon had a large number of mercenary troops in their city, to whom they could not pay the wages they owed. Accordingly they made proclamation that anyone, either citizen or alien, who had right of reprisal against any city or individual, and wished to exercise it, should have his name entered on a list. A large number of names was enrolled, and the people thus obtained a specious pretext for exercising reprisal upon ships that were passing on their way to the Pontus. They accordingly arrested the ships and fixed a period within which they would consider any claims that might be made in respect of them. Having now a large fund in hand, they paid off the mercenaries, and set up a tribunal to decide the claims; and those whose goods had been unjustly seized were compensated out of the revenues of the state.

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At Cyzicus, civil strife broke out between the democratic and oligarchic parties. The former proved victorious, and the rich citizens were placed under arrest. But as the city owed money to its troops, a resolution was passed that the lives of those under arrest should be spared, and that they should be allowed to depart into exile on paying a sum of money to the state.

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At Chios there was a law that all debts should be entered on a public register. Being in need of funds, the people resolved that debtors should pay their debts into the treasury, and that the state should meet the creditors’ interest out of its revenues until its former prosperity returned.

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Mausolus lord of Caria received from the King of PersiaProbably Artaxerxes II. who reigned 405-359 B.C. a demand for tribute. Therefore he summoned the wealthiest men in his dominion, and told them that the King was asking for the tribute, and he had not the means of paying it. Men whom he had previously suborned at once came forward and declared what each was ready to contribute. With this example before them, they who were wealthier than these, partly in shame and partly in alarm, promised and paid much larger sums than the others.

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Being again in lack of funds, Mausolus summoned a public meeting of the people of Mylassa and told them that the King of Persia was preparing to attack him; and that Mylassa his capital city was unfortified. He therefore bade the citizens contribute each as liberally as he could, saying that what they now paid in would afford security to the rest of their possessions. By these means he obtained large contributions. But though he kept the money, he declared that heaven, for the present, forbade the building of the walls.

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Condalus, who was a lieutenant-governor under Mausolus, whenever on his progress through the country he was presented with a sheep, a pig, or a calf, had a record made of the donor’s name and of the date. He then bade the man take the beast home and keep it until he should again pass that way. After what he considered a sufficient interval, he would demand the beast together with such profits as he reckoned it had produced. All trees, too, which projected over the king’s highway, or fell thereon, he sold as profits accruing to the State.

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When one of his soldiers died, he charged a drachma for the right of passing the body through the gates. This was not only a source of revenue, but a check on the commanders, who were thus prevented from falsifying the date of the man’s death.

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Noticing that the Lycians were fond of wearing their hair long, Condalus proclaimed that a dispatch had arrived from the King ordering him to send hair to make forelocks for his horses; and that Mausolus had therefore instructed him to shave their heads. However, if they would pay him a fixed sum per head, he would send to Greece for hair. They were glad to comply with his demand, and a large sum was collected, the number of those taxed being great.

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Aristoteles of Rhodes,Mentioned by Proclus in his commentary on the Timaeus of Plato. A coin of Phocaea is extant bearing the name. when governor of Phocaea, found himself in need of funds. Noticing that there were at Phocaea two opposing parties, he held a secret conference with one of them, at which he declared that the other party was offering him money if he would favor their pretensions; that he, however, preferred to receive from those now before him, and to entrust to them the administration of the city. On hearing this, they immediately contributed the money he asked, and gave it him. Thereupon he told the other party what he had received from them; and they in turn promised him at least an equal amount. Having thus taken the money of both factions, he effected a reconciliation between them.

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He also observed that there were many law-suits pending between the citizens, and that they had grave and long-standing plaints against one another which had arisen in course of war. He therefore appointed a tribunal, and made proclamation that all who failed to appear before it within a stated period should lose the right to a legal decision of their outstanding claims. Then, by taking into his own hands the court-fees for a number of suits, and also those appeal-cases which involved penalties, and receiving [through others] money from both sides, he obtained altogether a very considerable sum.

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The people of Clazomenae, suffering from dearth of grain and scarcity of funds, passed a resolution that any private citizens who had stores of oil should lend it to the State at interest; this being a produce which their land bears in abundance. The loan arranged, they hired vessels and sent them to the depots whence they obtained their grain, 〈and bought a consignment〉 on security of the value of the oil.

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The same people, owing their mercenaries twenty talents of pay and being unable to find it, were giving the leaders of the troop four talents of interest each year. But failing to reduce the capital debt, and committed to this fruitless drain on their revenue, they struck an iron coinage of twenty talents, bearing the face-value of the silver. This they distributed proportionately among the wealthiest citizens, and received from them silver to the same amount. Through this expedient, the private citizens possessed a currency which was good for their daily needs, and the state was relieved of its debt. Next, they proceeded to pay interest out of revenue to those who had advanced the silver; and little by little distributed repayment among them, recalling at the same time the currency of iron.Plut. Lycurgus speaks of an iron currency at Sparta, and Seneca De beneficiis of a leather one. These, not being exchangeable abroad, threw the nation upon its own resources and prevented the import of luxuries.

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The people of Selybria had a law, passed in time of famine, which forbade the export of grain. On one occasion, however, they were in need of funds; and as they possessed large stores of grain, they passed a resolution that citizens should deliver up their corn to the state at the regular fixed price, each retaining for himself a year’s supply. They then granted right of export to any who desired it, fixing what they deemed a suitable price.

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At Abydos civil strife had caused the land to remain uncultivated; while the resident aliens, to whom the city was already indebted, refused to make any further advances. A resolution was accordingly passed that anyone who would might lend money to enable the farmers to cultivate their land, on the understanding that the lender had the first claim on its produce; others taking from what was then left.

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The people of Ephesus, being in need of funds, passed a law forbidding their women to wear gold, and ordering them to lend the State what gold they had in their possession.

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They also offered to any citizen who was willing to pay a fixed sum the right of having his name inscribed on a certain pillar of their templeThis temple, dedicated to Artemis, was restored with great magnificence after its destruction by fire in 356 B.C. For its fame see Acts 19. Portions of the sculptured pillars are to be seen in the British Museum. as the donor thereof.

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Dionysius of Syracuse, being desirous of collecting funds, called a public assembly, and declared that Demeter had appeared to him, and bade him convey all the women’s ornaments into her temple. That he himself had done so with the ornaments of his own household; and the others must now follow his example, and thereby avoid any visitation of the goddess’s anger. Anyone who failed to comply would, he declared, be guilty of sacrilege. Through fear of the goddess as well as of the despot, all the citizens brought in whatever they had. Then Dionysius, after sacrificing to the goddess, removed the ornaments to his own treasury as a loan which he had borrowed from her. As time went on, the women again appeared with precious ornaments. Dionysius thereupon issued a decree that any woman who desired to wear gold should make an offering of a fixed amount in the temple.

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Intending to build a fleet of triremes, Dionysius knew that he should require funds for the purpose. He therefore called an assembly and declared that a certain city was offered to him by traitors, and he needed money to pay them. The citizens therefore must contribute two staters apiece.The stater was a Persian gold coin worth 20 drachmae. (See 3.) The money was paid; but after two or three days, Dionysius, pretending that the plot had failed, thanked the citizens and returned to each his contribution. In this way he won the confidence of the citizens; so that when he again asked for money, they contributed in the expectation that they would receive it back. But this time he kept it for building the fleet.

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On another occasion being in straits for silver he minted a coinage of tin, and summoning a public assembly, spoke at length in its favor. The citizens perforce voted that everyone should regard as silver, and not as tin, whatever he received.

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Again being in need of funds, he requested the citizens to contribute. On their declaring that they had not the wherewithal, he brought out the furnishings of his palace and offered them for sale, pretending to be compelled through lack of money. At the sale, he had a list made of the articles and their purchasers; and when they had all paid, he commanded every one to bring back the article he had bought.

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Finding that because of his imposts the citizens were ceasing to rear sheep and cattle, he made proclamation that he needed no more money until a certain 〈date〉; so that those who now became possessed of any stock would not be liable to taxation. A large number of citizens lost no time in acquiring a quantity of sheep and cattle, on the understanding that they would be free of impost. But Dionysius, when he thought the fitting time was come, had them all valued and imposed a tax. The citizens were angry at being thus deceived, and proceeded to kill and sell their beasts. On Dionysius’s making a decree that only such beasts should be slain as were needed each day, the owners retorted by offering their animals as sacrifices; whereupon the despot forbade the sacrifice of female beasts.

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Once more funds were lacking, and Dionysius ordered a list to be made for him of all houses whose heirs were orphan. Having obtained a complete list, he made use of the orphans’ property until each should come of age.

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After the capture of Rhegium, he summoned a meeting of the citizens, and told them why he had a good right to sell them as slaves. If, however, they would pay him the expenses of the war and three minaeSee 3. a head besides, he would release them. The people of Rhegium brought forth all their hoards; the poor borrowed from the wealthier and from the foreigners resident in the city; and so the amount demanded was paid. But though he received this money from them, none the less he sold them all for slaves, having succeeded 〈by his trick〉 in bringing to light the hoarded goods which they had previously concealed.

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On another occasion he had borrowed money from the citizens, promising to repay it. On their demanding its return, he bade each bring him, under pain of death, whatever silver he possessed. This silver when brought he coined into drachmae each bearing the face value of two: with these he repaid the 〈previous〉 debt and also what had just been brought in.

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He also made a raid on Tyrrhenia with a hundred ships, and rifled the temple of Leucothea of a large amount of gold and silver, besides a quantity of works of art. But being aware that his sailors too had taken much plunder, he made proclamation that each should bring him, under pain of death, one-half of what he had; the remainder of their takings they might keep. On the understanding that if they brought in half their plunder they would retain the rest in security, they obeyed. But when Dionysius had got the treasure into his hands, he commanded them to bring him the other half as well.

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The people of Mende used to meet the expenses of administration from harbor and other duties, but refrained from collecting the imposts on land and on houses. They kept, however, a register of the owners, and when the state was in need of funds, they collected the arrears. Meanwhile the owners had the advantage of trafficking with their whole property undiminished by any payment of percentages.

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The same city being at war with Olynthus and needing funds, passed a resolution that all the slaves they possessed, with the exception of one male and one female apiece, should be sold on behalf of the State, which was thus enabled to raise a loan from private citizens.Or:that citizens should sell to the state what slaves they possessed . . . as the equivalent of a loan from private persons to the city 〈of the slaves’ value〉.

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Callistratus, when in Macedonia, caused the harbor-dues, which were usually sold for twenty talents, to produce twice as much. For noticing that only the wealthier men were accustomed to buy them because the sureties for the twenty talents were obliged to show talent for talent, he issued a proclamation that anyone might buy the dues on furnishing securities for one-third of the amount, or as much more as could be procured in each case.

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Timotheus of Athens during his campaign against Olynthus was short of silver, and issued to his men a copper coinage instead. On their complaining, he told them that all the merchants and retailers would accept it in lieu of silver. But the merchants he instructed to buy in turn with the copper they received such produce of the land as was for sale, as well as any booty brought to them; such copper as remained on their hands he would exchange for silver.

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During the campaign of CorcyraApparently in 375 B.C. See the end of Xenophon’s fifth Book ofHellenicaXen. Hell. 5. this same Timotheus was reduced to sore straits. His men demanded their pay; refused to obey his orders; and declared they would desert to the enemy. Accordingly he summoned a meeting and told them that the stormy weather was delaying the arrival of the silver he expected; meanwhile, as he had on hand such abundance of provisions, he would charge them nothing for the three months’ ration of grain already advanced. The men, unable to believe that Timotheus would have sacrificed so large a sum to them unless he was in truth expecting the money, made no further claim for pay until he had completed his dispositions.

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At the siege of Samos,In 366 B.C. Timotheus sold the crops and other country property to the besieged Samians themselves, and thus obtained plenty of money to pay his men. But finding the camp was short of provisions owing to the arrival of reinforcements, he forbade the sale of milled corn, or of any measure less than 1 1/2 bushels of corn or 8 1/2 gallons of wine or oil. Accordingly the officers bought supplies wholesale and issued them to their men; the reinforcements thenceforth brought their own provisions, and sold any surplus on their departure. In this way the needs of the soldiers were satisfactorily met.

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Didales the Persian was able to provide for the daily needs of his mercenaries from the enemy’s country; but had no coined money to give them. When their pay became due, and they demanded it, he had recourse to the following trick. He called a meeting, and told the men that he had plenty of money, but that it was stored in a certain fortress, which he named. He then broke up his encampment and marched in that direction. On reaching the neighborhood of the fortress, he himself went on ahead, and entering the place seized all the silver vessels in the temples. He then loaded his mules in such a way that this plate was exposed, thus suggesting that silver formed the entire load; and so continued his march. The soldiers, beholding the plate and supposing that they convoyed a full load of silver, were cheered by the expectation of their pay. They were informed however by Didales that they would have to take it to Amisus to be coined—a journey of many days, and in the winter season. And during all this time, he continued to employ the army without giving it more than its necessary rations.

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Moreover, all the craftsmen in the army, and the hucksters who traded with the soldiers by barter, were under his personal control, and enjoyed a complete monopoly.

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When Taos,Called Tachos (Ταχώς) by Xenophon and Plutarch. Perhaps that form should be restored here. (Bonitz and Susemihl.) The name recurs in 37. king of Egypt, needed funds for an expedition he was making, Chabrias of Athens advised him to inform the priests that to save expense it was necessary to suppress some of the temples together with the majority of the attendant priests. On hearing this, each priesthood, being anxious to retain their own temple, offered him money from their private possessions 〈as well as from the temple funds〉. When the king had thus received money from them all, Chabrias bade him tell the priests to spend on the temple-service and on their own maintenance one-tenth of what they formerly spent, and lend him the remainder until he had made peace with the King 〈of Persia〉.

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Moreover, each inhabitant was to contribute a stated proportion of his household and personal possessions; and when grain was sold, buyer and seller were each to contribute, apart from the price, one obol per artabeThe artabe was a Persian measure containing nearly 50 quarts. The obol was 1/6 of a drachma of silver.; while a tax of one tenth was to be imposed on profits arising from ships and workshops and other sources of gain.

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Again, when Taos was on the point of setting out from Egypt, Chabrias advised him to make requisition of all uncoined gold and silver in the possession of the inhabitants; and when most of them complied, he bade the king make use of the bullion, and refer the lenders to the governors of his provinces for compensation out of the taxes.

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Iphicrates of Athens provided Cotys with money for a force which he had collected in the following manner. He bade him order 〈each〉 of his subjects to sow for him a piece of land bearing 4 1/2 bushels. A large quantity of grain was thus gathered, from the price of which, when brought to the depots on the coast, the king obtained as much money as he wanted.

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Cotys of Thrace asked the people of Peirinthus for a loan to enable him to raise an army. On their refusing, he begged them at any rate to let him have some of their citizens to garrison certain fortresses, and release for active service the men who were there on duty. They readily complied, thinking thus to obtain control of the fortresses. But Cotys placed in custody the men they sent, and told the citizens that they might have them back when they had sent him the amount of the loan he desired.

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Mentor of Rhodes, after taking Hermias prisoner and seizing his fortresses, left in their various districts the officials appointed by him. By this means he restored their confidence, so that they all took again to themselves the property they had hidden or had sent secretly out of the country. Then Mentor arrested them and stripped them of all they had.

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Memnon of Rhodes, on making himself master of Lampsacus, found he was in need of funds. He therefore assessed upon the wealthiest inhabitants a quantity of silver, telling them that they should recover it from the other citizens. But when the other citizens made their contributions, Memnon said they must lend him this money also, fixing a certain date for its repayment.

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Again being in need of funds, he asked for a contribution, to be recovered, as he said, from the city revenues. The citizens complied, thinking that they would speedily reimburse themselves. But when the revenue payments came in, he declared that he must have these also, and would repay the lenders subsequently with interest.

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His mercenary troops he requested to forgo six days’ pay and rations each year, on the plea that on those days they were neither on garrison duty nor on the march nor did they incur any expense. (He referred to the days omitted from alternate months.As the moon’s cycle is completed in 29 1/2 days, it was customary to alternatehollow months of 29 days with thefull months of 30 days. Memnon paid his men by the month, but deducted a day’s pay everyhollow month.)

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Moreover, being accustomed previously to issue his men’s rations of corn on the second day of the month, in the first month he postponed the distribution for three days, and in the second month for five; proceeding in this fashion until at length it took place on the last day of the month.

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Charidemus of Oreus, being in occupation of certain fortress-towns in Aeolis, and threatened with an attack by Artabazus,For the circumstances, and a (hostile) account of this commander’s adventures, see Demosthenes,Against AristocratesDem. 23. was in need of money to pay his troops. After their first contributions, the inhabitants declared they had no more to give. Charidemus then issued a proclamation to the town he deemed wealthiest, bidding the inhabitants send away to another fortress all the coin and valuables they possessed, under convoy which he would provide. He himself openly set the example with his own goods, and prevailed on them to comply. But when he had conducted them a little way out of the town, he made an inventory of their goods, took all he wanted, and led them home again.

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He had also issued a proclamation in the cities he governed forbidding anyone to keep arms in his house, under pain of a stated fine. At first, however, he took no care to enforce it, nor did he make any inquisition; so that the people treated his proclamation as nugatory, and made no attempt to get rid of what arms each possessed. Then Charidemus unexpectedly ordered a search to be made from house to house, and exacted the penalty from those who were found in possession of arms.

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A Macedonian named Philoxenus, who was governor of Caria, being in need of funds proclaimed that he intended to celebrate the festival of Dionysus. The wealthiest inhabitants were selected to provide the choruses, and were informed what they were expected to furnish. Noticing their disinclination, Philoxenus sent to them privately and asked what they would give to be relieved of the duty. They told him they were prepared to pay a much larger sum than they expected to spend 〈on the choruses〉 in order to avoid the trouble and the interruption of their business. Philoxenus accepted their offers, and proceeded to enrol a second levy. These also paid; and at last he received what he desired from each company.

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Euaises the Syrian, when governor of Egypt, received information that the local governors were meditating rebellion. He therefore summoned them to the palace and proceeded to hang them all, sending word to their relations that they were in prison. These accordingly made offers, each on behalf of his own kinsman, seeking by payment to secure their release. Euaises agreed to accept a certain sum for each, and when it had been paid returned to the relations the dead body.

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While Cleomenes of Alexandria was governor of Egypt,Cf. Dem. 56:Cleomenes . . . from the time that he received the government, has done immense mischief to your state, and still more to the rest of Greece, by buying up corn for resale and keeping it at his own price ( Kennedy’s translation). at a time when there was some scarcity in the land, but elsewhere a grievous famine, he forbade the export of grain. On the local governors representing that if there were no export of grain they would be unable to pay in their taxes, he allowed the export, but laid a heavy duty on the corn. By this means he obtained a large amount of duty from a small amount of export, and at the same time deprived the officials of their excuse.

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When Cleomenes was making a progress by water through the province where the crocodile is worshipped, one of his servants was carried off. Accordingly, summoning the priests, he told them that he intended to retaliate on the crocodiles for this unprovoked aggression; and gave orders for a battue. The priests, to save the credit of their god, collected all the gold they could, and succeeded in putting an end to the pursuit.

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King Alexander had given Cleomenes command to establish a town near the island of Pharus, and to transfer thither the market hitherto held at Canopus. Sailing therefore to Canopus he informed the priests and the men of property there that he was come to remove them. The priests and residents thereupon contributed money to induce him to leave their market where it was. He took what they offered, and departed; but afterwards returned, when all was ready to build the town, and proceeded to demand an excessive sum; which represented, he said, the difference the change of site would make to him. They however declared themselves unable to pay it, and were accordingly removed.

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On another occasion he sent an agent to make a certain purchase for him. Learning that the agent had made a good bargain, but intended to charge him a high price, he proceeded to inform the man’s associates that he had been told he had purchased the goods at an excessive price, and that therefore he did not intend to recognize the transaction; denouncing at the same time with feigned anger the fellow’s stupidity. They on hearing this asked him not to believe what was said against the agent until he himself arrived and rendered his account. On the man’s arrival, his associates told him what Cleomenes had said. He, desirous of winning their approval as well as that of Cleomenes, debited the latter with the actual price he had given.

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At a time when the price of grain in Egypt was ten drachmae 〈a measure〉 ,If the measure intended is the Attic medimnos , it is 1 1/2 bushels. The Persian artabe may however be meant, which was equal to 1 medimnos and 1/16th. In either case the price is very high compared with 3 drachmae per medimnos, the price at Athens in 390 B.C. Yet Polybius 9.44 says that at Rome during the war with Hannibal (210) corn was sold for fifteen drachmae per medimnos. As a contrast cf. what the same author says of the fertility of Gallia Cisalpina, where in time of peace this same measure of wheat was sold for four obols, and of barley for two. See note on 25. Cleomenes sent for the growers and asked them at what price they would contract to supply him with their produce. On their quoting a price lower than what they were charging the merchants, he offered them the full price they were accustomed to receive from others; and taking over the entire supply, sold it at a fixed rate of thirty-two drachmae 〈for the same measure〉.

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He also sent for the priests, and told them that the expenditure on the temples was very unevenly distributed in the country; and that some of these, together with the majority of the attendant priests, must accordingly be suppressed. The priests, supposing him to be in earnest, and wishing each to secure the continuance of his own temple and office, gave him money individually from their private possessions as well as collectively from the temple funds.Cf. 25.

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Antimenes of Rhodes, who was appointed by Alexander superintendent of highways in the province of Babylon, adopted the following means of raising funds. An ancient law of the country imposed a tax of one-tenth on all imports; but this had fallen into total abeyance. Antimenes kept a watch for all governors and soldiers whose arrival was expected, and upon the many ambassadors and craftsmen who were invited to the city, but brought with them others who dwelt there unofficially; and also upon the multitude of presents that were brought 〈to these persons〉 , on which he exacted the legal tax of a tenth.

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Another expedient was this. He invited the owners of any slaves in the camp to register them at whatever value they desired, undertaking at the same time to pay him eight drachmae a year. If the slave ran away, the owner was to recover the registered value. Many slaves were thus registered, and a large sum of money was paid 〈in premiums〉. And when a slave ran away, Antimenes instructed the governor of the 〈province〉 where the camp lay either to recover the man or to pay his master his value.

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Ophellas of Olynthus appointed an officer to superintend the revenues of the Province of Athribis. The local governors came to him, and told him they were willing to pay a much larger amount in taxes; but asked him to remove the present superintendent. Ophellas inquired if they were really able to pay what they promised; and on their assuring him that they were, left the superintendent in office and instructed him to demand from them the amount of tax which they themselves had assessed. And so, without being chargeable either with discountenancing the officer he had appointed, or with taxing the governors beyond their own estimate, he obtained from the latter many times his previous revenue.

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Pythocles the Athenian recommended his fellow-countrymen that the State should take over from private citizens the lead obtained from the mines of LauriumThese silver mines were state property; but mining rights therein were let to private citizens. Lead and silver were found in the same ore and had to be separated. The weight of the lead is not specified: it may have been a talent of 80 lbs. See Boeckh, Staatshaushaltung der Athener; and Xen. Ways. at the price of two drachmae 〈per talent〉 which they were asking, and should itself sell it at the fixed price of six drachmae.

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Chabrias had levied crews for a hundred and twenty ships to serve King Taos.See 25. Finding that Taos needed only sixty ships, he gave the crews of the superfluous sixty their choice between providing those who were to serve with two months’ rations, and themselves taking their place. Desiring to remain at their business, they gave what he demanded.

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Antimenes bade the governors of the provinces replenish, in accordance with the law of the country, the magazines along the royal highways. Whenever an army passed through the country or any other body of men unaccompanied by the king, he sent an officer to sell them the contents of the magazines.

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Cleomenes, as the beginning of the month approached when his soldiers’ allowance became due, deliberately sailed away down the river; and not till the month was advanced did he return and distribute the allowance. For the coming month, he omitted the distribution altogether until the following month began. Thus the men were quieted by the recent distribution, and Cleomenes, passing over a month each year, docked his troops of a month’s pay.σιταρχία (corn allowance) and μισθός (pay) here seem to be identified; possibly because in a land where grain was readily purchasable the former was given in money. Cf. 23, 29.

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Stabelbius, king of the Mysians, lacking pay to give his troops, summoned a meeting of the officers, and declared that he no longer needed the private soldiers, but only the officers. When he required troops, he would entrust a sum of money to each officer and send him to collect mercenaries; but that meanwhile he preferred to give the officers the pay he would otherwise have to give the men. Accordingly he bade each dismiss the men who were on his own muster-roll. The officers, scenting a source of gain for themselves, dismissed their men, as they were bidden. Shortly afterwards, Stabelbius called them together and informed them that a conductor without his chorus and an officer without his men were alike useless; wherefore let them depart from his country.

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When Dionysius was making a tour of the temples, wherever he saw a gold or silver table set, he bade them fill a cupin honor of the good spirit,Cf. Cic. De natura deorum 3.3.4 and Athenaeus Deipnosophistae 15.693. and then had the table carried away. Wherever, again, he saw a precious bowl set before one of the images, he would order its removal, with the words I accept it. He also stripped the images of their golden raiment and garlands, and declaring he would give them lighter and more fragrant wear, arrayed them in robes of white 〈linen〉 and garlands of white socks.

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ἡ οἰκονομικὴ καὶ πολιτικὴ διαφέρει οὐ μόνον τοσοῦτον ὅσον οἰκία καὶ πόλις ʽταῦτα μὲν γὰρ αὐταῖς ἐστι τὰ ὑποκείμενἀ, ἀλλὰ καὶ ὅτι ἡ μὲν πολιτικὴ ἐκ πολλῶν ἀρχόντων ἐστίν, ἡ οἰκονομικὴ δὲ μοναρχία.

ἔνιαι μὲν οὖν τῶν τεχνῶν διῄρηνται, καὶ οὐ τῆς αὐτῆς ἐστι ποιῆσαι καὶ χρήσασθαι τῷ ποιηθέντι, ὥσπερ λύρᾳ καὶ αὐλοῖς· τῆς δὲ πολιτικῆς ἐστι καὶ πόλιν ἐξ ἀρχῆς συστήσασθαι καὶ ὑπαρχούσῃ χρήσασθαι καλῶς· ὥστε δῆλον ὅτι καὶ τῆς οἰκονομικῆς ἂν εἴη καὶ κτήσασθαι οἶκον καὶ χρήσασθαι αὐτῷ.

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πόλις μὲν οὖν οἰκιῶν πλῆθός ἐστι καὶ χώρας καὶ κτημάτων αὔταρκες πρὸς τὸ εὖ ζῆν. φανερὸν δέ· ὅταν γὰρ μὴ δυνατοὶ ὦσι τούτου τυγχάνειν, διαλύεται καὶ ἡ κοινωνία. ἔτι δὲ ἕνεκα τούτου συνέρχονται. οὗ δὲ ἕνεκα ἕκαστόν ἐστι καὶ γέγονε, καὶ ἡ οὐσία αὐτοῦ τυγχάνει αὕτη οὖσα.

ὥστε δῆλον ὅτι πρότερον γενέσει ἡ οἰκονομικὴ πολιτικῆς ἐστι. καὶ γὰρ τὸ ἔργον. μόριον γὰρ οἰκία πόλεώς ἐστιν.

σκεπτέον οὖν περὶ τῆς οἰκονομικῆς καὶ τί τὸ ἔργον αὐτῆς.

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μέρη δὲ οἰκίας ἄνθρωπός τε καὶ κτῆσίς ἐστιν. ἐπεὶ δὲ πρῶτον ἐν τοῖς ἐλαχίστοις ἡ φύσιςἑκάστου θεωρεῖται, καὶ περὶ οἰκίας ἂν ὁμοίως ἔχοι. ὥστε καθʼ Ἡσίοδον δέοι ἂν ὑπάρχειν +

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μέρη δὲ οἰκίας ἄνθρωπός τε καὶ κτῆσίς ἐστιν. ἐπεὶ δὲ πρῶτον ἐν τοῖς ἐλαχίστοις ἡ φύσιςἑκάστου θεωρεῖται, καὶ περὶ οἰκίας ἂν ὁμοίως ἔχοι. ὥστε καθʼ Ἡσίοδον δέοι ἂν ὑπάρχειν οἶκον μὲν πρώτιστα γυναῖκά τε βοῦν τʼ ἀροτῆρα. Hes. WD 405 τὸ μὲν γὰρ τῆς τροφῆς πρῶτον, τὸ δὲ τῶν ἐλευθέρων. ὥστε δέοι ἂν τὰ περὶ τὴν τῆς γυναικὸς ὁμιλίαν οἰκονομήσασθαι καλῶς· τοῦτο δέ ἐστι τὸ ποίαν τινὰ δεῖ ταύτην εἶναι παρασκευάσαι.

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κτήσεως δὲ πρώτη ἐπιμέλεια ἡ κατὰ φύσιν. κατὰ φύσιν δὲ γεωργικὴ προτέρα, καὶ δεύτεραι ὅσαι ἀπὸ τῆς γῆς, οἷον μεταλλευτικὴ καὶ εἴ τις ἄλλη τοιαύτη. ἡ δὲ γεωργικὴ μάλιστα, ὅτι δικαία· οὐ γὰρ ἀπʼ ἀνθρώπων, οὔθʼ ἑκόντων, ὥσπερ καπηλεία καὶ αἱ μισθαρνικαί, οὔτʼ ἀκόντων, ὥσπερ αἱ πολεμικαί. ἔτι δὲ καὶ τῶν κατὰ φύσιν· φύσει γὰρ ἀπὸ τῆς μητρὸς ἡ τροφὴ πᾶσίν ἐστιν, ὥστε καὶ τοῖς ἀνθρώποις ἀπὸ τῆς γῆς.

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πρὸς δὲ τούτοις καὶ πρὸς ἀνδρίαν συμβάλλεται μεγάλα· οὐ γὰρ ὥσπερ αἱ βάναυσοι τὰ σώματα ἀχρεῖα ποιοῦσιν, ἀλλὰ δυνάμενα θυραυλεῖν καὶ πονεῖν, ἔτι δὲ δυνάμενα κινδυνεύειν πρὸς τοὺς πολεμίους· μόνων γὰρ τούτων τὰ κτήματα ἔξω τῶν ἐρυμάτων ἐστίν.

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κτήσεως δὲ πρώτη ἐπιμέλεια ἡ κατὰ φύσιν. κατὰ φύσιν δὲ γεωργικὴ προτέρα, καὶ δεύτεραι ὅσαι ἀπὸ τῆς γῆς, οἷον μεταλλευτικὴ καὶ εἴ τις ἄλλη τοιαύτη. ἡ δὲ γεωργικὴ μάλιστα, ὅτι δικαία· οὐ γὰρ ἀπʼ ἀνθρώπων, οὔθʼ ἑκόντων, ὥσπερ καπηλεία καὶ αἱ μισθαρνικαί, οὔτʼ ἀκόντων, ὥσπερ αἱ πολεμικαί. ἔτι δὲ καὶ τῶν κατὰ φύσιν· φύσει γὰρ ἀπὸ τῆς μητρὸς ἡ τροφὴ πᾶσίν ἐστιν, ὥστε καὶ τοῖς ἀνθρώποις ἀπὸ τῆς γῆς.

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πρὸς δὲ τούτοις καὶ πρὸς ἀνδρίαν συμβάλλεται μεγάλα· οὐ γὰρ ὥσπερ αἱ βάναυσοι τὰ σώματα ἀχρεῖα ποιοῦσιν, ἀλλὰ δυνάμενα θυραυλεῖν καὶ πονεῖν, ἔτι δὲ δυνάμενα κινδυνεύειν πρὸς τοὺς πολεμίους· μόνων γὰρ τούτων τὰ κτήματα ἔξω τῶν ἐρυμάτων ἐστίν.

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τῶν δὲ περὶ τοὺς ἀνθρώπους ἡ περὶ γυναῖκα πρώτη ἐπιμέλεια· κοινωνία γὰρ φύσει τῷ θήλει καὶ τῷ ἄρρενι μάλιστά ἐστιν. ὑπόκειται γὰρ ἡμῖν ἐν ἄλλοις ὅτι πολλὰ τοιαῦτα ἡ φύσις ἐφίεται ἀπεργάζεσθαι, ὥσπερ καὶ τῶν ζῴων ἕκαστον· ἀδύνατον δὲ τὸ θῆλυ ἄνευ τοῦ ἄρρενος ἢ τὸ ἄρρεν ἄνευ τοῦ θήλεος ἀποτελεῖν τοῦτο· ὥστʼ ἐξ ἀνάγκης αὐτῶν ἡ κοινωνία συνέστηκεν.

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ἐν μὲν οὖν τοῖς ἄλλοις ζῴοις ἀλόγως τοῦτο ὑπάρχει, καὶ ἐφʼ ὅσον μετέχουσι τῆς φύσεως, ἐπὶ τοσοῦτον, καὶ τεκνοποιίας μόνον χάριν· ἐν δὲ τοῖς ἡμέροις καὶ φρονιμωτέροις διήρθρωται μᾶλλον (φαίνονται γὰρ μᾶλλον βοήθειαι γινόμεναι καὶ εὔνοιαι καὶ συνεργίαι ἀλλήλοις),

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ἐν ἀνθρώπῳ δὲ μάλιστα, ὅτι οὐ μόνον τοῦ εἶναι ἀλλὰ καὶ τοῦ εὖ εἶναι συνεργὰ ἀλλήλοις τὸ θῆλυ καὶ τὸ ἄρρεν ἐστί. καὶ ἡ τῶν τέκνων κτῆσις οὐ λειτουργίας ἕνεκεν τῇ φύσει μόνον οὖσα τυγχάνει ἀλλὰ καὶ ὠφελείας· ἃ γὰρ ἂν δυνάμενοι εἰς ἀδυνάτους πονήσωσι, πάλιν κομίζονται παρὰ δυναμένων ἀδυνατοῦντες ἐν τῷ γήρᾳ.

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ἅμα δὲ καὶ ἡ φύσις ἀναπληροῖ ταύτῃ τῇ περιόδῳ τὸ ἀεὶ εἶναι, ἐπεὶ κατʼ ἀριθμὸν οὐ δύναται, ἀλλὰ κατὰ τὸ εἶδος. οὕτω προῳκονόμηται ὑπὸ τοῦ θείου ἑκατέρου ἡ φύσις, τοῦ τε ἀνδρὸς καὶ τῆς γυναικός, πρὸς τὴν κοινωνίαν. διείληπται γὰρ τῷ μὴ ἐπὶ ταὐτὰ πάντα χρήσιμον ἔχειν τὴν δύναμιν, ἀλλʼ ἔνια μὲν ἐπὶ τἀναντία, εἰς ταὐτὸν δὲ συντείνοντα· τὸ μὲν γὰρ ἰσχυρότερον τὸ δʼ ἀσθενέστερον ἐποίησεν, ἵνα τὸ μὲν φυλακτικώτερον ᾖ διὰ τὸν φόβον, τὸ δʼ ἀμυντικώτερον διὰ τὴν ἀνδρίαν, καὶ τὸ μὲν πορίζῃ τὰ ἔξωθεν, τὸ δὲ σῴζῃ τὰ ἔνδον· καὶ πρὸς τὴν ἐργασίαν τὸ μὲν δυνάμενον ἑδραῖον εἶναι, πρὸς δὲ τὰς ἔξωθεν θυραυλίας ἀσθενές, τὸ δὲ πρὸς μὲν τὰς ἡσυχίας χεῖρον, πρὸς δὲ τὰς κινήσεις ὑγιεινόν· καὶ περὶ τέκνων τὴν μὲν γένεσιν κοινήν, τὴν δὲ ὠφέλειαν ἴδιον· τῶν μὲν γὰρ τὸ θρέψαι, τῶν δὲ τὸ παιδεῦσαί ἐστιν.

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τῶν δὲ περὶ τοὺς ἀνθρώπους ἡ περὶ γυναῖκα πρώτη ἐπιμέλεια· κοινωνία γὰρ φύσει τῷ θήλει καὶ τῷ ἄρρενι μάλιστά ἐστιν. ὑπόκειται γὰρ ἡμῖν ἐν ἄλλοις ὅτι πολλὰ τοιαῦτα ἡ φύσις ἐφίεται ἀπεργάζεσθαι, ὥσπερ καὶ τῶν ζῴων ἕκαστον· ἀδύνατον δὲ τὸ θῆλυ ἄνευ τοῦ ἄρρενος ἢ τὸ ἄρρεν ἄνευ τοῦ θήλεος ἀποτελεῖν τοῦτο· ὥστʼ ἐξ ἀνάγκης αὐτῶν ἡ κοινωνία συνέστηκεν.

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ἐν μὲν οὖν τοῖς ἄλλοις ζῴοις ἀλόγως τοῦτο ὑπάρχει, καὶ ἐφʼ ὅσον μετέχουσι τῆς φύσεως, ἐπὶ τοσοῦτον, καὶ τεκνοποιίας μόνον χάριν· ἐν δὲ τοῖς ἡμέροις καὶ φρονιμωτέροις διήρθρωται μᾶλλον (φαίνονται γὰρ μᾶλλον βοήθειαι γινόμεναι καὶ εὔνοιαι καὶ συνεργίαι ἀλλήλοις),

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ἐν ἀνθρώπῳ δὲ μάλιστα, ὅτι οὐ μόνον τοῦ εἶναι ἀλλὰ καὶ τοῦ εὖ εἶναι συνεργὰ ἀλλήλοις τὸ θῆλυ καὶ τὸ ἄρρεν ἐστί. καὶ ἡ τῶν τέκνων κτῆσις οὐ λειτουργίας ἕνεκεν τῇ φύσει μόνον οὖσα τυγχάνει ἀλλὰ καὶ ὠφελείας· ἃ γὰρ ἂν δυνάμενοι εἰς ἀδυνάτους πονήσωσι, πάλιν κομίζονται παρὰ δυναμένων ἀδυνατοῦντες ἐν τῷ γήρᾳ.

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ἅμα δὲ καὶ ἡ φύσις ἀναπληροῖ ταύτῃ τῇ περιόδῳ τὸ ἀεὶ εἶναι, ἐπεὶ κατʼ ἀριθμὸν οὐ δύναται, ἀλλὰ κατὰ τὸ εἶδος. οὕτω προῳκονόμηται ὑπὸ τοῦ θείου ἑκατέρου ἡ φύσις, τοῦ τε ἀνδρὸς καὶ τῆς γυναικός, πρὸς τὴν κοινωνίαν. διείληπται γὰρ τῷ μὴ ἐπὶ ταὐτὰ πάντα χρήσιμον ἔχειν τὴν δύναμιν, ἀλλʼ ἔνια μὲν ἐπὶ τἀναντία, εἰς ταὐτὸν δὲ συντείνοντα· τὸ μὲν γὰρ ἰσχυρότερον τὸ δʼ ἀσθενέστερον ἐποίησεν, ἵνα τὸ μὲν φυλακτικώτερον ᾖ διὰ τὸν φόβον, τὸ δʼ ἀμυντικώτερον διὰ τὴν ἀνδρίαν, καὶ τὸ μὲν πορίζῃ τὰ ἔξωθεν, τὸ δὲ σῴζῃ τὰ ἔνδον· καὶ πρὸς τὴν ἐργασίαν τὸ μὲν δυνάμενον ἑδραῖον εἶναι, πρὸς δὲ τὰς ἔξωθεν θυραυλίας ἀσθενές, τὸ δὲ πρὸς μὲν τὰς ἡσυχίας χεῖρον, πρὸς δὲ τὰς κινήσεις ὑγιεινόν· καὶ περὶ τέκνων τὴν μὲν γένεσιν κοινήν, τὴν δὲ ὠφέλειαν ἴδιον· τῶν μὲν γὰρ τὸ θρέψαι, τῶν δὲ τὸ παιδεῦσαί ἐστιν.

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πρῶτον μὲν οὖν νόμοι πρὸς γυναῖκα, καὶ τὸ μὴ ἀδικεῖν· οὕτως γὰρ ἂν οὐδʼ αὐτὸς ἀδικοῖτο. τοῦθʼ ὑφηγεῖται δὲ ὃ καὶ ὁ κοινὸς νόμος, καθάπερ οἱ Πυθαγόρειοι λέγουσιν, ὥσπερ ἱκέτιν καὶ ἀφʼ ἑστίας ἠγμένην ὡς ἥκιστα δεῖν δοκεῖν ἀδικεῖν· ἀδικία δὲ ἀνδρὸς αἱ θύραζε συνουσίαι γιγνόμεναι.

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περὶ δὲ ὁμιλίας μήθʼ ὥστε δεῖσθαι μηθὲν μήθʼ ὡς ἀπόντος ἀδυνατεῖν ἡσυχάζειν, ἀλλʼ οὕτως ἐθίζειν ὥστε ἱκανῶς ἔχειν παρόντος καὶ μὴ παρόντος. εὖ δʼ ἔχει καὶ τὸ τοῦ Ἡσιόδου. παρθενικὴν δὲ γαμεῖν, ἵνα ἤθεα κεδνὰ διδάξῃς. Hes. WD 699 αἱ γὰρ ἀνομοιότητες τῶν ἠθῶν ἥκιστα φιλικόν.

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περὶ δὲ κοσμήσεως, ὥσπερ οὐδὲ τὰ ἤθη δεῖἀλαζονευομένους ἀλλήλοις πλησιάζειν, οὕτως οὐδὲ τὰ σώματα. ἡ δὲ διὰ τῆς κοσμήσεως οὐδὲν διαφέρουσά ἐστι τῆς τῶν τραγῳδῶν ἐν τῇ σκευῇ πρὸς ἀλλήλους ὁμιλία.

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πρῶτον μὲν οὖν νόμοι πρὸς γυναῖκα, καὶ τὸ μὴ ἀδικεῖν· οὕτως γὰρ ἂν οὐδʼ αὐτὸς ἀδικοῖτο. τοῦθʼ ὑφηγεῖται δὲ ὃ καὶ ὁ κοινὸς νόμος, καθάπερ οἱ Πυθαγόρειοι λέγουσιν, ὥσπερ ἱκέτιν καὶ ἀφʼ ἑστίας ἠγμένην ὡς ἥκιστα δεῖν δοκεῖν ἀδικεῖν· ἀδικία δὲ ἀνδρὸς αἱ θύραζε συνουσίαι γιγνόμεναι.

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περὶ δὲ ὁμιλίας μήθʼ ὥστε δεῖσθαι μηθὲν μήθʼ ὡς ἀπόντος ἀδυνατεῖν ἡσυχάζειν, ἀλλʼ οὕτως ἐθίζειν ὥστε ἱκανῶς ἔχειν παρόντος καὶ μὴ παρόντος. εὖ δʼ ἔχει καὶ τὸ τοῦ Ἡσιόδου. παρθενικὴν δὲ γαμεῖν, ἵνα ἤθεα κεδνὰ διδάξῃς. Hes. WD 699 αἱ γὰρ ἀνομοιότητες τῶν ἠθῶν ἥκιστα φιλικόν.

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περὶ δὲ κοσμήσεως, ὥσπερ οὐδὲ τὰ ἤθη δεῖἀλαζονευομένους ἀλλήλοις πλησιάζειν, οὕτως οὐδὲ τὰ σώματα. ἡ δὲ διὰ τῆς κοσμήσεως οὐδὲν διαφέρουσά ἐστι τῆς τῶν τραγῳδῶν ἐν τῇ σκευῇ πρὸς ἀλλήλους ὁμιλία.

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τῶν δὲ κτημάτων πρῶτον μὲν καὶ ἀναγκαιότατον τὸ βέλτιστον καὶ οἰκονομικώτατον· τοῦτο δὲ ἦν ἄνθρωπος. διὸ δεῖ πρῶτον δούλους παρασκευάζεσθαι σπουδαίους. δούλων δὲ εἴδη δύο, ἐπίτροπος καὶ ἐργάτης. ἐπεὶ δὲ ὁρῶμεν ὅτι αἱ παιδεῖαι ποιούς τινας ποιοῦσι τοὺς νέους, ἀναγκαῖον καὶ παρασκευασάμενον τρέφειν οἷς τὰ ἐλευθέρια τῶν ἔργων προστακτέον.

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ὁμιλία δὲ πρὸς δούλους ὡς μήτε ὑβρίζειν ἐᾶν μήτε ἀνιᾶν, καὶ τοῖς μὲν ἐλευθεριωτέροις τιμῆς μεταδιδόναι, τοῖς δʼ ἐργάταις τροφῆς πλῆθος. καὶ ἐπειδὴ ἡ τοῦ οἴνου πόσις καὶ τοὺς ἐλευθέρους ὑβριστὰς ποιεῖ, καὶ πολλὰ ἔθνη ἀπέχεται καὶ τῶν ἐλευθέρων, οἷον Καρχηδόνιοι ἐπὶ στρατιᾶς, φανερὸν ὅτι τούτου ἢ μηδὲν ἢ ὀλιγάκις μεταδοτέον.

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ὄντων δὲ τριῶν, ἔργου καὶ κολάσεως καὶ τροφῆς, τὸ μὲν μήτε κολάζεσθαι, μήτʼ ἐργάζεσθαι, τροφὴν δʼ ἔχειν, ὕβριν ἐμποιεῖ· τὸ δὲ ἔργα μὲν ἔχειν καὶ κολάσεις, τροφὴν δὲ μή, βίαιον καὶ ἀδυναμίαν ποιεῖ. λείπεται δὴ ἔργα παρέχειν καὶ τροφὴν ἱκανήν· ἀμίσθων γὰρ οὐχ οἷόν τε ἄρχειν, δούλῳ δὲ μισθὸς τροφή.

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τῶν δὲ κτημάτων πρῶτον μὲν καὶ ἀναγκαιότατον τὸ βέλτιστον καὶ οἰκονομικώτατον· τοῦτο δὲ ἦν ἄνθρωπος. διὸ δεῖ πρῶτον δούλους παρασκευάζεσθαι σπουδαίους. δούλων δὲ εἴδη δύο, ἐπίτροπος καὶ ἐργάτης. ἐπεὶ δὲ ὁρῶμεν ὅτι αἱ παιδεῖαι ποιούς τινας ποιοῦσι τοὺς νέους, ἀναγκαῖον καὶ παρασκευασάμενον τρέφειν οἷς τὰ ἐλευθέρια τῶν ἔργων προστακτέον.

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ὁμιλία δὲ πρὸς δούλους ὡς μήτε ὑβρίζειν ἐᾶν μήτε ἀνιᾶν, καὶ τοῖς μὲν ἐλευθεριωτέροις τιμῆς μεταδιδόναι, τοῖς δʼ ἐργάταις τροφῆς πλῆθος. καὶ ἐπειδὴ ἡ τοῦ οἴνου πόσις καὶ τοὺς ἐλευθέρους ὑβριστὰς ποιεῖ, καὶ πολλὰ ἔθνη ἀπέχεται καὶ τῶν ἐλευθέρων, οἷον Καρχηδόνιοι ἐπὶ στρατιᾶς, φανερὸν ὅτι τούτου ἢ μηδὲν ἢ ὀλιγάκις μεταδοτέον.

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ὄντων δὲ τριῶν, ἔργου καὶ κολάσεως καὶ τροφῆς, τὸ μὲν μήτε κολάζεσθαι, μήτʼ ἐργάζεσθαι, τροφὴν δʼ ἔχειν, ὕβριν ἐμποιεῖ· τὸ δὲ ἔργα μὲν ἔχειν καὶ κολάσεις, τροφὴν δὲ μή, βίαιον καὶ ἀδυναμίαν ποιεῖ. λείπεται δὴ ἔργα παρέχειν καὶ τροφὴν ἱκανήν· ἀμίσθων γὰρ οὐχ οἷόν τε ἄρχειν, δούλῳ δὲ μισθὸς τροφή.

ὥσπερ δὲ καὶ τοῖς ἄλλοις ὅταν μὴ γίγνηται τοῖς βελτίοσι βέλτιον μηδὲ ἆθλα ᾖ ἀρετῆς καὶ κακίας, γίγνονται χείρους, οὕτω καὶ περὶ οἰκέτας.

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διόπερ δεῖ ποιεῖσθαι σκέψιν καὶ διανέμειν τε καὶ ἀνιέναι κατʼ ἀξίαν ἕκαστα, καὶ τροφὴν καὶ ἐσθῆτα καὶ ἀργίαν καὶ κολάσεις, λόγῳ καὶ ἔργῳ μιμουμένους τὴν τῶν ἰατρῶν δύναμιν ἐν φαρμάκου λόγῳ, προσθεωροῦντας ὅτι ἡ τροφὴ οὐ φάρμακον διὰ τὸ συνεχές.

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γένη δὲ ἂν εἴη πρὸς τὰ ἔργα βέλτιστα μήτε δειλὰ μήτε ἀνδρῖα ἄγαν. ἀμφότερα γὰρ ἀδικοῦσι. καὶ γὰρ οἱ ἄγαν δειλοὶ οὐχ ὑπομένουσι καὶ οἱ θυμοειδεῖς οὐκ εὔαρχοι.

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χρὴ δὲ καὶ τέλος ὡρίσθαι πᾶσιν· δίκαιον γὰρ καὶ συμφέρον τὴν ἐλευθερίαν κεῖσθαι ἆθλον· βούλονται γὰρ πονεῖν, ὅταν ᾖ ἆθλον καὶ ὁ χρόνος ὡρισμένος. δεῖ δὲ καὶ ἐξομηρεύειν ταῖς τεκνοποιίαις· καὶ μὴ κτᾶσθαι ὁμοεθνεῖς πολλούς, ὥσπερ καὶ ἐν ταῖς πόλεσιν· καὶ τὰς θυσίας καὶ τὰς ἀπολαύσεις μᾶλλον τῶν δούλων ἕνεκα ποιεῖσθαι ἢ τῶν ἐλευθέρων·πλείονα γὰρ ἔχουσιν οὗτοι οὗπερ ἕνεκα τὰ τοιαῦτα ἐνομίσθη.

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εἴδη δὲ τοῦ οἰκονόμου τέτταρα ἃ δεῖ ἔχειν περὶ τὰ χρήματα. καὶ γὰρ τὸ κτᾶσθαι δυνατὸν χρὴ εἶναι καὶ φυλάττειν· εἰ δὲ μή, οὐδὲν ὄφελος τοῦ κτᾶσθαι· τῷ γὰρ ἠθμῷ ἀντλεῖν τοῦτʼ ἔστιν, καὶ ὁ λεγόμενος τετρημένος πίθος. ἔτι δὲ καὶ εἶναι κοσμητικὸν τῶν ὑπαρχόντων καὶ χρηστικόν· τούτων γὰρ ἕνεκα κἀκείνων δεόμεθα.

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διῃρῆσθαι δὲ δεῖ τούτων ἕκαστον, καὶ πλείω τὰ κάρπιμα εἶναι τῶν ἀκάρπων, καὶ τὰς ἐργασίας οὕτω νενεμῆσθαι, ὅπως μὴ ἅμα κινδυνεύσωσιν ἅπασιν. πρὸς δὲ φυλακὴν τοῖς τε Περσικοῖς συμφέρει χρῆσθαι καὶ τοῖς Λακωνικοῖς. καὶ ἡ Ἀττικὴ δὲ οἰκονομία χρήσιμος· ἀποδιδόμενοι γὰρ ὠνοῦνται, καὶ ἡ τοῦ ταμιείου θέσις οὐκ ἔστιν ἐν ταῖς μικροτέραις οἰκονομίαις.

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Περσικὰ δὲ ἦν τὸ πάντα τετάχθαι, καὶ πάντʼ ἐφορᾶν αὐτόν, καθʼ ὃ ἔλεγε Δίων περὶ Διονυσίου· οὐδεὶς γὰρ ἐπιμελεῖται ὁμοίως τῶν ἀλλοτρίων καὶ τῶν οἰκείων, ὥστε ὅσα ἐνδέχεται, διʼ ἑαυτοῦ ποιεῖσθαι χρὴ τὴν ἐπιμέλειαν. καὶ τὸ τοῦ Πέρσου καὶ τὸ τοῦ Λίβυος ἀπόφθεγμα εὖ ἂν ἔχοι. ὁ μὲν γὰρ ἐρωτηθεὶς τί μάλιστα ἵππον πιαίνει, ὁ τοῦ δεσπότου ὀφθαλμός ἔφη· ὁ δὲ Λίβυς ἐρωτηθεὶς ποία κόπρος ἀρίστη, τὰ τοῦ δεσπότου ἴχνη ἔφη.

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ἐπισκεπτέον οὖν τὰ μὲν αὐτόν, τὰ δὲ τὴν γυναῖκα, ὡς ἑκατέροις διαιρεῖται τὰ ἔργα τῆς οἰκονομίας. καὶ τοῦτο ποιητέον ἐν μικραῖς οἰκονομίαις ὀλιγάκις, ἐν δʼ ἐπιτροπευομέναις πολλάκις. οὐ γὰρ οἷόν τε μὴ καλῶς ὑποδεικνύντος καλῶς μιμεῖσθαι, οὔτʼ ἐν τοῖς ἄλλοις, οὔτʼ ἐν ἐπιτροπείᾳ, ὡς ἀδύνατον μὴ ἐπιμελῶν δεσποτῶν ἐπιμελεῖς εἶναι τοὺς ἐφεστῶτας.

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ἐπεὶ δὲ ταῦτα καὶ καλὰ πρὸς ἀρετὴν καὶ ὠφέλιμα πρὸς οἰκονομίαν, ἐγείρεσθαι χρὴ πρότερον δεσπότας οἰκετῶν καὶ καθεύδειν ὕστερον· καὶ μηδέποτε ἀφύλακτον οἰκίαν εἶναι, ὥσπερ πόλιν· ὅσα τε δεῖ ποιεῖν μήτε νυκτὸς μήτε ἡμέρας παριέναι· τό τε διανίστασθαι νύκτωρ· τοῦτο γὰρ καὶ πρὸς ὑγίειαν καὶ οἰκονομίαν καὶ φιλοσοφίαν χρήσιμον.

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ἐν μὲν οὖν ταῖς μικραῖς κτήσεσιν ὁ Ἀττικὸς τρόπος τῆς διαθέσεως τῶν ἐπικαρπιῶν χρήσιμος·ἐν δὲ ταῖς μεγάλαις, διαμερισθέντων καὶ τῶν πρὸς ἐνιαυτὸν καὶ τῶν κατὰ μῆνα δαπανωμένων, ὁμοίως δὲ καὶ περὶ σκευῶν χρήσεως τῶν καθʼ ἡμέραν καὶ τῶν ὀλιγάκις, ταῦτα παραδοτέον τοῖς ἐφεστῶσιν. ἐπὶ τούτοις καὶ τὴν ἐπίσκεψιν αὐτῶν διά τινος χρόνου ποιητέον, ἵνα μὴ λανθάνῃ τὸ σῳζόμενον καὶ τὸ ἐλλεῖπον.

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οἰκίαν δὲ πρός τε τὰ κτήματα ἀποβλέποντα κατασκευαστέον καὶ πρὸς ὑγίειαν καὶ πρὸς εὐημερίαν αὐτῶν· λέγω δὲ κτήματα μέν, οἷον καρποῖς καὶ ἐσθῆτι ποία συμφέρει, καὶ τῶν καρπῶν ποία ξηροῖς καὶ ποία ὑγροῖς, καὶ τῶν ἄλλων κτημάτων ποία ἐμψύχοις καὶ ποία ἀψύχοις, καὶ δούλοις καὶ ἐλευθέροις, καὶ γυναιξὶ καὶ ἀνδράσι, καὶ ξένοις καὶ ἀστοῖς. καὶ πρὸς εὐημερίαν δὲ καὶ πρὸς ὑγίειαν δεῖ εἶναι, εὔπνουν μὲν τοῦ θέρους, εὐήλιον δὲ τοῦ χειμῶνος.

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εἴη δʼ ἂν ἡ τοιαύτη κατάβορρος οὖσα καὶ μὴ ἰσοπλατής. δοκεῖ δὲ καὶ ἐν ταῖς μεγάλαις οἰκονομίαις χρήσιμος εἶναι θυρωρός, ὃς ἂν ᾖ ἄχρηστος τῶν ἄλλων ἔργων, πρὸς τὴν σωτηρίαν τῶν εἰσφερομένων καὶ ἐκφερομένων. πρὸς εὐχρηστίαν δὲ σκευῶν τὸ Λακωνικόν· χρὴ γὰρ ἓν ἕκαστον ἐν τῇ αὑτοῦ χώρᾳ κεῖσθαι· οὕτω γὰρ ἂν ἕτοιμον ὂν οὐ ζητοῖτο.

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διόπερ δεῖ ποιεῖσθαι σκέψιν καὶ διανέμειν τε καὶ ἀνιέναι κατʼ ἀξίαν ἕκαστα, καὶ τροφὴν καὶ ἐσθῆτα καὶ ἀργίαν καὶ κολάσεις, λόγῳ καὶ ἔργῳ μιμουμένους τὴν τῶν ἰατρῶν δύναμιν ἐν φαρμάκου λόγῳ, προσθεωροῦντας ὅτι ἡ τροφὴ οὐ φάρμακον διὰ τὸ συνεχές.

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γένη δὲ ἂν εἴη πρὸς τὰ ἔργα βέλτιστα μήτε δειλὰ μήτε ἀνδρῖα ἄγαν. ἀμφότερα γὰρ ἀδικοῦσι. καὶ γὰρ οἱ ἄγαν δειλοὶ οὐχ ὑπομένουσι καὶ οἱ θυμοειδεῖς οὐκ εὔαρχοι.

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χρὴ δὲ καὶ τέλος ὡρίσθαι πᾶσιν· δίκαιον γὰρ καὶ συμφέρον τὴν ἐλευθερίαν κεῖσθαι ἆθλον· βούλονται γὰρ πονεῖν, ὅταν ᾖ ἆθλον καὶ ὁ χρόνος ὡρισμένος. δεῖ δὲ καὶ ἐξομηρεύειν ταῖς τεκνοποιίαις· καὶ μὴ κτᾶσθαι ὁμοεθνεῖς πολλούς, ὥσπερ καὶ ἐν ταῖς πόλεσιν· καὶ τὰς θυσίας καὶ τὰς ἀπολαύσεις μᾶλλον τῶν δούλων ἕνεκα ποιεῖσθαι ἢ τῶν ἐλευθέρων·πλείονα γὰρ ἔχουσιν οὗτοι οὗπερ ἕνεκα τὰ τοιαῦτα ἐνομίσθη.

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εἴδη δὲ τοῦ οἰκονόμου τέτταρα ἃ δεῖ ἔχειν περὶ τὰ χρήματα. καὶ γὰρ τὸ κτᾶσθαι δυνατὸν χρὴ εἶναι καὶ φυλάττειν· εἰ δὲ μή, οὐδὲν ὄφελος τοῦ κτᾶσθαι· τῷ γὰρ ἠθμῷ ἀντλεῖν τοῦτʼ ἔστιν, καὶ ὁ λεγόμενος τετρημένος πίθος. ἔτι δὲ καὶ εἶναι κοσμητικὸν τῶν ὑπαρχόντων καὶ χρηστικόν· τούτων γὰρ ἕνεκα κἀκείνων δεόμεθα.

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διῃρῆσθαι δὲ δεῖ τούτων ἕκαστον, καὶ πλείω τὰ κάρπιμα εἶναι τῶν ἀκάρπων, καὶ τὰς ἐργασίας οὕτω νενεμῆσθαι, ὅπως μὴ ἅμα κινδυνεύσωσιν ἅπασιν. πρὸς δὲ φυλακὴν τοῖς τε Περσικοῖς συμφέρει χρῆσθαι καὶ τοῖς Λακωνικοῖς. καὶ ἡ Ἀττικὴ δὲ οἰκονομία χρήσιμος· ἀποδιδόμενοι γὰρ ὠνοῦνται, καὶ ἡ τοῦ ταμιείου θέσις οὐκ ἔστιν ἐν ταῖς μικροτέραις οἰκονομίαις.

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Περσικὰ δὲ ἦν τὸ πάντα τετάχθαι, καὶ πάντʼ ἐφορᾶν αὐτόν, καθʼ ὃ ἔλεγε Δίων περὶ Διονυσίου· οὐδεὶς γὰρ ἐπιμελεῖται ὁμοίως τῶν ἀλλοτρίων καὶ τῶν οἰκείων, ὥστε ὅσα ἐνδέχεται, διʼ ἑαυτοῦ ποιεῖσθαι χρὴ τὴν ἐπιμέλειαν. καὶ τὸ τοῦ Πέρσου καὶ τὸ τοῦ Λίβυος ἀπόφθεγμα εὖ ἂν ἔχοι. ὁ μὲν γὰρ ἐρωτηθεὶς τί μάλιστα ἵππον πιαίνει, ὁ τοῦ δεσπότου ὀφθαλμός ἔφη· ὁ δὲ Λίβυς ἐρωτηθεὶς ποία κόπρος ἀρίστη, τὰ τοῦ δεσπότου ἴχνη ἔφη.

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ἐπισκεπτέον οὖν τὰ μὲν αὐτόν, τὰ δὲ τὴν γυναῖκα, ὡς ἑκατέροις διαιρεῖται τὰ ἔργα τῆς οἰκονομίας. καὶ τοῦτο ποιητέον ἐν μικραῖς οἰκονομίαις ὀλιγάκις, ἐν δʼ ἐπιτροπευομέναις πολλάκις. οὐ γὰρ οἷόν τε μὴ καλῶς ὑποδεικνύντος καλῶς μιμεῖσθαι, οὔτʼ ἐν τοῖς ἄλλοις, οὔτʼ ἐν ἐπιτροπείᾳ, ὡς ἀδύνατον μὴ ἐπιμελῶν δεσποτῶν ἐπιμελεῖς εἶναι τοὺς ἐφεστῶτας.

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ἐπεὶ δὲ ταῦτα καὶ καλὰ πρὸς ἀρετὴν καὶ ὠφέλιμα πρὸς οἰκονομίαν, ἐγείρεσθαι χρὴ πρότερον δεσπότας οἰκετῶν καὶ καθεύδειν ὕστερον· καὶ μηδέποτε ἀφύλακτον οἰκίαν εἶναι, ὥσπερ πόλιν· ὅσα τε δεῖ ποιεῖν μήτε νυκτὸς μήτε ἡμέρας παριέναι· τό τε διανίστασθαι νύκτωρ· τοῦτο γὰρ καὶ πρὸς ὑγίειαν καὶ οἰκονομίαν καὶ φιλοσοφίαν χρήσιμον.

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ἐν μὲν οὖν ταῖς μικραῖς κτήσεσιν ὁ Ἀττικὸς τρόπος τῆς διαθέσεως τῶν ἐπικαρπιῶν χρήσιμος·ἐν δὲ ταῖς μεγάλαις, διαμερισθέντων καὶ τῶν πρὸς ἐνιαυτὸν καὶ τῶν κατὰ μῆνα δαπανωμένων, ὁμοίως δὲ καὶ περὶ σκευῶν χρήσεως τῶν καθʼ ἡμέραν καὶ τῶν ὀλιγάκις, ταῦτα παραδοτέον τοῖς ἐφεστῶσιν. ἐπὶ τούτοις καὶ τὴν ἐπίσκεψιν αὐτῶν διά τινος χρόνου ποιητέον, ἵνα μὴ λανθάνῃ τὸ σῳζόμενον καὶ τὸ ἐλλεῖπον.

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οἰκίαν δὲ πρός τε τὰ κτήματα ἀποβλέποντα κατασκευαστέον καὶ πρὸς ὑγίειαν καὶ πρὸς εὐημερίαν αὐτῶν· λέγω δὲ κτήματα μέν, οἷον καρποῖς καὶ ἐσθῆτι ποία συμφέρει, καὶ τῶν καρπῶν ποία ξηροῖς καὶ ποία ὑγροῖς, καὶ τῶν ἄλλων κτημάτων ποία ἐμψύχοις καὶ ποία ἀψύχοις, καὶ δούλοις καὶ ἐλευθέροις, καὶ γυναιξὶ καὶ ἀνδράσι, καὶ ξένοις καὶ ἀστοῖς. καὶ πρὸς εὐημερίαν δὲ καὶ πρὸς ὑγίειαν δεῖ εἶναι, εὔπνουν μὲν τοῦ θέρους, εὐήλιον δὲ τοῦ χειμῶνος.

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εἴη δʼ ἂν ἡ τοιαύτη κατάβορρος οὖσα καὶ μὴ ἰσοπλατής. δοκεῖ δὲ καὶ ἐν ταῖς μεγάλαις οἰκονομίαις χρήσιμος εἶναι θυρωρός, ὃς ἂν ᾖ ἄχρηστος τῶν ἄλλων ἔργων, πρὸς τὴν σωτηρίαν τῶν εἰσφερομένων καὶ ἐκφερομένων. πρὸς εὐχρηστίαν δὲ σκευῶν τὸ Λακωνικόν· χρὴ γὰρ ἓν ἕκαστον ἐν τῇ αὑτοῦ χώρᾳ κεῖσθαι· οὕτω γὰρ ἂν ἕτοιμον ὂν οὐ ζητοῖτο.

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τὸν οἰκονομεῖν μέλλοντά τι κατὰ τρόπον τῶν τε τόπων, περὶ οὓς ἂν πραγματεύηται, μὴ ἀπείρως ἔχειν, καὶ τῇ φύσει εὐφυῆ εἶναι καὶ τῇ προαιρέσει φιλόπονόν τε καὶ δίκαιον· ὅ τι γὰρ ἂν ἀπῇ τούτων τῶν μερῶν, πολλὰ διαμαρτήσεται περὶ τὴν πραγματείαν ἣν μεταχειρίζεται.

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τὸν οἰκονομεῖν μέλλοντά τι κατὰ τρόπον τῶν τε τόπων, περὶ οὓς ἂν πραγματεύηται, μὴ ἀπείρως ἔχειν, καὶ τῇ φύσει εὐφυῆ εἶναι καὶ τῇ προαιρέσει φιλόπονόν τε καὶ δίκαιον· ὅ τι γὰρ ἂν ἀπῇ τούτων τῶν μερῶν, πολλὰ διαμαρτήσεται περὶ τὴν πραγματείαν ἣν μεταχειρίζεται.

οἰκονομίαι δέ εἰσι τέσσαρες, ὡς ἐν τύπῳ διελέσθαι ʽτὰς γὰρ ἄλλας εἰς τοῦτο ἐμπιπτούσας εὑρήσομεν̓, βασιλική σατραπική πολιτική ἰδιωτική.

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τούτων δὲ μεγίστη μὲν καὶ ἁπλουστάτη ἡ βασιλική, , ποικιλωτάτη δὲ καὶ ῥᾴστη ἡ πολιτική, ἐλαχίστη δὲ καὶ ποικιλωτάτη ἡ ἰδιωτική. ἐπικοινωνεῖν μὲν τὰ πολλὰ ἀλλήλαις ἀναγκαῖόν ἐστιν· ὅσα δὲ μάλιστα διʼ αὐτῶν ἑκάστῃ συμβαίνει, ταῦτα ἐπισκεπτέον ἡμῖν ἐστιν.

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τούτων δὲ μεγίστη μὲν καὶ ἁπλουστάτη ἡ βασιλική, , ποικιλωτάτη δὲ καὶ ῥᾴστη ἡ πολιτική, ἐλαχίστη δὲ καὶ ποικιλωτάτη ἡ ἰδιωτική. ἐπικοινωνεῖν μὲν τὰ πολλὰ ἀλλήλαις ἀναγκαῖόν ἐστιν· ὅσα δὲ μάλιστα διʼ αὐτῶν ἑκάστῃ συμβαίνει, ταῦτα ἐπισκεπτέον ἡμῖν ἐστιν.

πρῶτον μὲν τοίνυν τὴν βασιλικὴν ἴδωμεν. ἔστι δὲ αὕτη δυναμένη μὲν τὸ καθόλου,εἴδη δὲ ἔχουσα τέσσαρα· περὶ νόμισμα, περὶ τὰ ἐξαγώγιμα, περὶ τὰ εἰσαγώγιμα, περὶ τὰ ἀναλώματα.

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τούτων δὲ ἕκαστον μὲν περὶ τὸ νόμισμα λέγω ποῖον καὶ πότε τίμιον ἢ εὔωνον ποιητέον, περὶ δὲ τὰ ἐξαγώγιμα καὶ εἰσαγώγιμα πότε καὶ τίνα παρὰ τῶν σατραπῶν ἐν τῇ ταγῇ ἐκλαβόντι αὐτῷ λυσιτελήσει διατίθεσθαι, περὶ δὲ τὰ ἀναλώματα τίνα περιαιρετέον καὶ πότε, καὶ πότερον δοτέον νόμισμα εἰς τὰς δαπάνας ἢ ἃ τῷ νομίσματι ὤνια.

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δεύτερον δὲ τὴν σατραπικήν. ἔστι δὲ ταύτης εἴδη ἓξ τῶν προσόδων ἀπὸ γῆς, ἀπὸ τῶν ἐν τῇ χώρᾳ ἰδίων γινομένων, ἀπὸ ἐμπορίων, ἀπὸ τελῶν, ἀπὸ βοσκημάτων, ἀπὸ τῶν ἄλλων.

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τούτων δὲ ἕκαστον μὲν περὶ τὸ νόμισμα λέγω ποῖον καὶ πότε τίμιον ἢ εὔωνον ποιητέον, περὶ δὲ τὰ ἐξαγώγιμα καὶ εἰσαγώγιμα πότε καὶ τίνα παρὰ τῶν σατραπῶν ἐν τῇ ταγῇ ἐκλαβόντι αὐτῷ λυσιτελήσει διατίθεσθαι, περὶ δὲ τὰ ἀναλώματα τίνα περιαιρετέον καὶ πότε, καὶ πότερον δοτέον νόμισμα εἰς τὰς δαπάνας ἢ ἃ τῷ νομίσματι ὤνια.

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δεύτερον δὲ τὴν σατραπικήν. ἔστι δὲ ταύτης εἴδη ἓξ τῶν προσόδων ἀπὸ γῆς, ἀπὸ τῶν ἐν τῇ χώρᾳ ἰδίων γινομένων, ἀπὸ ἐμπορίων, ἀπὸ τελῶν, ἀπὸ βοσκημάτων, ἀπὸ τῶν ἄλλων.

αὐτῶν δὲ τούτων πρώτη μὲν καὶ κρατίστη ἡ ἀπὸ τῆς γῆς ʽαὕτη δέ ἐστιν ἣν οἱ μὲν ἐκφόριον, οἱ δὲ δεκάτην προσαγορεύουσιν̓, δευτέρα δὲ ἡ ἀπὸ τῶν ἰδίων γινομένη, οὗ μὲν χρυσίον, οὗ δὲ ἀργύριον, οὗ δὲ χαλκός, οὗ δὲ ὁπόσα δύναται γίνεσθαι, τρίτη δὲ καὶ ἡ ἀπὸ τῶν ἐμπορίων τετάρτη δὲ καὶ ἡ ἀπὸ τῶν κατὰ γῆν τε καὶ ἀγοραίων τελῶν γινομένη, πέμπτη δὲ ἡ ἀπὸ τῶν βοσκημάτων, ἐπικαρπία τε καὶ δεκάτη καλουμένη, ἕκτη δὲ ἡ ἀπὸ τῶν ἄλλων, ἐπικεφάλαιόν τε καὶ χειρωνάξιον προσαγορευομένη.

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τρίτον δὲ τὴν πολιτικήν. ταύτης δὲ κρατίστη μὲν πρόσοδος ἡ ἀπὸ τῶν ἰδίων ἐν τῇ χώρᾳ γινομένων, εἶτα ἡ ἀπὸ τῶν ἐμπορίων καὶ διαγωγῶν, εἶτα ἡ ἀπὸ τῶν ἐγκυκλίων.

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τέταρτον δὲ καὶ τελευταῖον τὴν ἰδιωτικήν. αὕτη δέ ἐστιν ἀνώμαλος μὲν διὰ τὸ δεῖν μὴ πρὸς ἕνα σκοπὸν οἰκονομεῖν, ἐλαχίστη δὲ διὰ τὸ καὶ τὰς προσόδους καὶ τὰ ἀναλώματα βραχέα γίνεσθαι. αὐτῆς δὲ ταύτης κρατίστη μὲν πρόσοδος ἡ ἀπὸ γῆς γινομένη, δευτέρα δὲ ἡ ἀπὸ τῶν ἄλλων ἐγκλημάτων, τρίτη δὲ ἡ ἀπὸ ἀργυρίου. χωρὶς δὲ τούτων ὃ πάσαις μὲν ἐπικοινωνεῖται ταῖς οἰκονομίαις καὶ προσήκει σκοπεῖν αὐτὸ μὴ παρέργως, μάλιστα δὲ ταύτῃ, τὸ τἀναλώματα μὴ μείζω τῶν προσόδων γίνεσθαι.

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ἐπεὶ τοίνυν τὰς διαιρέσεις εἰρήκαμεν, μετὰ τοῦτο πάλιν νοητέον ἡμῖν, ἡ σατραπεία, περὶ ἣν ἂν πραγματευώμεθα, ἢ πόλις, πότερον ἃ πάντα ἄρτι διειλόμεθαἢ τὰ μέγιστα τούτων εἰ δυνατὴ φέρειν ἐστί, τούτοις χρηστέον· μετὰ δὲ τοῦτο ποῖαι τῶν προσόδων ἢ τὸ παράπαν οὐκ εἰσί, δυναταὶ δʼ εἰσὶ γενέσθαι, ἢ μικραὶ νῦν οὖσαι μείζους οἷαί τινες κατασκευασθῆναι, ἢ τῶν ἀναλωμάτων τῶν νῦν ἀναλουμένων, τίνα τε καὶ πόσα περιαιρεθέντα τὰ ὅλα μηθὲν βλάψει.

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τὰ μὲν οὖν περὶ τὰς οἰκονομίας τε καὶ τὰ μέρη τὰ τούτων εἰρήκαμεν· ὅσα δέ τινες τῶν πρότερον πεπράγασιν εἰς πόρον χρημάτων ἢ τεχνικῶς τι διῴκησαν, ἃ ὑπελαμβάνομεν ἀξιόλογα αὐτῶν εἶναι, συναγηόχαμεν. οὐδὲ γὰρ ταύτην τὴν ἱστορίαν ἀχρεῖον ὑπολαμβάνομεν εἶναι. ἔστι γὰρ ὅτε τούτων ἐφαρμόσει τοῖς οἷα ἂν αὐτὸς πραγματεύηται.

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τρίτον δὲ τὴν πολιτικήν. ταύτης δὲ κρατίστη μὲν πρόσοδος ἡ ἀπὸ τῶν ἰδίων ἐν τῇ χώρᾳ γινομένων, εἶτα ἡ ἀπὸ τῶν ἐμπορίων καὶ διαγωγῶν, εἶτα ἡ ἀπὸ τῶν ἐγκυκλίων.

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τέταρτον δὲ καὶ τελευταῖον τὴν ἰδιωτικήν. αὕτη δέ ἐστιν ἀνώμαλος μὲν διὰ τὸ δεῖν μὴ πρὸς ἕνα σκοπὸν οἰκονομεῖν, ἐλαχίστη δὲ διὰ τὸ καὶ τὰς προσόδους καὶ τὰ ἀναλώματα βραχέα γίνεσθαι. αὐτῆς δὲ ταύτης κρατίστη μὲν πρόσοδος ἡ ἀπὸ γῆς γινομένη, δευτέρα δὲ ἡ ἀπὸ τῶν ἄλλων ἐγκλημάτων, τρίτη δὲ ἡ ἀπὸ ἀργυρίου. χωρὶς δὲ τούτων ὃ πάσαις μὲν ἐπικοινωνεῖται ταῖς οἰκονομίαις καὶ προσήκει σκοπεῖν αὐτὸ μὴ παρέργως, μάλιστα δὲ ταύτῃ, τὸ τἀναλώματα μὴ μείζω τῶν προσόδων γίνεσθαι.

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ἐπεὶ τοίνυν τὰς διαιρέσεις εἰρήκαμεν, μετὰ τοῦτο πάλιν νοητέον ἡμῖν, ἡ σατραπεία, περὶ ἣν ἂν πραγματευώμεθα, ἢ πόλις, πότερον ἃ πάντα ἄρτι διειλόμεθαἢ τὰ μέγιστα τούτων εἰ δυνατὴ φέρειν ἐστί, τούτοις χρηστέον· μετὰ δὲ τοῦτο ποῖαι τῶν προσόδων ἢ τὸ παράπαν οὐκ εἰσί, δυναταὶ δʼ εἰσὶ γενέσθαι, ἢ μικραὶ νῦν οὖσαι μείζους οἷαί τινες κατασκευασθῆναι, ἢ τῶν ἀναλωμάτων τῶν νῦν ἀναλουμένων, τίνα τε καὶ πόσα περιαιρεθέντα τὰ ὅλα μηθὲν βλάψει.

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τὰ μὲν οὖν περὶ τὰς οἰκονομίας τε καὶ τὰ μέρη τὰ τούτων εἰρήκαμεν· ὅσα δέ τινες τῶν πρότερον πεπράγασιν εἰς πόρον χρημάτων ἢ τεχνικῶς τι διῴκησαν, ἃ ὑπελαμβάνομεν ἀξιόλογα αὐτῶν εἶναι, συναγηόχαμεν. οὐδὲ γὰρ ταύτην τὴν ἱστορίαν ἀχρεῖον ὑπολαμβάνομεν εἶναι. ἔστι γὰρ ὅτε τούτων ἐφαρμόσει τοῖς οἷα ἂν αὐτὸς πραγματεύηται.

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Κύψελος ὁ Κορίνθιος εὐξάμενος τῷ Διί, ἐὰν κύριος γένηται τῆς πόλεως, τὰ ὄντα Κορινθίοις πάντα ἀναθήσειν, ἐκέλευσεν αὐτοὺς ἀπογράψασθαι. ἀπογραψαμένων δὲ τούτων τὸ δέκατον μέρος παρʼ ἑκάστου ἔλαβε, τοῖς δὲ λοιποῖς ἐκέλευσεν ἐργάζεσθαι. περιελθόντος δὲ τοῦ ἐνιαυτοῦ τὸ αὐτὸ τοῦτο ἐποίησεν, ὥστε συνέβαινεν ἐν δέκα ἔτεσι κεῖνόν τε ἅπαντα ἔχειν, ἅπερ ἀνιέρωσεν, τούς τε Κορινθίους ἕτερα κεκτῆσθαι.

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Λύγδαμις Νάξιος ἐκβαλὼν φυγάδας, ἐπειδὴ τὰ κτήματα αὐτῶν οὐθεὶς ἠθέλησεν ἀλλʼ ἢ βραχέος ἀγοράζειν, αὐτοῖς τοῖς φυγάσιν ἀπέδοτο. τά τε ἀναθήματα, ὅσα ἦν αὐτῶν ἔν τισιν ἐργαστηρίοις ἡμίεργα ἀνακείμενα, ἐπώλει τοῖς τε φυγάσι καὶ τῶν ἄλλων τῷ βουλομένῳ ὥστʼ ἐπιγραφῆναι τὸ τοῦ πριαμένου ὄνομα.

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Βυζάντιοι δὲ δεηθέντες χρημάτων τὰ τεμένη τὰ δημόσια ἀπέδοντο, τὰ μὲν κάρπιμα χρόνον τινά, τὰ δὲ ἄκαρπα ἀεννάως· τά τε θιασωτικὰ καὶ τὰ πατριωτικὰ ὡσαύτως, καὶ ὅσα ἐν χωρίοις ἰδιωτικοῖς ἦν· ὠνοῦντο γὰρ πολλοῦ ὧν ἦν καὶ τὸ ἄλλο κτῆμα. τοῖς δὲ θιασώταις ἕτερα χωρία, τὰ δημόσια, ὅσα ἦν περὶ τὸ γυμνάσιον ἢ τὴν ἀγορὰν ἢ τὸν λιμένα,τούς τε τόπους τοὺς ἀγοραίους, ἐν οἷς ἐπώλει τίς τι· καὶ τῆς θαλάττης τὴν ἁλιείαν, καὶ τὴν τῶν ἁλῶν ἁλατοπωλίαν, τῶν τʼ ἐργαζομένων θαυματοποιῶν καὶ μάντεων καὶ φαρμακοπωλῶν καὶ τῶν ἄλλων τῶν τοιουτοτρόπων · τὸ τρίτον δὲ μέρος τοῦ ἐργαζομένου ἀποτελεῖν ἔταξαν. τῶν τε νομισμάτων τὴν καταλλαγὴν ἀπέδοντο μιᾷ τραπέζῃ, ἑτέρῳ δὲ οὐκ ἦν οὐθενὶ οὔτε ἀποδόσθαι ἑτέρῳ οὔτε πρίασθαι παρʼ ἑτέρου· εἰ δὲ μή, στέρησις ἦν.

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Κύψελος ὁ Κορίνθιος εὐξάμενος τῷ Διί, ἐὰν κύριος γένηται τῆς πόλεως, τὰ ὄντα Κορινθίοις πάντα ἀναθήσειν, ἐκέλευσεν αὐτοὺς ἀπογράψασθαι. ἀπογραψαμένων δὲ τούτων τὸ δέκατον μέρος παρʼ ἑκάστου ἔλαβε, τοῖς δὲ λοιποῖς ἐκέλευσεν ἐργάζεσθαι. περιελθόντος δὲ τοῦ ἐνιαυτοῦ τὸ αὐτὸ τοῦτο ἐποίησεν, ὥστε συνέβαινεν ἐν δέκα ἔτεσι κεῖνόν τε ἅπαντα ἔχειν, ἅπερ ἀνιέρωσεν, τούς τε Κορινθίους ἕτερα κεκτῆσθαι.

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Λύγδαμις Νάξιος ἐκβαλὼν φυγάδας, ἐπειδὴ τὰ κτήματα αὐτῶν οὐθεὶς ἠθέλησεν ἀλλʼ ἢ βραχέος ἀγοράζειν, αὐτοῖς τοῖς φυγάσιν ἀπέδοτο. τά τε ἀναθήματα, ὅσα ἦν αὐτῶν ἔν τισιν ἐργαστηρίοις ἡμίεργα ἀνακείμενα, ἐπώλει τοῖς τε φυγάσι καὶ τῶν ἄλλων τῷ βουλομένῳ ὥστʼ ἐπιγραφῆναι τὸ τοῦ πριαμένου ὄνομα.

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Βυζάντιοι δὲ δεηθέντες χρημάτων τὰ τεμένη τὰ δημόσια ἀπέδοντο, τὰ μὲν κάρπιμα χρόνον τινά, τὰ δὲ ἄκαρπα ἀεννάως· τά τε θιασωτικὰ καὶ τὰ πατριωτικὰ ὡσαύτως, καὶ ὅσα ἐν χωρίοις ἰδιωτικοῖς ἦν· ὠνοῦντο γὰρ πολλοῦ ὧν ἦν καὶ τὸ ἄλλο κτῆμα. τοῖς δὲ θιασώταις ἕτερα χωρία, τὰ δημόσια, ὅσα ἦν περὶ τὸ γυμνάσιον ἢ τὴν ἀγορὰν ἢ τὸν λιμένα,τούς τε τόπους τοὺς ἀγοραίους, ἐν οἷς ἐπώλει τίς τι· καὶ τῆς θαλάττης τὴν ἁλιείαν, καὶ τὴν τῶν ἁλῶν ἁλατοπωλίαν, τῶν τʼ ἐργαζομένων θαυματοποιῶν καὶ μάντεων καὶ φαρμακοπωλῶν καὶ τῶν ἄλλων τῶν τοιουτοτρόπων · τὸ τρίτον δὲ μέρος τοῦ ἐργαζομένου ἀποτελεῖν ἔταξαν. τῶν τε νομισμάτων τὴν καταλλαγὴν ἀπέδοντο μιᾷ τραπέζῃ, ἑτέρῳ δὲ οὐκ ἦν οὐθενὶ οὔτε ἀποδόσθαι ἑτέρῳ οὔτε πρίασθαι παρʼ ἑτέρου· εἰ δὲ μή, στέρησις ἦν.

ὄντος δὲ νόμου αὐτοῖς μὴ εἶναι πολίτην ὃς ἂν μὴ ἐξ ἀστῶν ἀμφοτέρων ᾖ, χρημάτων δεηθέντες ἐψηφίσαντο τὸν ἐξ ἑνὸς ὄντα ἀστοῦ καταβαλόντα μνᾶς τριάκοντα εἶναι πολίτην.

ἐν σιτοδείᾳ δὲ γενόμενοι καὶ ἀποροῦντες χρημάτων κατήγαγον τὰ πλοῖα τὰ ἐκ τοῦ Πόντου· χρόνου δὲ γενομένου, τῶν ἐμπόρων ἀγανακτούντων, ἐτέλουν αὐτοῖς τόκους ἐπιδεκάτους, τοῖς δʼ ὠνουμένοις τι ἔταξαν χωρὶς τῆς τιμῆς διδόναι τὸ ἐπιδέκατον.

μετοίκων δέ τινων ἐπιδεδανεικότων ἐπὶ κτήμασιν, οὐκ οὔσης αὐτοῖς ἐγκτήσεως ἐψηφίσαντο τὸ τρίτον μέρος εἰσφέροντα τοῦ δανείου τὸν βουλόμενον κυρίως ἔχειν τὸ κτῆμα.

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Ἱππίας ὁ Ἀθηναῖος τὰ ὑπερέχοντα τῶν ὑπερῴων εἰς τὰς δημοσίας ὁδοὺς καὶ τοὺς ἀναβαθμοὺς καὶ τὰ προφράγματα καὶ τὰς θύρας τὰς ἀνοιγομένας ἔξω ἐπώλησεν· ὠνοῦντο οὖν ὧν ἦν τὰ κτήματα, καὶ συνελέγη χρήματα οὕτω συχνά.

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Ἱππίας ὁ Ἀθηναῖος τὰ ὑπερέχοντα τῶν ὑπερῴων εἰς τὰς δημοσίας ὁδοὺς καὶ τοὺς ἀναβαθμοὺς καὶ τὰ προφράγματα καὶ τὰς θύρας τὰς ἀνοιγομένας ἔξω ἐπώλησεν· ὠνοῦντο οὖν ὧν ἦν τὰ κτήματα, καὶ συνελέγη χρήματα οὕτω συχνά.

τό τε νόμισμα τὸ ὂν Ἀθηναίοις ἀδόκιμον ἐποίησε, τάξας δὲ τιμὴν ἐκέλευσε πρὸς αὑτὸν ἀνακομίζειν· συνελθόντων δὲ ἐπὶ τῷ κόψαι ἕτερον χαρακτῆρα, ἐξέδωκε τὸ αὐτὸ ἀργύριον.

ὅσοι τε τριηραρχεῖν ἢ φυλαρχεῖν ἢ χορηγεῖν ἤ τινα εἰς ἑτέραν λειτουργίαν τοιαύτην ἤμελλον δαπανᾶν, τίμημα τάξας μέτριον ἐκέλευσε τὸν βουλόμενον ἀποτίσαντα τοῦτο ἐγγράφεσθαι εἰς τοὺς λελειτουργηκότας.

τῇ τε ἱερείᾳ τῇ τῆς Ἀθηνᾶς τῆς ἐν ἀκροπόλει ὑπὲρ τοῦ ἀποθανόντος φέρειν χοίνικα κριθῶν καὶ πυρῶν ἑτέραν καὶ ὀβολόν, καὶ ὅτῳ ἂν παιδάριον γένηται, τὸ αὐτὸ τοῦτο.

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Ἀθηναῖοι δὲ οἱ ἐν Ποτιδαίᾳ οἰκοῦντες δεόμενοι χρημάτων εἰς τὸν πόλεμον ἀπογράψασθαι ἅπασι συνέταξαν τὰς οὐσίας,μὴ ἁθρόας εἰς τὸν αὑτοῦ δῆμον ἕκαστον, ἀλλὰ κατὰ κτῆμα ἐν ᾧ τόπῳ ἕκαστον εἴη, ἵνα οἱ πένητες δύνωνται ὑποτιμᾶσθαι· ὅτῳ δὲ μὴ ἦν κτῆμα μηθέν, τὸ σῶμα διμναῖον τιμήσασθαι. ἀπὸ τούτων οὖν εἰσέφερον τὸ ἐπιγραφὲν ἕκαστος σῷον τῇ πόλει.

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Σωσίπολις Ἀντισσαῖος δέ, δεηθείσης τῆς πόλεως χρημάτων, εἰθισμένων δὲ αὐτῶν λαμπρῶς ἄγειν Διονύσια, ἐν οἷς ἄλλα τε πολλὰ ἀνήλισκον ἐξ ἐνιαυτοῦ παρασκευάζοντες καὶ ἱερεῖα πολυτελῆ, ὑπογύου δὲ οὔσης ταύτης τῆς ἑορτῆς, ἔπεισεν αὐτοὺς τῷ μὲν Διονύσῳ εὔξασθαι ἐς νέωτα ἀποδώσειν διπλάσια, ταῦτα δὲ συναγαγόντας ἀποδόσθαι. συνελέγη οὖν αὐτοῖς χρήματα οὐκ ὀλίγα πρὸς τὴν χρείαν.

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Λαμψακηνοὶ δὲ προσδοκίμων οὐσῶν τριηρῶν πολλῶν πρὸς αὐτούς, ὄντος μεδίμνου τῶν ἀλφίτων τετραδράχμου, προσέταξαν τοῖς ἀγοραίοις πωλεῖν ἑξάδραχμον, καὶ τοῦ ἐλαίου τὸν χοᾶ ὄντα δραχμῶν τριῶν, τεττάρων καὶ τριωβόλου, τοῦ τε οἴνου καὶ τῶν ἄλλων ὡσαύτως. τὴν μὲν οὖν ἀρχαίαν τιμὴν ἐλάμβανεν ὁ ἰδιώτης, τὸ δὲ πλέον ἡ πόλις, καὶ εὐπόρησε χρημάτων.

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Ἡρακλεῶται πέμποντες ναῦς τετταράκοντα ἐπὶ τοὺς ἐν Βοσπόρῳ τυράννους, οὐκ εὐπορούμενοι χρημάτων παρὰ τῶν ἐμπόρων συνηγόρασαν τόν τε σῖτον πάντα καὶ τὸ ἔλαιον καὶ τὸν οἶνον καὶ τὴν ἄλλην ἀγοράν χρόνου διισταμένου ἐν ᾧ ἔμελλον ἀποδώσειν τὴν τιμήν. τοῖς δὲ δὴ ἐμπόροις καλῶς εἶχε μὴ κοτυλίζειν, ἀλλʼ ἁθρόα τὰ φορτία πεπρᾶσθαι, ἐκεῖνοί τε διδόντες διʼ ἄλλην οὐ μισθὸν παρῆγον ἀλλὰ τὴν ἀγορὰν ἐν ὁλκάσι, καὶ ἄνδρα ταμίαν ἐπέστησαν ἐφʼ ἑκάστῃ τῶν νεῶν. ἀφικομένων δʼ εἰς τὴν πολεμίαν αὐτῶν ἠγόραζον οἱ στρατιῶται παρὰ τούτων ἅπαντα. πρότερον οὖν συνελέγη ἀργύριον ἤ ἐδίδοσαν οἱ στρατηγοὶ πάλιν τὸν μισθόν, ὥστε συνέβαινε ταὐτὸ τὸ ἀργύριον δίδοσθαι ἕως εἰς οἶκον ἀπῆλθον.

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Λακεδαιμόνιοι Σαμίων δεηθέντων χρήματα αὐτοῖς εἰς τὴν κάθοδον δοῦναι, ἐψηφίσαντο μίαν ἡμέραν καὶ αὐτοὺς καὶ τοὺς οἰκέτας καὶ τὰ ὑποζύγια νηστεῦσαι, ὅσον δὲ ἐδαπάνα ἕκαστος, τοσοῦτον δοῦναι τοῖς Σαμίοις.

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Χαλκηδόνιοι δέ, ξένων ἐν τῇ πόλει συχνῶν παρʼ αὐτοῖς γινομένων, ὀφείλοντες αὐτοῖς μισθὸν οὐκ ἠδύναντο διαλῦσαι. ἀνήγγειλαν οὖν, εἴ τις τῶν πολιτῶν ἢ μετοίκων σῦλον ἔχει κατὰ πόλεως ἢ ἰδιώτου καὶ βούλεται λαβεῖν, ἀπογράψασθαι. ἀπογραψαμένων δὲ συχνῶν, τὰ πλοῖα τὰ πλέοντα εἰς τὸν Πόντον ἐσύλων μετὰ προφάσεως εὐλόγου. ἔταξαν δὲ χρόνον ἐν ᾧ λόγον ὑπὲρ αὐτῶν ἔφασαν ποιήσασθαι. συλλεγέντων δὲ χρημάτων συχνῶν, τοὺς μὲν στρατιώτας ἀπήλλαξαν, ὑπὲρ δὲ τῶν σύλων διεδικάσαντο. τοῖς δὲ μὴ δικαίως συληθεῖσιν ἡ πόλις ἀπὸ τῶν προσόδων ἀπεδίδου.

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Κυζικηνοὶ δὲ στασιάσαντες πρὸς ἀλλήλους, ἐπικρατήσαντος τοῦ δήμου, τῶν δὲ πλουσίων συνειλημμένων, ὀφείλοντες χρήματα στρατιώταις ἐψηφίσαντο μὴ θανατῶσαι τοὺς συνειλημμένους, ἀλλὰ χρήματα πραξαμένους φυγαδεῦσαι.

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Χῖοι δέ, νόμου ὄντος αὐτοῖς ἀπογράφεσθαι τὰ χρέα εἰς τὸ δημόσιον, δεηθέντες χρημάτων ἐψηφίσαντο τοὺς ὀφείλοντας μὲν ἀποδοῦναι τῇ πόλει τὰ δάνεια, τὴν δὲ πόλιν ἐκ τῶν προσόδων τοὺς τόκους τοῖς δεδανεικόσι καταφέρειν, ἕως ἂν καὶ τὸ ἀρχαῖον εὐπορήσωσιν.

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Μαύσωλος ὁ Καρίας τύραννος, πέμποντος βασιλέως πρὸς αὐτὸν ἐπὶ τῷ τοὺς φόρους δοῦναι, συναγαγὼν τοὺς εὐπορωτάτους ἐν τῇ χώρᾳ ἔλεγεν ὅτι ὁ βασιλεὺς αἰτεῖ τοὺς φόρους, αὐτὸς δὲ οὐκ εὐπορεῖται. κατασκευαστοὶ δʼ ἄνδρες αὐτῷ εὐθέως ἐπηγγέλλοντο ὅσον εἰσοίσει ἕκαστος. τούτων δὲ τοῦτο πραξάντων, οἱ εὐπορώτεροι τὰ μὲν αἰσχυνόμενοι τὰ δὲ φοβούμενοι πολλῷ τούτων πλείω ἐπηγγέλλοντο καὶ εἰσέφερον.

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Ἀθηναῖοι δὲ οἱ ἐν Ποτιδαίᾳ οἰκοῦντες δεόμενοι χρημάτων εἰς τὸν πόλεμον ἀπογράψασθαι ἅπασι συνέταξαν τὰς οὐσίας,μὴ ἁθρόας εἰς τὸν αὑτοῦ δῆμον ἕκαστον, ἀλλὰ κατὰ κτῆμα ἐν ᾧ τόπῳ ἕκαστον εἴη, ἵνα οἱ πένητες δύνωνται ὑποτιμᾶσθαι· ὅτῳ δὲ μὴ ἦν κτῆμα μηθέν, τὸ σῶμα διμναῖον τιμήσασθαι. ἀπὸ τούτων οὖν εἰσέφερον τὸ ἐπιγραφὲν ἕκαστος σῷον τῇ πόλει.

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Σωσίπολις Ἀντισσαῖος δέ, δεηθείσης τῆς πόλεως χρημάτων, εἰθισμένων δὲ αὐτῶν λαμπρῶς ἄγειν Διονύσια, ἐν οἷς ἄλλα τε πολλὰ ἀνήλισκον ἐξ ἐνιαυτοῦ παρασκευάζοντες καὶ ἱερεῖα πολυτελῆ, ὑπογύου δὲ οὔσης ταύτης τῆς ἑορτῆς, ἔπεισεν αὐτοὺς τῷ μὲν Διονύσῳ εὔξασθαι ἐς νέωτα ἀποδώσειν διπλάσια, ταῦτα δὲ συναγαγόντας ἀποδόσθαι. συνελέγη οὖν αὐτοῖς χρήματα οὐκ ὀλίγα πρὸς τὴν χρείαν.

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Λαμψακηνοὶ δὲ προσδοκίμων οὐσῶν τριηρῶν πολλῶν πρὸς αὐτούς, ὄντος μεδίμνου τῶν ἀλφίτων τετραδράχμου, προσέταξαν τοῖς ἀγοραίοις πωλεῖν ἑξάδραχμον, καὶ τοῦ ἐλαίου τὸν χοᾶ ὄντα δραχμῶν τριῶν, τεττάρων καὶ τριωβόλου, τοῦ τε οἴνου καὶ τῶν ἄλλων ὡσαύτως. τὴν μὲν οὖν ἀρχαίαν τιμὴν ἐλάμβανεν ὁ ἰδιώτης, τὸ δὲ πλέον ἡ πόλις, καὶ εὐπόρησε χρημάτων.

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Ἡρακλεῶται πέμποντες ναῦς τετταράκοντα ἐπὶ τοὺς ἐν Βοσπόρῳ τυράννους, οὐκ εὐπορούμενοι χρημάτων παρὰ τῶν ἐμπόρων συνηγόρασαν τόν τε σῖτον πάντα καὶ τὸ ἔλαιον καὶ τὸν οἶνον καὶ τὴν ἄλλην ἀγοράν χρόνου διισταμένου ἐν ᾧ ἔμελλον ἀποδώσειν τὴν τιμήν. τοῖς δὲ δὴ ἐμπόροις καλῶς εἶχε μὴ κοτυλίζειν, ἀλλʼ ἁθρόα τὰ φορτία πεπρᾶσθαι, ἐκεῖνοί τε διδόντες διʼ ἄλλην οὐ μισθὸν παρῆγον ἀλλὰ τὴν ἀγορὰν ἐν ὁλκάσι, καὶ ἄνδρα ταμίαν ἐπέστησαν ἐφʼ ἑκάστῃ τῶν νεῶν. ἀφικομένων δʼ εἰς τὴν πολεμίαν αὐτῶν ἠγόραζον οἱ στρατιῶται παρὰ τούτων ἅπαντα. πρότερον οὖν συνελέγη ἀργύριον ἤ ἐδίδοσαν οἱ στρατηγοὶ πάλιν τὸν μισθόν, ὥστε συνέβαινε ταὐτὸ τὸ ἀργύριον δίδοσθαι ἕως εἰς οἶκον ἀπῆλθον.

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Λακεδαιμόνιοι Σαμίων δεηθέντων χρήματα αὐτοῖς εἰς τὴν κάθοδον δοῦναι, ἐψηφίσαντο μίαν ἡμέραν καὶ αὐτοὺς καὶ τοὺς οἰκέτας καὶ τὰ ὑποζύγια νηστεῦσαι, ὅσον δὲ ἐδαπάνα ἕκαστος, τοσοῦτον δοῦναι τοῖς Σαμίοις.

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Χαλκηδόνιοι δέ, ξένων ἐν τῇ πόλει συχνῶν παρʼ αὐτοῖς γινομένων, ὀφείλοντες αὐτοῖς μισθὸν οὐκ ἠδύναντο διαλῦσαι. ἀνήγγειλαν οὖν, εἴ τις τῶν πολιτῶν ἢ μετοίκων σῦλον ἔχει κατὰ πόλεως ἢ ἰδιώτου καὶ βούλεται λαβεῖν, ἀπογράψασθαι. ἀπογραψαμένων δὲ συχνῶν, τὰ πλοῖα τὰ πλέοντα εἰς τὸν Πόντον ἐσύλων μετὰ προφάσεως εὐλόγου. ἔταξαν δὲ χρόνον ἐν ᾧ λόγον ὑπὲρ αὐτῶν ἔφασαν ποιήσασθαι. συλλεγέντων δὲ χρημάτων συχνῶν, τοὺς μὲν στρατιώτας ἀπήλλαξαν, ὑπὲρ δὲ τῶν σύλων διεδικάσαντο. τοῖς δὲ μὴ δικαίως συληθεῖσιν ἡ πόλις ἀπὸ τῶν προσόδων ἀπεδίδου.

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Κυζικηνοὶ δὲ στασιάσαντες πρὸς ἀλλήλους, ἐπικρατήσαντος τοῦ δήμου, τῶν δὲ πλουσίων συνειλημμένων, ὀφείλοντες χρήματα στρατιώταις ἐψηφίσαντο μὴ θανατῶσαι τοὺς συνειλημμένους, ἀλλὰ χρήματα πραξαμένους φυγαδεῦσαι.

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Χῖοι δέ, νόμου ὄντος αὐτοῖς ἀπογράφεσθαι τὰ χρέα εἰς τὸ δημόσιον, δεηθέντες χρημάτων ἐψηφίσαντο τοὺς ὀφείλοντας μὲν ἀποδοῦναι τῇ πόλει τὰ δάνεια, τὴν δὲ πόλιν ἐκ τῶν προσόδων τοὺς τόκους τοῖς δεδανεικόσι καταφέρειν, ἕως ἂν καὶ τὸ ἀρχαῖον εὐπορήσωσιν.

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Μαύσωλος ὁ Καρίας τύραννος, πέμποντος βασιλέως πρὸς αὐτὸν ἐπὶ τῷ τοὺς φόρους δοῦναι, συναγαγὼν τοὺς εὐπορωτάτους ἐν τῇ χώρᾳ ἔλεγεν ὅτι ὁ βασιλεὺς αἰτεῖ τοὺς φόρους, αὐτὸς δὲ οὐκ εὐπορεῖται. κατασκευαστοὶ δʼ ἄνδρες αὐτῷ εὐθέως ἐπηγγέλλοντο ὅσον εἰσοίσει ἕκαστος. τούτων δὲ τοῦτο πραξάντων, οἱ εὐπορώτεροι τὰ μὲν αἰσχυνόμενοι τὰ δὲ φοβούμενοι πολλῷ τούτων πλείω ἐπηγγέλλοντο καὶ εἰσέφερον.

πάλιν δεηθεὶς χρημάτων ἐξεκκλησιάσας τοῖς Μυλασσεῦσιν ἔλεγεν ὅτι μητρόπολις οὖσα ἡ πόλις αὐτοῦ αὕτη ἀτείχιστός ἐστιν, ὁ δὲ βασιλεὺς ἐπʼ αὐτὸν στρατεύει. ἐκέλευσεν οὖν τοὺς Μυλασσεῖς φέρειν ἕκαστον ὅτι πλεῖστα χρήματα, φάσκων αὐτοὺς τοῖς νῦν εἰσενεχθεῖσι καὶ τὰ λοιπὰ σῴζειν. εἰσενεχθέντων δὲ πολλῶν τὰ μὲν χρήματα εἶχε, τὸ δὲ τεῖχος οὐκ ἔφη τὸν θεὸν ἐᾶν ἐν τῷ παρόντι οἰκοδομεῖν.

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Κόνδαλος Μαυσώλου ὕπαρχος, ὁπότε διαπορευομένῳ αὐτῷ διὰ τῆς χώρας προσενέγκοι τις πρόβατονἢ ὗν ἢ μόσχον, ἀπογραψάμενος τὸν δόντα καὶ τὸν χρόνον, ἀπαγαγόντα εἰς οἶκον ἐκέλευε τρέφειν ἕως ἂν ἐπανέλθοι· ὁπότε δὲ δοκοίη χρόνος ἱκανὸς εἶναι, αὐτό τε τὸ τραφὲν καὶ τὴν ἐπικαρπίαν λογισάμενος ἀπῄτει. τῶν τε δένδρων τὰ ὑπερέχοντα ἢ πίπτοντα εἰς τὰς ὁδοὺς τὰς βασιλικὰς ἐπώλει ὡς τὰς ἐπικαρπίας.

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Κόνδαλος Μαυσώλου ὕπαρχος, ὁπότε διαπορευομένῳ αὐτῷ διὰ τῆς χώρας προσενέγκοι τις πρόβατονἢ ὗν ἢ μόσχον, ἀπογραψάμενος τὸν δόντα καὶ τὸν χρόνον, ἀπαγαγόντα εἰς οἶκον ἐκέλευε τρέφειν ἕως ἂν ἐπανέλθοι· ὁπότε δὲ δοκοίη χρόνος ἱκανὸς εἶναι, αὐτό τε τὸ τραφὲν καὶ τὴν ἐπικαρπίαν λογισάμενος ἀπῄτει. τῶν τε δένδρων τὰ ὑπερέχοντα ἢ πίπτοντα εἰς τὰς ὁδοὺς τὰς βασιλικὰς ἐπώλει ὡς τὰς ἐπικαρπίας.

τῶν δὲ στρατιωτῶν εἴ τις τελευτήσειε, διαπύλιον ἀπῄτει δραχμὴν τοῦ σώματος· ἅμα τε οὖν ἐντεῦθεν καὶ ἀργύριον ἐλάμβανεν, ἅμα τε οἱ ἡγεμόνες οὐ παρεκρούοντο αὐτόν, πότε τετελεύτηκεν ὁ στρατιώτης.

τούς τε Λυκίους ὁρῶν ἀγαπῶντας τὸ τρίχωμα φορεῖν, ἔφησε γράμματα ἥκειν παρὰ βασιλέως, κόμας ἀποστεῖλαι εἰς προκόμια, προστετάχθαι οὖν αὐτῷ ὑπὸ Μαυσώλου ἀποκεῖραι αὐτούς. ἔφησεν οὖν, εἰ βούλονται ἐπικεφάλαιον τακτὸν αὐτῷ δοῦναι, μεταπέμψασθαι ἐκ τῆς Ἑλλάδος κόμην, οἱ δὲ ἀσμένως ἔδοσαν ὃ ᾔτει, καὶ συνελέγη χρήματα πολλὰ ἀπὸ ὄχλου πολλοῦ.

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Ἀριστοτέλης Ῥόδιος ἄρχων Φωκαίας, ἀπορῶν χρημάτων, ὁρῶν στάσεις οὔσας δύο τῶν Φωκαίων, λόγους ἐποιήσατο πρὸς τὴν ἑτέραν στάσιν ἐν ἀπορρήτοις, φάσκων αὑτῷ διδόναι χρήματα τοὺς ἑτέρους ἐφʼ ᾧ αὐτοῖς τὰ πράγματα ἐγκλῖναι, αὐτὸς δὲ μᾶλλον βούλεσθαι παρὰ τούτων λαβεῖν καὶ τὰ περὶ τὴν πόλιν τούτοις διοικεῖν παραδοῦναι. ἀκούσαντες δὲ ταῦτα εὐθέως τὰ χρήματα οἱ παρόντες πορίσαντες ὅσα ἐκέλευσεν ἔδωκαν. ὁ δὲ τοῖς ἑτέροις πάλιν ἔδειξεν ἃ εἰληφὼς εἴη παρὰ τῶν ἑτέρων· οἱ δὲ καὶ αὐτοὶ ἔφασαν οὐκ ἐλάττω δώσειν. λαβὼν δὲ παρʼ ἀμφοτέρων κατήλλαξεν αὐτοὺς πρὸς ἀλλήλους.

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Ἀριστοτέλης Ῥόδιος ἄρχων Φωκαίας, ἀπορῶν χρημάτων, ὁρῶν στάσεις οὔσας δύο τῶν Φωκαίων, λόγους ἐποιήσατο πρὸς τὴν ἑτέραν στάσιν ἐν ἀπορρήτοις, φάσκων αὑτῷ διδόναι χρήματα τοὺς ἑτέρους ἐφʼ ᾧ αὐτοῖς τὰ πράγματα ἐγκλῖναι, αὐτὸς δὲ μᾶλλον βούλεσθαι παρὰ τούτων λαβεῖν καὶ τὰ περὶ τὴν πόλιν τούτοις διοικεῖν παραδοῦναι. ἀκούσαντες δὲ ταῦτα εὐθέως τὰ χρήματα οἱ παρόντες πορίσαντες ὅσα ἐκέλευσεν ἔδωκαν. ὁ δὲ τοῖς ἑτέροις πάλιν ἔδειξεν ἃ εἰληφὼς εἴη παρὰ τῶν ἑτέρων· οἱ δὲ καὶ αὐτοὶ ἔφασαν οὐκ ἐλάττω δώσειν. λαβὼν δὲ παρʼ ἀμφοτέρων κατήλλαξεν αὐτοὺς πρὸς ἀλλήλους.

τοῖς τε πολίταις κατιδὼν οὔσας δίκας πολλὰς, καὶ μεγάλας ἐκ πολλοῦ χρόνου ἀδικίας τουτοῖς διὰ πολέμου, δικαστήριον καθίσας προεῖπεν, ὅσοι ἂν μὴ δικάσωνται χρόνῷ ὃν ἐθηκε, μηκέτι εἶναι ὑπὲρ τῶν προτέρων ἐγκλημάτων κρίσεις. τότε δὴ παραβόλιον πολλῶν δικῶν καὶ τὰς ἐκκλήτους μετʼ ἐπιτιμίων ἐφʼ αὑτὸν ποιούμενος καὶ παρʼ ἑκατέρων ἀργύριον διʼ ἑτέρων λαμβάνων, συνήγαγεν οὐκ ὀλίγα χρήματα.

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Κλαζομένιοι δʼ ἐν σιτοδείᾳ ὄντες χρημάτων τε ἀποροῦντες ἐψηφίσαντο, παρʼ οἷς ἔλαιόν ἐστι τῶν ἰδιωτῶν, δανεῖσαι τῇ πόλει ἐπὶ τόκῳ· γίνεται δὲ πολὺς οὗτος ὁ καρπὸς ἐν τῇ χώρᾳ αὐτῶν.δανεισάντων δὲ μισθωσάμενοι πλοῖα ἀπέστειλαν εἰς τὰ ἐμπόρια, ὅθεν αὐτοῖς ἧκε σῖτος, ὑποθήκης γενομένης τῆς τοῦ ἐλαίου τιμῆς.

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Κλαζομένιοι δʼ ἐν σιτοδείᾳ ὄντες χρημάτων τε ἀποροῦντες ἐψηφίσαντο, παρʼ οἷς ἔλαιόν ἐστι τῶν ἰδιωτῶν, δανεῖσαι τῇ πόλει ἐπὶ τόκῳ· γίνεται δὲ πολὺς οὗτος ὁ καρπὸς ἐν τῇ χώρᾳ αὐτῶν.δανεισάντων δὲ μισθωσάμενοι πλοῖα ἀπέστειλαν εἰς τὰ ἐμπόρια, ὅθεν αὐτοῖς ἧκε σῖτος, ὑποθήκης γενομένης τῆς τοῦ ἐλαίου τιμῆς.

ὀφείλοντές στρατιώταις μισθὸν εἴκοσι τάλαντα καὶ οὐ δοῦναι δυνάμενοι τόκον ἔφερον τοῖς ἡγεμόσι τέτταρα τάλαντα τοῦ ἐνιαυτοῦ· ἐπεὶ δὲ τοῦ μὲν ἀρχαίου ἀπέκοπτον οὐθέν, ἀεὶ δὲ μάτην ἐδαπάνων, νόμισμα ἔκοψαν σιδηροῦν εἰς ἀργυρίου λόγον εἴκοσι ταλάντων, εἶτα διδόντες τοῖς εὐπορωτάτοις ἐν τῇ πόλει κατὰ λόγον ἑκάστῳ ἀργύριον παρʼ ἐκείνων ἔλαβον ἴσον. οἵ τε οὖν ἰδιῶται εἶχον εἰς τὰς καθʼ ἡμέραν χρείας ἀναλίσκειν καὶ ἡ πόλις τοῦ χρέους ἀπηλλάγη. δεύτερον δὲ ἐκ τῶν προσόδων ἐκείνοις τόν τε τόκον κατέφερον καὶ ἀεὶ διαιροῦντες ἑκάστῳ πρὸς μέρος διεδίδοσαν, τοὺς δὲ σιδηροῦς ἐκομίζοντο.

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Σηλυβριανοὶ δὲ δεηθέντες χρημάτων, νόμου ὄντος αὐτοῖς σίτου μὴ ἐξάγειν ἐν λιμῷ γενομένοις, ἐκείνοις δὲ ὑπάρχοντος σίτου παλαιοῦ, ἐψηφίσαντο τῇ πόλει παραδοῦναι τοὺς ἰδιώτας τὸν σῖτον τῆς τεταγμένης τιμῆς, ὑπολειπόμενον ἕκαστον ἐνιαυτοῦ τροφήν· εἶτα ἐξαγωγὴν ἔδωκαν τῷ βουλομένῳ, τάξαντες τιμὴν ἣν ἐδόκει καλῶς ἔχειν αὐτοῖς.

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Ἀβυδηνοὶ δέ, διὰ στασιασμὸν τῆς χώρας ἀργοῦ γενομένης, καὶ τῶν μετοίκων οὐ προϊεμένων αὐτοῖς οὐδὲν διὰ τὸ καὶ ἔτι ὀφείλειν, ἐψηφίσαντο τὸν βουλόμενον τοῖς γεωργοῖς δανείζειν, ὡς ἐργάσωνται, ὡς πρώτοις αὐτοῖς ἐσομένης τῆς κομιδῆς ἐκ τοῦ καρποῦ, τοῖς δὲ ἄλλοις ἐκ τῶν λειπομένων.

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Σηλυβριανοὶ δὲ δεηθέντες χρημάτων, νόμου ὄντος αὐτοῖς σίτου μὴ ἐξάγειν ἐν λιμῷ γενομένοις, ἐκείνοις δὲ ὑπάρχοντος σίτου παλαιοῦ, ἐψηφίσαντο τῇ πόλει παραδοῦναι τοὺς ἰδιώτας τὸν σῖτον τῆς τεταγμένης τιμῆς, ὑπολειπόμενον ἕκαστον ἐνιαυτοῦ τροφήν· εἶτα ἐξαγωγὴν ἔδωκαν τῷ βουλομένῳ, τάξαντες τιμὴν ἣν ἐδόκει καλῶς ἔχειν αὐτοῖς.

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Ἀβυδηνοὶ δέ, διὰ στασιασμὸν τῆς χώρας ἀργοῦ γενομένης, καὶ τῶν μετοίκων οὐ προϊεμένων αὐτοῖς οὐδὲν διὰ τὸ καὶ ἔτι ὀφείλειν, ἐψηφίσαντο τὸν βουλόμενον τοῖς γεωργοῖς δανείζειν, ὡς ἐργάσωνται, ὡς πρώτοις αὐτοῖς ἐσομένης τῆς κομιδῆς ἐκ τοῦ καρποῦ, τοῖς δὲ ἄλλοις ἐκ τῶν λειπομένων.

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Ἐφέσιοι δεηθέντες χρημάτων νόμον ἔθεντο μὴ φορεῖν χρυσὸν τὰς γυναῖκας, ὅσον δὲ νῦν ἔχουσι δανεῖσαι τῇ πόλει.

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Ἐφέσιοι δεηθέντες χρημάτων νόμον ἔθεντο μὴ φορεῖν χρυσὸν τὰς γυναῖκας, ὅσον δὲ νῦν ἔχουσι δανεῖσαι τῇ πόλει.

τῶν τε κιόνων τισὶ τῶν ἐν τῷ νεῷ τάξαντες ἀργύριον ὃ δεῖ καταβαλεῖν εἴων ἐπιγράφεσθαι τὸ ὄνομα τοῦ δόντος τὸ ἀργύριον ὡς ἀνατεθεικότος.

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Διονύσιος Συρακούσιος βουλόμενος χρήματα συναγαγεῖν, ἐκκλησίαν ποιήσας ἔφησεν ἑωρακέναι τὴν Δήμητραν, καὶ κελεύειν τὸν τῶν γυναικῶν κόσμον εἰς τὸ ἱερὸν ἀποκομίζειν. αὐτὸς μὲν οὖν τῶν παρʼ αὑτῷ γυναικῶν τὸν κόσμον τοῦτο πεποιηκέναι· ἠξίου δὲ καὶ τοὺς ἄλλους, μή τι μήνιμα παρὰ τῆς θεοῦ γένηται· τὸν δὲ μὴ τοῦτο ποιήσαντα ἔνοχον ἔφησεν ἱεροσυλίας ἔσεσθαι.ἀνενεγκάντων δὲ πάντων ἃ εἶχον διά τε τὴν θεὸν καὶ διʼ ἐκεῖνον, θύσας τῇ θεῷ τὸν κόσμον ἀπηνέγκατο ὡς παρὰ τῆς θεοῦ δεδανεισμένος. προελθόντος δὲ χρόνου καὶ τῶν γυναικῶν πάλιν φορουσῶν, ἐκέλευσε τὴν βουλομένην χρυσοφορεῖν τάγμα τι ἀνατιθέναι ἐν τῷ ἱερῷ.

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Διονύσιος Συρακούσιος βουλόμενος χρήματα συναγαγεῖν, ἐκκλησίαν ποιήσας ἔφησεν ἑωρακέναι τὴν Δήμητραν, καὶ κελεύειν τὸν τῶν γυναικῶν κόσμον εἰς τὸ ἱερὸν ἀποκομίζειν. αὐτὸς μὲν οὖν τῶν παρʼ αὑτῷ γυναικῶν τὸν κόσμον τοῦτο πεποιηκέναι· ἠξίου δὲ καὶ τοὺς ἄλλους, μή τι μήνιμα παρὰ τῆς θεοῦ γένηται· τὸν δὲ μὴ τοῦτο ποιήσαντα ἔνοχον ἔφησεν ἱεροσυλίας ἔσεσθαι.ἀνενεγκάντων δὲ πάντων ἃ εἶχον διά τε τὴν θεὸν καὶ διʼ ἐκεῖνον, θύσας τῇ θεῷ τὸν κόσμον ἀπηνέγκατο ὡς παρὰ τῆς θεοῦ δεδανεισμένος. προελθόντος δὲ χρόνου καὶ τῶν γυναικῶν πάλιν φορουσῶν, ἐκέλευσε τὴν βουλομένην χρυσοφορεῖν τάγμα τι ἀνατιθέναι ἐν τῷ ἱερῷ.

τριηρεῖς τε ναυπηγεῖσθαι μέλλων ᾔδει ὅτι δεήσοιτο χρημάτων. ἐκκλησίαν οὖν συναγαγὼν ἔφη πόλιν αὑτῷ τινα προδίδοσθαι, εἰς ἣν δεῖσθαι χρημάτων, ἠξίου τε αὑτῷ τοὺς πολίτας εἰσενέγκαι δύο στατῆρας ἕκαστον· οἳ δʼ εἰσήνεγκαν. διαλιπὼν δὲ δύο ἢ τρεῖς ἡμέρας, ὡς διημαρτηκὼς τῆς πράξεως, ἐπαινέσας αὐτοὺς ἀπέδωκεν ἑκάστῳ ὃ εἰσήνεγκαν. ποιήσας δὲ τοῦτο ἀνεκτήσατο τοὺς πολίτας. εἶτα πάλιν οἰόμενοι ἀπολήψεσθαι εἰσήνεγκαν· ὃ δὲ λαβὼν εἶχεν εἰς τὴν ναυπηγίαν.

οὐκ εὐπορῶν δὲ ἀργυρίου νόμισμα ἔκοψε καττιτέρου, καὶ συναγαγὼν ἐκκλησίαν πολλὰ τοῦ κεκομμένου νομίσματος ὑπερεῖπεν· οἳ δὲ ἐψηφίσαντο καὶ μὴ βουλόμενοι ἕκαστος ὃ ἂν εἵλετο ἔχειν ὡς ἀργυροῦν ἀλλὰ μὴ καττιτέρινον.

πάλιν τε δεηθεὶς χρημάτων ἠξίου τοὺς πολίτας εἰσενεγκεῖν αὑτῷ· οἳ δʼ οὐκ ἔφασαν ἔχειν. ἐξενέγκας οὖν τὰ σκεύη τὰ παρʼ αὑτοῦ ἐπώλει, ὡς δὴ διʼ ἀπορίαν τοῦτο ποιῶν· ἀγοραζόντων δὲ Συρακουσίων ἀπεγράφετο τί ἕκαστος ἀγοράσειεν· ἐπεὶ δὲ τὴν τιμὴν κατέβαλον, ἐκέλευσε τὸ σκεῦος ἀναφέρειν ἕκαστον ὃ ἠγόρασεν.

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Ῥήγιόν τε καταλαβών, ἐκκλησίαν συναγαγὼν εἶπε διότι δικαίως μὲν ἂν ἐξανδραποδισθεῖεν ὑπʼ αὐτοῦ,νῦν μέντοι τὰ εἰς τὸν πόλεμον ἀνηλωμένα χρήματα κομισάμενος καὶ ὑπὲρ ἑκάστου σώματος τρεῖς μνᾶς ἀφήσειν αὐτούς. οἱ δὲ Ῥηγῖνοι ὅσα ποτʼ ἦν αὐτοῖς ἀποκεκρυμμένα ἐμφανῆ ἐποίουν καὶ οἱ ἄποροι παρὰ τῶν εὐπορωτέρων καὶ παρὰ τῶν ξένων δανειζόμενοι ἐπόρισαν ἃ ἐκέλευσε χρήματα. λαβὼν δὲ ταῦτα παρʼ αὐτῶν τά τε σώματα πάντα οὐδὲν ἧττον ἀπέδοτο τά τε σκεύη, ἃ τότε ἦν ἀποκεκρυμμένα, ἐμφανῆ ἅπαντα ἔλαβε.

δανεισάμενός τε παρὰ τῶν πολιτῶν χρήματα ἐπʼ ἀποδόσει, ὡς ἀπῄτουν αὐτόν, ἐκέλευσεν ἀναφέρειν ὅσον ἔχει τις ἀργύριον πρὸς αὐτόν· εἰ δὲ μή, θάνατον ἔταξε τὸ ἐπιτίμιον. ἀνενεχθέντος δὲ τοῦ ἀργυρίου, ἐπικόψας χαρακτῆρα ἐξέδωκε τὴν δραχμὴν δύο δυναμένην δραχμὰς καὶ τό τε ὀφειλόμενον πρότερον ἀνήνεγκαν πρὸς αὐτόν.

εἰς Τυρρηνίαν τε πλεύσας ναυσὶν ἑκατόν, ἔλαβεν ἐκ τοῦ τῆς Λευκοθέας ἱεροῦ χρυσίον τε καὶ ἀργύριον πολὺ καὶ τὸν ἄλλον κόσμον οὐκ ὀλίγον. εἰδὼς δὲ ὅτι καὶ οἱ ναῦται πολλὰ ἔχουσι, κήρυγμα ἐποιήσατο τὰ ἡμίσεα ὧν ἔχει ἕκαστος ἀναφέρειν πρὸς αὑτόν, τὰ δʼ ἡμίσεα ἔχειν τὸν λαβόντα· τῷ δὲ μὴ ἀνενέγκαντι θάνατον ἔταξε τὸ ἐπιτίμιον. ὑπολαβόντες δὲ οἱ ναῦται ἀνενεγκόντες τὰ ἡμίσεα τὰ κατάλοιπα ἔχειν, ἀδεῶς ἀνήνεγκαν· ὃ δʼ ἐπείπερ ἐκεῖνα ἔλαβεν, ἐκέλευσε πάλιν τὰ ἡμίσεα ἀναφέρειν.

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Μενδαῖοι δὲ τὰ μὲν ἀπὸ λιμένων καὶ τῶν ἄλλων τελῶν αὐτοῖς προσπορευόμενα ἐχρῶντο εἰς διοίκησιν τῆς πόλεως, τὰ δὲ ἀπὸ τῆς γῆς καὶ οἰκιῶν τέλη οὐκ ἔπραττον, ἀλλʼ ἀνέγραφον τοὺς ἔχοντας· ὁπότε δὲ δεηθεῖεν χρημάτων, ἀπεδίδοσαν οι ὀφείλοντες· ἐκέρδαινον οὖν τὸν παρεληλυθότα χρόνον ἀτόκοις τοῖς χρήμασιν ἀποκεχρημένοι.

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Μενδαῖοι δὲ τὰ μὲν ἀπὸ λιμένων καὶ τῶν ἄλλων τελῶν αὐτοῖς προσπορευόμενα ἐχρῶντο εἰς διοίκησιν τῆς πόλεως, τὰ δὲ ἀπὸ τῆς γῆς καὶ οἰκιῶν τέλη οὐκ ἔπραττον, ἀλλʼ ἀνέγραφον τοὺς ἔχοντας· ὁπότε δὲ δεηθεῖεν χρημάτων, ἀπεδίδοσαν οι ὀφείλοντες· ἐκέρδαινον οὖν τὸν παρεληλυθότα χρόνον ἀτόκοις τοῖς χρήμασιν ἀποκεχρημένοι.

πολεμοῦντες τὲ πρὸς Ὀλυνθίους καὶ δεόμενοι χρημάτων, ὄντων αὐτοῖς ἀνδραπόδων, ἐψηφίσαντο καταλειπομένων ἑνὶ ἑκάστῳ θήλεος καὶ ἄρρενος τὰ ἄλλα ἀποδόσθαι τῇ πόλει, ὡς ἐκδανεῖσαι τοὺς ἰδιώτας χρήματα.

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Καλλίστρατος ἐν Μακεδονίᾳ πωλουμένου τοῦ ἐλλιμενίου ὡς ἐπὶ τὸ πολὺ εἴκοσι ταλάντων, ἐποίησεν εὑρεῖν τὸ διπλάσιον· κατιδὼν γὰρ ὠνουμένους τοὺς εὐπορωτέρους ἀεὶ διὰ τὸ δεῖν ταλαντιαίους καθιστάναι τοὺς ἐγγύους τῶν εἴκοσι ταλάντων,προεκήρυξεν ὠνεῖσθαι τὸν βουλόμενον καὶ τοὺς ἐγγύους καθιστάναι τοῦ τρίτου μέρους καὶ καθʼ ὁπόσον ἕκαστος δύνηται πείθειν.

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Τιμόθεος Ἀθηναῖος πολεμῶν πρὸς Ὀλυνθίους καὶ ἀπορούμενος ἀργυρίου, κόψας χαλκὸν διεδίδου τοῖς στρατιώταις. ἀγανακτούντων δὲ τῶν στρατιωτῶν ἔφη αὐτοῖς τοὺς ἐμπόρους τε καὶ ἀγοραίους ἅπαντα ὡσαύτως πωλήσειν. τοῖς δʼ ἐμπόροις προεῖπεν, ὃν ἄν τις λάβῃ χαλκόν, τούτου πάλιν ἀγοράζειν τά τʼ ἐκ τῆς χώρας ὤνια καὶ τὰ ἐκ τῶν λειῶν ἀγόμενα· ὃς δʼ ἂν περιλειφθῇ αὐτοῖς χαλκός, πρὸς αὐτὸν ἀναφέροντας ἀργύριον λαμβάνειν.

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Καλλίστρατος ἐν Μακεδονίᾳ πωλουμένου τοῦ ἐλλιμενίου ὡς ἐπὶ τὸ πολὺ εἴκοσι ταλάντων, ἐποίησεν εὑρεῖν τὸ διπλάσιον· κατιδὼν γὰρ ὠνουμένους τοὺς εὐπορωτέρους ἀεὶ διὰ τὸ δεῖν ταλαντιαίους καθιστάναι τοὺς ἐγγύους τῶν εἴκοσι ταλάντων,προεκήρυξεν ὠνεῖσθαι τὸν βουλόμενον καὶ τοὺς ἐγγύους καθιστάναι τοῦ τρίτου μέρους καὶ καθʼ ὁπόσον ἕκαστος δύνηται πείθειν.

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Τιμόθεος Ἀθηναῖος πολεμῶν πρὸς Ὀλυνθίους καὶ ἀπορούμενος ἀργυρίου, κόψας χαλκὸν διεδίδου τοῖς στρατιώταις. ἀγανακτούντων δὲ τῶν στρατιωτῶν ἔφη αὐτοῖς τοὺς ἐμπόρους τε καὶ ἀγοραίους ἅπαντα ὡσαύτως πωλήσειν. τοῖς δʼ ἐμπόροις προεῖπεν, ὃν ἄν τις λάβῃ χαλκόν, τούτου πάλιν ἀγοράζειν τά τʼ ἐκ τῆς χώρας ὤνια καὶ τὰ ἐκ τῶν λειῶν ἀγόμενα· ὃς δʼ ἂν περιλειφθῇ αὐτοῖς χαλκός, πρὸς αὐτὸν ἀναφέροντας ἀργύριον λαμβάνειν.

περὶ Κέρκυραν δὲ πολεμῶν καὶ ἀπόρως διακείμενος καὶ τῶν στρατιωτῶν αἰτούντων τοὺς μισθοὺς καὶ ἀπειθούντων αὐτῷ καὶ πρὸς τοὺς ὑπεναντίους φασκόντων ἀποπορεύεσθαι, ἐκκλησίαν συναγαγὼν ἔφησεν οὐ δύνασθαι διὰ τοὺς χειμῶνας παραγενέσθαι αὑτῷ ἀργύριον, ἐπεὶ τοσαύτην εἶναι περὶ αὑτὸν εὐπορίαν, ὥστε τὴν προδεδομένην τριμήνου σιταρχίαν δωρεὰν αὐτοῖς διδόναι· οἱ δὲ ὑπολαβόντες οὐκ ἄν ποτε προέσθαι τοσαῦτα χρήματα τὸν Τιμόθεον αὐτοῖς, εἰ μὴ τῇ ἀληθείᾳ προσδόκιμα ἦν τὰ χρήματα πρὸς αὐτόν, ἡσυχίαν εἶχον ὑπὲρ τῶν μισθῶν ἕως ἐκεῖνος διῳκήσατο ἃ ἐβούλετο.

Σάμον δὲ πολιορκῶν τοὺς καρποὺς καὶ τὰ ἐπὶ τῶν ἀγρῶν ἀπεδίδοτο αὐτοῖς τοῖς Σαμίοις, ὥστε εὐπόρησε χρημάτων εἰς μισθοὺς τοῖς στρατιώταις. τῶν τε ἐπιτηδείων ἐπεὶ σπάνις ἦν ἐν τῷ στρατοπέδῳ διὰ τοὺς ἀφικνουμένους, ἀπηγόρευσε μὴ πωλεῖν σῖτον ἀληλεσμένον μηδὲ μέτρον ἔλασσον ἢ μέδιμνον, μηδὲ τῶν ὑγρῶν μηθὲν ἔλαττον ἢ μετρητήν. οἱ μὲν οὖν ταξίαρχοί τε καὶ λοχαγοὶ ἀγοράζοντες ἀθρόα διεδίδοσαν τοῖς στρατιώταις, οἱ δὲ εἰσαφικνούμενοι ἦγον αὑτοῖς τὰ ἐπιτήδεια· ὁπότε δὲ ἀπαλλάττοιντο, εἴ τι περίλοιπον εἴη αὐτοῖς, ἐπώλουν. ὥστε συνέβαινεν εὐπορεῖσθαι τοὺς στρατιώτας τῶν ἐπιτηδείων.

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Διδάλης Πέρσης ἔχων στρατιώτας τὰ μὲν καθʼ ἡμέραν πορίζειν ἐδύνατο ἐκ τῆς πολεμίας αὐτοῖς, νόμισμα δὲ οὐκ ἔχων διδόναι, ἀπαιτούμενος δέ, χρόνου γενομένου οὗ ὤφειλε, τεχνάζει τοιόνδε.ἐκκλησίαν συναγαγὼν ἔφη οὐκ ἀπορεῖσθαι χρημάτων, ἀλλʼ εἶναι αὑτῷ ἐν χωρίῳ τινί, λέγων ἐν ᾧ εἴη. καὶ ἀναζεύξας ἐβάδιζεν ἐπʼ αὐτό· εἶτα, ὡς ἐγγὺς τοῦ χωρίου ἐγένετο, προελθὼν εἰς αὐτὸ ἔλαβεν ἐκ τῶν ἐνόντων ἱερῶν ὅσος ἐνῆν κοῖλος ἄργυρος· εἶτʼ ἐπισκευάσας τὰς ἡμιόνους ὡς ἀγούσας ἀργύριον παραφαινούσας τε ταῦτα ἐβάδιζεν. ἰδόντες δὲ οἱ στρατιῶται καὶ νομίσαντες ἅπαντα εἶναι ἄργυρον τὰ ἀγόμενα, ἐθάρρησαν ὡς κομιούμενοι τὸν μισθόν. ὁ δὲ ἔφη δεῖν εἰς Ἀμισὸν ἐλθόντας ἐπισημήνασθαι· ἦν δʼ εἰς τὴν Ἀμισὸν ὁδὸς πολλῶν τε ἡμερῶν καὶ χειμέριος· τὸν δὴ χρόνον τοῦτον ἀπεχρᾶτο τῷ στρατοπέδῳ τὰ ἐπιτήδεια μόνον διδούς.

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Διδάλης Πέρσης ἔχων στρατιώτας τὰ μὲν καθʼ ἡμέραν πορίζειν ἐδύνατο ἐκ τῆς πολεμίας αὐτοῖς, νόμισμα δὲ οὐκ ἔχων διδόναι, ἀπαιτούμενος δέ, χρόνου γενομένου οὗ ὤφειλε, τεχνάζει τοιόνδε.ἐκκλησίαν συναγαγὼν ἔφη οὐκ ἀπορεῖσθαι χρημάτων, ἀλλʼ εἶναι αὑτῷ ἐν χωρίῳ τινί, λέγων ἐν ᾧ εἴη. καὶ ἀναζεύξας ἐβάδιζεν ἐπʼ αὐτό· εἶτα, ὡς ἐγγὺς τοῦ χωρίου ἐγένετο, προελθὼν εἰς αὐτὸ ἔλαβεν ἐκ τῶν ἐνόντων ἱερῶν ὅσος ἐνῆν κοῖλος ἄργυρος· εἶτʼ ἐπισκευάσας τὰς ἡμιόνους ὡς ἀγούσας ἀργύριον παραφαινούσας τε ταῦτα ἐβάδιζεν. ἰδόντες δὲ οἱ στρατιῶται καὶ νομίσαντες ἅπαντα εἶναι ἄργυρον τὰ ἀγόμενα, ἐθάρρησαν ὡς κομιούμενοι τὸν μισθόν. ὁ δὲ ἔφη δεῖν εἰς Ἀμισὸν ἐλθόντας ἐπισημήνασθαι· ἦν δʼ εἰς τὴν Ἀμισὸν ὁδὸς πολλῶν τε ἡμερῶν καὶ χειμέριος· τὸν δὴ χρόνον τοῦτον ἀπεχρᾶτο τῷ στρατοπέδῳ τὰ ἐπιτήδεια μόνον διδούς.

τούς τε τεχνίτας τοὺς ἐν τῷ στρατοπέδῳ αὐτὸς εἶχε καὶ τοὺς καπήλους τοὺς μεταβαλλομένους τι· ἄλλῳ δὲ οὐκ ἦν οὐθενὶ οὐθὲν τούτων ποιεῖν.

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Χαβρίας Ἀθηναῖος Ταῲ τῷ Αἰγυπτίων βασιλεῖ ἐκστρατεύοντι καὶ δεομένῳ χρημάτων συνεβούλευε τῶν τε ἱερῶν τινα καὶ τῶν ἱερέων τὸ πλῆθος φάναι πρὸς τοὺς ἱερεῖς δεῖν παραλυθῆναι διὰ τὴν δαπάνην. ἀκούσαντες δὲ οἱ ἱερεῖς καὶ τὸ ἱερὸν παρʼ αὑτοῖς ἕκαστοι βουλόμενοι εἶναι, καὶ ἴδια αὐτοῖς οἱ ἱερεῖς ἐδίδοσαν χρήματα. ἐπεὶ δὲ παρὰ πάντων εἰλήφει, προστάξαι αὐτοῖς ἐκέλευσεν εἰς μὲν τὸ ἱερὸν καὶ εἰς αὑτὸν τῆς δαπάνης ἧς πρότερον ἐποιοῦντο τὸ δέκατον μέρος ποιεῖσθαι, τὰ δὲ λοιπὰ αὑτῷ δανεῖσαι, ἕως ὁ πόλεμος ὁ πρὸς βασιλέα διαλυθῇ.

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Χαβρίας Ἀθηναῖος Ταῲ τῷ Αἰγυπτίων βασιλεῖ ἐκστρατεύοντι καὶ δεομένῳ χρημάτων συνεβούλευε τῶν τε ἱερῶν τινα καὶ τῶν ἱερέων τὸ πλῆθος φάναι πρὸς τοὺς ἱερεῖς δεῖν παραλυθῆναι διὰ τὴν δαπάνην. ἀκούσαντες δὲ οἱ ἱερεῖς καὶ τὸ ἱερὸν παρʼ αὑτοῖς ἕκαστοι βουλόμενοι εἶναι, καὶ ἴδια αὐτοῖς οἱ ἱερεῖς ἐδίδοσαν χρήματα. ἐπεὶ δὲ παρὰ πάντων εἰλήφει, προστάξαι αὐτοῖς ἐκέλευσεν εἰς μὲν τὸ ἱερὸν καὶ εἰς αὑτὸν τῆς δαπάνης ἧς πρότερον ἐποιοῦντο τὸ δέκατον μέρος ποιεῖσθαι, τὰ δὲ λοιπὰ αὑτῷ δανεῖσαι, ἕως ὁ πόλεμος ὁ πρὸς βασιλέα διαλυθῇ.

ἀπʼ οἰκίας δὲ ἑκάστης κελεῦσαι ἅπαντας εἰσενέγκαι τάξαντα ὃ δεῖ, καὶ ἀπὸ τοῦ σώματος ὡσαύτως· τοῦ σίτου τε πωλουμένου χωρὶς τῆς τιμῆς διδόναι τὸν πωλοῦντα καὶ ὠνούμενον ἀπὸ τῆς ἀρτάβης τὸν ὀβολόν· ἀπό τῶν πλοίων τε καὶ ἐργαστηρίων καὶ τῶν ἄλλην τινὰ ἐργασίαν εχόντων τῆς ἐργασίας μέρος τὸ δέκατον κελεῦσαι ἀποτελεῖν.

ἐκστρατεύειν δʼ αὐτῷ μέλλοντι ἐκ τῆς χώρας, εἴ τίς τι ἔχει ἄσημον ἀργύριον ἢ χρυσίον, κελεῦσαι ἐνέγκαι πρὸς αὑτόν· ἐνεγκάντων δὲ τῶν πλείστων, ἐκέλευσε τούτῳ μὲν ἐκεῖνον χρῆσθαι, τοὺς δὲ δανείσαντας συστῆσαι τοῖς νομάρχαις, ὥστʼ ἐκ τῶν φόρων αὐτοῖς ἀποδοῦναι.

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Ἰφικράτης Ἀθηναῖος, Κότυος συναγαγόντος στρατιώτας, ἐπόρισεν αὐτῷ χρήματα τρόπον τοιοῦτον.ἐκέλευσε τῶν ἀνθρώπων ὧν ἦρχε προστάξαι κατασπεῖραι αὐτῷ γῆν τριῶν μεδίμνων· τούτου δὲ πραχθέντος συνελέγη σίτου πολὺ πλῆθος. καταγαγὼν οὖν ἐπὶ τὰ ἐμπόρια ἀπέδοτο, καὶ εὐπόρησε χρημάτων.

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Κότυς Θρᾷξ παρὰ Περινθίων ἐδανείζετο χρήματα εἰς τοὺς στρατιώτας συναγαγεῖν· οἱ δὲ Περίνθιοι οὐκ ἐδίδοσαν αὐτῷ. ἠξίωσεν οὖν αὐτοὺς ἄνδρας γε τῶν πολιτῶν φρουροὺς δοῦναι εἰς χωρία τινά, ἵνα τοῖς ἐκεῖ στρατιώταις νῦν φρουροῦσι σχῇ ἀποχρήσασθαι. οἱ δὲ τοῦτο ταχέως ἐποίησαν, οἰόμενοι τῶν χωρίων κύριοι ἔσεσθαι. ὁ δὲ Κότυς τοὺς ἀποσταλέντας εἰς φυλακὴν ποιήσας τὰ χρήματα αὐτοὺς ἐκέλευσεν ἀποστείλαντας, ἃ ἐδανείζετο παρʼ αὐτῶν, κομίσασθαι.

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Μέντωρ Ῥόδιος Ἑρμείαν συλλαβὼν καὶ τὰ χωρία αὐτοῦ κατασχὼν τοὺς ἐπιμελητὰς εἴασε κατὰ χώραν τοὺς ὑπὸ τοῦ Ἑρμείου καθεστηκότας. ἐπεὶ δὲ ἐθάρρησάν τε ἅπαντες καί, εἴ τί ποτʼ ἦν αὐτοῖς ἀποκεκρυμμένον ἢ ὑπεκκείμενον, μεθʼ αὑτῶν εἶχον, συλλαβὼν αὐτοὺς πάντα παρείλετο ἃ εἶχον.

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Μέμνων Ῥόδιος κυριεύσας Λαμψάκου δεηθεὶς χρημάτων ἐπέγραψε τοῖς πλουσιωτάτοις αὐτῶν πλῆθός τι ἀργυρίου, τούτοις δὲ τὴν κομιδὴν ἔσεσθαι παρὰ τῶν ἄλλων πολιτῶν ἔφησεν· ἐπεὶ δὲ οἱ ἄλλοι πολῖται εἰσήνεγκαν, ἐκέλευσε καὶ ταῦτα αὑτῷ δανεῖσαι ἐν χρόνῳ διειπάμενος ἐν ᾧ πάλιν αὐτοῖς ἀποδώσει.

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Ἰφικράτης Ἀθηναῖος, Κότυος συναγαγόντος στρατιώτας, ἐπόρισεν αὐτῷ χρήματα τρόπον τοιοῦτον.ἐκέλευσε τῶν ἀνθρώπων ὧν ἦρχε προστάξαι κατασπεῖραι αὐτῷ γῆν τριῶν μεδίμνων· τούτου δὲ πραχθέντος συνελέγη σίτου πολὺ πλῆθος. καταγαγὼν οὖν ἐπὶ τὰ ἐμπόρια ἀπέδοτο, καὶ εὐπόρησε χρημάτων.

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Κότυς Θρᾷξ παρὰ Περινθίων ἐδανείζετο χρήματα εἰς τοὺς στρατιώτας συναγαγεῖν· οἱ δὲ Περίνθιοι οὐκ ἐδίδοσαν αὐτῷ. ἠξίωσεν οὖν αὐτοὺς ἄνδρας γε τῶν πολιτῶν φρουροὺς δοῦναι εἰς χωρία τινά, ἵνα τοῖς ἐκεῖ στρατιώταις νῦν φρουροῦσι σχῇ ἀποχρήσασθαι. οἱ δὲ τοῦτο ταχέως ἐποίησαν, οἰόμενοι τῶν χωρίων κύριοι ἔσεσθαι. ὁ δὲ Κότυς τοὺς ἀποσταλέντας εἰς φυλακὴν ποιήσας τὰ χρήματα αὐτοὺς ἐκέλευσεν ἀποστείλαντας, ἃ ἐδανείζετο παρʼ αὐτῶν, κομίσασθαι.

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Μέντωρ Ῥόδιος Ἑρμείαν συλλαβὼν καὶ τὰ χωρία αὐτοῦ κατασχὼν τοὺς ἐπιμελητὰς εἴασε κατὰ χώραν τοὺς ὑπὸ τοῦ Ἑρμείου καθεστηκότας. ἐπεὶ δὲ ἐθάρρησάν τε ἅπαντες καί, εἴ τί ποτʼ ἦν αὐτοῖς ἀποκεκρυμμένον ἢ ὑπεκκείμενον, μεθʼ αὑτῶν εἶχον, συλλαβὼν αὐτοὺς πάντα παρείλετο ἃ εἶχον.

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Μέμνων Ῥόδιος κυριεύσας Λαμψάκου δεηθεὶς χρημάτων ἐπέγραψε τοῖς πλουσιωτάτοις αὐτῶν πλῆθός τι ἀργυρίου, τούτοις δὲ τὴν κομιδὴν ἔσεσθαι παρὰ τῶν ἄλλων πολιτῶν ἔφησεν· ἐπεὶ δὲ οἱ ἄλλοι πολῖται εἰσήνεγκαν, ἐκέλευσε καὶ ταῦτα αὑτῷ δανεῖσαι ἐν χρόνῳ διειπάμενος ἐν ᾧ πάλιν αὐτοῖς ἀποδώσει.

πάλιν τε δεηθεὶς χρημάτων ἠξίωσεν αὐτοὺς εἰσενέγκαι, κομίσασθαι δὲ ἐκ τῶν προσόδων· οἳ δʼ εἰσήνεγκαν ὡς διὰ ταχέων αὐτοῖς ἐσομένης τῆς κομιδῆς· ἐπεὶ δὲ καὶ αἱ καταβολαὶ τῶν προσόδων παρῆσαν, ἔφησεν ἐπʼ αὐτῷ χρείαν εἶναι καὶ τούτων, ἐκείνοις δὲ ὕστερον ἀποδώσειν σὺν τόκῳ.

τῶν τε στρατευομένων παρʼ αὐτῷ παρῃρεῖτο τὰς σιταρχίας καὶ τοὺς μισθοὺς ἓξ ἡμερῶν τὸν ἐνιαυτόν, φάσκων ταύταις ταῖς ἡμέραις οὔτε φυλακὴν αὐτοῖς οὐδεμίαν οὔτε πορείαν οὔτε δαπάνην ποιεῖσθαι, τὰς ἐξαιρεσίμους λέγων.

τόν τε πρὸ τοῦ χρόνον διδοὺς τοῖς στρατιώταις τῇ δευτέρᾳ τῆς νουμηνίας τὴν σιταρχίαν, τῷ μὲν πρώτῳ μηνὶ παρέβη τρεῖς ἡμέρας, τῷ δʼ ἐχομένῳ πέντε. τοῦτον δὲ τὸν τρόπον προῆγεν, ἕως εἰς τὴν τριακάδα ἦλθεν.

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Χαρίδημος Ὠρείτης ἔχων τῆς Αἰολίδος τινὰ χωρία, ἐπιστρατεύοντος ἐπʼ αὐτὸν Ἀρταβάζου χρημάτων ἐδεῖτο εἰς τοὺς στρατιώτας. τὸ μὲν οὖν πρῶτον εἰσέφερον αὐτῷ, εἶτα οὐκέτι ἔφασαν ἔχειν· ὁ δὲ Χαρίδημος, ὃ ᾤετο χωρίον εὐπορώτατον εἶναι, ἐκέλευσεν καὶ εἴ τι νόμισμα ἔχουσιν ἤ τι ἄλλο σκεῦος ἀξιόλογον, εἰς ἕτερον χωρίον ἀποστέλλειν, παραπομπὴν δὲ δώσειν· ἅμα δὲ καὶ αὐτὸς τοῦτο ποιῶν φανερὸς ἦν. πεισθέντων δὲ τῶν ἀνθρώπων, προαγαγὼν αὐτοὺς τῆς πόλεως μικρὸν καὶ ἐρευνήσας ἃ εἶχον, ἔλαβεν ὅσων ἐδεῖτο, ἐκείνους δὲ πάλιν εἰς τὸ χωρίον ἀπῆγεν.

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Χαρίδημος Ὠρείτης ἔχων τῆς Αἰολίδος τινὰ χωρία, ἐπιστρατεύοντος ἐπʼ αὐτὸν Ἀρταβάζου χρημάτων ἐδεῖτο εἰς τοὺς στρατιώτας. τὸ μὲν οὖν πρῶτον εἰσέφερον αὐτῷ, εἶτα οὐκέτι ἔφασαν ἔχειν· ὁ δὲ Χαρίδημος, ὃ ᾤετο χωρίον εὐπορώτατον εἶναι, ἐκέλευσεν καὶ εἴ τι νόμισμα ἔχουσιν ἤ τι ἄλλο σκεῦος ἀξιόλογον, εἰς ἕτερον χωρίον ἀποστέλλειν, παραπομπὴν δὲ δώσειν· ἅμα δὲ καὶ αὐτὸς τοῦτο ποιῶν φανερὸς ἦν. πεισθέντων δὲ τῶν ἀνθρώπων, προαγαγὼν αὐτοὺς τῆς πόλεως μικρὸν καὶ ἐρευνήσας ἃ εἶχον, ἔλαβεν ὅσων ἐδεῖτο, ἐκείνους δὲ πάλιν εἰς τὸ χωρίον ἀπῆγεν.

κήρυγμά τε ποιησάμενος ἐν ταῖς πόλεσιν, ὧν ἦρχε, μηδένα μηδὲν ὅπλον κεκτῆσθαι ἐν τῇ οἰκίᾳ, εἰ δὲ μή, ἀποτείσειν ἀργύριον ὃ ἐπεκήρυξεν, ἠμέλει καὶ οὐδεμίαν ἐπιστροφὴν ἐποιεῖτο. τῶν δὲ ἀνθρώπων οἰομένων τὸ κήρυγμα μάτην αὐτὸν πεποιῆσθαι, εἶχον ἃ ἔτυχον ἕκαστοι κεκτημένοι κατὰ χώραν. ὁ δʼ ἔρευναν ἐξαίφνης ποιησάμενος τῶν οἰκιῶν, παρʼ οἷς εὗρεν ὅπλον τι, ἐπράττετο τὸ ἐπιτίμιον.

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Φιλόξενός τις Μακεδὼν Καρίας σατραπεύων δεηθεὶς χρημάτων Διονύσια ἔφασκε μέλλειν ἄγειν, καὶ χοραγοὺς προέγραψε τῶν Καρῶν τοὺς εὐπορωτάτους καὶ προσέταττεν αὐτοῖς ἃ δεῖ παρασκευάζειν. ὁρῶν δʼ αὐτοὺς δυσχεραίνοντας, ὑποπέμπων τινὰς ἠρώτα, τί βούλονται δόντες ἀπαλλαγῆναι τῆς λειτουργίας. οἱ δὲ πολλῷ πλέον ἢ ὅσον ᾤοντο ἀναλώσειν ἔφασαν δώσειν τοῦ μὴ ὀχλεῖσθαι καὶ ἀπὸ τῶν ἰδίων ἀπεῖναι. ὁ δὲ παρὰ τούτων λαβὼν ὃ ἐδίδοσαν ἑτέρους κατέγραψεν, ἕως ἔλαβε παρὰ τούτων ἃ ἐβούλετο καὶ προσῆν παρʼ ἑκάστοις.

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Εὐαίσης Σύρος Αἰγύπτου σατραπεύων, ἀφίστασθαι μελλόντων τῶν νομαρχῶν ἀπʼ αὐτοῦ αἰσθόμενος, καλέσας αὐτοὺς εἰς τὰ βασίλεια ἐκρέμα ἅπαντας· πρὸς δὲ τοὺς οἰκείους ἐκέλευσε λέγειν ὅτι ἐν φυλακῇ εἰσιν. ἕκαστος οὖν τῶν οἰκείων ἔπραττον ὑπὲρ ἑκάστου, καὶ χρημάτων ἐξεωνοῦντο τοὺς συνειλημμένους. ὁ δὲ διομολογησάμενος ὑπὲρ ἑκάστου καὶ λαβὼν τὰ ὁμολογηθέντα ἀπέδωκεν ἑκάστοις τὸν νεκρόν.

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Κλεομένης Ἀλεξανδρεὺς Αἰγύπτου σατραπεύων, λιμοῦ γενομένου ἐν μὲν τοῖς ἄλλοις τόποις σφόδρα, ἐν Αἰγύπτῳ δὲ μετρίως, ἀπέκλεισε τὴν ἐξαγωγὴν τοῦ σίτου. τῶν δὲ νομαρχῶν φασκόντωνοὐ δυνήσεσθαι τοὺς φόρους ἀποδοῦναι τῷ μὴ ἐξάγεσθαι τὸν σῖτον, ἐξαγωγὴν μὲν ἐποίησε, τέλος δὲ πολὺ τῷ σίτῳ ἐπέβαλεν, ὥστε συνέβαινεν αὐτῷ, εἰ μὴ , ἐξαγομένου ὀλίγου πολὺ τέλος λαμβάνειν, αὐτούς τε τοὺς νομάρχας πεπαῦσθαι τῆς προφάσεως.

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Φιλόξενός τις Μακεδὼν Καρίας σατραπεύων δεηθεὶς χρημάτων Διονύσια ἔφασκε μέλλειν ἄγειν, καὶ χοραγοὺς προέγραψε τῶν Καρῶν τοὺς εὐπορωτάτους καὶ προσέταττεν αὐτοῖς ἃ δεῖ παρασκευάζειν. ὁρῶν δʼ αὐτοὺς δυσχεραίνοντας, ὑποπέμπων τινὰς ἠρώτα, τί βούλονται δόντες ἀπαλλαγῆναι τῆς λειτουργίας. οἱ δὲ πολλῷ πλέον ἢ ὅσον ᾤοντο ἀναλώσειν ἔφασαν δώσειν τοῦ μὴ ὀχλεῖσθαι καὶ ἀπὸ τῶν ἰδίων ἀπεῖναι. ὁ δὲ παρὰ τούτων λαβὼν ὃ ἐδίδοσαν ἑτέρους κατέγραψεν, ἕως ἔλαβε παρὰ τούτων ἃ ἐβούλετο καὶ προσῆν παρʼ ἑκάστοις.

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Εὐαίσης Σύρος Αἰγύπτου σατραπεύων, ἀφίστασθαι μελλόντων τῶν νομαρχῶν ἀπʼ αὐτοῦ αἰσθόμενος, καλέσας αὐτοὺς εἰς τὰ βασίλεια ἐκρέμα ἅπαντας· πρὸς δὲ τοὺς οἰκείους ἐκέλευσε λέγειν ὅτι ἐν φυλακῇ εἰσιν. ἕκαστος οὖν τῶν οἰκείων ἔπραττον ὑπὲρ ἑκάστου, καὶ χρημάτων ἐξεωνοῦντο τοὺς συνειλημμένους. ὁ δὲ διομολογησάμενος ὑπὲρ ἑκάστου καὶ λαβὼν τὰ ὁμολογηθέντα ἀπέδωκεν ἑκάστοις τὸν νεκρόν.

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Κλεομένης Ἀλεξανδρεὺς Αἰγύπτου σατραπεύων, λιμοῦ γενομένου ἐν μὲν τοῖς ἄλλοις τόποις σφόδρα, ἐν Αἰγύπτῳ δὲ μετρίως, ἀπέκλεισε τὴν ἐξαγωγὴν τοῦ σίτου. τῶν δὲ νομαρχῶν φασκόντωνοὐ δυνήσεσθαι τοὺς φόρους ἀποδοῦναι τῷ μὴ ἐξάγεσθαι τὸν σῖτον, ἐξαγωγὴν μὲν ἐποίησε, τέλος δὲ πολὺ τῷ σίτῳ ἐπέβαλεν, ὥστε συνέβαινεν αὐτῷ, εἰ μὴ , ἐξαγομένου ὀλίγου πολὺ τέλος λαμβάνειν, αὐτούς τε τοὺς νομάρχας πεπαῦσθαι τῆς προφάσεως.

διαπλέοντος δʼ αὐτοῦ τὸν νομόν, οὗ ἐστι θεὸς ὁ κροκόδειλος, ἡρπάσθη τις τῶν παίδων αὐτοῦ. καλέσας οὖν τοὺς ἱερεῖς ἔφη πρότερος ἀδικηθεὶς ἀμύνεσθαι τοὺς κροκοδείλους, καὶ προσέταξε θηρεύειν αὐτούς. οἱ δὲ ἱερεῖς, ἵνα μὴ ὁ θεὸς αὐτῶν καταφρονηθῇ, συναγαγόντες ὅσον ἠδύναντο χρυσίον ἔδοσαν αὐτῷ καὶ οὕτως ἐπαύσατο.

Ἀλεξάνδρου τοῦ βασιλέως ἐντειλαμένου αὐτῷ οἰκίσαι πόλιν πρὸς τῇ Φάρῳ καὶ τὸ ἐμπόριον τὸ πρότερον ὂν ἐπὶ τοῦ Κανώβου ἐνταῦθα ποιῆσαι, καταπλεύσας εἰς τὸν Κάνωβον πρὸς τοὺς ἱερεῖς καὶ τοὺς κτήματα ἔχοντας ἐκεῖ ἐπὶ τούτῳ ἥκειν ἔφη ὥστε μετοικίσαι αὐτούς. οἱ δὲ ἱερεῖς καὶ οἱ κάτοικοι εἰσενέγκαντες χρήματα ἔδωκαν, ἵνʼ ἐᾷ κατὰ χώραν αὐτοῖς τὸ ἐμπόριον. ὁ δὲ λαβὼν τότε μὲν ἀπηλλάγη, εἶτα δὲ καταπλεύσας, ἐπεὶ ἦν εὐτρεπῆ αὐτῷ τὰ πρὸς τὴν οἰκοδομίαν, ᾔτει αὐτοὺς χρήματα ὑπερβαλὼν τῷ πλήθει· τοῦτο γὰρ αὑτῷ τὸ διάφορον εἶναι, τὸ αὐτοῦ εἶναι τὸ ἐμπόριον καὶ μὴ ἐκεῖ. ἐπεὶ δʼ οὐκ ἂν ἔφασαν δύνασθαι δοῦναι, μετῴκισεν αὐτούς.

ἀποστείλας τέ τινα ἐπʼ ἀγοράσμά τε καὶ αἰσθόμενος ὅτι εὐώνων ἐπιτετύχηκεν, αὐτῷ δὲ μέλλει ἐκτετιμημένα λογίζεσθαι, πρὸς τοὺς συνήθεις τοῦ ἀγοραστοῦ ἔλεγεν ὅτι ἀκηκοὼς εἴη τὰ ἀγοράσματα αὐτὸν ὑπερτίμια ἠγορακέναι· αὐτὸς οὖν οὐ προσέξειν· καὶ ἅμα τὴν ἀβελτερίαν αὐτοῦ ἐλοιδόρει μετʼ ὀργῆς προσποιητοῦ. οἱ δὲ ταῦτα ἀκούοντες οὐκ ἔφασαν δεῖν πιστεύειν αὐτὸν τοῖς λέγουσί τι κατʼ ἐκείνου, ἕως αὐτὸς παραγενόμενος τὸν λόγον αὐτῷ δῷ. ἀφικομένου δὲ τοῦ ἀγοραστοῦ ἀπήγγειλαν αὐτῷ τὰ παρὰ τοῦ Κλεομένους· ὁ δʼ ἐκείνοις τε βουλόμενος ἐνδείξασθαι καὶ τῷ Κλεομένει, ἀνήνεγκε τὰς τιμὰς ὧνπερ ἦν ἠγορακώς.

τοῦ τε σίτου πωλουμένου ἐν τῇ χώρᾳ δεκαδράχμου, καλέσας τοὺς ἐργαζομένους ἠρώτα, πόσου βούλονται αὑτῷ ἐργάζεσθαι· οἱ δʼ ἔφασαν ἐλάσσονος ἢ ὅσου ἂν τοῖς ἐμπόροις ἐπώλουν. ὁ δʼ ἐκείνους μὲν ἐκέλευσεν αὑτῷ παραδιδόναι ὅσουπερ ἐπώλουν τοῖς ἄλλοις· αὐτὸς δὲ τάξας τριάκοντα καὶδύο δραχμὰς τοῦ σίτου τιμὴν οὕτως ἐπώλει.

τούς τε ἱερεῖς καλέσας ἔφησε πολὺ τὸ ἀνώμαλον ἀνάλωμα ἐν τῇ χώρᾳ γίνεσθαι εἰς τὰ ἱερά· δεῖν οὖν καὶ τῶν ἱερῶν τινα καὶ τῶν ἱερέων τὸ πλῆθος καταλυθῆναι. οἱ δὲ ἱερεῖς καὶ ἰδίᾳ ἕκαστος καὶ κοινῇ τὰ ἱερὰ χρήματα ἐδίδοσαν, οἰόμενοί τε αὐτὸν τῇ ἀληθείᾳ μέλλειν τοῦτο ποιεῖν, καὶ ἕκαστος βουλόμενος τό τε ἱερὸν τὸ αὑτοῦ μείναι κατὰ χώραν καὐτὸς ἱερεύς.

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Ἀντιμένης Ῥόδιος ἡμιόδιος γενόμενος Ἀλεξάνδρου περὶ Βαβυλῶνα ἐπόρισε χρήματα ὧδε. νόμου ὄντος ἐν Βαβυλωνίᾳ παλαιοῦ δεκάτην εἶναι τῶν εἰσαγομένων, χρωμένου δὲ αὐτῷ οὐθενός, τηρήσας τούς τε σατράπας ἅπαντας προσδοκίμους ὄντας καὶ στρατιώτας, οὐκ ὀλίγους τε πρέσβεις καὶ τεχνίτας κλητοὺς ἄλλους τοὺς ἄγοντας καὶ ἰδίᾳ ἀποδημοῦντας, καὶ δῶρα πολλὰ ἀναγόμενα, τὴν δεκάτην ἔπρασσε κατὰ τὸν νόμον τὸν κείμενον.

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Ἀντιμένης Ῥόδιος ἡμιόδιος γενόμενος Ἀλεξάνδρου περὶ Βαβυλῶνα ἐπόρισε χρήματα ὧδε. νόμου ὄντος ἐν Βαβυλωνίᾳ παλαιοῦ δεκάτην εἶναι τῶν εἰσαγομένων, χρωμένου δὲ αὐτῷ οὐθενός, τηρήσας τούς τε σατράπας ἅπαντας προσδοκίμους ὄντας καὶ στρατιώτας, οὐκ ὀλίγους τε πρέσβεις καὶ τεχνίτας κλητοὺς ἄλλους τοὺς ἄγοντας καὶ ἰδίᾳ ἀποδημοῦντας, καὶ δῶρα πολλὰ ἀναγόμενα, τὴν δεκάτην ἔπρασσε κατὰ τὸν νόμον τὸν κείμενον.

πάλιν τε πορίζων τἀνδράποδα τὰ ἐπὶ στρατοπέδῳ ὄντα ἐκέλευσε τὸν βουλόμενον ἀπογράφεσθαι ὁπόσου θέλοι, μέλλειν δὲ τοῦ ἐνιαυτοῦ ὀκτὼ δραχμάς ἀποτίσαι, ἂν δὲ ἀποδρᾷ τὸ ἀνδράποδον, κομίζεσθαι τὴν τιμὴν ἧς ἀνεγράψατο. ἀπογραφέντων οὖν πολλῶν ἀνδραπόδων οὐκ ὀλίγον συνετελεῖ ἀργύριον. εἰ δέ τι ἀποδρῴη ἀνδράποδον, ἐκέλευε τὸν σατράπην τῆς ἐν ᾗ ἐστι τὸ στρατόπεδον, ἀνασῴζειν ἢ τὴν τιμὴν τῷ κυρίῳ ἀποδοῦναι.

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Ὀφέλας Ὀλύνθιος καταστήσας ἐπιμελητὴν εἰς τὸν νομὸν τὸν Ἀθριβίτην, ἐπεὶ προσελθόντες αὐτῷ οἱ νομάρχαι οἱ ἐκ τοῦ τόπου τούτου ἔφασαν βούλεσθαι πλείω αὐτοὶ πολὺ φέρειν, τὸν δʼ ἐπιμελητὴν τὸν νῦν καθεστηκότα ἀπαλλάξαι αὐτὸν ἠξίουν, ἐπερωτήσας αὐτοὺς εἰ δυνήσονται συντελεῖν ἅπερ ἐπαγγέλλονται, φησάντων αὐτῶν, τὸν μὲν ἐπιμελητὴν κατὰ χώραν εἴα, τοὺς δὲ φόρους πράσσεσθαι ἐκέλευεν ὅσους αὐτοὶ ὑπετιμήσαντο. οὔτε οὖν ὃν κατέστησεν ἀτιμάσαι ἐδόκει οὔτʼ ἐκείνοις πλείους φόρους ἐπιβαλεῖν ἢ αὐτοὶ ἔταξαν, χρήματα δὲ πολλαπλάσια αὐτὸς ἐλάμβανεν.

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Πυθοκλῆς Ἀθηναῖος Ἀθηναίοις συνεβούλευσε τὸν μόλυβδον τὸν ἐκ τῶν Λαυρίων παραλαμβάνειν παρὰ τῶν ἰδιωτῶν τὴν πόλιν, ὥσπερ ἐπώλουν, δίδραχμον, εἶτα τάξαντας αὐτοὺς τιμὴν ἑξαδράχμου οὕτω πωλεῖν.

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Χαβρίας πληρωμάτων τε κατειλεγμένων εἰς ἑκατὸν καὶ εἴκοσι ναῦς, τῷ δὲ Ταῲ ἑξήκοντα μόνον οὔσης χρείας, προσέταξε τοῖς ἐκ τῶν ἑξήκοντα νεῶν αὐτοῦ τῶν ὑπομενουσῶν τοὺς πλέοντας εἰς δίμηνον σιτηρεσιάσαι, ἢ αὐτοὺς πλέειν. οἱ δὲ βουλόμενοι ἐπὶ τῶν ἰδίων μεῖναι ἔδωκαν ἃ προσέταξεν.

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Ἀντιμένης τούς τε θησαυροὺς τοὺς παρὰ τὰς ὁδοὺς τὰς βασιλικὰς ἀναπληροῦν ἐκέλευε τοὺς σατράπας κατὰ τὸν νόμον τὸν τῆς χώρας· ὁπότε δὲ διαπορεύοιτο στρατόπεδον ἢ ἕτερος ὄχλος ἄνευ τοῦ βασιλέως, πέμψας τινὰ παρʼ αὑτοῦ ἐπώλει τὰ ἐκ τῶν θησαυρῶν.

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Κλεομένης προσπορευομένης τε τῆς νουμηνίας καὶ δέον τοῖς στρατιώταις σιταρχίαν δοῦναι, κατέπλευσεν ἐξεπίτηδες· προπορευομένου δὲ τοῦ μηνὸς ἀναπλεύσας διέδωκε τὴν σιταρχίαν, εἶτα τοῦ εἰσιόντος μηνὸς διέλιπεν ἕως τῆς νουμηνίας. οἱ μὲν οὖν στρατιῶται διὰ τὸ νεωστὶ εἰληφέναι τὴν σιταρχίαν ἡσυχίαν εἶχον, ἐκεῖνος δὲ παραλλάξας ἕνα μῆνα παρὰ τὸν ἐνιαυτὸν ἀφῄρει μισθὸν ἀεὶ μηνός.

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Σταβέλβιος ὁ Μυσῶν στρατιώταις μισθὸν συγκαλέσας ἔφησεν αὑτῷ τῶν μὲν ἰδιωτῶν οὐδεμίαν χρείαν εἶναι, τῶν δὲ ἡγεμόνων, ὅταν δὲ δέηται στρατιωτῶν, ἐκείνων ἑκάστῳ δοὺς ἀργύριον ἀποστέλλειν ἐπὶ ξενολογίαν, τούς τε μισθοὺς οὓς δεῖ ἐκείνοις δοῦναι, τοῖς ἡγεμόσιν ἂν ἥδιον διδόναι· ἐκέλευεν οὖν αὐτοὺς ἀποστέλλειν ἕκαστον τοὺς αὑτῶν καταλόγους ἐκ τῆς χώρας. τῶν δὲ ἡγεμόνων ὑπολαβόντων χρηματισμὸν αὑτοῖς ἔσεσθαι, ἀπέστειλαν τοὺς στρατιώτας, καθάπερ ἐκεῖνος προσέταξε. διαλιπὼν δὲ ὀλίγον χρόνον καὶ συναγαγὼν αὐτοὺς οὔτε αὐλητὴν ἄνευ χοροῦ οὔτε ἡγεμόνας ἄνευ ἰδιωτῶν οὐδὲν ἔφη χρησίμους εἶναι· ἐκέλευεν οὖν αὐτοὺς ἀπαλλάττεσθαι ἐκ τῆς χώρας.

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Διονύσιος τά ἱερὰ περιπορευόμενος, εἰ μὲν τράπεζαν ἴδοι παρακειμένην χρυσῆν ἢ ἀργυρᾶν, ἀγαθοῦ δαίμονος κελεύσας ἐγχέαι ἐκέλευεν ἀφαιρεῖν, ὅσα δὲ τῶν ἀγαλμάτων φιάλην εἶχε προτετακότα, εἴπας ἂν ὅτι δέχομαι, ἐξαιρεῖν ἐκέλευε. τά θʼ ἱμάτια τά τε χρυσᾶ καὶ τοὺς στεφάνους τοὺς περιῄρει τῶν ἀγαλμάτων φάσκων αὐτὸς καὶ κουφότερα καὶ εὐωδέστερα δοῦναι· εἶτα ἱμάτια μὲν λευκά, στεφάνους δὲ λευκοΐνους περιετίθει.

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Ὀφέλας Ὀλύνθιος καταστήσας ἐπιμελητὴν εἰς τὸν νομὸν τὸν Ἀθριβίτην, ἐπεὶ προσελθόντες αὐτῷ οἱ νομάρχαι οἱ ἐκ τοῦ τόπου τούτου ἔφασαν βούλεσθαι πλείω αὐτοὶ πολὺ φέρειν, τὸν δʼ ἐπιμελητὴν τὸν νῦν καθεστηκότα ἀπαλλάξαι αὐτὸν ἠξίουν, ἐπερωτήσας αὐτοὺς εἰ δυνήσονται συντελεῖν ἅπερ ἐπαγγέλλονται, φησάντων αὐτῶν, τὸν μὲν ἐπιμελητὴν κατὰ χώραν εἴα, τοὺς δὲ φόρους πράσσεσθαι ἐκέλευεν ὅσους αὐτοὶ ὑπετιμήσαντο. οὔτε οὖν ὃν κατέστησεν ἀτιμάσαι ἐδόκει οὔτʼ ἐκείνοις πλείους φόρους ἐπιβαλεῖν ἢ αὐτοὶ ἔταξαν, χρήματα δὲ πολλαπλάσια αὐτὸς ἐλάμβανεν.

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Πυθοκλῆς Ἀθηναῖος Ἀθηναίοις συνεβούλευσε τὸν μόλυβδον τὸν ἐκ τῶν Λαυρίων παραλαμβάνειν παρὰ τῶν ἰδιωτῶν τὴν πόλιν, ὥσπερ ἐπώλουν, δίδραχμον, εἶτα τάξαντας αὐτοὺς τιμὴν ἑξαδράχμου οὕτω πωλεῖν.

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Χαβρίας πληρωμάτων τε κατειλεγμένων εἰς ἑκατὸν καὶ εἴκοσι ναῦς, τῷ δὲ Ταῲ ἑξήκοντα μόνον οὔσης χρείας, προσέταξε τοῖς ἐκ τῶν ἑξήκοντα νεῶν αὐτοῦ τῶν ὑπομενουσῶν τοὺς πλέοντας εἰς δίμηνον σιτηρεσιάσαι, ἢ αὐτοὺς πλέειν. οἱ δὲ βουλόμενοι ἐπὶ τῶν ἰδίων μεῖναι ἔδωκαν ἃ προσέταξεν.

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Ἀντιμένης τούς τε θησαυροὺς τοὺς παρὰ τὰς ὁδοὺς τὰς βασιλικὰς ἀναπληροῦν ἐκέλευε τοὺς σατράπας κατὰ τὸν νόμον τὸν τῆς χώρας· ὁπότε δὲ διαπορεύοιτο στρατόπεδον ἢ ἕτερος ὄχλος ἄνευ τοῦ βασιλέως, πέμψας τινὰ παρʼ αὑτοῦ ἐπώλει τὰ ἐκ τῶν θησαυρῶν.

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Κλεομένης προσπορευομένης τε τῆς νουμηνίας καὶ δέον τοῖς στρατιώταις σιταρχίαν δοῦναι, κατέπλευσεν ἐξεπίτηδες· προπορευομένου δὲ τοῦ μηνὸς ἀναπλεύσας διέδωκε τὴν σιταρχίαν, εἶτα τοῦ εἰσιόντος μηνὸς διέλιπεν ἕως τῆς νουμηνίας. οἱ μὲν οὖν στρατιῶται διὰ τὸ νεωστὶ εἰληφέναι τὴν σιταρχίαν ἡσυχίαν εἶχον, ἐκεῖνος δὲ παραλλάξας ἕνα μῆνα παρὰ τὸν ἐνιαυτὸν ἀφῄρει μισθὸν ἀεὶ μηνός.

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Σταβέλβιος ὁ Μυσῶν στρατιώταις μισθὸν συγκαλέσας ἔφησεν αὑτῷ τῶν μὲν ἰδιωτῶν οὐδεμίαν χρείαν εἶναι, τῶν δὲ ἡγεμόνων, ὅταν δὲ δέηται στρατιωτῶν, ἐκείνων ἑκάστῳ δοὺς ἀργύριον ἀποστέλλειν ἐπὶ ξενολογίαν, τούς τε μισθοὺς οὓς δεῖ ἐκείνοις δοῦναι, τοῖς ἡγεμόσιν ἂν ἥδιον διδόναι· ἐκέλευεν οὖν αὐτοὺς ἀποστέλλειν ἕκαστον τοὺς αὑτῶν καταλόγους ἐκ τῆς χώρας. τῶν δὲ ἡγεμόνων ὑπολαβόντων χρηματισμὸν αὑτοῖς ἔσεσθαι, ἀπέστειλαν τοὺς στρατιώτας, καθάπερ ἐκεῖνος προσέταξε. διαλιπὼν δὲ ὀλίγον χρόνον καὶ συναγαγὼν αὐτοὺς οὔτε αὐλητὴν ἄνευ χοροῦ οὔτε ἡγεμόνας ἄνευ ἰδιωτῶν οὐδὲν ἔφη χρησίμους εἶναι· ἐκέλευεν οὖν αὐτοὺς ἀπαλλάττεσθαι ἐκ τῆς χώρας.

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Διονύσιος τά ἱερὰ περιπορευόμενος, εἰ μὲν τράπεζαν ἴδοι παρακειμένην χρυσῆν ἢ ἀργυρᾶν, ἀγαθοῦ δαίμονος κελεύσας ἐγχέαι ἐκέλευεν ἀφαιρεῖν, ὅσα δὲ τῶν ἀγαλμάτων φιάλην εἶχε προτετακότα, εἴπας ἂν ὅτι δέχομαι, ἐξαιρεῖν ἐκέλευε. τά θʼ ἱμάτια τά τε χρυσᾶ καὶ τοὺς στεφάνους τοὺς περιῄρει τῶν ἀγαλμάτων φάσκων αὐτὸς καὶ κουφότερα καὶ εὐωδέστερα δοῦναι· εἶτα ἱμάτια μὲν λευκά, στεφάνους δὲ λευκοΐνους περιετίθει.

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- - - - - - -English -Greek - - - -EpiDoc and CTS conversion and general header review. -fixed Aristotle bibls -fixed bad bibl refs -fixed bad bibl refs -cleaned up bad place tags in a few texts and cleaned up the document format -fixed bibls for Plut. Mor. to correct work title -more reorganizing of texts module by collection -began reorganizing texts module by collection. created separate work directory in texts module to keep hopper files separate from in progress files -edited entity tags CEH -fixed bad bibls -fixed bad bibls -fixed bibl errors through book 14 - zr -fixed bibl errors through book 13 - zr -fixed bibl errors through book 12 - zr -fixed bibl errors through book 11 - zr -fixed bibl errors through book 9 - zr -fixed bibl errors through book 6 - zr -fixed bibl errors through book 4 - zr -fixed bibl errors through book 3 - zr -fixed bibl errors through book 1 - zr -added cvs log keyword -Put Bekker line 1 milestone tags at the beginning of each section so that the incoming list creator would work. Changed RREFDECL. -Tagged in conformance with Prose.e dtd. -Text was scanned at St. Olaf Spring, 1992. - - - - - - -
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All men naturally desire knowledge. An indication of this is our esteem for the senses; for apart from their use we esteem them for their own sake, and most of all the sense of sight. Not only with a view to action, but even when no action is contemplated, we prefer sight, generally speaking, to all the other senses.

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The reason of this is that of all the senses sight best helps us to know things, and reveals many distinctions.

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Now animals are by nature born with the power of sensation, and from this some acquire the faculty of memory, whereas others do not. Accordingly the former are more intelligent and capable of learning than those which cannot remember.

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Such as cannot hear sounds (as the bee, and any other similar type of creature) are intelligent, but cannot learn; those only are capable of learning which possess this sense in addition to the faculty of memory.

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Thus the other animals live by impressions and memories, and have but a small share of experience; but the human race lives also by art and reasoning.

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It is from memory that men acquire experience, because the numerous memories of the same thing eventually produce the effect of a single experience. Experience seems very similar to science and art,

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but actually it is through experience that men acquire science and art; for as Polus rightly says, experience produces art, but inexperience chance. Plat. Gorgias 448c, Plat. Gorg. 462b-c. Art is produced when from many notions of experience a single universal judgement is formed with regard to like objects.

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To have a judgement that when Callias was suffering from this or that disease this or that benefited him, and similarly with Socrates and various other individuals, is a matter of experience; but to judge that it benefits all persons of a certain type, considered as a class, who suffer from this or that disease (e.g. the phlegmatic or bilious when suffering from burning fever) is a matter of art.

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It would seem that for practical purposes experience is in no way inferior to art; indeed we see men of experience succeeding more than those who have theory without experience.

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The reason of this is a that experience is knowledge of particulars, but art of universals; and actions and the effects produced are all concerned with the particular. For it is not man that the physician cures, except incidentally, but Callias or Socrates or some other person similarly named, who is incidentally a man as well.

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So if a man has theory without experience, and knows the universal, but does not know the particular contained in it, he will often fail in his treatment; for it is the particular that must be treated.

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Nevertheless we consider that knowledge and proficiency belong to art rather than to experience, and we assume that artists are wiser than men of mere experience (which implies that in all cases wisdom depends rather upon knowledge);

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and this is because the former know the cause, whereas the latter do not. For the experienced know the fact, but not the wherefore; but the artists know the wherefore and the cause. For the same reason we consider that the master craftsmen in every profession are more estimable and know more and are wiser than the artisans, because they know the reasons of the things which are done; but we think that the artisans, like certain inanimate objects, do things, but without knowing what they are doing (as, for instance, fire burns);

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only whereas inanimate objects perform all their actions in virtue of a certain natural quality, artisans perform theirs through habit. Thus the master craftsmen are superior in wisdom, not because they can do things, but because they possess a theory and know the causes.

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In general the sign of knowledge or ignorance is the ability to teach, and for this reason we hold that art rather than experience is scientific knowledge; for the artists can teach, but the others cannot.

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Further, we do not consider any of the senses to be Wisdom. They are indeed our chief sources of knowledge about particulars, but they do not tell us the reason for anything, as for example why fire is hot, but only that it is hot.

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It is therefore probable that at first the inventor of any art which went further than the ordinary sensations was admired by his fellow-men, not merely because some of his inventions were useful, but as being a wise and superior person.

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And as more and more arts were discovered, some relating to the necessities and some to the pastimes of life, the inventors of the latter were always considered wiser than those of the former, because their branches of knowledge did not aim at utility.

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Hence when all the discoveries of this kind were fully developed, the sciences which relate neither to pleasure nor yet to the necessities of life were invented, and first in those places where men had leisure. Thus the mathematical sciences originated in the neighborhood of Egypt, because there the priestly class was allowed leisure.Cf. Plat. Phaedrus 274, Hdt. 2.109.

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The difference between art and science and the other kindred mental activities has been stated in theEthicsAristot. Nic. Eth. 6.1139b 14-1141b 8.; the reason for our present discussion is that it is generally assumed that what is called Wisdomi.e. Metaphysics. is concerned with the primary causes and principles, so that, as has been already stated, the man of experience is held to be wiser than the mere possessors of any power of sensation, the artist than the man of experience, the master craftsman than the artisan; and the speculative sciences to be more learned than the productive. Thus it is clear that Wisdom is knowledge of certain principles and causes.

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Since we are investigating this kind of knowledge, we must consider what these causes and principles are whose knowledge is Wisdom. Perhaps it will be clearer if we take the opinions which we hold about the wise man.

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We consider first, then, that the wise man knows all things, so far as it is possible, without having knowledge of every one of them individually; next, that the wise man is he who can comprehend difficult things, such as are not easy for human comprehension (for sense-perception, being common to all, is easy, and has nothing to do with Wisdom); and further that in every branch of knowledge a man is wiser in proportion as he is more accurately informed and better able to expound the causes.

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Again among the sciences we consider that that science which is desirable in itself and for the sake of knowledge is more nearly Wisdom than that which is desirable for its results, and that the superior is more nearly Wisdom than the subsidiary; for the wise man should give orders, not receive them; nor should he obey others, but the less wise should obey him.

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Such in kind and in number are the opinions which we hold with regard to Wisdom and the wise. Of the qualities there described the knowledge of everything must necessarily belong to him who in the highest degree possesses knowledge of the universal, because he knows in a sense all the particulars which it comprises. These things, viz. the most universal, are perhaps the hardest for man to grasp, because they are furthest removed from the senses.

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Again, the most exact of the sciences are those which are most concerned with the first principles; for those which are based on fewer principles are more exact than those which include additional principles; e.g., arithmetic is more exact than geometry.

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Moreover, the science which investigates causes is more instructive than one which does not, for it is those who tell us the causes of any particular thing who instruct us. Moreover, knowledge and understanding which are desirable for their own sake are most attainable in the knowledge of that which is most knowable. For the man who desires knowledge for its own sake will most desire the most perfect knowledge, and this is the knowledge of the most knowable, and the things which are most knowable are first principles and causes; for it is through these and from these that other things come to be known, and not these through the particulars which fall under them.

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And that science is supreme, and superior to the subsidiary, which knows for what end each action is to be done; i.e. the Good in each particular case, and in general the highest Good in the whole of nature.

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Thus as a result of all the above considerations the term which we are investigating falls under the same science, which must speculate about first principles and causes; for the Good, i.e. the end , is one of the causes.

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That it is not a productive science is clear from a consideration of the first philosophers.

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It is through wonder that men now begin and originally began to philosophize; wondering in the first place at obvious perplexities, and then by gradual progression raising questions about the greater matters too, e.g. about the changes of the moon and of the sun, about the stars and about the origin of the universe.

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Now he who wonders and is perplexed feels that he is ignorant (thus the myth-lover is in a sense a philosopher, since myths are composed of wonders); therefore if it was to escape ignorance that men studied philosophy, it is obvious that they pursued science for the sake of knowledge, and not for any practical utility.

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The actual course of events bears witness to this; for speculation of this kind began with a view to recreation and pastime, at a time when practically all the necessities of life were already supplied. Clearly then it is for no extrinsic advantage that we seek this knowledge; for just as we call a man independent who exists for himself and not for another, so we call this the only independent science, since it alone exists for itself.

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For this reason its acquisition might justly be supposed to be beyond human power, since in many respects human nature is servile; in which case, as SimonidesSimon. Fr. 3 (Hiller). says, God alone can have this privilege, and man should only seek the knowledge which is within his reach.

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Indeed if the poets are right and the Deity is by nature jealous, it is probable that in this case He would be particularly jealous, and all those who excel in knowledge unfortunate. But it is impossible for the Deity to be jealous (indeed, as the proverbCf. Solon, Fr. 26 (Hiller); Leutsch and Schneidwin, Paroemiographi, 1.371. says, poets tell many a lie), nor must we suppose that any other form of knowledge is more precious than this; for what is most divine is most precious.

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Now there are two ways only in which it can be divine. A science is divine if it is peculiarly the possession of God, or if it is concerned with divine matters. And this science alone fulfils both these conditions; for (a) all believe that God is one of the causes and a kind of principle, and (b) God is the sole or chief possessor of this sort of knowledge. Accordingly, although all other sciences are more necessary than this, none is more excellent.

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The acquisition of this knowledge, however, must in a sense result in something which is the reverse of the outlook with which we first approached the inquiry. All begin, as we have said, by wondering that things should be as they are, e.g. with regard to marionettes, or the solstices, or the incommensurabilityi.e. the fact that the diagonal of a square cannot be rationally expressed in terms of the side. of the diagonal of a square; because it seems wonderful to everyone who has not yet perceived the cause that a thing should not be measurable by the smallest unit.

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But we must end with the contrary and (according to the proverb)i.e. δευτέρον ἀμεινόνων(second thoughts are better). Leutsch and Schneidwin 1.62. the better view, as men do even in these cases when they understand them; for a geometrician would wonder at nothing so much as if the diagonal were to become measurable.

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Thus we have stated what is the nature of the science which we are seeking, and what is the object which our search and our whole investigation must attain.

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It is clear that we must obtain knowledge of the primary causes, because it is when we think that we understand its primary cause that we claim to know each particular thing. Now there are four recognized kinds of cause. Of these we hold that one is the essence or essential nature of the thing (since the reason why of a thing is ultimately reducible to its formula, and the ultimate reason why is a cause and principle); another is the matter or substrate; the third is the source of motion; and the fourth is the cause which is opposite to this, namely the purpose or good;

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for this is the end of every generative or motive process. We have investigated these sufficiently in the PhysicsPhys. 2.3, Phys. 2.7; however, let us avail ourselves of the evidence of those who have before us approached the investigation of reality and philosophized about Truth. For clearly they too recognize certain principles and causes, and so it will be of some assistance to our present inquiry if we study their teaching; because we shall either discover some other kind of cause, or have more confidence in those which we have just described.

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Most of the earliest philosophers conceived only of material principles as underlying all things. That of which all things consist, from which they first come and into which on their destruction they are ultimately resolved, of which the essence persists although modified by its affections—this, they say, is an element and principle of existing things. Hence they believe that nothing is either generated or destroyed, since this kind of primary entity always persists. Similarly we do not say that Socrates comes into being absolutely when he becomes handsome or cultured, nor that he is destroyed when he loses these qualities; because the substrate, Socrates himself, persists.

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In the same way nothing else is generated or destroyed; for there is some one entity (or more than one) which always persists and from which all other things are generated.

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All are not agreed, however, as to the number and character of these principles. Thales,Thales of Miletus, fl. 585 B.C. the founder of this school of philosophy,That of the Ionian monists, who sought a single material principle of everything. says the permanent entity is water (which is why he also propounded that the earth floats on water). Presumably he derived this assumption from seeing that the nutriment of everything is moist, and that heat itself is generated from moisture and depends upon it for its existence (and that from which a thing is generated is always its first principle). He derived his assumption, then, from this; and also from the fact that the seeds of everything have a moist nature, whereas water is the first principle of the nature of moist things.

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There are someCf. Plat. Crat. 402b, Plat. Theaet. 152e, Plat. Theaet. 180c,d. who think that the men of very ancient times, long before the present era, who first speculated about the gods, also held this same opinion about the primary entity. For theycf. Hom. Il. 14. 201, Hom. Il. 14.246. represented Oceanus and Tethys to be the parents of creation, and the oath of the gods to be by water— Styx,Cf. Hom. Il. 2.755, Hom. Il. 14.271, Hom. Il.15.37. as they call it. Now what is most ancient is most revered, and what is most revered is what we swear by.

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Whether this view of the primary entity is really ancient and time-honored may perhaps be considered uncertain; however, it is said that this was Thales’ opinion concerning the first cause. (I say nothing of Hippo,Hippo of Samos, a medical writer and eclectic philosopher who lived in the latter half of the fifth century B.C. Cf.Aristot. De Anima 405b 2. because no one would presume to include him in this company, in view of the paltriness of his intelligence.)

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AnaximenesThe third Milesian monist; fl. circa 545 B.C. and DiogenesDiogenes of Apollonia, an eclectic philosopher roughly contemporary with Hippo. held that air is prior to water, and is of all corporeal elements most truly the first principle. HippasusA Pythagorean, probably slightly junior to Heraclitus. of Metapontum and HeraclitusFl. about 500 B.C. of Ephesus hold this of fire; and EmpedoclesOf Acragas; fl. 450 B.C.—adding earth as a fourth to those already mentioned—takes all four. These, he says, always persist, and are only generated in respect of multitude and paucity, according as they are combined into unity or differentiated out of unity.Cf. Empedocles, Fr. 17 (Diels), R.P. 166; Burnet, E.G.P. 108-109.

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Anaxagoras of Clazomenae—prior to Empedocles in point of age, but posterior in his activities—says that the first principles are infinite in number. For he says that as a general rule all things which are, like fire and water,This is Aristotle’s illustration; apparently Anaxagoras did not regard the elements as homoeomerous (i.e. composed of parts which are similar to one another and to the whole). Cf. Aristot. De Caelo 302a 28, Aristot. De Gen. et Corr. 314a 24. homoeomerous, are generated and destroyed in this sense only, by combination and differentiation; otherwise they are neither generated nor destroyed, but persist eternally.Cf. Anaxagoras Fr. 4 (Diels); and see Burnet, E.G.P. 130.

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From this account it might be supposed that the only cause is of the kind called material. But as men proceeded in this way, the very circumstances of the case led them on and compelled them to seek further; because if it is really true that all generation and destruction is out of some one entity or even more than one, why does this happen, and what is the cause?

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It is surely not the substrate itself which causes itself to change. I mean, e.g., that neither wood nor bronze is responsible for changing itself; wood does not make a bed, nor bronze a statue, but something else is the cause of the change. Now to investigate this is to investigate the second type of cause: the source of motion, as we should say.

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Those who were the very first to take up this inquiry, and who maintained that the substrate is one thing, had no misgivings on the subject; but some of thosei.e. the Eleatic school. who regard it as one thing, being baffled, as it were, by the inquiry, say that that one thing (and indeed the whole physical world) is immovable in respect not only of generation and destruction (this was a primitive belief and was generally admitted) but of all other change. This belief is peculiar to them.

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None of those who maintained that the universe is a unity achieved any conception of this type of cause, except perhaps ParmenidesFounder of the above; fl. about 475.; and him only in so far as he admits, in a sense, not one cause only but two.i.e. in the Δόξα. Parmenides Fr. 8 (Diels); R.P. 121.

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But those who recognize more than one entity, e.g. hot and cold, or fire and earth, are better able to give a systematic explanation, because they avail themselves of fire as being of a kinetic nature, and of water, earth, etc., as being the opposite.Aristotle is probably thinking of Empedocles. Cf. Aristot. Met. 4.8.

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After these thinkers and the discovery of these causes, since they were insufficient to account for the generation of the actual world, men were again compelled (as we have said) by truth itself to investigate the next first principle.

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For presumably it is unnatural that either fire or earth or any other such element should cause existing things to be or become well and beautifully disposed; or indeed that those thinkers should hold such a view. Nor again was it satisfactory to commit so important a matter to spontaneity and chance.

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Hence when someoneAnaxagoras. said that there is Mind in nature, just as in animals, and that this is the cause of all order and arrangement, he seemed like a sane man in contrast with the haphazard statements of his predecessors.Cf. Plat. Phaedo 97b-98b.

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We know definitely that Anaxagoras adopted this view; but HermotimusA semi-mythical person supposed to have been a preincarnation of Pythagoras. of Clazomenae is credited with having stated it earlier. Those thinkers, then, who held this view assumed a principle in things which is the cause of beauty, and the sort of cause by which motion is communicated to things.

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It might be inferred that the first person to consider this question was Hesiod, or indeed anyone else who assumed Love or Desire as a first principle in things; e.g. Parmenides. For he says, where he is describing the creation of the universe, Love sheProbably Aphrodite (so Simplicius, Plutarch). created first of all the gods . . . Parmenides Fr. 13 (Diels)And Hesiod says,Hes. Th. 116-20. The quotation is slightly inaccurate. First of all things was Chaos made, and then/Broad-bosomed Earth . . ./And Love, the foremost of immortal beings, thus implying that there must be in the world some cause to move things and combine them.

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The question of arranging these thinkers in order of priority may be decided later. Now since it was apparent that nature also contains the opposite of what is good, i.e. not only order and beauty, but disorder and ugliness; and that there are more bad and common things than there are good and beautiful: in view of this another thinker introduced Love and StrifeEmpedocles Fr. 17, 26 (Diels); R.P. 166. Cf. Burnet, E.G.P. 108 ff. as the respective causes of these things—

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because if one follows up and appreciates the statements of Empedocles with a view to his real meaning and not to his obscure language, it will be found that Love is the cause of good, and Strife of evil. Thus it would perhaps be correct to say that Empedocles in a sense spoke of evil and good as first principles, and was the first to do so—that is, if the cause of all good things is absolute good.

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These thinkers then, as I say, down to the time of Empedocles, seem to have grasped two of the causes which we have defined in the PhysicsAristot. Phys. 2.3, 7.: the material cause and the source of motion; but only vaguely and indefinitely. They are like untrained soldiers in a battle, who rush about and often strike good blows, but without science; in the same way these thinkers do not seem to understand their own statements, since it is clear that upon the whole they seldom or never apply them.

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Anaxagoras avails himself of Mind as an artificial device for producing order, and drags it in whenever he is at a loss to explain some necessary result; but otherwise he makes anything rather than Mind the cause of what happens.Cf. Plat. Phaedo 98b, Plat. Laws 967b; also Aristot. Met. 7.5. Again, Empedocles does indeed use causes to a greater degree than Anaxagoras, but not sufficiently; nor does he attain to consistency in their use.

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At any rate Love often differentiates and Strife combines: because whenever the universe is differentiated into its elements by Strife, fire and each of the other elements are agglomerated into a unity; and whenever they are all combined together again by Love, the particles of each element are necessarily again differentiated.

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Empedocles, then, differed from his predecessors in that he first introduced the division of this cause, making the source of motion not one but two contrary forces.

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Further, he was the first to maintain that the so-called material elements are four—not that he uses them as four, but as two only, treating fire on the one hand by itself, and the elements opposed to it—earth, air and water—on the other, as a single nature.Cf. 3.14. This can be seen from a study of his writings.e.g. Empedocles, Fr. 62 (Diels).

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Such, then, as I say, is his account of the nature and number of the first principles.

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Leucippus,Of Miletus; fl. circa 440 (?) B.C. See Burnet, E.G.P. 171 ff. however, and his disciple DemocritusOf Abdera; fl. circa 420 B.C. E.G.P loc. cit. hold that the elements are the Full and the Void—calling the one what is and the other what is not. Of these they identify the full or solid with what is, and the void or rare with what is not (hence they hold that what is not is no less real than what is,For the probable connection between the Atomists and the Eleatics see E.G.P. 173, 175, and cf. De Gen. et Corr. 324b 35-325a 32. because Void is as real as Body); and they say that these are the material causes of things.

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And just as those who make the underlying substance a unity generate all other things by means of its modifications, assuming rarity and density as first principles of these modifications, so these thinkers hold that the differencesi.e., of the atoms. are the causes of everything else.

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These differences, they say, are three: shape, arrangement, and position; because they hold that what is differs only in contour, inter-contact, and inclination .Cf. R.P. 194.(Of these contour means shape, inter-contact arrangement, and inclination position.) Thus, e.g., A differs from N in shape, AN from NA in arrangement, and Z from NThese letters will convey Aristotle’s point better to the English reader, but see critical note. in position.

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As for motion, whence and how it arises in things, they casually ignored this point, very much as the other thinkers did. Such, then, as I say, seems to be the extent of the inquiries which the earlier thinkers made into these two kinds of cause.

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At the same time, however, and even earlier the so-calledAristotle seems to have regarded Pythagoras as a legendary person. Pythagoreans applied themselves to mathematics, and were the first to develop this sciencePythagoras himself (fl. 532 B.C.) is said by Aristoxenus (ap. Stobaeus 1.20.1) to have been the first to make a theoretical study of arithmetic.; and through studying it they came to believe that its principles are the principles of everything.

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And since numbers are by nature first among these principles, and they fancied that they could detect in numbers, to a greater extent than in fire and earth and water, many analoguesCf. Aristot. Met. 14.6ff.. of what is and comes into being—such and such a property of number being justice ,Apparently (cf. infra, Aristot. Met. 1.17) they identified these not only with properties of number but with numbers themselves. Thus justice (properly=squareness)=4, the first square number; soul or mind=1, opportunity=7 (Alexander). and such and such soul or mind , another opportunity , and similarly, more or less, with all the rest—and since they saw further that the properties and ratios of the musical scales are based on numbers,Pythagoras himself is credited with having discovered the ratios of the octave (2 : 1), the fifth (3 : 2) and the fourth (4 : 3). Burnet, E.G.P. 51. and since it seemed clear that all other things have their whole nature modelled upon numbers, and that numbers are the ultimate things in the whole physical universe, they assumed the elements of numbers to be the elements of everything, and the whole universe to be a proportionOr harmony. Cf. Aristot. De Caelo 2.9, and E.G.P. 152. or number. Whatever analogues to the processes and parts of the heavens and to the whole order of the universe they could exhibit in numbers and proportions, these they collected and correlated;

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and if there was any deficiency anywhere, they made haste to supply it, in order to make their system a connected whole. For example, since the decad is considered to be a complete thing and to comprise the whole essential nature of the numerical system, they assert that the bodies which revolve in the heavens are ten; and there being only nineEarth, sun, moon, five planets, and the sphere of the fixed stars. that are visible, they make the antichthoni.e. counter-earth; a planet revolving round the central fire in such a way as to be always in opposition to the earth. the tenth.

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We have treated this subject in greater detail elsewhereIn the lost work On the Pythagoreans; but cf. Aristot. De Caelo 2.13.; but the object of our present review is to discover from these thinkers too what causes they assume and how these coincide with our list of causes.

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Well, it is obvious that these thinkers too consider number to be a first principle, both as the materialSee Burnet, E.G.P 143-146. of things and as constituting their properties and states.i.e., as a formal principle. Cf. Ross ad loc. The elements of number, according to them, are the Even and the Odd. Of these the former is limited and the latter unlimited; Unity consists of both (since it is both odd and even)Either because by addition it makes odd numbers even and even odd (Alexander, Theo Smyrnaeus) or because it was regarded as the principle of both odd and even numbers (Heath).; number is derived from Unity; and numbers, as we have said, compose the whole sensible universe.

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OthersZeller attributes the authorship of this theory to Philolaus. of this same school hold that there are ten principles, which they enunciate in a series of corresponding pairs: (1.) Limit and the Unlimited; (2.) Odd and Even; (3.) Unity and Plurality; (4.) Right and Left; (5.) Male and Female; (6.) Rest and Motion; (7.) Straight and Crooked; (8.) Light and Darkness; (9.) Good and Evil; (10.) Square and Oblong.

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Apparently Alcmaeon of Croton speculated along the same lines, and either he derived the theory from them or they from him; for [Alcmaeon was contemporary with the old age of Pythagoras, and]This statement is probably true, but a later addition. his doctrines were very similar to theirs.He was generally regarded as a Pythagorean. He says that the majority of things in the world of men are in pairs; but the contraries which he mentions are not, as in the case of the Pythagoreans, carefully defined, but are taken at random, e.g. white and black, sweet and bitter, good and bad, great and small.

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Thus Alcmaeon only threw out vague hints with regard to the other instances of contrariety, but the Pythagoreans pronounced how many and what the contraries are. Thus from both these authoritiesThe section of Pythagoreans mentioned in 6, and Alcmaeon. we can gather thus much, that the contraries are first principles of things; and from the former, how many and what the contraries are.

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How these can be referred to our list of causes is not definitely expressed by them, but they appear to reckon their elements as material; for they say that these are the original constituents of which Being is fashioned and composed.

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From this survey we can sufficiently understand the meaning of those ancients who taught that the elements of the natural world are a plurality. Others, however, theorized about the universe as though it were a single entity; but their doctrines are not all alike either in point of soundness or in respect of conformity with the facts of nature.

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For the purposes of our present inquiry an account of their teaching is quite irrelevant, since they do not, while assuming a unity, at the same time make out that Being is generated from the unity as from matter, as do some physicists, but give a different explanation; for the physicists assume motion also, at any rate when explaining the generation of the universe; but these thinkers hold that it is immovable. Nevertheless thus much is pertinent to our present inquiry.

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It appears that Parmenides conceived of the Unity as one in definition,His argument was Everything that is is one, if what is has one meaning (πάντα ἕν, εἰ τὸ ὂν ἓν σημαίνει, Aristot. Phys. 187a 1); but he probably believed, no less than Melissus, in the material unity of reality. Cf. Melissus Fr. 8 (Diels). It has been suggested, however (by the Rev. C. F. Angus), that he was simply trying to convey in figurative language a conception of absolute existence. but MelissusOf Samos; defeated the Athenian fleet in 441 B.C. as materially one. Hence the former says that it is finite,Melissus Fr. 8, ll. 32-3, 42-3. and the latter that it is infinite.Melissus Fr. 3. But Xenophanes,Of Colophon, b. 565 (?) B.C. Criticized and ridiculed most of the views of his day, especially the anthropomorphic conception of the gods. Burnet, E.G.P. 55 ff., esp. 61-62. Cf. Xenophanes Fr. 23 (Diels). the first exponent of the Unity (for Parmenides is said to have been his disciple), gave no definite teaching, nor does he seem to have grasped either of these conceptions of unity; but regarding the whole material universe he stated that the Unity is God.

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This school then, as we have said, may be disregarded for the purposes of our present inquiry; two of them, Xenophanes and Melissus, may be completely ignored, as being somewhat too crude in their views. Parmenides, however, seems to speak with rather more insight. For holding as he does that Not-being, as contrasted with Being, is nothing, he necessarily supposes that Being is one and that there is nothing else (we have discussed this point in greater detail in the Physics Aristot. Phys. 1.3 ); but being compelled to accord with phenomena, and assuming that Being is one in definition but many in respect of sensation, he posits in his turn two causes, i.e. two first principles, Hot and Cold; or in other words, Fire and Earth. Of these he ranks Hot under Being and the other under Not-being.Cf. note on Aristot. Met. 3.13.

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From the account just given, and from a consideration of those thinkers who have already debated this question, we have acquired the following information. From the earliest philosophers we have learned that the first principle is corporeal (since water and fire and the like are bodies); some of them assume one and others more than one corporeal principle, but both parties agree in making these principles material. Others assume in addition to this cause the source of motion, which some hold to be one and others two.

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Thus down to and apart from the ItalianThe Pythagoreans; so called because Pythagoras founded his society at Croton. philosophers the other thinkers have expressed themselves vaguely on the subject, except that, as we have said, they actually employ two causes, and one of these—the source of motion —some regard as one and others as two. The Pythagoreans, while they likewise spoke of two principles, made this further addition, which is peculiar to them: they believed, not that the Limited and the Unlimited are separate entities, like fire or water or some other such thing, but that the Unlimited itself and the One itself are the essence of those things of which they are predicated, and hence that number is the essence of all things.

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Such is the nature of their pronouncements on this subject. They also began to discuss and define the what of things; but their procedure was far too simple. They defined superficially, and supposed that the essence of a thing is that to which the term under consideration first applies—e.g. as if it were to be thought that double and 2 are the same, because 2 is the first number which is double another.

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But presumably to be double a number is not the same as to be the number 2. Otherwise, one thing will be many—a consequence which actually followed in their system.i.e., the same number might be the first to which each of several definitions applied; then that number would be each of the concepts so defined. This much, then, can be learned from other and earlier schools of thought.

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The philosophies described above were succeeded by the system of Plato,Compare Aristot. Met. 12.4.2-5. which in most respects accorded with them, but contained also certain peculiar features distinct from the philosophy of the Italians.

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In his youth Plato first became acquainted with CratylusCf. Aristot. Met. 4.5.18. and the Heraclitean doctrines—that the whole sensible world is always in a state of flux,Plat. Crat. 402a (fr. 41 Bywater). and that there is no scientific knowledge of it—and in after years he still held these opinions. And when Socrates, disregarding the physical universe and confining his study to moral questions, sought in this sphere for the universal and was the first to concentrate upon definition, Plato followed him and assumed that the problem of definition is concerned not with any sensible thing but with entities of another kind; for the reason that there can be no general definition of sensible things which are always changing.

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These entities he called Ideas,I have translated ἰδέα by Idea and εἶδος by Form wherever Aristotle uses the words with reference to the Platonic theory. Plato apparently uses them indifferently, and so does Aristotle in this particular connection, but he also uses εἶδος in the sense of form in general. For a discussion of the two words see Taylor, Varia Socratica, 178-267, and Gillespie, Classical Quarterly, 6.179-203. and held that all sensible things are named afterFor this interpretation of παρὰ ταῦτα see Ross’s note ad loc. them sensible and in virtue of their relation to them; for the plurality of things which bear the same name as the Forms exist by participation in them. (With regard to the participation, it was only the term that he changed; for whereas the Pythagoreans say that things exist by imitation of numbers, Plato says that they exist by participation—merely a change of term.

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As to what this participation or imitation may be, they left this an open question.)

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Further, he states that besides sensible things and the Forms there exists an intermediate class, the objects of mathematics,i.e. arithmetical numbers and geometrical figures. which differ from sensible things in being eternal and immutable, and from the Forms in that there are many similar objects of mathematics, whereas each Form is itself unique.

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Now since the Forms are the causes of everything else, he supposed that their elements are the elements of all things. Accordingly the material principle is the Great and Small, and the essence <or formal principle> is the One, since the numbers are derived from the Great and Small by participation in the the One.

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In treating the One as a substance instead of a predicate of some other entity, his teaching resembles that of the Pythagoreans, and also agrees with it in stating that the numbers are the causes of Being in everything else; but it is peculiar to him to posit a duality instead of the single Unlimited, and to make the Unlimited consist of the Great and Small. He is also peculiar in regarding the numbers as distinct from sensible things, whereas they hold that things themselves are numbers, nor do they posit an intermediate class of mathematical objects.

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His distinction of the One and the numbers from ordinary things (in which he differed from the Pythagoreans) and his introduction of the Forms were due to his investigation of logic (the earlier thinkers were strangers to Dialectic)See Aristot. Met. 4.2.19-20, and cf. Aristot. Met. 8.4.4.; his conception of the other principle as a duality to the belief that numbers other than primesἔξω τῶν πρώτων is very difficult, but it can hardly be a gloss, and no convincing emendation has been suggested. Whatever the statement means, it is probably (as the criticism which follows is certainly) based upon a misunderstanding. From Plat. Parm. 143c, it might be inferred that the Great and Small (the Indeterminate Dyad) played no part in the generation of numbers; but there the numbers are not Ideal, as here they must be. In any case Aristotle is obsessed with the notion that the Dyad is a duplicative principle (Aristot. Met. 13.8.14), which if true would imply that it could generate no odd number. Hence Heinze proposed reading περιττῶν(odd) for πρώτων(which may be right, although the corruption is improbable) and Alexander tried to extract the meaning of odd from πρώτων by understanding it as prime to 2. However, as Ross points out (note ad loc.), we may keep πρώτων in the sense of prime if we suppose Aristotle to be referring either (a) to the numbers within the decad (Aristot. Met. 13.8.17) and forgetting 9—the other odd numbers being primes; or (b) to numbers in general, and forgetting the entire class of compound odd numbers. Neither of these alternatives is very satisfactory, but it seems better to keep the traditional text. can be readily generated from it, as from a matrix.For a similar use of the word ἐκμαγεῖον cf. Plat. Tim. 50c.

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The fact, however, is just the reverse, and the theory is illogical; for whereas the Platonists derive multiplicity from matter although their Form generates only once,Aristotle’s objection is that it is unreasonable that a single operation of the formal upon the material principle should result in more than one product; i.e. that the material principle should be in itself duplicative. it is obvious that only one table can be made from one piece of timber, and yet he who imposes the form upon it, although he is but one, can make many tables. Such too is the relation of male to female: the female is impregnated in one coition, but one male can impregnate many females. And these relations are analogues of the principles referred to.

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This, then, is Plato’s verdict upon the question which we are investigating. From this account it is clear that he only employed two causesPlato refers several times in the dialogues to an efficient cause (e.g. the Demiurgus,Plat. Soph. 265b-d, Plat. Tim. 28c ff.) and a final cause (e.g. Plat. Phil. 20d, 53e, Plat. Tim. 29d ff.); but Aristotle does not seem to take these allusions seriously.: that of the essence, and the material cause; for the Forms are the cause of the essence in everything else, and the One is the cause of it in the Forms.

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He also tells us what the material substrate is of which the Forms are predicated in the case of sensible things, and the One in that of the Forms—that it is this the duality, the Great and Small. Further, he assigned to these two elements respectively the causation of goodCf. Plat. Phil. 25e-26b. and of evil; a problem which, as we have said,Aristot. Met. 3.17; 4.3. had also been considered by some of the earlier philosophers, e.g. Empedocles and Anaxagoras.

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We have given only a concise and summary account of those thinkers who have expressed views about the causes and reality, and of their doctrines. Nevertheless we have learned thus much from them: that not one of those who discuss principle or cause has mentioned any other type than those which we we have distinguished in the Physics. Aristot. Phys. 2.3 Clearly it is after these types that they are groping, however uncertainly.

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Some speak of the first principle as material, whether they regard it as one or several, as corporeal or incorporeal: e.g. Plato speaks of the Great and Small; the ItaliansSee note on Aristot. Met. 5.15. of the Unlimited; Empedocles of Fire, Earth, Water and Air; Anaxagoras of the infinity of homoeomeries.

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All these have apprehended this type of cause; and all those too who make their first principle air or water or something denser than fire but rarer than airThe various references in Aristotle to material principles intermediate between certain pairs of elements have been generally regarded as applying to Anaximander’s ἄπειρον or Indeterminate; but the references are so vague (cf. Aristot. Met. 7.6, Aristot. Phys.187a 14, 189b 3, 203a 18) that it seems better to connect them with later and minor members of the Milesian school. Cf. Ross’s note ad loc.(for some have so described the primary element). These, then, apprehended this cause only, but others apprehended the source of motion—e.g. all such as make Love and Strife, or Mind, or Desire a first principle.

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As for the essence or essential nature, nobody has definitely introduced it; but the inventors of the Forms express it most nearly. For they do not conceive of the Forms as the matter of sensible things (and the One as the matter of the Forms), nor as producing the source of motion (for they hold that they are rather the cause of immobility and tranquillity); but they adduce the Forms as the essential nature of all other things, and the One as that of the Forms.

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The end towards which actions, changes and motions tend they do in a way treat as a cause, but not in this sense, i.e. not in the sense in which it is naturally a cause. Those who speak of Mind or Love assume these causes as being something good; but nevertheless they do not profess that anything exists or is generated for the sake of them, but only that motions originate from them.Cf. Aristot. Met. 3.17.

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Similarly also those who hold that Unity or Being is an entity of this kind state that it is the cause of existence, but not that things exist or are generated for the sake of it. So it follows that in a sense they both assert and deny that the Good is a cause; for they treat it as such not absolutely, but incidentally.

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It appears, then, that all these thinkers too (being unable to arrive at any other cause) testify that we have classified the causes rightly, as regards both number and nature. Further, it is clear that all the principles must be sought either along these lines or in some similar way.

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Let us next examine the possible difficulties arising out of the statements of each of these thinkers, and out of his attitude to the first principles.

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All those who regard the universe as a unity, and assume as its matter some one nature, and that corporeal and extended, are clearly mistaken in many respects. They only assume elements of corporeal things, and not of incorporeal ones, which also exist. They attempt to state the causes of generation and destruction, and investigate the nature of everything; and at the same time do away with the cause of motion.

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Then there is their failure to regard the essence or formula as a cause of anything; and further their readiness to call any one of the simple bodies—except earth—a first principle, without inquiring how their reciprocal generation is effected. I refer to fire, water, earth and air. Of these some are generated from each other by combination and others by differentiation;

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and this difference is of the greatest importance in deciding their relative priority. In one way it might seem that the most elementary body is that from which first other bodies are produced by combination; and this will be that body which is rarest and composed of the finest particles.

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Hence all who posit Fire as first principle will be in the closest agreement with this theory. However, even among the other thinkers everyone agrees that the primary corporeal element is of this kind. At any rate none of the Monists thought earth likely to be an element—obviously on account of the size of its particles—

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but each of the other three has had an advocate; for some name fire as the primary element, others water, and others air.Cf. Aristot. Met. 3.5, 8. And yet why do they not suggest earth too, as common opinion does? for people say Everything is earth.

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And Hesiod too saysCf. Aristot. Met. 4.1. that earth was generated first of corporeal things—so ancient and popular is the conception found to be. Thus according to this theory anyone who suggests any of these bodies other than fire, or who assumes something denser than air but rarer than water,Cf. Aristot. Met. 7.3 n. will be wrong.

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On the other hand if what is posterior in generation is prior in nature, and that which is developed and combined is posterior in generation, then the reverse will be the case; water will be prior to air, and earth to water. So much for those who posit one cause such as we have described.

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The same will apply too if anyone posits more than one, as e.g. Empedocles says that matter consists of four bodies;

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objections must occur in his case also, some the same as before, and some peculiar to him. First, we can see things being generated from each other in a way which shows that fire and earth do not persist as the same corporeal entity. (This subject has been treated in my works on Natural Science.Aristot. De Caelo, 3.7; Aristot. De Gen. et Corr. 2.6.) Again with regard to the cause of motion in things, whether one or two should be assumed, it must not be thought that his account is entirely correct or even reasonable.Cf. Aristot. Met. 4.6.

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And in general those who hold such views as these must of necessity do away with qualitative alteration; for on such a theory cold will not come from hot nor hot from cold, because to effect this there must be something which actually takes on these contrary qualities: some single element which becomes both fire and water—which Empedocles denies.

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If one were to infer that Anaxagoras recognized twoMind, and the mixture of homoeomerous particles. elements, the inference would accord closely with a view which, although he did not articulate it himself, he must have accepted as developed by others.

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To say that originally everything was a mixture is absurd for various reasons, but especially since (a) it follows that things must have existed previously in an unmixed state; (b) it is contrary to nature for anything to mix with anything ; (c) moreover affections and attributes would then be separable from their substances (because what is mixed can also be separated). At the same time, if one were to follow his doctrine carefully and interpret its meaning, perhaps it would be seen to be more up-to-date;

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because when nothing was yet differentiated, obviously nothing could be truly predicated of that substance—e.g. that it was white or black or buff or any other color. It must necessarily have been colorless, since otherwise it would have had one of these colors.

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Similarly by the same argument it had no taste or any other such attribute; for it cannot have had any quality or magnitude or individuality. Otherwise some particular form would have belonged to it; but this is impossible on the assumption that everything was mixed together, for then the form would have been already differentiated, whereas he says that everything was mixed together except Mind, which alone was pure and unmixed.Anaxagoras. Fr. 12 (Diels).

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It follows from this that he recognizes as principles the One (which is simple and unmixed) and the Other, which is such as we suppose the Indeterminate to be before it is determined and partakes of some form. Thus his account is neither correct nor clear, but his meaning approximates to more recent theories and what is now more obviously true.

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However, these thinkers are really concerned only with the theories of generation and destruction and motion (for in general it is only with reference to this aspect of reality that they look for their principles and causes).

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Those, however, who make their study cover the whole of reality, and who distinguish between sensible and non-sensible objects, clearly give their attention to both kinds; hence in their case we may consider at greater length what contributions, valuable or otherwise, they make to the inquiry which is now before us.

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The so-called Pythagoreans employ abstruser principles and elements than the physicists. The reason is that they did not draw them from the sensible world; for mathematical objects, apart from those which are connected with astronomy, are devoid of motion.

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Nevertheless all their discussions and investigations are concerned with the physical world. They account for the generation of the sensible universe, and observe what happens in respect of its parts and affections and activities, and they use up their principles and causes in this connection, as though they agreed with the others—the physicists—that reality is just so much as is sensible and is contained in the so-called heavens.

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All the same, as we have said,Aristot. Met. 1.8.17. the causes and principles which they describe are capable of application to the remoter class of realities as well, and indeed are better fitted to these than to their physical theories.

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But as to how there is to be motion, if all that is premissed is Limit and the Unlimited, and Odd and Even, they do not even hint; nor how, without motion and change, there can be generation and destruction, or the activities of the bodies which traverse the heavens.

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And further, assuming that it be granted to them or proved by them that magnitudeAristotle uses the word μέγεθος both of magnitude in general and of spatial magnitude or extension. Here the meaning seems to be the former. Numbers obviously have magnitude, and might be regarded as causing it; but (except on the Number-Atomism theory,) they are no more the cause of extension than that of gravity. is composed of these factors, yet how is it to be explained that some bodies are light, and others have weight? For in their premisses and statements they are speaking just as much about sensible as about mathematical objects; and this is why they have made no mention of fire or earth or other similar bodies, because, I presume, they have no separate explanation of sensible things.

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Again, how are we to understand that number and the modifications of number are the causes of all being and generation, both in the beginning and now, and at the same time that there is no other number than the number of which the universe is composed?i.e., how can number be both reality and the cause of reality?

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Because when they make out that Opinion and Opportunity are in such and such a region, and a little above or below them Injustice and Separation or Mixture, and when they state as proof of this that each of these abstractions is a number; and that also in this region there is already a plurality of the magnitudes composed of number, inasmuch as these modifications of number correspond to these several regions,—is the number which we must understand each of these abstractions to be the same number which is present in the sensible universe, or another kind of number?The point seems to be this. The Pythagoreans say that Opinion is a number, 3 (or 2, according to another version), and is located in a certain region of the universe because that region is proper to a corporeal magnitude composed of the number 3 (air was so composed according to Syrianus). Are we to understand, says Aristotle, that the abstract number identified with Opinion is the same as the concrete number of which air consists? The difficulty is probably due to an attempt to combine two different Pythagorean views of number.

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Plato at least says that it is another. It is true that he too supposes that numbers are both these magnitudes and their causes; but in his view the causative numbers are intelligible and the others sensible.

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The Pythagoreans, then, may be dismissed for the present, for it is enough to touch upon them thus briefly. As for those who posit the Forms as causes,For a discussion of the Ideal theory and Aristotle’s conception of it see Introduction; and with the whole contents of Aristot. Met. 9.1-15 cf. Aristot. Met. 13.4.6-5. in the first place in their attempt to find the causes of things in our sensible world, they introduced an equal number of other entities—as though a man who wishes to count things should suppose that it would be impossible when they are few, and should attempt to count them when he has added to them. For the Forms are as many as, or not fewer than, the things in search of whose causes these thinkers were led to the Forms; because corresponding to each thing there is a synonymous entity apart from the substances (and in the case of non-substantial things there is a One over the ManyAn Idea which represents their common denominator.), both in our everyday world and in the realm of eternal entities.The heavenly bodies.

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Again, not one of the arguments by which weAristotle is here speaking as a Platonist. Contrast the language of Aristot. Met. 13.4.7ff., and see Introduction. try to prove that the Forms exist demonstrates our point: from some of them no necessary conclusion follows, and from others it follows that there are Forms of things of which we hold that there are no Forms.

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For according to the arguments from the sciencesScientific knowledge must have a permanent object (cf. Aristot. Met. 1.4.2. there will be Forms of all things of which there are sciencesIncluding artificial products; cf. Aristot. Met. 1.15.; and according to the One-over-Many argument,The fact that several particulars can have a common quality or nature implies a single Idea of which they all partake (Plat. Rep. 596a). of negations too; and according to the argument that we have some conception of what has perished, of perishable things; because we have a mental picture of these things.The theory always admitted Ideas of perishable things, e.g. man. The objection here is that if the memory of dead men establishes the Idea of man, the memory of a dead individual establishes an Idea of that (perishable) individual. Again, of Plato’s more exact arguments some establish Ideas of relations,Plat. Phaedo 74a-77a, Plat. Rep. 479a-480a. which we do not hold to form a separate genus;

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and others state the Third Man. Several arguments bore this name. Here the reference is probably to the following: If X is a man because he resembles the Idea of Man, there must be a third man in whom the humanity of these two is united. Cf.Plat. Parm. 132a-133a. And in general the arguments for the Forms do away with things which are more important to us exponents of the Forms than the existence of the Ideas; for they imply that it is not the Dyad that is primary, but NumberThe Indeterminate Dyad, being to Aristotle a glorified 2, falls under the Idea of Number, which is therefore prior to it.; and that the relative is prior to the absoluteThis seems to be a development of the same objection. Number, which is relative, becomes prior to the supposedly self-subsistent Dyad.; and all the other conclusions in respect of which certain persons, by following up the views held about the Ideas, have gone against the principles of the theory.

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Again, according to the assumption by which we hold that the Ideas exist, there will be Forms not only of substances but of many other things (since the concept is one not only in the case of substances, but also in the case of all other things; and there are sciences not only of substances but of other things as well; and there are a thousand other similar consequences); but according to logical necessity, and from the views generally held about them, it follows that if the Forms are participated in, then there can only be Ideas of substances. For they are not participated in qua accidents; each Form can only be participated in in so far as it is not predicated of a subject.

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I mean, e.g., that if anything participates in absolute Doubleness it participates also in eternal, but only accidentally; because it is an accident of Doubleness to be eternal.Sensible double things are not eternal; therefore they do not, in the proper sense of participation, participate in the Idea of Doubleness qua having the accidental attribute eternal. Therefore Ideas, qua participated in, are not attributes but substances.

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Thus the Forms must be substance. But the same names denote substance in the sensible as in the Ideal world; otherwise what meaning will there be in saying that something exists beside the particulars, i.e. the unity comprising their multiplicity?

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If the form of the Ideas and of the things which participate in them is the same, they will have something in common (for why should Duality mean one and the same thing in the case of perishable twosi.e. pairs of sensible objects. and the twos which are many but eternal,i.e. mathematical 2s. and not in the case of the Idea of Duality and a particular two?); but if the form is not the same, they will simply be homonyms; just as though one were to call both Callias and a piece of wood man, without remarking any property common to them.The argument of 7-8 is: Ideas are substances. The common name which an idea shares with its particulars must mean the same of both; otherwise participation is merely homonymy. But as applied to Ideas it denotes substance; therefore particulars must be substances.

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Above all we might examine the question what on earth the Forms contribute to sensible things, whether eternal or subject to generation and decay; for they are not the cause of any motion or change in them.

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Again, they are no help towards the knowledge of other thingsThis objection, like the next, is chiefly directed against the transcendence of the Ideas. It is anticipated by Plato in Plat. Parm. 134d.(for they are not the substance of things, otherwise they would be in things), nor to their existence, since they are not present in the things which partake of them. If they were, it might perhaps seem that they are causes, in the sense in which the admixture of white causes a thing to be white;

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but this theory, which was first stated by AnaxagorasAnaxagoras Fr. 12ad fin. and later by EudoxusSee note on Aristot. Met. 12.8.9. Apparently he was a Platonist who regarded the Ideas as immanent in particulars. and others, is very readily refutable, for it is easy to adduce plenty of impossibilities against such a view. Again, other things are not in any accepted sense derived from the Forms.

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To say that the Forms are patterns, and that other things participate in them, is to use empty phrases and poetical metaphors; for what is it that fashions things on the model of the IdeasPlato says the Demiurgus?Plat. Tim. 28c, Plat. Tim. 29a. Besides, anything may both be and become like something else without being imitated from it; thus a man may become just like Socrates whether Socrates exists or not,

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and even if Socrates were eternal, clearly the case would be the same. Also there will be several patterns, and hence Forms, of the same thing; e.g. animal and two-footed will be patterns of man, and so too will the Idea of Man.Why this consequence is objectionable is not quite clear. Perhaps it is on the ground that to account for appearances in this way is not economical.

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Further, the Forms will be patterns not only of sensible things but of themselves (e.g. genus in the sense of genus of species), and thus the same thing will be both pattern and copy.The species will be the pattern of individuals, and the genus of the species. Further, it would seem impossible that the substance and the thing of which it is the substance exist in separation; hence how can the Ideas, if they are the substances of things, exist in separation from them?Cf. Aristot. Met. 1.10. It is stated in the PhaedoPlat. Phaedo 100d. that the Forms are the causes both of existence and of generation.

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Yet, assuming that the Forms exist, still the things which participate in them are not generated unless there is something to impart motion; while many other things are generated (e.g. house, ring) of which we hold that there are no Forms. Thus it is clearly possible that all other things may both exist and be generated for the same causes as the things just mentioned.

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Further, if the Forms are numbers, in what sense will they be causes? Is it because things are other numbers, e.g. such and such a number Man, such and such another Socrates, such and such another Callias? then why are those numbers the causes of these? Even if the one class is eternal and the other not, it will make no difference.

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And if it is because the things of our world are ratios of numbers (e.g. a musical concord), clearly there is some one class of things of which they are ratios. Now if there is this something, i.e. their matter , clearly the numbers themselves will be ratios of one thing to another.

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I mean, e.g., that if Callias is a numerical ratio of fire, earth, water and air, the corresponding Idea too will be a number of certain other things which are its substrate. The Idea of Man, too, whether it is in a sense a number or not, will yet be an arithmetical ratio of certain things, and not a mere number; nor, on these grounds, will any Idea be a number.The point, which is not very clearly expressed, is that the Ideas will not be pure numerical expressions or ratios, but will have a substrate just as particulars have.

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Again, one number can be composed of several numbers, but how can one Form be composed of several Forms? And if the one number is not composed of the other numbers themselves, but of their constituents (e.g. those of the number 10,000), what is the relation of the units? If they are specifically alike, many absurdities will result, and also if they are not (whether (a) the units in a given number are unlike, or (b) the units in each number are unlike those in every other number).That the words in brackets give the approximate sense seems clear from Aristot. Met. 13.6.2-3, Aristot. Met. 13.7.15; but it is difficult to get it out of the Greek. For in what can they differ, seeing that they have no qualities? Such a view is neither reasonable nor compatible with our conception of units.

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Further, it becomes necessary to set up another kind of number (with which calculation deals), and all the objects which are called intermediate by some thinkers.Cf. vi. 4. But how or from what principles can these be derived? or on what grounds are they to be considered intermediate between things here and Ideal numbers? Further, each of the units in the number 2 comes from a prior 2; but this is impossible.i.e., if 2 is derived from a prior 2 (the Indeterminate Dyad; Aristotle always regards this as a number 2), and at the same time consists of two units or 1s, 2 will be prior both to itself and to 1.

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Further, why should a number <of units>, taken together, be one thing? And further, in addition to the above objections, if the units are unlike, they should be treated as the thinkers who assume two or four elements treat those elements; for not one of them applies the term element to the common substrate, e.g. body, but to fire and earth—whether there is a common substrate (i.e. body) or not.In the Aristot. De Gen. et Corr. 320b 23Aristotle says that there is not.

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As it is, the One is spoken of as though it were homogeneous, like fire or water. But if this is so, the numbers will not be substances. And if there is an absolute One which is a principle, clearly the term one is ambiguous; otherwise this is impossible.This last sentence shows that in what goes before A. has been regarding the Platonic One as a unit. If this is so, he says, substance cannot be composed of it. If on the other hand the One is something different from the unit, they ought to make this clear.

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When we wish to refer substances to their principles we derive linesThe lines, planes, and solids here discussed are probably the Ideal lines, etc., which are immediately posterior to the Idea-Numbers. Cf. 30, Aristot. Met. 13.6.10, Aristot. Met. 13.9.2, and see Introduction. from Long and Short, a kind of Great and Small; and the plane from Wide and Narrow, and the solid body from Deep and Shallow. But in this case how can the plane contain a line,

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or the solid a line and a plane? for Wide and Narrow and Deep and Shallow are different genera. Nor is Number contained in these objects (because Many and Few is yet another class); and in the same way it is clear that none of the other higher genera will be contained in the lower. Nor, again, is the Broad the genus of which the Deep is a species; for then body would be a kind of plane.

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Further, how will it be possible for figures to contain points?Lines, planes, and solids are generated from varieties of the Great and Small, but points cannot be, having no magnitude; how, then, can the latter be present in the former? Plato steadily rejected this class of objects as a geometrical fiction, but he recognized the beginning of a line, and he frequently assumed this latter class, i.e. the indivisible lines. That Plato denied the existence of the point and asserted that of indivisible lines is not directly stated elsewhere, but the same views are ascribed to Xenocrates, and were attacked in the treatise Xenocrates De lineis insecabilibus. See Ross ad loc. But these must have some limit; and so by the same argument which proves the existence of the line, the point also exists.Sc. if the point is the limit of the line.

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In general, although Wisdom is concerned with the cause of visible things, we have ignored this question (for we have no account to give of the cause from which change arises),Cf. Aristot. Met. 7.5 and Aristot. Met. 1.9. and in the belief that we are accounting for their substance we assert the existence of other substances; but as to how the latter are the substances of the former, our explanation is worthless—for participation, as we have said before,Aristot. Met. 1.12. means nothing.

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And as for that which we can see to be the cause in the sciences, and through which all mind and all nature works—this causeThe final cause. Cf. Aristot. Met. 1.6.9-10. which we hold to be one of the first principles—the Forms have not the slightest bearing upon it either. Philosophy has become mathematics for modern thinkers,e.g. Speusippus, for whom see Aristot. Met. 7.2.4. although they professCf. Plat. Rep.531c-d that mathematics is only to be studied as a means to some other end.

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Further, one might regard the substance which they make the material substrate as too mathematical, and as being a predicate and differentia of substance or matter rather than as matter itself, I mean the Great and Small, which is like the Rare and Dense of which the physicists speak,Cf. iv. 10. holding that they are the primary differentiae of the substrate; because these qualities are a species of excess and defect.

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Also with regard to motion, if the Great and Small is to constitute motion, obviously the Forms will be moved; if not, whence did it come? On this view the whole study of physics is abolished. And what is supposed to be easy, to prove that everything is One, does not follow; because from their expositionThe word ἔκθεσις has various technical meanings. The process referred to here apparently consisted in taking, e.g., particular men, and reducing them with reference to their common nature to a single unit or universal, man; then taking man, horse, dog, etc. and treating them in the same way, until a unit is reached which embraces everything (Alexander). it does not follow, even if you grant them all their assumptions that everything is One, but only that there is an absolute One—

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and not even this, unless you grant that the universal is a class; which is impossible in some cases.Probably those of relative or negative terms. Cf. Aristot. Met. 1.3. Nor is there any explanation of the lines, planes and solids which come after the NumbersSee note on Aristot. Met. 1.23.: neither as to how they exist or can exist, nor as to what their importance is. They cannot be Forms (since they are not numbers) or Intermediates (which are the objects of mathematics) or perishables; clearly they form yet another fourth class.

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In general, to investigate the elements of existing things without distinguishing the various senses in which things are said to exist is a hopeless task; especially when one inquires along these lines into the nature of the elements of which things are composed. For (a) we cannot surely conceive of the elements of activity or passivity or straightness; this is possible, if at all, only in the case of substances. Hence to look for, or to suppose that one has found, the elements of everything that exists, is a mistake.

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(b) How can one apprehend the elements of everything ? Obviously one could not have any previous knowledge of anything; because just as a man who is beginning to learn geometry can have previous knowledge of other facts, but no previous knowledge of the principles of that science or of the things about which he is to learn, so it is in the case of all other branches of knowledge.

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Hence if there is a science which embraces everythinge.g. Plato’s Dialectic.(as some say), the student of it can have no previous knowledge at all. But all learning proceeds, wholly or in part, from what is already known; whether it is through demonstration or through definition—since the parts of the definition must be already known and familiar. The same is true of induction.

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On the other hand, assuming that this knowledge should turn out to be innate,Cf. the doctrine of ἀνάμνησις (recollection), Plat. Meno 81c, Plat. Phaedo 72e. it is astonishing that we should possess unawares the most important of the sciences. Further, how is one to know of what elements things consist? how is it to be established?

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Even this presents a difficulty, because the facts might be disputed, as happens in the case of certain syllables—for some say that ZA is composed of S, D and A, while others say that it is a distinct sound and not any one of those which are familiar to us.στοιχεῖον means both an element and a letter of the alphabet; hence letters are often used as analogues of the material elements. The point here is: Is Z or rather the Greek ζ) a στοιχεῖον, or is it further analyzable? Since this can be disputed, we must expect differences of opinion about the elements in general.

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Further, how can one gain knowledge of the objects of a particular sense-perception without possessing that sense? Yet it should be possible, that if the elements of which all things consist, as composite sounds consist of their peculiar Peculiar to them as sounds, not as individual sounds. If sights and sounds had the same elements, sight, which knows those elements as composing sights, would know them as composing sounds; i.e., we could see sounds. elements, are the same.

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Thus it is obvious, from the statements of earlier thinkers also, that all inquiry is apparently directed towards the causes described in the Physics,Aristot. Phys. 2.3, 7. and that we cannot suggest any other cause apart from these. They were, however, only vaguely conceived; and although in one sense they have all been stated before, in another they have not been stated at all.

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For the earliest philosophy speaks falteringly, as it were, on all subjects; being new and in its infancy. Even Empedocles says that bone exists by virtue of its ratio,Empedocles Fr. 96, 98 (Diels), Ritter and Preller 175. Aristotle says that Empedocles had some idea of the essence or formal cause, but did not apply it generally. which is the definition or essence of a thing.

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But by similar reasoning both flesh and every other thing, or else nothing at all, must be ratio; for it must be because of this, and not because of their matter—which he calls fire, earth, water and air—that flesh and bone and every other thing exists.

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If anyone else had stated this, he would necessarily have agreed, but his own statement was not clear.

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These and similar points have been explained already. We will now return to the difficulties which might be raised about these same questions, for they may throw some light upon subsequent difficulties.The reference is to Book 3. See Introduction.

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The study of Truth is in one sense difficult, in another easy. This is shown by the fact that whereas no one person can obtain an adequate grasp of it, we cannot all fail in the attempt; each thinker makes some statement about the natural world, and as an individual contributes little or nothing to the inquiry; but a combination of all conjectures results in something considerable.

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Thus in so far as it seems that Truth is like the proverbial door which no one can miss,Leutsch and Schneidewin, Paroemiographi, 2.678. in this sense our study will be easy; but the fact that we cannot, although having some grasp of the whole, grasp a particular part, shows its difficulty. However, since difficulty also can be accounted for in two ways, its cause may exist not in the objects of our study but in ourselves:

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just as it is with bats’ eyes in respect of daylight, so it is with our mental intelligence in respect of those things which are by nature most obvious.

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It is only fair to be grateful not only to those whose views we can share but also to those who have expressed rather superficial opinions. They too have contributed something; by their preliminary work they have formed our mental experience.

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If there had been no Timotheus,Of Miletus, 446 (?)—357 B.C. we should not possess much of our music; and if there had been no Phrynis,Of Mytilene; he is referred to as still alive in Aristoph. Cl. 971. Both Phrynis and Timotheus are criticized in the fragment of Pherecrates Chirontranslated by Rogers in the appendix to his ed. of the Clouds. there would have been no Timotheus. It is just the same in the case of those who have theorized about reality: we have derived certain views from some of them, and they in turn were indebted to others.

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Moreover, philosophy is rightly called a knowledge of Truth. The object of theoretic knowledge is truth, while that of practical knowledge is action; for even when they are investigating how a thing is so, practical men study not the eternal principle but the relative and immediate application.

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But we cannot know the truth apart from the cause. Now every thing through which a common quality is communicated to other things is itself of all those things in the highest degree possessed of that quality (e.g. fire is hottest, because it is the cause of heat in everything else); hence that also is most true which causes all subsequent things to be true.

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Therefore in every case the first principles of things must necessarily be true above everything else—since they are not merely sometimes true, nor is anything the cause of their existence, but they are the cause of the existence of other things,—and so as each thing is in respect of existence, so it is in respect of truth.

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Moreover, it is obvious that there is some first principle, and that the causes of things are not infinitely many either in a direct sequence or in kind. For the material generation of one thing from another cannot go on in an infinite progression (e.g. flesh from earth, earth from air, air from fire, and so on without a stop); nor can the source of motion (e.g. man be moved by air, air by the sun, the sun by Strife,Aristotle is evidently thinking of Empedocles’ system. with no limit to the series).

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In the same way neither can the Final Cause recede to infinity—walking having health for its object, and health happiness, and happiness something else: one thing always being done for the sake of another.

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And it is just the same with the Formal Cause. For in the case of all intermediate terms of a series which are contained between a first and last term, the prior term is necessarily the cause of those which follow it; because if we had to say which of the three is the cause, we should say the first. At any rate it is not the last term, because what comes at the end is not the cause of anything. Neither, again, is the intermediate term, which is only the cause of one

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(and it makes no difference whether there is one intermediate term or several, nor whether they are infinite or limited in number). But of series which are infinite in this way, and in general of the infinite, all the parts are equally intermediate, down to the present moment. Thus if there is no first term, there is no cause at all.

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On the other hand there can be no infinite progression downwards (where there is a beginning in the upper direction) such that from fire comes water, and from water earth, and in this way some other kind of thing is always being produced. There are two senses in which one thing comes from another—apart from that in which one thing is said to come after another, e.g. the Olympian fromἐκ means not only from but after; Aristotle dismisses this latter meaning. The Isthmian fell alternatively in the same year as the Olympian festival; when this happened the former was held in the spring and the latter in the summer. Cf. Aristot. Met. 5.24.5. the Isthmian games—either as a man comes from a child as it develops, or as air comes from water.

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Now we say that a man comes from a child in the sense that that which has become something comes from that which is becoming: i.e. the perfect from the imperfect. (For just as becoming is always intermediate between being and not-being, so is that which is becoming between what is and what is not. The learner is becoming informed, and that is the meaning of the statement that the informed person comes from the learner.)

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On the other hand A comes from B in the sense that water comes from air by the destruction of B. Hence the former class of process is not reversible (e.g. a child cannot come from a man, for the result of the process of becoming is not the thing which is becoming, but that which exists after the process is complete. So day comes from early dawn, because it is after dawn; and hence dawn does not come from day). But the other class is reversible.

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In both cases progression to infinity is impossible; for in the former the intermediate terms must have an end, and in the second the process is reversible, for the destruction of one member of a pair is the generation of the other. At the same time the first cause, being eternal, cannot be destroyed; because, since the process of generation is not infinite in the upper direction, that cause which first, on its destruction, became something else, cannot possibly be eternal.The argument is elliptical and confused. The meaning is this: Since there is an upward limit, there is a first cause which is eternal, being independent of any other cause. Therefore this cause cannot cause other things by its destruction, in the manner just described.

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Further, the Final cause of a thing is an end , and is such that it does not happen for the sake of some thing else, but all other things happen for its sake. So if there is to be a last term of this kind, the series will not be infinite; and if there is no such term, there will be no Final cause. Those who introduce infinity do not realize that they are abolishing the nature of the Good (although no one would attempt to do anything if he were not likely to reach some limit);

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nor would there be any intelligence in the world, because the man who has intelligence always acts for the sake of something, and this is a limit, because the end is a limit.

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Nor again can the Formal cause be referred back to another fuller definition;

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for the prior definition is always closer, and the posterior is not; and where the original definition does not apply, neither does the subsequent one. Further, those who hold such a view do away with scientific knowledge, for on this view it is impossible to know anything until one comes to terms which cannot be analyzed.

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Understanding, too, is impossible; for how can one conceive of things which are infinite in this way? It is different in the case of the line, which, although in respect of divisibility it never stops, yet cannot be conceived of unless we make a stop (which is why, in examining an infinitei.e. infinitely divisible. line, one cannot count the sections).It does not follow that we can apprehend that which is infinite because we can apprehend a line which is infinitely divisible. We can only really apprehend the line by setting a limit to its divisibility and regarding it simply as divisible into a very great (but not infinite) number of sections. An infinite number of sections can neither be apprehended nor counted.

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Even matter has to be conceived under the form of something which changes,Matter too, which is infinite in its varieties, can only be apprehended in the form of concrete sensible objects which are liable to change. This seems to be the meaning of the text, but Ross’s reading and interpretation may be right: see his note ad loc. and there can be nothing which is infinite.i.e. not actually, but only potentially. In any case the concept of infinity is not infinite.Cf. the third note above.

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Again, if the kinds of causes were infinite in number it would still be impossible to acquire knowledge; for it is only when we have become acquainted with the causes that we assume that we know a thing; and we cannot, in a finite time, go completely through what is additively infinite.

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The effect of a lecture depends upon the habits of the listener; because we expect the language to which we are accustomed, and anything beyond this seems not to be on the same level, but somewhat strange and unintelligible on account of its unfamiliarity; for it is the familiar that is intelligible. The powerful effect of familiarity is clearly shown by the laws, in which the fanciful and puerile survivals prevail, through force of habit, against our recognition of them.

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Thus some people will not accept the statements of a speaker unless he gives a mathematical proof; others will not unless he makes use of illustrations; others expect to have a poet adduced as witness. Again, some require exactness in everything, while others are annoyed by it, either because they cannot follow the reasoning or because of its pettiness; for there is something about exactness which seems to some people to be mean, no less in an argument than in a business transaction.

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Hence one must have been already trained how to take each kind of argument, because it is absurd to seek simultaneously for knowledge and for the method of obtaining it; and neither is easy to acquire. Mathematical accuracy is not to be demanded in everything, but only in things which do not contain matter.

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Hence this method is not that of natural science, because presumably all nature is concerned with matter. Hence we should first inquire what nature is; for in this way it will become clear what the objects of natural science are [and whether it belongs to one science or more than one to study the causes and principles of things].These words have evidently been inserted to form a kind of link with the subject matter of the Metaphysics. The book is almost certainly part of a quite independent treatise; see Introduction.

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It is necessary, with a view to the science which we are investigating, that we first describe the questions which should first be discussed. These consist of all the divergent views which are held about the first principles; and also of any other view apart from these which happens to have been overlooked.

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Now for those who wish to get rid of perplexities it is a good plan to go into them thoroughly; for the subsequent certainty is a release from the previous perplexities, and release is impossible when we do not know the knot. The perplexity of the mind shows that there is a knot in the subject; for in its perplexity it is in much the same condition as men who are fettered: in both cases it is impossible to make any progress.

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Hence we should first have studied all the difficulties, both for the reasons given and also because those who start an inquiry without first considering the difficulties are like people who do not know where they are going; besides, one does not even know whether the thing required has been found or not. To such a man the end is not clear; but it is clear to one who has already faced the difficulties.

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Further, one who has heard all the conflicting theories, like one who has heard both sides in a lawsuit, is necessarily more competent to judge.

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The first difficulty is concerned with the subjectsThe principles and causes referred to in Book I. which we discussed in our prefatory remarks. (1.) Does the study of the causes belong to one science or to more than one?The problem is discussed Aristot. Met. 3.2.1-10, and answered Aristot. Met. 4.1.(2.) Has that science only to contemplate the first principles of substance, or is it also concerned with the principles which all use for demonstration—e.g. whether it is possible at the same time to assert and deny one and the same thing, and other similar principles?Discussed Aristot. Met. 3.2.10-15; answered Aristot. Met. 4.2.

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And if it is concerned with substance, (3.) is there one science which deals with all substances, or more than one; and if more than one, are they all cognate, or should we call some of them kinds of Wisdom and others something different?Discussed Aristot. Met. 3.2.15-17; answered Aristot. Met. 4.2.9-10, Aristot. Met. 6.1.

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This too is a question which demands inquiry: (iv.) should we hold that only sensible substances exist, or that there are other besides? And should we hold that there is only one class of non-sensible substances, or more than one (as do those who posit the Forms and the mathematical objects as intermediate between the Forms and sensible things)?Discussed Aristot. Met. 3.2.20-30 answered Aristot. Met. 12.6-10, and also by the refutation of the Platonic Ideas and Intermediates in Books 13 and 14.

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These questions, then, as I say, must be considered; and also (v.) whether our study is concerned only with substances, or also with the essential attributes of substance;

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and further, with regard to Same and Other, and Like and Unlike and Contrariety, and Prior and Posterior, and all other such terms which dialecticians try to investigate, basing their inquiry merely upon popular opinions; we must consider whose province it is to study all of these.

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Further, we must consider all the essential attributes of these same things, and not merely what each one of them is, but also whether each one has one oppositeDiscussed Aristot. Met. 3.2.18-19; answered Aristot. Met. 4.2.8-25.; and (vi.) whether the first principles and elements of things are the genera under which they fall or the pre-existent parts into which each thing is divided; and if the genera, whether they are those which are predicated ultimately of individuals, or the primary genera—e.g., whether animal or man is the first principle and the more independent of the individual.DiscussedAristot. Met. 3.3; answered Aristot. Met. 7.10, 12-13

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Above all we must consider and apply ourselves to the question (7.) whether there is any other cause per se besides matter, and if so whether it is dissociable from matter, and whether it is numerically one or several; and whether there is anything apart from the concrete thing (by the concrete thing I mean matter together with whatever is predicated of it) or nothing; or whether there is in some cases but not in others; and what these cases are.Discussed iv. 1-8. For answers to these questions see Aristot. Met. 7.8, 13-14; Aristot. Met. 12.6-10; Aristot. Met. 13.10.

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Further, (8.) we must ask whether the first principles are limited in number or in kindDiscussed Aristot. Met. 3.4.8-10; answered Aristot. Met. 12.4-5, Aristot. Met. 13.10.—both those in the definitions and those in the substrate—and (ix.) whether the principles of perishable and of imperishable things are the same or different; and whether all are imperishable, or those of perishable things are perishable.Discussed Aristot. Met. 3.4.11-23; for Aristotle’s general views on the subject see Aristot. Met. 7.7-10, Aristot. Met. 12.1-7.

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Further, there is the hardest and most perplexing question of all: (x.) whether Unity and Being (as the Pythagoreans and Plato maintained) are not distinct, but are the substance of things; or whether this is not so, and the substrate is something distinctDiscussed Aristot. Met. 3.4.24-34; answered Aristot. Met. 7.16.3-4, Aristot. Met. 10.2.(as Empedocles holds of Love,Actually Love was no more the universal substrate than was any other of Empedocles’ elements; Aristotle appears to select it on account of its unifying function. another thinkerHeraclitus. of fire, and another Thales. of water or airAnaximenes.);

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and (xi.) whether the first principles are universal or like individual thingsDiscussed Aristot. Met. 3.6.7-9; for the answer see Aristot. Met. 7.13-15, Aristot. Met. 13.10.; and (12.) whether they exist potentially or actually; and further whether their potentiality or actuality depends upon anything other than motionDiscussed Aristot. Met. 3.6.5-6; for the relation of potentiality to actuality see Aristot. Met. 9.1-9; for actuality and motion see Aristot. Met. 12.6-7.; for these questions may involve considerable difficulty.

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Moreover we must ask (13.) whether numbers and lines and figures and points are substances in any sense, or not; and if they are, whether they are separate from sensible things or inherent in them.Discussed Aristot. Met. 3.5; answered Aristot. Met. 13.1-3, 6-9; Aristot. Met. 14.1-3, 5, 6. With regard to these problems not only is it difficult to attain to the truth, but it is not even easy to state all the difficulties adequately.For another statement of the problems sketched in this chapter see Aristot. Met. 9.1, 2.

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(1.) Firstly, then, with respect to the first point raised: whether it is the province of one science or of more than one to study all the kinds of causes. How can one science comprehend the first principles unless they are contraries? Again, in many things they are not all present.

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How can a principle of motion be in immovable things? or the nature of the Good? for everything which is good in itself and of its own nature is an end and thus a cause, because for its sake other things come to be and exist; and the end and purpose is the end of some action, and all actions involve motion; thus it would be impossible either for this principle to exist in motionless things or for there to be any absolute Good.

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Hence in mathematics too nothing is proved by means of this cause, nor is there any demonstration of the kind because it is better or worse; indeed no one takes any such consideration into account.

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And so for this reason some of the sophists, e.g. Aristippus,Founder of the Cyrenaic school in the early fourth century. spurned mathematics, on the ground that in the other arts, even the mechanical ones such as carpentry and cobbling, all explanation is of the kind because it is better or worse, while mathematics takes no account of good and bad.For a defense of mathematics see Aristot. Met. 13.3.10-12.

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On the other hand if there are several sciences of the causes, and a different one for each different principle, which of them shall we consider to be the one which we are seeking, or whom of the masters of these sciences shall we consider to be most learned in the subject which we are investigating?

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For it is possible for all the kinds of cause to apply to the same object; e.g. in the case of a house the source of motion is the art and the architect; the final cause is the function; the matter is earth and stones, and the form is the definition. Now to judge from our discussion some time agoCf. Aristot. Met. 1.2.5-6. as to which of the sciences should be called Wisdom, there is some case for applying the name to each of them.

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Inasmuch as Wisdom is the most sovereign and authoritative kind of knowledge, which the other sciences, like slaves, may not contradict, the knowledge of the end and of the Good resembles Wisdom (since everything else is for the sake of the end ); but inasmuch as it has been defined as knowledge of the first principles and of the most knowable, the knowledge of the essence will resemble Wisdom.

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For while there are many ways of understanding the same thing, we say that the man who recognizes a thing by its being something knows more than he who recognizes it by its not being something; and even in the former case one knows more than another, and most of all he who knows what it is, and not he who knows its size or quality or natural capacity for acting or being acted upon.

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Further, in all other cases too, even in such as admit of demonstration, we consider that we know a particular thing when we know what it is (e.g. what is the squaring of a rectangle? answer, the finding of a mean proportional to its sides; and similarly in other instances); but in the case of generations and actions and all kinds of change, when we know the source of motion.

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This is distinct from and opposite to the end . Hence it might be supposed that the study of each of these causes pertained to a different science.See Aristot. Met. 4.1

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(2.) Again, with respect to the demonstrative principles as well, it may be disputed whether they too are the objects of one sciencesc. the science which studies the four causes. or of several.Cf. Aristot. Met. 3.1.5.

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By demonstrative I mean the axioms from which all demonstration proceeds, e.g. everything must be either affirmed or denied, and it is impossible at once to be and not to be, and all other such premisses. Is there one science both of these principles and of substance, or two distinct sciences? and if there is not one, which of the two should we consider to be the one which we are now seeking?

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It is not probable that both subjects belong to one science; for why should the claim to understand these principles be peculiar to geometry rather than to any other science? Then if it pertains equally to any science, and yet cannot pertain to all, comprehension of these principles is no more peculiar to the science which investigates substances than to any other science.

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Besides, in what sense can there in be a science of these principles? We know already just what each of them is; at any rate other sciences employ them as being known to us.sc. and so there can be no science which defines them. If, however there is a demonstrative science of them, there will have to be some underlying genus, and some of the principles will be derived from axioms, and others will be unproved

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(for there cannot be demonstration of everything), since demonstration must proceed from something, and have some subject matter, and prove something. Thus it follows that there is some one genus of demonstrable things; for all the demonstrative sciences employ axioms.

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On the other hand, if the science of substance is distinct from the science of these principles, which is of its own nature the more authoritative and ultimate?

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The axioms are most universal, and are the first principles of everything. And whose province will it be, if not the philosopher’s, to study truth and error with respect to them?For the answer see Aristot. Met. 4.3.

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(3.) And in general, is there one science of all substances, or more than one?Cf. Aristot. Met. 3.1.6. if there is not one, with what sort of substance must we assume that this science is concerned?

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On the other hand, it is not probable that there is one science of all substances; for then there would be one demonstrative of all attributes—assuming that every demonstrative science proceeds from accepted beliefs and studies the essential attributes concerned with some definite subject matter.

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Thus to study the essential attributes connected with the same genus is the province of the same science proceeding from the same beliefs. For the subject matter belongs to one science, and so do the axioms, whether to the same science or to a different one; hence so do the attributes, whether they are studied by these sciences themselves or by one derived from them.For the answer see Aristot. Met. 4.2.9-10, Aristot. Met. 6.1.

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(v.) Further, is this study concerned only with substances, or with their attributes as well?Cf. Aristot. Met. 3.1.8-10. I mean, e.g., if the solid is a kind of substance, and so too lines and planes, is it the province of the same science to investigate both these and their attributes, in every class of objects about which mathematics demonstrates anything, or of a different science?

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If of the same, then the science of substance too would be in some sense demonstrative; but it does not seem that there is any demonstration of the what is it? And if of a different science, what will be the science which studies the attributes of substance? This is a very difficult question to answer.This problem, together with the appendix to it stated in Aristot. Met. 3.1.9-10, is answered in Aristot. Met. 4.2.8-25.

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(iv.) Further, are we to say that only sensible substances exist, or that others do as well? and is there really only one kind of substance, or more than one (as they hold who speak of the Forms and the Intermediates, which they maintain to be the objects of the mathematical sciences)?

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In what sense we Platonists hold the Forms to be both causes and independent substances has been statedAristot. Met. 1.6. in our original discussion on this subject. But while they involve difficulty in many respects, not the least absurdity is the doctrine that there are certain entities apart from those in the sensible universe, and that these are the same as sensible things except in that the former are eternal and the latter perishable.As it stands this is a gross misrepresentation; but Aristotle’s objection is probably directed against the conception of Ideas existing independently of their particulars. See Introduction.

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For Platonists say nothing more or less than that there is an absolute Man, and Horse, and Health; in which they closely resemble those who state that there are Gods, but of human form; for as the latter invented nothing more or less than eternal men, so the former simply make the Forms eternal sensibles.

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Again, if anyone posits Intermediates distinct from Forms and sensible things, he will have many difficulties;

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because obviously not only will there be lines apart from both Ideal and sensible lines, but it will be the same with each of the other classes.sc. of objects of mathematical sciences. Thus since astronomy is one of the mathematical sciences, there will have to be a heaven besides the sensible heaven, and a sun and moon, and all the other heavenly bodies.

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But how are we to believe this? Nor is it reasonable that the heaven should be immovable; but that it should move is utterly impossible.The reference is to the supposed intermediate heaven. A heaven (including heavenly bodies) without motion is unthinkable; but a non-sensible heaven can have no motion. It is the same with the objects of optics and the mathematical theory of harmony; these too, for the same reasons, cannot exist apart from sensible objects. Because if there are intermediate objects of sense and sensations, clearly there will also be animals intermediate between the Ideal animals and the perishable animals.If there are intermediate, i.e. non-sensible, sights and sounds, there must be intermediate faculties of sight and hearing, and intermediate animals to exercise these faculties; which is absurd.

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One might also raise the question with respect to what kind of objects we are to look for these sciences. For if we are to take it that the only difference between mensuration and geometry is that the one is concerned with things which we can perceive and the other with things which we cannot, clearly there will be a science parallel to medicine (and to each of the other sciences), intermediate between Ideal medicine and the medicine which we know.

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Yet how is this possible? for then there would be a class of healthy things apart from those which are sensible and from the Ideally healthy. Nor, at the same time, is it true that mensuration is concerned with sensible and perishable magnitudes; for then it would perish as they do. Nor, again, can astronomy be concerned with sensible magnitudes or with this heaven of ours;

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for as sensible lines are not like those of which the geometrician speaks (since there is nothing sensible which is straight or curved in that sense; the circlei.e., the visible circle which we draw. Like the ruler, it is geometrically imperfect; thus they touch at more than one point. touches the ruler not at a point, but <along a line> as Protagoras used to say in refuting the geometricians), so the paths and orbits of our heaven are not like those which astronomy discusses, nor have the symbols of the astronomer the same nature as the stars.

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Some, however, say that these so-called Intermediates between Forms and sensibles do exist: not indeed separately from the sensibles, but in them. It would take too long to consider in detail all the impossible consequences of this theory, but it will be sufficient to observe the following.

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On this view it is not logical that only this should be so; in clearly it would be possible for the Forms also to be in sensible things; for the same argument applies to both. Further, it follows necessarily that two solids must occupy the same space; and that the Forms cannot be immovable, being present in sensible things, which move.

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And in general, what is the object of assuming that Intermediates exist, but only in sensible things? The same absurdities as before will result: there will be a heaven besides the sensible one, only not apart from it, but in the same place; which is still more impossible.The problem is dealt with partly in Aristot. Met. 12.6-10, where Aristotle describes the eternal moving principles, and partly in Books 13 and 14, where he argues against the Platonic non-sensible substances.

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Thus it is very difficult to say, not only what view we should adopt in the foregoing questions in order to arrive at the truth, but also in the case of the first principles (vi.) whether we should assume that the genera, or the simplest constituents of each particular thing, are more truly the elements and first principles of existing things. E.g., it is generally agreed that the elements and first principles of speech are those things of which, in their simplest form, all speech is composed; and not the common term speech; and in the case of geometrical propositions we call those the elementsCf. Aristot. Met. 5.3.3. whose proofs are embodied in the proofs of all or most of the rest.

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Again, in the case of bodies, both those who hold that there are several elements and those who hold that there is one call the things of which bodies are composed and constituted first principles. E.g., Empedocles states that fire and water and the other things associated with them are the elements which are present in things and of which things are composed; he does not speak of them as genera of things.

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Moreover in the case of other things too, if a man wishes to examine their nature he observes, e.g., of what parts a bed consists and how they are put together; and then he comprehends its nature. Thus to judge from these arguments the first principles will not be the genera of things.

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But from the point of view that it is through definitions that we get to know each particular thing, and that the genera are the first principles of definitions, the genera must also be the first principles of the things defined.

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And if to gain scientific knowledge of things is to gain it of the species after which things are named, the genera are first principles of the species. And apparently some even of thoseThe Pythagoreans and Plato. who call Unity or Being or the Great and Small elements of things treat them as genera.

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Nor again is it possible to speak of the first principles in both senses.

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The formula of substance is one; but the definition by genera will be different from that which tells us of what parts a thing is composed.

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Moreover, assuming that the genera are first principles in the truest sense, are we to consider the primary genera to be first principles, or the final terms predicated of individuals? This question too involves some dispute.

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For if universals are always more truly first principles, clearly the answer will be the highest genera, since these are predicated of everything. Then there will be as many first principles of things as there are primary genera, and so both Unity and Being will be first principles and substances, since they are in the highest degree predicated of all things.

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But it is impossible for either Unity or Being to be one genus of existing things. For there must be differentiae of each genus, and each differentia must be onei.e., each differentia must have Being and Unity predicated of it.; but it is impossible either for the species of the genus to be predicated of the specific differentiae, or for the genus to be predicated without its species.The reasons are given in Aristot. Topica, 144a 36-b11. Hence if Unity or Being is a genus, there will be no differentia Being or Unity.

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But if they are not genera, neither will they be first principles, assuming that it is the genera that are first principles. And further, the intermediate terms, taken together with the differentiae, will be genera, down to the individuals; but in point of fact, although some are thought to be such, others are not. Moreover the differentiae are more truly principles than are the genera; and if they also are principles, we get an almost infinite number of principles, especially if one makes the ultimate genus a principle.

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Moreover, if Unity is really more of the nature of a principle, and the indivisible is a unity, and every thing indivisible is such either in quantity or in kind, and the indivisible in kind is prior to the divisible, and the genera are divisible into species, then it is rather the lowest predicate that will be a unity (for man is not the genussc. but the species. of individual men).

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Further, in the case of things which admit of priority and posteriority, that which is predicated of the things cannot exist apart from them. E.g., if 2 is the first number, there will be no Number apart from the species of number; and similarly there will be no Figure apart from the species of figures. But if the genera do not exist apart from the species in these cases, they will scarcely do so in others; because it is assumed that genera are most likely to exist in these cases.

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In individuals, however, there is no priority and posteriority. Further, where there is a question of better or worse, the better is always prior; so there will be no genus in these cases either.

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From these considerations it seems that it is the terms predicated of individuals, rather than the genera, that are the first principles. But again on the other hand it is not easy to say in what sense we are to understand these to be principles;

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for the first principle and cause must be apart from the things of which it is a principle, and must be able to exist when separated from them. But why should we assume that such a thing exists alongside of the individual, except in that it is predicated universally and of all the terms? And indeed if this is a sufficient reason, it is the more universal concepts that should rather be considered to be principles; and so the primary genera will be the principles.For partial solutions to the problem see Aristot. Met. 7.10, 12-13.

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In this connection there is a difficulty which is the hardest and yet the most necessary of all to investigate, and with which our inquiry is now concerned. (7.) If nothing exists apart from individual things, and these are infinite in number, how is it possible to obtain knowledge of the numerically infinite? For we acquire our knowledge of all things only in so far as they contain something universal, some one and identical characteristic.

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But if this is essential, and there must be something apart from individual things, it must be the genera; either the lowest or the highest; but we have just concluded that this is impossible.In Aristot. Met. 3.3.

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Further, assuming that when something is predicated of matter there is in the fullest sense something apart from the concrete whole, if there is something, must it exist apart from all concrete wholes, or apart from some but not others, or apart from none?

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If nothing exists apart from individual things, nothing will be intelligible; everything will be sensible, and there will be no knowledge of anything—unless it be maintained that sense-perception is knowledge. Nor again will anything be eternal or immovable, since sensible things are all perishable and in motion.

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Again, if nothing is eternal, even generation is impossible; for there must be something which becomes something, i.e. out of which something is generated, and of this series the ultimate term must be ungenerated; that is if there is any end to the series and generation cannot take place out of nothing.

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Further, if there is generation and motion, there must be limit too. For (a) no motion is infinite, but every one has an end; (b) that which cannot be completely generated cannot begin to be generated, and that which has been generated must be as soon as it has been generated.

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Further, if matter exists apart in virtue of being ungenerated, it is still more probable that the substance, i.e. that which the matter is at any given time becoming, should exist. And if neither one nor the other exists, nothing will exist at all. But if this is impossible, there must be something, the shape or form, apart from the concrete whole.

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But again, if we assume this, there is a difficulty: in what cases shall we, and in what shall we not, assume it? Clearly it cannot be done in all cases; for we should not assume that a particular house exists apart from particular houses. Moreover, are we to regard the essence of all things, e.g. of men, as one? This is absurd; for all things whose essence is one are one.

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Then is it many and diverse? This too is illogical. And besides, how does the matter become each individual one of these things, and how is the concrete whole both matter and form?For answers to these questions see Aristot. Met. 7.8, 13-14; Aristot. Met. 12.6-10; Aristot. Met. 13.10.

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(8.) Further, the following difficulty might be raised about the first principles. If they are one in kind, none of them will be one in number, not even the Idea of Unity or of Being. And how can there be knowledge unless there is some universal term?If the principles are one in kind only, particular things cannot be referred to the same principle but only to like principles; i.e., there will be no universal terms, without which there can be no knowledge.

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On the other hand if they are numerically one, and each of the principles is one, and not, as in the case of sensible things, different in different instances (e.g. since a given syllable is always the same in kind, its first principles are always the same in kind, but only in kind, since they are essentially different in number)—if the first principles are one, not in this sense, but numerically, there will be nothing else apart from the elements; for numerically one and individual are identical in meaning. This is what we mean by individual: the numerically one; but by universal we mean what is predicable of individuals.

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Hence just as, if the elements of languageOr letters of the alphabet. Cf. Aristot. Met. 1.9.36n. were limited in number, the whole of literature would be no more than those elements—that is, if there were not two nor more than two of the same <so it would be in the case of existing things and their principles>.For the answer to the problem see Aristot. Met. 12.4-5, Aristot. Met. 13.10.

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(ix.) There is a difficulty, as serious as any, which has been left out of account both by present thinkers and by their predecessors: whether the first principles of perishable and imperishable things are the same or different. For if they are the same, how is it that some things are perishable and others imperishable, and for what cause?

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The school of Hesiod, and all the cosmologists, considered only what was convincing to themselves, and gave no consideration to us. For they make the first principles Gods or generated from Gods, and say that whatever did not taste of the nectar and ambrosia became mortal—clearly using these terms in a sense significant to themselves;

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but as regards the actual applications of these causes their statements are beyond our comprehension. For if it is for pleasure that the Gods partake of them, the nectar and ambrosia are in no sense causes of their existence; but if it is to support life, how can Gods who require nourishment be eternal?

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However, it is not worth while to consider seriously the subtleties of mythologists; we must ascertain by cross-examining those who offer demonstration of their statements why exactly things which are derived from the same principles are some of an eternal nature and some perishable. And since these thinkers state no reason for this view, and it is unreasonable that things should be so, obviously the causes and principles of things cannot be the same.

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Even the thinker who might be supposed to speak most consistently, Empedocles, is in the same case; for he posits Strife as a kind of principle which is the cause of destruction, but none the less Strife would seem to produce everything except the One; for everything except GodThe expressions the One and God refer to Empedocles’ Sphere: the universe as ordered and united by Love. Cf. Empedocles, Fr. 26-29 (Diels). proceeds from it.

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At any rate he says

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From which grew all that was and is and shall be

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In time to come: the trees, and men and women,

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The beasts and birds and water-nurtured fish,

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And the long-living Gods.Empedocles, Fr. 21. 9-12.

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And it is obvious even apart from this; for if there had not been Strife in things, all things would have been one, he says; for when they came together then Strife came to stand outermost. Empedocles, Fr. 36. 7. Hence it follows on his theory that God, the most blessed being, is less wise than the others, since He does not know all the elements; for He has no Strife in Him, and knowledge is of like by like:

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By earth (he says) we earth perceive, by water water,

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By air bright air, by fire consuming fire,

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Love too by love, and strife by grievous strife.Empedocles, Fr. 109.

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But—and this is the point from which we started—thus much is clear: that it follows on his theory that Strife is no more the cause of destruction than it is of Being. Nor, similarly, is Love the cause of Being; for in combining things into one it destroys everything else.Cf. Aristot. Met. 1.4.6.

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Moreover, of the actual process of change he gives no explanation, except that it is so by nature:

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But when Strife waxing great among the membersi.e., of the Sphere.

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Sprang up to honor as the time came round

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Appointed them in turn by a mighty oath,Empedocles, Fr. 30.

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as though change were a necessity; but he exhibits no cause for the necessity.

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However, thus much of his theory is consistent: he does not represent some things to be perishable and others imperishable, but makes everything perishable except the elements. But the difficulty now being stated is why some things are perishable and others not, assuming that they are derived from the same principles.

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The foregoing remarks may suffice to show that the principles cannot be the same.

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If however they are different, one difficulty is whether they too are to be regarded as imperishable or as perishable. For if they are perishable, it is clearly necessary that they too must be derived from something else, since everything passes upon dissolution into that from which it is derived. Hence it follows that there are other principles prior to the first principles;

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but this is impossible, whether the series stops or proceeds to infinity. And further, how can perishable things exist if their principles are abolished? On the other hand if the principles are imperishable, why should some imperishable principles produce perishable things, and others imperishable things? This is not reasonable; either it is impossible or it requires much explanation.

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Further, no one has so much as attempted to maintain different principles; they maintain the same principles for everything. But they swallow down the difficulty which we raised firsti.e., whether all things have the same principles. as though they took it to be trifling.For Aristotle’s views about the principles of perishable and imperishable things see Aristot. Met. 7.7-10, Aristot. Met. 12.1-7.

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But the hardest question of all to investigate and also the most important with a view to the discovery of the truth, is whether after all Being and Unity are substances of existing things, and each of them is nothing else than Being and Unity respectively, or whether we should inquire what exactly Being and Unity are, there being some other nature underlying them.

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Some take the former, others the latter view of the nature of Being and Unity. Plato and the Pythagoreans hold that neither Being nor Unity is anything else than itself, and that this is their nature, their essence being simply Being and Unity.

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But the physicists, e.g. Empedocles, explain what Unity is by reducing it to something, as it were, more intelligible—or it would seem that by Love Empedocles means Unity; at any rate Love is the cause of Unity in all things. Others identify fire and others air with this Unity and Being of which things consist and from which they have been generated.

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Those who posit more numerous elements also hold the same view; for they too must identify Unity and Being with all the principles which they recognize. And it follows that unless one assumes Unity and Being to be substance in some sense, no other universal term can be substance; for Unity and Being are the most universal of all terms,

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and if there is no absolute Unity or absolute Being, no other concept can well exist apart from the so-called particulars. Further, if Unity is not substance, clearly number cannot be a separate characteristic of things; for number is units, and the unit is simply a particular kind of one.

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On the other hand, if there is absolute Unity and Being, their substance must be Unity and Being; for no other term is predicated universally of Unity and Being, but only these terms themselves. Again, if there is to be absolute Being and absolute Unity, it is very hard to see how there can be anything else besides these; I mean, how things can be more than one.

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For that which is other than what is, is not; and so by Parmenides’ argumentBy τὸ ὄν Parmenides meant what is, i.e. the real universe, which he proved to be one thing because anything else must be what is not, or non-existent. The Platonists meant by it being in the abstract. Aristotle ignores this distinction. it must follow that all things are one, i.e. Being. In either case there is a difficulty; for whether Unity is not a substance or whether there is absolute Unity, number cannot be a substance.

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It has already been stated why this is so if Unity is not a substance; and if it is, there is the same difficulty as about Being. For whence, if not from the absolute One or Unity, can there be another one? It must be not-one; but all things are either one, or many of which each is one. Further, if absolute Unity is indivisible, by Zeno’s axiom it will be nothing.

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For that which neither when added makes a thing greater nor when subtracted makes it smaller is not an existent thing, he saysCf. Zeno, Fr. 2, and see Burnet, E.G.P. sects. 157 ff.; clearly assuming that what exists is spatial magnitude. And if it is a spatial magnitude it is corporeal, since the corporeal exists in all dimensions, whereas the other magnitudes, the plane or line, when added to a thing in one way will increase it, but when added in another will not; and the point or unit will not increase a thing in any way whatever.

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But since Zeno’s view is unsound, and it is possible for a thing to be indivisible in such a way that it can be defended even against his argument (for such a thinge.g., a point is indivisible and has no magnitude, yet added to other points it increases their number. when added will increase a thing in number though not in size)—still how can a magnitude be composed of one or more such indivisible things? It is like saying that the line is composed of points.

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Moreover, even if one supposes the case to be such that number is generated, as some say, from the One itself and from something else which is not one, we must none the less inquire why and how it is that the thing generated will be at one time number and at another magnitude, if the not-one was inequality and the same principle in both cases.The reference is to the Platonists. Cf. Aristot. Met. 14.1.5, 6; Aristot. Met. 14.2.13, 14. For it is not clear how magnitude can be generated either from One and this principle, or from a number and this principle.For the answer to this problem see Aristot. Met. 7.16.3, 4; Aristot. Met. 10.2; and cf. Aristot. Met. 13.8.

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(13.) Out of this arises the question whether numbers, bodies, planes and points are substances or not. If not, the question of what Being is, what the substances of things are, baffles us; for modifications and motions and relations and dispositions and ratios do not seem to indicate the substance of anything; they are all predicated of a substrate, and none of them is a definite thing.

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As for those things which might be especially supposed to indicate substance—water, earth, fire and air, of which composite bodies are composed— their heat and cold and the like are modifications, not substances; and it is only the body which undergoes these modifications that persists as something real and a kind of substance.

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Again, the body is less truly substance than the plane, and the plane than the line, and the line than the unit or point; for it is by these that the body is defined, and it seems that they are possible without the body, but that the body cannot exist without them.

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This is why the vulgar and the earlier thinkers supposed that substance and Being are Body, and everything else the modifications of Body; and hence also that the first principles of bodies are the first principles of existing things; whereas later thinkers with a greater reputation for wisdom supposed that substance and Being are numbers.

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As we have said, then, if these things are not substance, there is no substance or Being at all; for the attributes of these things surely have no right to be called existent things. On the other hand, if it be agreed that lines and points are more truly substance than bodies are, yet unless we can see to what kind of bodies they belong (for they cannot be in sensible bodies) there will still be no substance.

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Further, it is apparent that all these lines are divisions of Body, either in breadth or in depth or in length. Moreover every kind of shape is equally present in a solid, so that if Hermes is not in the stone,Apparently a proverbial expression. neither is the half-cube in the cube as a determinate shape.

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Hence neither is the plane; for if any kind of plane were in it, so would that plane be which defines the half-cube. The same argument applies to the line and to the point or unit. Hence however true it may be that body is substance, if planes, lines and points are more truly substance than Body is, and these are not substance in any sense, the question of what Being is and what is the substance of things baffles us.

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Because, in addition to the above arguments, absurd results follow from a consideration of generation and destruction; for it seems that if substance, not having existed before, now exists, or having existed before, subsequently does not exist it suffers these changes in the process of generation and destruction. But points, lines and planes, although they exist at one time and at another do not, cannot be in process of being either generated or destroyed;

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for whenever bodies are joined or divided, at one time, when they are joined one surface is instantaneously produced, and at another, when they are divided, two. Thus when the bodies are combined the surface does not exist but has perished; and when they are divided, surfaces exist which did not exist before. (The indivisible point is of course never divided into two.) And if they are generated and destroyed, from what are they generated?

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It is very much the same with the present moment in time. This too cannot be generated and destroyed; but nevertheless it seems always to be different, not being a substance. And obviously it is the same with points, lines and planes, for the argument is the same; they are all similarly either limits or divisions.For arguments against the substantiality of numbers and mathematical objects see Aristot. Met. 13.1-3, 6-9; Aristot. Met. 14.1-3, 5, 6.

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In general one might wonder why we should seek for other entities apart from sensible things and the Intermediates:Cf. Aristot. Met. 3.2.20ff.. e.g., for the Forms which we Platonists assume.

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If it is for the reason that the objects of mathematics, while differing from the things in our world in another respect, resemble them in being a plurality of objects similar in form, so that their principles cannot be numerically determined (just as the principles of all language in this world of ours are determinate not in number but in kind—unless one takes such and such a particular syllable or sound, for the principles of these are determinate in number too—

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and similarly with the Intermediates, for in their case too there is an infinity of objects similar in form), then if there is not another set of objects apart from sensible and mathematical objects, such as the Forms are said to be, there will be no substance which is one both in kind and in number, nor will the principles of things be determinate in number, but in kind only.

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Thus if this is necessarily so, it is necessary for this reason to posit the Forms also. For even if their exponents do not articulate their theory properly, still this is what they are trying to express, and it must be that they maintain the Forms on the ground that each of them is a substance, and none of them exists by accident.

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On the other hand, if we are to assume that the Forms exist, and that the first principles are one in number but not in kind, we have already statedAristot. Met. 3.4.9, 10. the impossible consequences which must follow.This problem is not stated in ch. 1., but is akin to problems 5. and 8., which see.

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(12.) Closely connected with these questions is the problem whether the elements exist potentially or in some other sense.

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If in some other sense, there will be something else prior to the first principles. For the potentiality is prior to the actual cause, and the potential need not necessarily always become actual. On the other hand, if the elements exist potentially, it is possible for nothing to exist; for even that which does not yet exist is capable of existing. That which does not exist may come to be, but nothing which cannot exist comes to be.For the relation of potentiality to actuality see Aristot. Met. 9.1-9. The second point raised in this connection in ch. 1 is not discussed here; for actuality and motion see Aristot. Met. 12.6, 7.

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(xi.) Besides the foregoing problems about the first principles we must also raise the question whether they are universal or such as we describe the particulars to be. For if they are universal, there will be no substances; for no common term denotes an individual thing, but a type; and substance is an individual thing.

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But if the common predicate be hypostatized as an individual thing, Socrates will be several beings: himself, and Man, and Animal—that is, if each predicate denotes one particular thing.

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These then are the consequences if the principles are universal. If on the other hand they are not universal but like particulars, they will not be knowable; for the knowledge of everything is universal. Hence there will have to be other universally predicated principles prior to the first principles, if there is to be any knowledge of them.For the answer to this problem see Aristot. Met. 7.13-15, Aristot. Met. 13.10.

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There is a science which studies Being qua Being, and the properties inherent in it in virtue of its own nature. This science is not the same as any of the so-called particular sciences, for none of the others contemplates Being generally qua Being; they divide off some portion of it and study the attribute of this portion, as do for example the mathematical sciences.

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But since it is for the first principles and the most ultimate causes that we are searching, clearly they must belong to something in virtue of its own nature. Hence if these principles were investigated by those also who investigated the elements of existing things, the elements must be elements of Being not incidentally, but qua Being. Therefore it is of Being qua Being that we too must grasp the first causes.

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The term being is used in various senses, but with reference to one central idea and one definite characteristic, and not as merely a common epithet. Thus as the term healthy always relates to health (either as preserving it or as producing it or as indicating it or as receptive of it),

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and as medical relates to the art of medicine (either as possessing it or as naturally adapted for it or as being a function of medicine)—and we shall find other terms used similarly to these—

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so being is used in various senses, but always with reference to one principle. For some things are said to be because they are substances; others because they are modifications of substance; others because they are a process towards substance, or destructions or privations or qualities of substance, or productive or generative of substance or of terms relating to substance, or negations of certain of these terms or of substance. (Hence we even say that not-being is not-being.)

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And so, just as there is one science of all healthy things, so it is true of everything else. For it is not only in the case of terms which express one common notion that the investigation belongs to one science, but also in the case of terms which relate to one particular characteristic; for the latter too, in a sense, express one common notion. Clearly then the study of things which are, qua being, also belongs to one science.

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Now in every case knowledge is principally concerned with that which is primary, i.e. that upon which all other things depend, and from which they get their names. If, then, substance is this primary thing, it is of substances that the philosopher must grasp the first principles and causes.

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Now of every single class of things, as there is one perception, so there is one science: e.g., grammar, which is one science, studies all articulate sounds.

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Hence the study of all the species of Being qua Being belongs to a science which is generically one, and the study of the several species of Being belongs to the specific parts of that science.

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Now if Being and Unity are the same, i.e. a single nature, in the sense that they are associated as principle and cause are, and not as being denoted by the same definition (although it makes no difference but rather helps our argument if we understand them in the same sense),

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since one man and man and existent man and man are the same thing, i.e. the duplication in the statement he is a man and an existent man gives no fresh meaning (clearly the concepts of humanity and existence are not dissociated in respect of either coming to be or ceasing to be), and similarly in the case of the term one, so that obviously the additional term in these phrases has the same significance, and Unity is nothing distinct from Being;

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and further if the substance of each thing is one in no accidental sense, and similarly is of its very nature something which is—then there are just as many species of Being as of Unity. And to study the essence of these species (I mean, e.g., the study of Same and Other and all the other similar concepts—

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roughly speaking all the contraries are reducible to this first principle; but we may consider that they have been sufficiently studied in the Selection of ContrariesIt is uncertain to what treatise Aristotle refers; in any case it is not extant.) is the province of a science which is generically one.

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And there are just as many divisions of philosophy as there are kinds of substance; so that there must be among them a First Philosophy and one which follows upon it.

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For Being and Unity at once entail genera, and so the sciences will correspond to these genera. The term philosopher is like the term mathematician in its uses; for mathematics too has divisions—there is a primary and a secondary science, and others successively, in the realm of mathematics.

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Now since it is the province of one science to study opposites, and the opposite of unity is plurality, and it is the province of one science to study the negation and privation of Unity, because in both cases we are studying Unity, to which the negation (or privation) refers, stated either in the simple form that Unity is not present, or in the form that it is not present in a particular class; in the latter case Unity is modified by the differentia, apart from the content of the negation (for the negation of Unity is its absence); but in privation there is a substrate of which the privation is predicated.—

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The opposite of Unity, then, is Plurality; and so the opposites of the above-mentioned concepts—Otherness, Dissimilarity, Inequality and everything else which is derived from these or from Plurality or Unity— fall under the cognizance of the aforesaid science. And one of them is Oppositeness; for this is a form of Difference, and Difference is a form of Otherness.

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Hence since the term one is used in various senses, so too will these terms be used; yet it pertains to one science to take cognizance of them all. For terms fall under different sciences, not if they are used in various senses, but if their definitions are neither identical nor referable to a common notion.

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And since everything is referred to that which is primary, e.g. all things which are called one are referred to the primary One, we must admit that this is also true of Identity and Otherness and the Contraries. Thus we must first distinguish all the senses in which each term is used, and then attribute them to the primary in the case of each predicate, and see how they are related to it; for some will derive their name from possessing and others from producing it, and others for similar reasons.

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Thus clearly it pertains to one science to give an account both of these concepts and of substance (this was one of the questions raised in the DifficultiesSee Aristot. Met. 3.1.8-10, Aristot. Met. 3.2.18, 19.), and it is the function of the philosopher to be able to study all subjects.

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If this is not so, who is it who in will investigate whether Socrates and Socrates seated are the same thing; or whether one thing has one contrary, or what the contrary is, or how many meanings it has?Cf. Aristot. Met. 10.4. and similarly with all other such questions.

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Thus since these are the essential modifications of Unity qua Unity and of Being qua Being, and not qua numbers or lines or fire, clearly it a pertains to that sciencei.e., Philosophy or Metaphysics. to discover both the essence and the attributes of these concepts.

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And those who investigate them err, not in being unphilosophical, but because the substance, of which they have no real knowledge, is prior. For just as number qua number has its peculiar modifications, e.g. oddness and evenness, commensurability and equality, excess and defect, and these things are inherent in numbers both considered independently and in relation to other numbers; and as similarly other peculiar modifications are inherent in the solid and the immovable and the moving and the weightless and that which has weight; so Being qua Being has certain peculiar modifications, and it is about these that it is the philosopher’s function to discover the truth. And here is evidence of this fact.

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Dialecticians and sophists wear the same appearance as the philosopher, for sophistry is Wisdom in appearance only, and dialecticians discuss all subjects, and Being is a subject common to them all; but clearly they discuss these concepts because they appertain to philosophy.

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For sophistry and dialectic are concerned with the same class of subjects as philosophy, but philosophy differs from the former in the nature of its capability and from the latter in its outlook on life. Dialectic treats as an exercise what philosophy tries to understand, and sophistry seems to be philosophy; but is not.

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Further, the second column of contraries is privative, and everything is reducible to Being and Not being, and Unity and Plurality; e.g. Rest falls under Unity and Motion under Plurality. And nearly everyone agrees that substance and existing things are composed of contraries; at any rate all speak of the first principles as contraries—

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some as Odd and Even,The Pythagoreans. some as Hot and Cold,Perhaps Parmenides. some as Limit and Unlimited,The Platonists. some as Love and Strife.Empedocles. And it is apparent that all other things also are reducible to Unity and Plurality (we may assume this reduction); and the principles adduced by other thinkers fall entirely under these as genera.

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It is clear, then, from these considerations also, that it pertains to a single science to study Being qua Being; for all things are either contraries or derived from contraries, and the first principles of the contraries are Unity and Plurality. And these belong to one science, whether they have reference to one common notion or not. Probably the truth is that they have not; but nevertheless even if the term one is used in various senses, the others will be related to the primary sense (and similarly with the contraries)—

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even if Being or Unity is not a universal and the same in all cases, or is not separable from particulars (as it presumably is not; the unity is in some cases one of reference and in others one of succession). For this very reason it is not the function of the geometrician to inquire what is Contrariety or Completeness or Being or Unity or Identity or Otherness, but to proceed from the assumption of them.

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Clearly, then, it pertains to one science to study Being qua Being, and the attributes inherent in it qua Being; and the same science investigates, besides the concepts mentioned above, Priority and Posteriority, Genus and Species, Whole and Part, and all other such concepts.

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We must pronounce whether it pertains to the same science to study both the so-called axioms in mathematics and substance, or to different sciences. It is obvious that the investigation of these axioms too pertains to one science, namely the science of the philosopher; for they apply to all existing things, and not to a particular class separate and distinct from the rest. Moreover all thinkers employ them—because they are axioms of Being qua Being, and every genus possesses Being—

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but employ them only in so far as their purposes require; i.e., so far as the genus extends about which they are carrying out their proofs. Hence since these axioms apply to all things qua Being (for this is what is common to them), it is the function of him who studies Being qua Being to investigate them as well.

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For this reason no one who is pursuing a particular inquiry—neither a geometrician nor an arithmetician—attempts to state whether they are true or false; but some of the physicists did so, quite naturally; for they alone professed to investigate nature as a whole, and Being.

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But inasmuch as there is a more ultimate type of thinker than the natural philosopher (for nature is only a genus of Being), the investigation of these axioms too will belong to the universal thinker who studies the primary reality. Natural philosophy is a kind of Wisdom, but not the primary kind.

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As for the attempts of some of those who discuss how the truth should be received, they are due to lack of training in logic; for they should understand these things before they approach their task, and not investigate while they are still learning.

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Clearly then it is the function of the philosopher, i.e. the student of the whole of reality in its essential nature, to investigate also the principles of syllogistic reasoning. And it is proper for him who best understands each class of subject to be able to state the most certain principles of that subject; so that he who understands the modes of Being qua Being should be able to state the most certain principles of all things.

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Now this person is the philosopher, and the most certain principle of all is that about which one cannot be mistaken; for such a principle must be both the most familiar (for it is about the unfamiliar that errors are always made), and not based on hypothesis.

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For the principle which the student of any form of Being must grasp is no hypothesis; and that which a man must know if he knows anything he must bring with him to his task.

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Clearly, then, it is a principle of this kind that is the most certain of all principles. Let us next state what this principle is.

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It is impossible for the same attribute at once to belong and not to belong to the same thing and in the same relation; and we must add any further qualifications that may be necessary to meet logical objections. This is the most certain of all principles, since it possesses the required definition;

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for it is impossible for anyone to suppose that the same thing is and is not, as some imagine that Heraclitus saysFor examples of Heraclitus’s paradoxes cf. Heraclitus Fr. 36, 57, 59 (Bywater); and for their meaning see Burnet, E.G.P. 80.—for what a man says does not necessarily represent what he believes.

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And if it is impossible for contrary attributes to belong at the same time to the same subject (the usual qualifications must be added to this premiss also), and an opinion which contradicts another is contrary to it, then clearly it is impossible for the same man to suppose at the same time that the same thing is and is not; for the man who made this error would entertain two contrary opinions at the same time.

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Hence all men who are demonstrating anything refer back to this as an ultimate belief; for it is by nature the starting-point of all the other axioms as well.

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There are some, however, as we have said, who both state themselves that the same thing can be and not be, and say that it is possible to hold this view. Many even of the physicists adopt this theory. But we have just assumed that it is impossible at once to be and not to be, and by this means we have proved that this is the most certain of all principles.

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Some, indeed, demand to have the law proved, but this is because they lack educationsc., in logic.; for it shows lack of education not to know of what we should require proof, and of what we should not. For it is quite impossible that everything should have a proof; the process would go on to infinity, so that even so there would be no proof.Every proof is based upon some hypothesis, to prove which another hypothesis must be assumed, and so on ad infinitum.

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If on the other hand there are some things of which no proof need be sought, they cannot say what principle they think to be more self-evident. Even in the case of this law, however, we can demonstrate the impossibility by refutation, if only our opponent makes some statement. If he makes none, it is absurd to seek for an argument against one who has no arguments of his own about anything, in so far as he has none; for such a person, in so far as he is such, is really no better than a vegetable.

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And I say that proof by refutation differs from simple proof in that he who attempts to prove might seem to beg the fundamental question, whereas if the discussion is provoked thus by someone else, refutation and not proof will result.

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The starting-point for all such discussions is not the claim that he should state that something is or is not so (because this might be supposed to be a begging of the question), but that he should say something significant both to himself and to another (this is essential if any argument is to follow; for otherwise such a person cannot reason either with himself or with another);

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and if this is granted, demonstration will be possible, for there will be something already defined. But the person responsible is not he who demonstrates but he who acquiesces; for though he disowns reason he acquiesces to reason. Moreover, he who makes such an admission as this has admitted the truth of something apart from demonstration [so that not everything will be so and not so].

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Thus in the first place it is obvious that this at any rate is true: that the term to be or not to be has a definite meaning; so that not everything can be so and not so. Again, if man has one meaning, let this be two-footed animal.

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By has one meaning I mean this: if X means man, then if anything is a man, its humanity will consist in being X. And it makes no difference even if it be said that man has several meanings, provided that they are limited in number; for one could assign a different name to each formula.

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For instance, it might be said that man has not one meaning but several, one of which has the formula two-footed animal, and there might be many other formulae as well, if they were limited in number; for a particular name could be assigned to each for formula.

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If on the other hand it be said that man has an infinite number of meanings, obviously there can be no discourse; for not to have one meaning is to have no meaning, and if words have no meaning there is an end of discourse with others, and even, strictly speaking, with oneself; because it is impossible to think of anything if we do not think of one thing; and even if this were possible, one name might be assigned to that of which we think.

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Now let this name, as we said at the beginning, have a meaning; and let it have one meaning. Now it is impossible that being man should have the same meaning as not being man, that is, if man is not merely predicable of one subject but has one meaning

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(for we do not identify having one meaning with being predicable of one subject, since in this case cultured and white and man would have one meaning, and so all things would be one; for they would all have the same meaning). And it will be impossible for the same thing to be and not to be, except by equivocation, as e.g. one whom we call man others might call not-man;

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but the problem is whether the same thing can at once be and not be man, not in name , but in fact . If man and not-man have not different meanings, clearly not being a man will mean nothing different from being a man; and so being a man will be not being a man; they will be one.

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For to be one means, as in the case of garment and coat, that the formula is one. And if being man and being not-man are to be one, they will have the same meaning; but it has been proved above that they have different meanings. If then anything can be truly said to be man, it must be two-footed animal; for this is what man was intended to mean.

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And if this is necessarily so, it is impossible that at the same time the same thing should not be two-footed animal. For to be necessarily so means this: that it is impossible not to be so. Thus it cannot be true to say at the same time that the same thing is and is not man.

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And the same argument holds also in the case of not being man; because being man and being not-man have different meanings if being white and being man have different meanings (for the opposition is much stronger in the former case so as to produce different meanings).

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And if we are told that white too means one and the same thing,i.e. the same as man. we shall say again just what we said before,Aristot. Met. 4.4.12. that in that case all things, and not merely the opposites, will be one. But if this is impossible, what we have stated follows; that is, if our opponent answers our question; but if when asked the simple question he includes in his answer the negations, he is not answering our question.

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There is nothing to prevent the same thing from being man and white and a multitude of other things; but nevertheless when asked whether it is true to say that X is man, or not, one should return an answer that means one thing, and not add that X is white and large. It is indeed impossible to enumerate all the infinity of accidents; and so let him enumerate either all or none.

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Similarly therefore, even if the same thing is ten thousand times man and not-man, one should not include in one’s answer to the question whether it is man that it is at the same time also not-man, unless one is also bound to include in one’s answer all the other accidental things that the subject is or is not. And if one does this, he is not arguing properly.

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In general those who talk like this do away with substance and essence,

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for they are compelled to assert that all things are accidents, and that there is no such thing as being essentially man or animal. For if there is to be such a thing as being essentially man, this will not be being not-man nor not-being man (and yet these are negations of it); for it was intended to have one meaning, i.e. the substance of something.

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But to denote a substance means that the essence is that and nothing else; and if for it being essentially man is the same as either being essentially not-man or essentially not-being man, the essence will be something else.

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Thus they are compelled to say that nothing can have such a definition as this, but that all things are accidental; for this is the distinction between substance and accident: white is an accident of man, because although he is white, he is not white in essence.

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And since the accidental always implies a predication about some subject, if all statements are accidental, there will be nothing primary about which they are made; so the predication must proceed to infinity. But this is impossible, for not even more than two accidents can be combined in predication. An accident cannot be an accident of an accident unless both are accidents of the same thing.

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I mean, e.g., that white is cultured and cultured white merely because both are accidents of a man. But it is not in this sense—that both terms are accidents of something else—that Socrates is cultured. Therefore since some accidents are predicated in the latter and some in the former sense, such as are predicated in the way that white is of Socrates cannot be an infinite series in the upper direction; e.g. there cannot be another accident of white Socrates, for the sum of these predications does not make a single statement.

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Nor can white have a further accident, such as cultured; for the former is no more an accident of the latter than vice versa; and besides we have distinguished that although some predicates are accidental in this sense, others are accidental in the sense that cultured is to Socrates; and whereas in the former case the accident is an accident of an accident, it is not so in the latter; and thus not all predications will be of accidents.

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Therefore even so there will be something which denotes substance. And if this is so, we have proved that contradictory statements cannot be predicated at the same time.

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Again, if all contradictory predications of the same subject at the same time are true, clearly all things will be one.

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For if it is equally possible either to affirm or deny anything of anything, the same thing will be a trireme and a wall and a man; which is what necessarily follows for those who hold the theory of Protagoras.i.e., that all appearances and opinions are true. For if anyone thinks that a man is not a trireme, he is clearly not a trireme; and so he also is a trireme if the contradictory statement is true.

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And the result is the dictum of Anaxagoras, all things mixed together Fr. 1 (Diels). ; so that nothing truly exists. It seems, then, that they are speaking of the Indeterminate; and while they think that they are speaking of what exists, they are really speaking of what does not; for the Indeterminate is that which exists potentially but not actually.

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But indeed they must admit the affirmation or negation of any predicate of any subject, for it is absurd that in the case of each term its own negation should be true, and the negation of some other term which is not true of it should not be true. I mean, e.g., that if it is true to say that a man is not a man, it is obviously also true to say that he is or is not a trireme.

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Then if the affirmation is true, so must the negation be true; but if the affirmation is not true the negation will be even truer than the negation of the original term itself. Therefore if the latter negation is true, the negation of trireme will also be true; and if this is true, the affirmation will be true too.

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And not only does this follow for those who hold this theory, but also that it is not necessary either to affirm or to deny a statement.

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For if it is true that X is both man and not-man, clearly he will be neither man nor not-man; for to the two statements there correspond two negations, and if the former is taken as a single statement compounded out of two, the latter is also a single statement and opposite to it.

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Again, either this applies to all terms, and the same thing is both white and not-white, and existent and non-existent, and similarly with all other assertions and negations; or it does not apply to all, but only to some and not to others.

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And if it does not apply to all, the exceptions will be admittedi.e., it will be admitted that in certain cases where an attribute is true of a subject, the negation is not true; and therefore some propositions are indisputable.; but if it does apply to all, again either (a) the negation will be true wherever the affirmation is true, and the affirmation will be true wherever the negation is true, or (d) the negation will be true wherever the assertion is true, but the assertion will not always be true where the negation is true.

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And in the latter case there will be something which definitely is not, and this will be a certain belief; and if that it is not is certain and knowable, the opposite assertion will be still more knowable. But if what is denied can be equally truly asserted, it must be either true or false to state the predicates separately and say, e.g., that a thing is white, and again that it is not-white.

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And if it is not-true to state them separately, our opponent does not say what he professes to say, and nothing exists; and how can that which does not exist speak or walk?If our opponent holds that you can only say A is B and not B, (1) he contradicts every statement that he makes; (2) he must say that what exists does not exist. Therefore nothing exists, and so he himself does not exist; but how can he speak or walk if he does not exist? And again all things will be one, as we said before,Aristot. Met. 4.4.27. and the same thing will be man and God and trireme and the negations of these terms.

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For if it is equally possible to assert or deny anything of anything, one thing will not differ from another; for if anything does differ, it will be true and unique. And similarly even if it is possible to make a true statement while separating the predicates, what we have stated follows. Moreover it follows that all statements would be true and all false; and that our opponent himself admits that what he says is false. Besides, it is obvious that discussion with him is pointless, because he makes no real statement.

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For he says neither yes nor no, but yes and no; and again he denies both of these and says neither yes nor no; otherwise there would be already some definite statement.

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Again, if when the assertion is true the negation is false, and when the latter is true the affirmation is false, it will be impossible to assert and deny with truth the same thing at the same time.

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But perhaps it will be said that this is the point at issue.

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Again, is the man wrong who supposes that a thing is so or not so, and he who supposes both right? If he is right, what is the meaning of saying that such is the nature of reality?If everything is both so and not so, nothing has any definite nature. And if he is not right, but is more right than the holder of the first view, reality will at once have a definite nature, and this will be true, and not at the same time not-true.

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And if all men are equally right and wrong, an exponent of this view can neither speak nor mean anything, since at the same time he says both yes and no. And if he forms no judgement, but thinks and thinks not indifferently, what difference will there be between him and the vegetables?

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Hence it is quite evident that no one, either of those who profess this theory or of any other school, is really in this position.

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Otherwise, why does a man walk to Megara and not stay at home, when he thinks he ought to make the journey? Why does he not walk early one morning into a well or ravine, if he comes to it, instead of clearly guarding against doing so, thus showing that he does not think that it is equally good and not good to fall in? Obviously then he judges that the one course is better and the other worse.

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And if this is so, he must judge that one thing is man and another not man, and that one thing is sweet and another not sweet. For when, thinking that it is desirable to drink water and see a man, he goes to look for them, he does not look for and judge all things indifferently; and yet he should, if the same thing were equally man and not-man.

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But as we have said, there is no one who does not evidently avoid some things and not others. Hence, as it seems, all men form unqualified judgements, if not about all things, at least about what is better or worse.

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And if they do this by guesswork and without knowledge, they should be all the more eager for truth; just as a sick man should be more eager for health than a healthy man; for indeed the man who guesses, as contrasted with him who knows, is not in a healthy relation to the truth.

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Again, however much things may be so and not so, yet differences of degree are inherent in the nature of things. For we should not say that 2 and 3 are equally even; nor are he who thinks that 4 is 5, and he who thinks it is 1000, equally wrong: hence if they are not equally wrong, the one is clearly less wrong, and so more right.

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If then that which has more the nature of something is nearer to that something, there will be some truth to which the more true is nearer. And even if there is not, still there is now something more certain and true, and we shall be freed from the undiluted doctrine which precludes any mental determination.

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From the same view proceeds the theory of Protagoras, and both alike must be either true or false. For if all opinions and appearances are true, everything must be at once true and false; for many people form judgements which are opposite to those of others, and imagine that those who do not think the same as themselves are wrong: hence the same thing must both be and not be.

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And if this is so, all opinions must be true; for those who are wrong and those who are right think contrarily to each other. So if reality is of this nature, everyone will be right.

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Clearly then both these theories proceed from the same mental outlook. But the method of approach is not the same for all cases; for some require persuasion and others compulsion.

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The ignorance of those who have formed this judgement through perplexity is easily remedied, because we are dealing not with the theory but with their mental outlook; but those who hold the theory for its own sake can only be cured by refuting the theory as expressed in their own speech and words.

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This view comes to those who are perplexed from their observation of sensible things. (1.) The belief that contradictions and contraries can be true at the same time comes to them from seeing the contraries generated from the same thing.

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Then if what is not cannot be generated, the thing must have existed before as both contraries equally—just as Anaxagoras saysCf. Aristot. Met. 4.4.28. that everything is mixed in everything; and also Democritus, for he too saysCf. Aristot. Met. 1.4.9. that Void and Plenum are present equally in any part, and yet the latter is , and the former is not.

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To those, then, who base their judgement on these considerations, we shall say that although in one sense their theory is correct, in another they are mistaken. For being has two meanings, so that there is a sense in which something can be generated from not-being, and a sense in which it cannot; and a sense in which the same thing can at once be and not be; but not in the same respect. For the same thing can be contraries at the same time potentially, but not actually.

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And further, we shall request them to conceive another kind also of substance of existing things, in which there is absolutely no motion or destruction or generation. And (2.) similarly the theory that there is truth in appearances has come to some people from an observation of sensible things.

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They think that the truth should not be judged by the number or fewness of its upholders; and they say that the same thing seems sweet to some who taste it, and bitter to others; so that if all men were diseased or all insane, except two or three who were healthy or sane, the latter would seem to be diseased or insane, and not the others.

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And further they say that many of the animals as well get from the same things impressions which are contrary to ours, and that the individual himself does not always think the same in matters of sense-perception. Thus it is uncertain which of these impressions are true or false; for one kind is no more true than another, but equally so. And hence Democritus saysCf. Ritter and Preller, 204. that either there is no truth or we cannot discover it.

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And in general it is because they suppose that thought is sense-perception, and sense-perception physical alteration, that they say that the impression given through sense-perception is necessarily true; for it is on these grounds that both Empedocles and Democritus and practically all the rest have become obsessed by such opinions as these.

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For Empedocles says that those who change their bodily condition change their thought:

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For according to that which is present to them doth thought increase in men.Empedocles Fr. 106.

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And in another passage he says:

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And as they change into a different nature, so it ever comes to them to think differently.Empedocles Fr. 108.

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And Parmenides too declares in the same way:

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For as each at any time hath the temperament of his many-jointed limbs, so thought comes to men. For for each and every man the substance of his limbs is that very thing which thinks; for thought is that which preponderates.Empedocles Fr. 16; quoted also (in a slightly different form; see critical notes) by Theophrastus, De Sensu 3.

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There is also recorded a saying of Anaxagoras to some of his disciples, that things would be for them as they judged them to be.

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And they say that in Homer too clearly held this view, because he made Hector,The only passage in our text of Homer to which this reference could apply isHom. Il. 23.698; but there the subject is Euryalus, not Hector. when he was stunned by the blow, lie with thoughts deranged—thus implying that even those who are out of their minds still think, although not the same thoughts. Clearly then, if both are kinds of thought, reality also will be both so and not so.

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It is along this path that the consequences are most difficult; for if those who have the clearest vision of such truth as is possible (and these are they who seek and love it most) hold such opinions and make these pronouncements about the truth, surely those who are trying to be philosophers may well despair; for the pursuit of truth will be chasing birds in the air. Cf. Leutsch and Schneidewin, Paroemiographi Graeci, 2.677.

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But the reason why these men hold this view is that although they studied the truth about reality, they supposed that reality is confined to sensible things, in which the nature of the Indeterminate, i.e. of Being in the sense which we have explained,Aristot. Met. 4.4.28. is abundantly present. (Thus their statements, though plausible, are not true;

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this form of the criticism is more suitable than that which EpicharmusFl. early 5th century; held views partly Pythagorean, partly Heraclitean. applied to Xenophanes.) And further, observing that all this indeterminate substance is in motion, and that no true predication can be made of that which changes, they supposed that it is impossible to make any true statement about that which is in all ways and entirely changeable.

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For it was from this supposition that there blossomed forth the most extreme view of those which we have mentioned, that of the professed followers of Heraclitus, and such as Cratylus held, who ended by thinking that one need not say anything, and only moved his finger; and who criticized Heraclitus for saying that one cannot enter the same river twice,Heraclitus Fr. 41 (Bywater). for he himself held that it cannot be done even once.

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But we shall reply to this theory also that although that which is changeable supplies them, when it changes, with some real ground for supposing that it is not, yet there is something debatable in this; for that which is shedding any quality retains something of that which is being shed, and something of that which is coming to be must already exist.

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And in general if a thing is ceasing to be, there will be something there which is ; and if a thing is coming to be, that from which it comes and by which it is generated must be ; and this cannot go on to infinity. But let us leave this line of argument and remark that quantitative and qualitative change are not the same.

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Let it be granted that there is nothing permanent in respect of quantity; but it is by the form that we recognize everything. And again those who hold the theory that we are attacking deserve censure in that they have maintained about the whole material universe what they have observed in the case of a mere minority of sensible things.

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For it is only the realm of sense around us which continues subject to destruction and generation, but this is a practically negligible part of the whole; so that it would have been fairer for them to acquit the former on the ground of the latter than to condemn the latter on account of the former.

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Further, we shall obviously say to these thinkers too the same as we said some time agoAristot. Met. 4.5.7.; for we must prove to them and convince them that there is a kind of nature that is not moved

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(and yet those who claim that things can at once be and not be are logically compelled to admit rather that all things are at rest than that they are in motion; for there is nothing for them to change into, since everything exists in everything). And as concerning reality, that not every appearance is real, we shall say, first, that indeed the perception, at least of the proper object of a sense, is not false, but the impression we get of it is not the same as the perception.

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And then we may fairly express surprise if our opponents raise the question whether magnitudes and colors are really such as they appear at a distance or close at hand, as they appear to the healthy or to the diseased; and whether heavy things are as they appear to the weak or to the strong; and whether truth is as it appears to the waking or to the sleeping.

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For clearly they do not really believe the latter alternative—at any rate no one, if in the night he thinks that he is at Athens whereas he is really in Africa, starts off to the Odeum.A concert-hall (used also for other purposes) built by Pericles. It lay to the south-east of the Acropolis. And again concerning the future (as indeed Plato saysPlat. Theaet. 171e, 178cff..) the opinion of the doctor and that of the layman are presumably not equally reliable, e.g. as to whether a man will get well or not.

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And again in the case of the senses themselves, our perception of a foreign object and of an object proper to a given sense, or of a kindred object and of an actual object of that sense itself, is not equally reliableAn object of taste is foreign to the sense of sight; a thing may look sweet without tasting sweet. Similarly although the senses of taste and smell (and therefore their objects) are kindred (Aristot. De Sensu 440b 29), in judging tastes the sense of taste is the more reliable.; but in the case of colors sight, and not taste, is authoritative, and in the case of flavor taste, and not sight. But not one of the senses ever asserts at the same time of the same object that it is so and not so.

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Nor even at another time does it make a conflicting statement about the quality, but only about that to which the quality belongs. I mean, e.g., that the same wine may seem, as the result of its own change or of that of one’s body, at one time sweet and at another not; but sweetness, such as it is when it exists, has never yet changed, and there is no mistake about it, and that which is to be sweet is necessarily of such a nature.

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Yet all these theories destroy the possibility of anything’s existing by necessity, inasmuch as they destroy the existence of its essence; for the necessary cannot be in one way and in another; and so if anything exists of necessity, it cannot be both so and not so.

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And in general, if only the sensible exists, without animate things there would be nothing; for there would be no sense-faculty.

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That there would be neither sensible qualities nor sensations is probably trueCf. Aristot. De Anima 425b 25-426b 8.(for these depend upon an effect produced in the percipient), but that the substrates which cause the sensation should not exist even apart from the sensation is impossible.

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For sensation is not of itself, but there is something else too besides the sensation, which must be prior to the sensation; because that which moves is by nature prior to that which is moved, and this is no less true if the terms are correlative.

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But there are some, both of those who really hold these convictions and of those who merely profess these views, who raise a difficulty; they inquire who is to judge of the healthy man, and in general who is to judge rightly in each particular case. But such questions are like wondering whether we are at any given moment asleep or awake;

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and all problems of this kind amount to the same thing. These people demand a reason for everything. They want a starting-point, and want to grasp it by demonstration; while it is obvious from their actions that they have no conviction. But their case is just what we have stated beforeAristot. Met. 4.4.2.; for they require a reason for things which have no reason, since the starting-point of a demonstration is not a matter of demonstration.

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The first class, then, may be readily convinced of this, because it is not hard to grasp. But those who look only for cogency in argument look for an impossibility, for they claim the right to contradict themselves, and lose no time in doing so.

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Yet if not everything is relative, but some things are self-existent, not every appearance will be true; for an appearance is an appearance to someone. And so he who says that all appearances are true makes everything relative.

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Hence those who demand something cogent in argument, and at the same time claim to make out a case, must guard themselves by saying that the appearance is true; not in itself, but for him to whom it appears, and at, the time when it appears, and in the way and manner in which it appears. And if they make out a case without this qualification, as a result they will soon contradict themselves;

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for it is possible in the case of the same man for a thing to appear honey to the sight, but not to the taste, and for things to appear different to the sight of each of his two eyes, if their sight is unequal. For to those who assert (for the reasons previously stated Aristot. Met. 4.5.7-17. ) that appearances are true, and that all things are therefore equally false and true, because they do not appear the same to all, nor always the same to the same person, but often have contrary appearances at the same time

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(since if one crosses the fingers touch says that an object is two, while sight says that it is only oneCf. Aristot. Problemata 958b 14, 959a 5, 965a 36.), we shall say but not to the same sense or to the same part of it in the same way and at the same time; so that with this qualification the appearance will be true. But perhaps it is for this reason that those who argue not from a sense of difficulty but for argument’s sake are compelled to say that the appearance is not true in itself, but true to the percipient;

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and, as we have said before, are compelled also to make everything relative and dependent upon opinion and sensation, so that nothing has happened or will happen unless someone has first formed an opinion about it; otherwise clearly all things would not be relative to opinion.

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Further, if a thing is one, it is relative to one thing or to something determinate. And if the same thing is both a half and an equal, yet the equal is not relative to the double.

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If to the thinking subject man and the object of thought are the same, man will be not the thinking subject but the object of thought; and if each thing is to be regarded as relative to the thinking subject, the thinking subject will be relative to an infinity of specifically different things.

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That the most certain of all beliefs is that opposite statements are not both true at the same time, and what follows for those who maintain that they are true, and why these thinkers maintain this, may be regarded as adequately stated. And since the contradiction of a statement cannot be true at the same time of the same thing, it is obvious that contraries cannot apply at the same time to the same thing.

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For in each pair of contraries one is a privation no less than it is a contrary—a privation of substance. And privation is the negation of a predicate to some defined genus. Therefore if it is impossible at the same time to affirm and deny a thing truly, it is also impossible for contraries to apply to a thing at the same time; either both must apply in a modified sense, or one in a modified sense and the other absolutely.

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Nor indeed can there be any intermediate between contrary statements, but of one thing we must either assert or deny one thing, whatever it may be. This will be plain if we first define truth and falsehood. To say that what is is not, or that what is not is, is false; but to say that what is is, and what is not is not, is true; and therefore also he who says that a thing is or is not will say either what is true or what is false.

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But neither what is nor what is not is said not to be or to be. Further, an intermediate between contraries will be intermediate either as grey is between black and white, or as neither man nor horse is between man and horse. If in the latter sense, it cannot change (for change is from not-good to good, or from good to not-good);

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but in fact it is clearly always changing; for change can only be into the opposite and the intermediate. And if it is a true intermediate, in this case too there would be a kind of change into white not from not-white; but in fact this is not seen.It is not qua grey (i.e. intermediate between white and black) that grey changes to white, but qua not-white (i.e. containing a certain proportion of black). Further, the understanding either affirms or denies every object of understanding or thought (as is clear from the definitionAristot. Met. 4.7.1.)

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whenever it is right or wrong. When, in asserting or denying, it combines the predicates in one way, it is right; when in the other, it is wrong.

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Again, unless it is maintained merely for argument’s sake, the intermediate must exist beside all contrary terms; so that one will say what is neither true nor false. And it will exist beside what is and what is not; so that there will be a form of change beside generation and destruction.

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Again, there will also be an intermediate in all classes in which the negation of a term implies the contrary assertion; e.g., among numbers there will be a number which is neither odd nor not-odd. But this is impossible, as is clear from the definition.What definition Aristotle had in mind we cannot tell; but it must have stated that every number is either even or odd.

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Again, there will be an infinite progression, and existing things will be not only half as many again, but even more.

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For again it will be possible to deny the intermediate in reference both to its assertion and to its negation, and the result will be somethingIf besides A and not-A there is an intermediate B, besides B and not-B there will be an intermediate C which is neither B nor not-B; and so on.; for its essence is something distinct.

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Again, when a man is asked whether a thing is white and says no, he has denied nothing except that it is <white>, and its not-being <white> is a negation.

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Now this view has occurred to certain people in just the same way as other paradoxes have also occurred; for when they cannot find a way out from eristic arguments, they submit to the argument and admit that the conclusion is true. Some, then, hold the theory for this kind of reason, and others because they require an explanation for everything. In dealing with all such persons the starting-point is from definition;

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and definition results from the necessity of their meaning something; because the formula, which their term implies, will be a definition.Cf. Aristot. Met. 4.4.5, 6. The doctrine of Heraclitus, which says that everything is and is not,Cf. Aristot. Met. 4.3.10. seems to make all things true; and that of AnaxagorasCf. Aristot. Met. 4.4.28. seems to imply an intermediate in contradiction, so that all things are false; for when things are mixed, the mixture is neither good nor not-good; and so no statement is true.

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It is obvious from this analysis that the one-sided and sweeping statements which some people make cannot be substantially true—some maintaining that nothing is true (for they say that there is no reason why the same rule should not apply to everything as applies to the commensurability of the diagonal of a squareA stock example of impossibility and falsity; see Index.), and some that everything is true.

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These theories are almost the same as that of Heraclitus. For the theory which says that all things are true and all false also makes each of these statements separately; so that if they are impossible in combination they are also impossible individually. And again obviously there are contrary statements, which cannot be true at the same time. Nor can they all be false, although from what we have said, this might seem more possible.

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But in opposing all such theories we must demand, as was said in our discussion above,Aristot. Met. 4.4.5. not that something should be or not be, but some significant statement; and so we must argue from a definition, having first grasped what falsehood or truth means. And if to assert what is true is nothing else than to deny what is false, everything cannot be false; for one part of the contradiction must be true.

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Further, if everything must be either asserted or denied, both parts cannot be false; for one and only one part of the contradiction is false. Indeed, the consequence follows which is notorious in the case of all such theories, that they destroy themselves;

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for he who says that everything is true makes the opposite theory true too, and therefore his own untrue (for the opposite theory says that his is not true); and he who says that everything is false makes himself a liar.

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And if they make exceptions, the one that the opposite theory alone is not true, and the other that his own theory alone is not false, it follows none the less that they postulate an infinite number of true and false statements. For the statement that the true statement is true is also true; and this will go on to infinity.

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Nor, as is obvious, are those right who say that all things are at rest; nor those who say that all things are in motion. For if all things are at rest, the same things will always be true and false, whereas this state of affairs is obviously subject to change; for the speaker himself once did not exist, and again he will not exist. And if all things are in motion, nothing will be true, so everything will be false; but this has been proved to be impossible.

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Again, it must be that which is that changes, for change is from something into something. And further, neither is it true that all things are at rest or in motion sometimes, but nothing continuously; for there is something The sphere of the fixed stars; cf. Aristot. Met. 12.6, 12.7.1, 12.8.18. which always moves that which is moved, and the prime mover is itself unmoved.Cf. Aristot. Met. 12.7.

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Beginningἀρχή means starting-point, principle, rule or ruler. means: (a) That part of a thing from which one may first move; eg., a line or a journey has one beginning here , and another at the opposite extremity. (b) The point from which each thing may best come into being; e.g., a course of study should sometimes be begun not from what is primary or from the starting-point of the subject, but from the point from which it is easiest to learn. (c) That thing as a result of whose presence something first comes into being; e.g., as the keel is the beginning of a ship, and the foundation that of a house, and as in the case of animals some thinkers suppose the heartThis was Aristotle’s own view,Aristot. De Gen. An. 738b 16. to be the beginning, others the brain,So Plato held,Plat. Tim. 44 d. and others something similar, whatever it may be. (d) That from which, although not present in it, a thing first comes into being, and that from which motion and change naturally first begin, as the child comes from the father and mother, and fighting from abuse. (e) That in accordance with whose deliberate choice that which is moved is moved, and that which is changed is changed; such as magistracies, authorities, monarchies and despotisms.

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(f) Arts are also called beginnings,As directing principles. especially the architectonic arts. (g) Again, beginning means the point from which a thing is first comprehensible, this too is called the beginning of the thing; e.g. the hypotheses of demonstrations. (Cause can have a similar number of different senses, for all causes are beginnings. )

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It is a common property, then, of all beginnings to be the first thing from which something either exists or comes into being or becomes known; and some beginnings are originally inherent in things, while others are not. Hence nature is a beginning, and so is element and understanding and choice and essence and final cause—for in many cases the Good and the Beautiful are the beginning both of knowledge and of motion.

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Cause means: (a) in one sense, that as the result of whose presence something comes into being—e.g. the bronze of a statue and the silver of a cup, and the classessc. of material—metal, wood, etc. which contain these; (b) in another sense, the form or pattern; that is, the essential formula and the classes which contain it—e.g. the ratio 2:1 and number in general is the cause of the octave—and the parts of the formula.

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(c) The source of the first beginning of change or rest; e.g. the man who plans is a cause, and the father is the cause of the child, and in general that which produces is the cause of that which is produced, and that which changes of that which is changed. (d) The same as end; i.e. the final cause; e.g., as the end of walking is health.

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For why does a man walk? To be healthy, we say, and by saying this we consider that we have supplied the cause. (e) All those means towards the end which arise at the instigation of something else, as, e.g. fat-reducing, purging, drugs and instruments are causes of health; for they all have the end as their object, although they differ from each other as being some instruments, others actions.

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These are roughly all the meanings of cause, but since causes are spoken of with various meanings, it follows that there are several causes (and that not in an accidental sense) of the same thing. E.g., both statuary and bronze are causes of the statue; not in different connections, but qua statue. However, they are not causes in the same way, but the one as material and the other as the source of motion. And things are causes of each other; as e.g. labor of vigor, and vigor of labor—but not in the same way; the one as an end , and the other as source of motion .

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And again the same thing is sometimes the cause of contrary results; because that which by its presence is the cause of so-and-so we sometimes accuse of being, by its absence, the cause of the contrary—as, e.g., we say that the absence of the pilot is the cause of a capsize, whereas his presence was the cause of safety.

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And both, presence and privation, are moving causes.

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Now there are four senses which are most obvious under which all the causes just described may be classed.

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The components of syllables; the material of manufactured articles; fire, earth and all such bodies; the parts of a whole; and the premisses of a syllogistic conclusion; are causes in the material sense. Of these some are causes as substrate: e.g. the parts; and others as essence : the whole, and the composition, and the form.

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The seed and the physician and the contriver and in general that which produces, all these are the source of change or stationariness. The remainder represent the end and good of the others; for the final cause tends to be the greatest good and end of the rest.

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Let it be assumed that it makes no difference whether we call it good or apparent good. In kind , then, there are these four classes of cause.

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The modes of cause are numerically many, although these too are fewer when summarized.

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For causes are spoken of in many senses, and even of those which are of the same kind, some are causes in a prior and some in a posterior sense; e.g., the physician and the expert are both causes of health; and the ratio 2:1 and number are both causes of the octave; and the universals which include a given cause are causes of its particular effects.

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Again, a thing may be a cause in the sense of an accident, and the classes which contain accidents; e.g., the cause of a statue is in one sense Polyclitus and in another a sculptor, because it is an accident of the sculptor to be Polyclitus. And the universal terms which include accidents are causes; e.g., the cause of a statue is a man, or even, generally, an animal; because Polyclitus is a man, and man is an animal.

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And even of accidental causes some are remoter or more proximate than others; e.g., the cause of the statue might be said to be white man or cultured man, and not merely Polyclitus or man.

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And besides the distinction of causes as proper and accidental , some are termed causes in a potential and others in an actual sense; e.g., the cause of building is either the builder or the builder who builds.

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And the same distinctions in meaning as we have already described will apply to the effects of the causes; e.g. to this statue, or a statue, or generally an image; and to this bronze, or bronze, or generally material.Effects, just like causes (10), may be particular or general. The metal-worker produces (a) the bronze for a particular statue by the sculptor, (b) bronze for a statue, (c) metal for an image. And it is the same with accidental effects. Again, the proper and accidental senses will be combined; e.g., the cause is neither Polyclitus nor a sculptor but the sculptor Polyclitus.

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However, these classes of cause are in all six in number, each used in two senses. Causes are (1.) particular, (2.) generic, (3.) accidental, (4.) generically accidental; and these may be either stated singly or (5, 6) in combinationThe cause of a statue may be said to be (1) a sculptor, (2) an artist, (3) Polyclitus, (4) a man, (5) the sculptor Polyclitus (combination of (1) and (3)), (6) an artistic man (combination of (2) and (4)).; and further they are all either actual or potential.

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And there is this difference between them, that actual and particular causes coexist or do not coexist with their effects (e.g. this man giving medical treatment with this man recovering his health, and this builder with this building in course of erection); but potential causes do not always do so; for the house and the builder do not perish together.

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Element means (a) the primary immanent thing, formally indivisible into another form, of which something is composed. E.g., the elements of a sound are the parts of which that sound is composed and into which it is ultimately divisible, and which are not further divisible into other sounds formally different from themselves. If an element be divided, the parts are formally the same as the whole: e.g., a part of water is water; but it is not so with the syllable.

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(b) Those who speak of the elements of bodies similarly mean the parts into which bodies are ultimately divisible, and which are not further divisible into other parts different in form. And whether they speak of one such element or of more than one, this is what they mean.

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(c) The term is applied with a very similar meaning to the elements of geometrical figures, and generally to the elements of demonstrations; for the primary demonstrations which are contained in a number of other demonstrations are called elements of demonstrations.Cf. Aristot. Met. 3.3.1. Such are the primary syllogisms consisting of three terms and with one middle term.

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(d) The term element is also applied metaphorically to any small unity which is useful for various purposes; and so that which is small or simple or indivisible is called an element.

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(e) Hence it comes that the most universal things are elements; because each of them, being a simple unity, is present in many things—either in all or in as many as possible. Some too think that unity and the point are first principles.

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(f) Therefore since what are called generaThis must refer to the highest genera, which have no definition because they cannot be analyzed into genus and differentia ( Ross). are universal and indivisible (because they have no formula), some people call the genera elements, and these rather than the differentia, because the genus is more universal. For where the differentia is present, the genus also follows; but the differentia is not always present where the genus is. And it is common to all cases that the element of each thing is that which is primarily inherent in each thing.

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NatureOn the meaning of φύσις cf. Burnet, E.G.P. pp. 10-12, 363-364. means: (a) in one sense, the genesis of growing things—as would be suggested by pronouncing the υ of φύσις long—and (b) in another, that immanent thingProbably the seed (Bonitz). from which a growing thing first begins to grow. (c) The source from which the primary motion in every natural object is induced in that object as such. All things are said to grow which gain increase through something else by contact and organic unity (or adhesion, as in the case of embryos).

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Organic unity differs from contact; for in the latter case there need be nothing except contact, but in both the things which form an organic unity there is some one and the same thing which produces, instead of mere contact, a unity which is organic, continuous and quantitative (but not qualitative).

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Again, nature means (d) the primary stuff, shapeless and unchangeable from its own potency, of which any natural object consists or from which it is produced; e.g., bronze is called the nature of a statue and of bronze articles, and wood that of wooden ones, and similarly in all other cases.

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For each article consists of these natures, the primary material persisting. It is in this sense that men call the elements of natural objects the nature, some calling it fire, others earth or air or water, others something else similar, others some of these, and others all of them.

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Again in another sense nature means (e) the substance of natural objects; as in the case of those who say that the nature is the primary composition of a thing, or as Empedocles says: Of nothing that exists is there nature, but only mixture and separation of what has been mixed; nature is but a name given to these by men.Empedocles Fr. 8 (Diels).

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Hence as regards those things which exist or are produced by nature, although that from which they naturally are produced or exist is already present, we say that they have not their nature yet unless they have their form and shape.

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That which comprises both of these exists by nature; e.g. animals and their parts. And nature is both the primary matter (and this in two senses: either primary in relation to the thing, or primary in general; e.g., in bronze articles the primary matter in relation to those articles is bronze, but in general it is perhaps water—that is if all things which can be melted are water) and the form or essence, i.e. the end of the process, of generation. Indeed from this sense of nature, by an extension of meaning, every essence in general is called nature, because the nature of anything is a kind of essence.

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From what has been said, then, the primary and proper sense of nature is the essence of those things which contain in themselves as such a source of motion; for the matter is called nature because it is capable of receiving the nature, and the processes of generation and growth are called nature because they are motions derived from it. And nature in this sense is the source of motion in natural objects, which is somehow inherent in them, either potentially or actually.

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Necessary means: (a) That without which, as a concomitant condition, life is impossible; e.g. respiration and food are necessary for an animal, because it cannot exist without them. (b) The conditions without which good cannot be or come to be, or without which one cannot get rid or keep free of evil—e.g., drinking medicine is necessary to escape from ill-health, and sailing to Aegina is necessary to recover one’s money.

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(c) The compulsory and compulsion; i.e. that which hinders and prevents, in opposition to impulse and purpose. For the compulsory is called necessary, and hence the necessary is disagreeable; as indeed EvenusOf Poros; sophist and poet, contemporary with Socrates. says: For every necessary thing is by nature grievous. Evenus Fr. 8 (Hiller).

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And compulsion is a kind of necessity, as Sophocles says: Compulsion makes me do this of necessity. Soph. El. 256 (the quotation is slightly inaccurate).

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And necessity is held, rightly, to be something inexorable; for it is opposed to motion which is in accordance with purpose and calculation. (d) Again, what cannot be otherwise we say is necessarily so.

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It is from this sense of necessary that all others are somehow derived; for the term compulsory is used of something which it is necessary for one to do or suffer only when it is impossible to act according to impulse, because of the compulsion: which shows that necessity is that because of which a thing cannot be otherwise; and the same is true of the concomitant conditions of living and of the good. For when in the one case good, and in the other life or existence, is impossible without certain conditions, these conditions are necessary, and the cause is a kind of necessity.

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(e) Again, demonstration is a necessary thing, because a thing cannot be otherwise if the demonstration has been absolute. And this is the result of the first premisses, when it is impossible for the assumptions upon which the syllogism depends to be otherwise.

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Thus of necessary things, some have an external cause of their necessity, and others have not, but it is through them that other things are of necessity what they are.

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Hence the necessary in the primary and proper sense is the simple , for it cannot be in more than one condition. Hence it cannot be in one state and in another; for if so it would ipso facto be in more than one condition. Therefore if there are certain things which are eternal and immutable, there is nothing in them which is compulsory or which violates their nature.

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The term one is used (1.) in an accidental, (2.) in an absolute sense. (1.) In the accidental sense it is used as in the case of CoriscusCoriscus of Scepsis was a Platonist with whom Aristotle was probably acquainted; but the name is of course chosen quite arbitrarily. and cultured and cultured Coriscus (for Coriscus and cultured and cultured Coriscus mean the same);

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and cultured and upright and cultured upright Coriscus. For all these terms refer accidentally to one thing; upright and cultured because they are accidental to one substance, and cultured and Coriscus because the one is accidental to the other.

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And similarly in one sense cultured Coriscus is one with Coriscus, because one part of the expression is accidental to the other, e.g. cultured to Coriscus; and cultured Coriscus is one with upright Coriscus,

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because one part of each expression is one accident of one and the same thing. It is the same even if the accident is applied to a genus or a general term; e.g., man and cultured man are the same, either because cultured is an accident of man, which is one substance, or because both are accidents of some individual, e.g. Coriscus.

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But they do not both belong to it in the same way; the one belongs presumably as genus in the substance, and the other as condition or affection of the substance. Thus all things which are said to be one in an accidental sense are said to be so in this way.

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(2.) Of those things which are said to be in themselves one, (a) some are said to be so in virtue of their continuity; e.g., a faggot is made continuous by its string, and pieces of wood by glue; and a continuous line, even if it is bent, is said to be one, just like each of the limbs; e.g. the leg or arm. And of these things themselves those which are naturally continuous are one in a truer sense than those which are artificially continuous.

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Continuous means that whose motion is essentially one, and cannot be otherwise; and motion is one when it is indivisible, i.e. indivisible in time . Things are essentially continuous which are one not by contact only; for if you put pieces of wood touching one another you will not say that they are one piece of wood, or body, or any other continuous thing.

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And things which are completely continuous are said to be one even if they contain a joint, and still more those things which contain no joint; e.g., the shin or the thigh is more truly one than the leg, because the motion of the leg may not be one.

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And the straight line is more truly one than the bent. We call the line which is bent and contains an angle both one and not one, because it may or may not move all at once; but the straight line always moves all at once, and no part of it which has magnitude is at rest while another moves, as in the bent line.

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(b) Another sense of one is that the substrate is uniform in kind.

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Things are uniform whose form is indistinguishable to sensation; and the substrate is either that which is primary, or that which is final in relation to the end. For wine is said to be one, and water one, as being something formally indistinguishable. And all liquids are said to be one (e.g. oil and wine), and melted things; because the ultimate substrate of all of them is the same, for all these things are water or vapor.

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(c) Things are said to be one whose genus is one and differs in its opposite differentiae. All these things too are said to be one because the genus, which is the substrate of the differentiae, is one (e.g., horse, man and dog are in a sense one, because they are all animals); and that in a way very similar to that in which the matter is one.

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Sometimes these things are said to be one in this sense, and sometimes their higher genus is said to be one and the same (if they are final species of their genus)—the genus, that is, which is above the genera of which their proximate genus is one; e.g., the isosceles and equilateral triangles are one and the same figure (because they are both triangles), but not the same triangles.

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(d) Again, things are said to be one when the definition stating the essence of one is indistinguishable from a definition explaining the other; for in itself every definition is distinguishable <into genus and differentiae>. In this way that which increases and decreases is one, because its definition is one; just as in the case of planes the definition of the form is one.

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And in general those things whose concept, which conceives the essence, is indistinguishable and cannot be separated either in time or in place or in definition, are in the truest sense one; and of these such as are substances are most truly one. For universally such things as do not admit of distinction are called one in so far as they do not admit of it; e.g., if man qua man does not admit of distinction, he is one man; and similarly if qua animal, he is one animal; and if qua magnitude, he is one magnitude.

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Most things, then, are said to be one because they produce, or possess, or are affected by, or are related to, some other one thing; but some are called one in a primary sense, and one of these is substance. It is one either in continuity or in form or in definition; for we reckon as more than one things which are not continuous, or whose form is not one, or whose definition is not one.

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Again, in one sense we call anything whatever one if it is quantitative and continuous; and in another sense we say that it is not one unless it is a whole of some kind, i.e. unless it is one in form (e.g., if we saw the parts of a shoe put together anyhow, we should not say that they were one — except in virtue of their continuity; but only if they were so put together as to be a shoe, and to possess already some one form).

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Hence the circumference of a circle is of all lines the most truly one, because it is whole and complete.

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The essence of one is to be a kind of starting point of number; for the first measure is a starting point, because that by which first we gain knowledge of a thing is the first measure of each class of objects. The one, then, is the starting-point of what is knowable in respect of each particular thing. But the unit is not the same in all classes,

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for in one it is the quarter-tone, and in another the vowel or consonant; gravity has another unit, and motion another. But in all cases the unit is indivisible, either quantitatively or formally.

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Thus that which is quantitatively and qua quantitative wholly indivisible and has no position is called a unit; and that which is wholly indivisible and has position, a point; that which is divisible in one sense, a line; in two senses, a plane; and that which is quantitatively divisible in all three senses, a body.

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And reversely that which is divisible in two senses is a plane, and in one sense a line; and that which is in no sense quantitatively divisible is a point or a unit; if it has no position, a unit, and if it has position, a point.

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Again, some things are one numerically, others formally, others generically, and others analogically; numerically, those whose matter is one; formally, those whose definition is one; generically, those which belong to the same category; and analogically, those which have the same relation as something else to some third object.

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In every case the latter types of unity are implied in the former: e.g., all things which are one numerically are also one formally, but not all which are one formally are one numerically; and all are one generically which are one formally, but such as are one generically are not all one formally, although they are one analogically; and such as are one analogically are not all one generically.

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It is obvious also that many will have the opposite meanings to one. Some things are called many because they are not continuous; others because their matter (either primary or ultimate) is formally divisible; others because the definitions of their essence are more than one.

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Being means (1.) accidental being, (2.) absolute being. (1.) E.g., we say that the upright person is cultured, and that the man is cultured, and that the cultured person is a man; very much as we say that the cultured person builds, because the builder happens to be cultured, or the cultured person a builder; for in this sense X is Y means that Y is an accident of X.

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And so it is with the examples cited above; for when we say that the man is cultured and the cultured person is a man or the white is cultured or the cultured is white, in the last two cases it is because both predicates are accidental to the same subject, and in the first case because the predicate is accidental to what is ; and we say that the cultured is a man because the cultured is accidental to a man.

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(Similarly not-white is said to be, because the subject of which not-white is an accident, is .) These, then, are the senses in which things are said to be accidentally: either because both predicates belong to the same subject, which is ; or because the predicate belongs to the subject, which is ; or because the subject to which belongs that of which it is itself predicated itself is .

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(2.) The senses of essential being are those which are indicated by the figures of predicationThe categories. For the full list of these see Aristot. Categories 1b 25-27.; for being has as many senses as there are ways of predication. Now since some predicates indicate (a) what a thing is, and others its (b) quality, (c) quantity, (d) relation, (e) activity or passivity, (f) place, (g) time, to each of these corresponds a sense of being.

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There is no difference between the man is recovering and the man recovers; or between the man is walking or cutting and the man walks or cuts; and similarly in the other cases.

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(3.) Again, to be and is mean that a thing is true, and not to be that it is false.

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Similarly too in affirmation and negation; e.g., in Socrates is cultured is means that this is true; or in Socrates is not-white that this is true; but in the diagonal is not commensurableCf. Aristot. Met. 1.2.15.is not means that the statement is false. (4.) Again, to be <or is> means that some of these statements can be made in virtue of a potentiality and others in virtue of an actuality.

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For we say that both that which sees potentially and that which sees actually is a seeing thing. And in the same way we call understanding both that which can use the understanding, and that which does ; and we call tranquil both that in which tranquillity is already present, and that which is potentially tranquil.

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Similarly too in the case of substances. For we say that Hermes is in the stone,Cf. Aristot. Met. 3.5.6. and the half of the line in the whole; and we call corn what is not yet ripe. But when a thing is potentially existent and when not, must be defined elsewhere.Aristot. Met. 9.9.

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Substance means (a) simple bodies, e.g. earth, fire, water and the like; and in general bodies, and the things, animal or divine, including their parts, which are composed of bodies. All these are called substances because they are not predicated of any substrate, but other things are predicated of them.

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(b) In another sense, whatever, being immanent in such things as are not predicated of a substrate, is the cause of their being; as, e.g., the soul is the cause of being for the animal.

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(c) All parts immanent in things which define and indicate their individuality, and whose destruction causes the destruction of the whole; as, e.g., the plane is essential to the body (as someThe Pythagoreans and Platonists. hold) and the line to the plane. And number in general is thought by someThe Pythagoreans and Platonists. to be of this nature, on the ground that if it is abolished nothing exists, and that it determines everything.

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(d) Again, the essence , whose formula is the definition, is also called the substance of each particular thing.

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Thus it follows that substance has two senses: the ultimate subject, which cannot be further predicated of something else; and whatever has an individual and separate existence. The shape and form of each particular thing is of this nature.

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The same means (a) accidentally the same. E.g., white and cultured are the same because they are accidents of the same subject; and man is the same as cultured, because one is an accident of the other; and cultured is the same as man because it is an accident of man; and cultured man is the same as each of the terms cultured and man, and vice versa; for both man and cultured are used in the same way as cultured man, and the latter in the same way as the former.

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Hence none of these predications can be made universally. For it is not true to say that every man is the same as the cultured; because universal predications are essential to things, but accidental predications are not so, but are made of individuals and with a single application. Socrates and cultured Socrates seem to be the same; but Socrates is not a class-name, and hence we do not say every Socrates as we say every man.

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Some things are said to be the same in this sense, but (b) others in an essential sense, in the same number of senses as the one is essentially one; for things whose matter is formally or numerically one, and things whose substance is one, are said to be the same. Thus sameness is clearly a kind of unity in the being, either of two or more things, or of one thing treated as more than one; as, e.g., when a thing is consistent with itself; for it is then treated as two.

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Things are called other of which either the forms or the matter or the definition of essence is more than one; and in general other is used in the opposite senses to same.

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Things are called different which, while being in a sense the same, are other not only numerically, but formally or generically or analogically; also things whose genus is not the same; and contraries; and all things which contain otherness in their essence.

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Things are called like which have the same attributes in all respects; or more of those attributes the same than different; or whose quality is one. Also that which has a majority or the more important of those attributes of something else in respect of which change is possible (i.e. the contraries) is like that thing. And unlike is used in the opposite senses to like.

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The term opposite is applied to (a) contradiction; (b) contraries; (c) relative terms; (d) privation; (e) state; (f) extremes; e.g. in the process of generation and destruction. And (g) all things which cannot be present at the same time in that which admits of them both are called opposites; either themselves or their constituents. Grey and white do not apply at the same time to the same thing, and hence their constituents are opposite.

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Contrary means: (a) attributes, generically different, which cannot apply at the same time to the same thing. (b) The most different attributes in the same genus; or (c) in the same subject; or (d) falling under the same faculty. (e) Things whose difference is greatest absolutely, or in genus, or in species.

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Other things are called contrary either because they possess attributes of this kind, or because they are receptive of them, or because they are productive of or liable to them, or actually produce or incur them, or are rejections or acquisitions or possessions or privations of such attributes.

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And since one and being have various meanings, all other terms which are used in relation to one and being must vary in meaning with them; and so same, other and contrary must so vary, and so must have a separate meaning in accordance with each category.

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Things are called other in species (a) which belong to the same genus and are not subordinate one to the other; or (b) which are in the same genus and contain a differentia; or (c) which contain a contrariety in their essence.

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(d) Contraries, too (either all of them or those which are called so in a primary sense), are other in species than one another; and (e) so are all things of which the formulae are different in the final species of the genus (e.g., man and horse are generically indivisible, but their formulae are different); and (f) attributes of the same substance which contain a difference. The same in species has the opposite meanings to these.

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Prior and posterior mean: (1.) (a) In one sense (assuming that there is in each genus some primary thing or starting-point) that which is nearer to some starting-point, determined either absolutely and naturally, or relatively, or locally, or by some agency; e.g., things are prior in space because they are nearer either to some place naturally determined, such as the middle or the extreme, or to some chance relation; and that which is further is posterior.

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(b) In another sense, prior or posterior in time . Some things are prior as being further from the present, as in the case of past events (for the Trojan is prior to the Persian war, because it is further distant from the present); and others as being nearer the present, as in the case of future events (for the Nemean are prior to the Pythian games because they are nearer to the present, regarded as a starting-point and as primary).

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(c) In another sense, in respect of motion (for that which is nearer to the prime mover is prior; e.g., the boy is prior to the man). This too is a kind of starting point in an absolute sense. (d) In respect of potency; for that which is superior in potency, or more potent, is prior. Such is that in accordance with whose will the other, or posterior, thing must follow, so that according as the former moves or does not move, the latter is or is not moved. And the will is a starting-point.

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(e) In respect of order; such are all things which are systematically arranged in relation to some one determinate object. E.g., he who is next to the leader of the chorus is prior to him who is next but one, and the seventh string is prior to the eighthThe octachord to which Aristotle refers was composed of the following notes: E (ὑπάτη ) F (παρυπάτη) G (λιχανός) A (μέση) B (παραμέση) C (τρίτη) D (παρανήτη) E (νήτη).; for in one case the leader is the starting-point, and in the other the middleStrictly speaking there was no middle string in the octachord; the name was taken over from the earlier heptachord EFGABbCD, in which there was no παραμέση. The μέση was apparently what we should call the tonic. Cf. Aristot. Met. 14.6.5; Aristot. Problemata 919b 20. string.

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In these examples prior has this sense; but (2.) in another sense that which is prior in knowledge is treated as absolutely prior; and of things which are prior in this sense the prior in formula are different from the prior in perception . Universals are prior in formula, but particulars in perception. And in formula the attribute is prior to the concrete whole: e.g. cultured to the cultured man; for the formula will not be a whole without the part.

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Yet cultured cannot exist apart from some cultured person.

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Again, (3.) attributes of prior subjects are called prior; e.g., straightness is prior to smoothness, because the former is an attribute of the line in itself, and the latter of a surface.

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Some things, then, are called prior and posterior in this sense; but others (iv.) in virtue of their nature and substance, namely all things which can exist apart from other things, whereas other things cannot exist without them. This distinction was used by Plato.Not, apparently, in his writings.(And since being has various meanings, (a) the substrate, and therefore substance, is prior; (b) potential priority is different from actual priority.

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Some things are prior potentially, and some actually; e.g., potentially the half-line is prior to the whole, or the part to the whole, or the matter to the substance; but actually it is posterior, because it is only upon dissolution that it will actually exist.)

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Indeed, in a sense all things which are called prior or posterior are so called in this connection; for some things can exist apart from others in generation (e.g. the whole without the parts), and others in destruction (e.g. the parts without the whole). And similarly with the other examples.

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PotencyOr capacity or potentiality. means: (a) the source of motion or change which is in something other than the thing changed, or in it qua other. E.g., the science of building is a potency which is not present in the thing built; but the science of medicine, which is a potency, may be present in the patient, although not qua patient.

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Thus potency means the source in general of change or motion in another thing, or in the same thing qua other; or the source of a thing’s being moved or changed by another thing, or by itself qua other (for in virtue of that principle by which the passive thing is affected in any way we call it capable of being affected; sometimes if it is affected at all, and sometimes not in respect of every affection, but only if it is changed for the better).

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(b) The power of performing this well or according to intention; because sometimes we say that those who can merely take a walk, or speak, without doing it as well as they intended, cannot speak or walk. And similarly in the case of passivity.

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(c) All states in virtue of which things are unaffected generally, or are unchangeable, or cannot readily deteriorate, are called potencies. For things are broken and worn out and bent and in general destroyed not through potency but through impotence and deficiency of some sort; and things are unaffected by such processes which are scarcely or slightly affected because they have a potency and are potent and are in a definite state.

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Since potency has all these meanings, potent (or capable) will mean (a) that which contains a source of motion or change (for even what is static is potent in a sense) which takes place in another thing, or in itself qua other. (b) That over which something else has a potency of this kind. (c) That which has the potency of changing things, either for the worse or for the better (for it seems that even that which perishes is capable of perishing; otherwise, if it had been incapable, it would not have perished. As it is, it has a kind of disposition or cause or principle which induces such an affection.

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Sometimes it seems to be such as it is because it has something, and sometimes because it is deprived of something; but if privation is in a sense a state or habit, everything will be potent through having something; and so a thing is potent in virtue of having a certain habit or principle, and also in virtue of having the privation of that habit, if it can have privation; and if privation is not in a sense habit, the term potent is equivocal).

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(d) A thing is potent if neither any other thing nor itself qua other contains a potency or principle destructive of it. (e) All these things are potent either because they merely might chance to happen or not to happen, or because they might do so well . Even in inanimate things this kind of potency is found; e.g. in instruments; for they say that one lyre can be played, and another not at all, if it has not a good tone.

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Impotence is a privation of potency—a kind of abolition of the principle which has been described—either in general or in something which would naturally possess that principle, or even at a time when it would naturally already possess it (for we should not use impotence—in respect of begetting—in the same sense of a boy, a man and a eunuch). Again, there is an impotence corresponding to each kind of potency; both to the kinetic and to the successfully kinetic.

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Some things are said to be impotent in accordance with this meaning of impotence, but others in a different sense, namely possible and impossible. Impossible means: (a) that whose contrary is necessarily true; e.g., it is impossible that the diagonal of a square should be commensurable with the sides, because such a thing is a lie, whose contrary is not only true but inevitable. Hence that it is commensurable is not only a lie but necessarily a lie.

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And the contrary of the impossible, i.e. the possible, is when the contrary is not necessarily a lie; e.g., it is possible that a man should be seated, for it is not necessarily a lie that he should not be seated. Possible, then, means in one sense, as we have said, that which is not necessarily a lie; in another, that which is true; and in another, that which may be true.

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(The power in geometryA square was called a δύναμις. Plat. Rep 587d; Plat. Tim. 31c. is so called by an extension of meaning.)

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These are the senses of potent which do not correspond to potency. Those which do correspond to it all refer to the first meaning, i.e. a source of change which exists in something other than that in which the change takes place, or in the same thing qua other.

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Other things are said to be potentsc. in a passive sense, which the English word potent cannot bear. because something else has such a potency over them; others because it does not possess it; others because it possesses it in a particular way. The term impotent is similarly used. Thus the authoritative definition of potency in the primary sense will be a principle producing change, which is in something other than that in which the change takes place, or in the same thing qua other.

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Quantity means that which is divisible into constituent parts, eachi.e., if there are only two. or every one of which is by nature some one individual thing. Thus plurality, if it is numerically calculable, is a kind of quantity; and so is magnitude, if it is measurable. Plurality means that which is potentially divisible into non-continuous parts; and magnitude that which is potentially divisible into continuous parts. Of kinds of magnitude, that which is continuous in one direction is length; in two directions, breadth; in three, depth.

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And of these, plurality, when limited, is a number; length, a line; breadth, a plane; depth, a body. Again, some things are essentially quantitative, but others only accidentally; e.g. the line is essentially, but cultured accidentally quantitative.

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And of the former class some are quantitative in virtue of their substance, e.g. the fine (because the definition which describes it is quantitative in some form); and others are attributes and conditions of a substance of this kind— e.g., much and little, long and short, broad and narrow, deep and shallow, heavy and light, etc.

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Moreover, great and small, and greater and smaller, whether used absolutely or relatively to one another, are essential attributes of quantity; by an extension of meaning, however, these terms are also applied to other things.

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Of things called quantitative in an accidental sense, one kind is so called in the sense in which we said above that cultured or white is quantitative—because the subject to which they belong is quantitative; and others in the sense that motion and time are so called—for these too are said in a sense to be quantitative and continuous, since the subjects of which they are attributes are divisible. I mean, not the thing moved, but that through or along which the motion has taken place; for it is because the latter is quantitative that the motion is quantitative, and because the motion is quantitative that the time is also.

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Quality means (a) in one sense, the differentia of essence; e.g., a man is an animal of a certain quality because he is two-footed; and so is a horse, because it is four-footed. Also a circle is a geometrical figure of a certain quality, because it has no angles; which shows that the essential differentia is quality.

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In this one sense, then, quality means differentia of essence; but (b) in another it is used as of immovable and mathematical objects, in the sense that numbers are in a way qualitative—e.g. such as are composite and are represented geometrically not by a line but by a plane or solid (these are products respectively of two and of three factors)—and in general means that which is present besides quantity in the essence. For the essence of each number is that which goes into it once; e.g. that of 6 is not what goes twice or three times, but what goes once; for 6 is once 6.

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(c) All affections of substance in motion in respect of which bodies become different when they (the affections) change—e.g. heat and cold, whiteness and blackness, heaviness and lightness, etc. (d) The term is used with reference to goodness and badness, and in general to good and bad.

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Thus there are, roughly speaking, two meanings which the term quality can bear, and of these one is more fundamental than the other. Quality in the primary sense is the differentia of the essence; and quality in numbers falls under this sense, because it is a kind of differentia of essences, but of things either not in motion or not qua in motion. Secondly, there are the affections of things in motion qua in motion, and the differentiae of motions.

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Goodness and badness fall under these affections, because they denote differentiae of the motion or functioning in respect of which things in motion act or are acted upon well or badly. For that which can function or be moved in such-and-such a way is good, and that which can function in such-and-such a way and in the contrary way is bad. Quality refers especially to good and bad in the case of living things, and of these especially in the case of such as possess choice.

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Things are called relative (a) In the sense that the double is relative to the half, and the triple to the third; and in general the many times greater to the many times smaller, and that which exceeds to the thing exceeded. (b) In the sense that the thing which heats or cuts is relative to the thing heated or cut; and in general the active to the passive. (c) In the sense that the measurable is relative to the measure, and the knowable to knowledge, and the sensible to sensation.

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(a) In the first sense they are said to be numerically relative; either simply, or in a definite relation to numbers or to 1. E.g., the double in relation to 1 is a definite number; the many times as great is in a numerical relation to 1, but not in a definite relation such as this or that;

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the relation of that which is 1.5 times something else to that something is a definite numerical relation to a number; and that which is (n+1)/n times something else is in an indefinite relation to a number, just as the many times as great is in an indefinite relation to 1.

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The relation of that which exceeds to that which is exceeded is numerically quite indefinite, for number is commensurate, and is not predicated of the incommensurate; whereas that which exceeds, in relation to that which is exceeded, is so much plus something more; and this something more is indefinite, for it is indifferently equal or not equal to the so much.

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Thus not only are all these things said to be relative in respect of number, but also the equal and like and same, though in another way: for all these terms are used in respect of one. Things are the same whose essence is one; like whose quality is one; equal whose quantity is one. Now one is the starting-point and standard of number; and so all these relations involve number, though not all in the same way.

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(b) Active and passive things are called relative in virtue of an active or passive potentiality or actualization of the potentialities; e.g., that which can heat is called relative to that which can be heated, because it can heat; and again the thing heating is called relative to the thing heated, and the thing cutting to the thing cut, because their potentialities are actualized. Numerical relations, on the other hand, are not actualized (except as has been described elsewhere)The reference is quite uncertain, but cf. Aristot. Met. 9.9.4, 5. The point is that the actualization of a numerical (or geometrical) relation does not imply an active functioning, as in the case of the potentialities just described.; they have no actualizations in respect of motion.

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Of things potentially relative, some are further relative in respect of particular times; as, e.g., that which has made or will make is relative to that which has been or will be made. It is in this way that a father is called father of a son; the one has acted, and the other has been acted upon, in a particular way. Again, some things are relative in virtue of a privation of their potentiality; such is the impossible and all similar terms, e.g. the invisible.

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Thus relative terms which involve number and potentiality are all relative because their very essence contains a reference to something else; but not because something else is related to their essence. But (c) that which is measurable or knowable or thinkable is called relative because something else is related to its essence.

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For thinkable signifies that there is a thought which thinks it; but thought is not relative to that of which it is the thought (for then the same thing would have been said twice). And similarly sight is the sight of something; not of that of which it is the sight, although this is of course true—it is relative to some color or other similar thing.

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To describe it in the other way—the sight of the object of sight—would be to say the same thing twice. Things, then, which are called relative of their own nature are so called, some in these senses, and others because the classes which contain them are of this kind. E.g., medicine is reckoned as relative because its genus, science, is thought to be a relative thing.

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Further, there are the properties in virtue of which the things which possess them are called relative; e.g., equality is relative because the equal is relative, and similarity because the similar is relative. Other things are accidentally relative; e.g., a man is relative because he happens to be double something else, and double is a relative term; or white is relative if the same thing happens to be white as well as double.

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Perfect <or complete> means: (a) That outside which it is impossible to find even a single one of its parts; e.g., the complete time of each thing is that outside which it is impossible to find any time which is a part of it. (b) That which, in respect of goodness or excellence, cannot be surpassed in its kind; e.g., a doctor and a musician are perfect when they have no deficiency in respect of the form of their peculiar excellence.

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And thus by an extension of the meaning we use the term in a bad connection, and speak of a perfect humbug and a perfect thief; since indeed we call them good— e.g. a good thief and a good humbug.

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(c) And goodness is a kind of perfection. For each thing, and every substance, is perfect when, and only when, in respect of the form of its peculiar excellence, it lacks no particle of its natural magnitude. (d) Things which have attained their end, if their end is good, are called perfect; for they are perfect in virtue of having attained the end.

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Hence, since the end is an ultimate thing, we extend the meaning of the term to bad senses, and speak of perishing perfectly or being perfectly destroyed, when the destruction or calamity falls short in no respect but reaches its extremity. Hence, by an extension of the meaning, death is called an end, because they are both ultimate things. And the ultimate object of action is also an end.

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Things, then, which are called perfect in themselves are so called in all these senses; either because in respect of excellence they have no deficiency and cannot be surpassed, and because no part of them can be found outside them; or because, in general, they are unsurpassed in each particular class, and have no part outside. All other things are so called in virtue of these, because they either produce or possess something of this kind, or conform to it, or are referred in some way or other to things which are perfect in the primary sense.

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Limit means: (a) The furthest part of each thing, and the first point outside which no part of a thing can be found, and the first point within which all parts are contained. (b) Any form of magnitude or of something possessing magnitude.

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(c) The end of each thing. (This end is that to which motion and action proceed, and not the end from which. But sometimes it is both the end from which and the end to which, i.e. the final cause.) (d) The reality or essence of each thing; for this is the limit of our knowledge of it, and if it is a limit of the knowledge, it is also a limit of the thing. Thus it is obvious that limit has not only as many senses as beginning but even more; because the beginning is a kind of limit, but not every limit is a beginning.

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That in virtue of which has various meanings. (a) The form or essence of each individual thing; e.g., that in virtue of which a man is good is goodness itself. (b) The immediate substrate in which a thing is naturally produced; as, e.g., color is produced in the surface of things. Thus that in virtue of which in the primary sense is the form , and in the secondary sense, as it were, the matter of each thing, and the immediate substrate.

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And in general that in virtue of which will exist in the same number of senses as cause. For we say indifferently in virtue of what has he come? or for what reason has he come? and in virtue of what has he inferred or inferred falsely? or what is the cause of his inference or false inference? (And further, there is the positional sense of καθ’ ὅ, in which he stands, or in which he walks; all these examples denote place or position.)

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Hence in virtue of itself must also have various meanings. It denotes (a) The essence of each particular; e.g., Callias is in virtue of himself Callias and the essence of Callias. (b) Everything contained in the definition; e.g., Callias is in virtue of himself an animal, because animal is present in the definition, since Callias is a kind of animal.

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(c) Any attribute which a thing has received directly in itself or in any of its parts; e.g., the surface is white in virtue of itself; and man lives in virtue of himself, because the soul is a part of the man, and life is directly contained in it. (d) That which has no other cause. Man has many causes: animal, twofooted, etc.; but nevertheless man is in virtue of himself man. (e) All things which belong to a thing alone and qua alone; and hence that which is separate is in virtue of itself. This seems to be a slightly irrelevant reference to καθ’ ἁυτό in the sense of independent; but corruption in the text has made the true reading uncertain.

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Disposition means arrangement of that which has parts, either in space or in potentiality or in form. It must be a kind of position, as indeed is clear from the word, disposition.

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Havingἕξις means not only having but habit or state. Cf. Latin, habitus. means (a) In one sense an activity, as it were, of the haver and the thing had, or as in the case of an action or motion; for when one thing makes and another is made, there is between them an act of making. In this way between the man who has a garment and the garment which is had, there is a having. Clearly, then, it is impossible to have a having in this sense; for there will be an infinite series if we can have the having of what we have.

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But (b) there is another sense of having which means a disposition, in virtue of which the thing which is disposed is disposed well or badly, and either independently or in relation to something else. E.g., health is a state, since it is a disposition of the kind described. Further, any part of such a disposition is called a state; and hence the excellence of the parts is a kind of state.

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Affection means (a) In one sense, a quality in virtue of which alteration is possible; e.g., whiteness and blackness, sweetness and bitterness, heaviness and lightness, etc. (b) The actualizations of these qualities; i.e. the alterations already realized. (c) More particularly, hurtful alterations and motions, and especially hurts which cause suffering. (d) Extreme cases of misfortune and suffering are called affections. The English equivalent for πάθος in this sense would be calamity or disaster.

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We speak of privation: (a) In one sense, if a thing does not possess an attribute which is a natural possession, even if the thing itself would not naturally possess itThis is not a proper sense of privation, as Aristotle implies by choosing an example from everyday speech.; e.g., we say that a vegetable is deprived of eyes. (b) If a thing does not possess an attribute which it or its genus would naturally possess. E.g., a blind man is not deprived of sight in the same sense that a mole is; the latter is deprived in virtue of its genus, but the former in virtue of himself.i.e., a mole is blind as being a member of a blind genus, whereas a man is blind only as an individual. Of course moles are not really blind, but we still speak as though they were.

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(c) If a thing has not an attribute which it would naturally possess, and when it would naturally possess it (for blindness is a form of privation; but a man is not blind at any age, but only if he lacks sight at the age when he would naturally possess itThe qualification refers, I suppose, to the fact that an embryo does not naturally possess sight.), and similarly if itThe subject seems to be indefinite, but no doubt Aristotle is thinking primarily of the particular example which he has just given. A man is not called blind if he does not see in the dark, or if he does not see with his ears, or if he does not see sound, or if he does not see what is behind him or too far away ( Ross). lacks an attribute in the medium and organ and relation and manner in which it would naturally possess it.

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(d) The forcible removal of anything is called privation. (e) Privation has as many senses as there are senses of negation derived from the negative affix (ἀ-). For we call a thing unequal because it does not possess equality (though it would naturally do so); and invisible either because it has no color at all or because it has only a faint one; and footless either because it has no feet at all or because it has rudimentary feet.

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Again, a negative affix may mean having something in a small degree—e.g. stoneless— that is, having it in some rudimentary manner. Again, it may mean having it not easily or not well; e.g., uncutable means not only that which cannot be cut, but that which cannot be cut easily or well. And again, it may mean not having a thing at all; for it is not the one-eyed man, but the man who lacks sight in both eyes, who is called blind. Hence not every man is good or bad, moral or immoral; there is also the intermediate state.

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To have <or possess> is used in various senses. (a) To direct in accordance with one’s own nature or impulse; whence we say that fever possesses a man, and despots possess cities, and people who wear clothes possess them. (b) We speak of anything as having in which, as receptive material, something is present. E.g., the bronze has the shape of the statue, and the body has the disease.

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(c) In the sense that the container holds the contained; for when A is contained in B, we say that A is held by B. E.g., we say that the vessel holds the liquid, and the city holds men, and the ship holds sailors, and so too that the whole holds the parts.

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(d) The same term is applied to that which prevents anything from moving or acting in accordance with its own impulse; as pillars hold <up> the weights which are imposed upon them, and as the poets make AtlasCf. Hes. Th. 517. hold up the heaven, because otherwise it would fall upon the earth (as some of the physicistse.g., Empedocles held that the heavens were kept in place by the velocity of their rotation;Aristot. De Caelo 284a 24, 295a 16 (Ritter and Preller, 170 b). maintain also).

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It is in this sense that we say that that which holds together holds what it holds together; because otherwise the latter would disperse, each part in accordance with its own impulse.

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To be in a thing is used similarly in senses corresponding to those of to have.

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To come from something means: (a) In one sense, to come from something as matter, and this in two ways: in respect either of the primary genus or of the ultimate species. E.g., in the one sense everything liquefiable comes from water, and in the other the statue comes from bronze.

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(b) To come from something as the first moving principle; e.g., from what comes fighting? From abuse; because this is the beginning of a fight. (c) To come from the combination of matter and form (as the parts come from the whole, and the verse from the Iliad , and the stones from the house); for the shape is an end, and that is a complete thing which has attained its end.

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(d) In the sense that the form is made out of the part of its definition; as, e.g., man is made out of two-footed and the syllable out of its elementIn the sense that στοιχεῖον(letter) forms part of the definition of syllable. (this is a different way from that in which the statue is made out of the bronze; for the composite entity is made out of perceptible material, but the form is also made out of the material of the form).

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These, then, are some of the meanings of from <or out of>, but (e) sometimes one of these senses only partially applies; e.g., the child comes from the father and mother, and plants from the earth, because they come from some part of those things. (f) It means after in time; e.g., we say that night comes from day, and storm from fine weather, because one comes after the other.

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And we speak thus of some of these things in view of their alternation with each other, as in the examples just mentioned, and of others in view merely of their succession in time; e.g., the voyage was made from the equinox, meaning that it was made after it; and the Thargelia are from the Dionysia, meaning after the Dionysia.The (city) Dionysia were celebrated in March; the Thargelia (a festival in honor of Apollo and Artemis) at the end of May.

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Part means: (a) That into which a quantity can be in any way divided; for that which is taken from a quantity qua quantity is always called a part of that quantity—e.g., we call 2 part (in a sense) of 3. (b) In another sense the term is only applied to those parts in sense (a) which measure the whole; hence in one sense we call 2 part of 3, and in another not.

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Again, (c) those divisions into which the form, apart from quantity, can be divided, are also called parts of the form. Hence species are called parts of their genus. (d) That into which the whole (either the form or that which contains the form) is divided, or of which it is composed. E.g., of a bronze sphere or cube not only is the bronze

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(i.e. the material which contains the form) a part, but also the angle. (e) The elements in the definition of each thing are also called parts of the whole. Hence the genus is even called a part of the species, whereas in another sense the species is part of the genus.

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Whole means: (a) That from which no part is lacking of those things as composed of which it is called a natural whole. (b) That which so contains its contents that they form a unity; and this in two ways, either in the sense that each of them is a unity, or in the sense that the unity is composed of them.

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For (i) the universal, or term generally applied as being some whole thing, is universal in the sense that it contains many particulars; because it is predicated of each of them, and each and all of them (e.g. man, horse, god) are one; because they are all living things. And (2) that which is continuous and limited is a whole when it is a unity composed of several parts (especially if the parts are only potentially present in it; but otherwise even if they are present actually).

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And of these things themselves, those which are so naturally are more truly wholes than those which are so artificially; just as we said of the one, because wholeness is a kind of oneness. Again, since a quantity has a beginning, middle and end, those to which position makes no difference we describe as all, and those to which position makes a difference we describe as whole, and those to which both descriptions can be applied, as both all and whole.

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These are all things whose nature remains the same in transposition, but whose shape does not; e.g. wax or a coat. They are described as both whole and all; for they have both characteristics. Water, however, and all liquids, and number, are described as all; we do not speak of a whole number or whole water except by an extension of meaning. Things are described as all in the plural qua differentiated which are described as all in the singular qua one; all this number, all these units.

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We do not describe any chance quantity as mutilated; it must have parts, and must be a whole. The number 2 is not mutilated if one of its 1’s is taken away—because the part lost by mutilation is never equal to the remainder—nor in general is any number mutilated; because the essence must persist. If a cup is mutilated, it must still be a cup; but the number is no longer the same.

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Moreover, not even all things which have dissimilar parts are mutilated; for a number has in a sense dissimilar as well as similar parts—e.g. 2, 3. But in general of things whose position makes no difference, e.g. water or fire, none is mutilated;— to be mutilated, things must be such as have their position according to their essence.

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Further, they must be continuous; for a musical scale is composed of dissimilar parts, and has position; but it does not become mutilated. Moreover, even things which are wholes are not mutilated by the removal of any of their parts; the parts removed must be neither proper to their essence nor in any chance location. E.g., a cup is not mutilated if a hole is made in it, but only if the handle or some projection is broken;

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and a man is not mutilated if he loses flesh or his spleen, but if he loses some extremity; and not every extremity, but only such as cannot grow again when completely removed. Hence bald people are not mutilated.

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The term genus <or race> is used: (a) When there is a continuous generation of things of the same type; e.g., as long as the human race exists means as long as the generation of human beings is continuous. (b) Of anything from which things derive their being as the prime mover of them into being. Thus some are called Hellenes by race, and others Ionians, because some have Hellen and others Ion as their first ancestor.

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(Races are called after the male ancestor rather than after the material.Aristotle regards the mother as providing the material, and the father the formal element of the child. Cf. Aristot. Met. 1.6.8, Aristot. Met. 8.4.5. Some derive their race from the female as well; e.g. the descendants of PyrrhaWife of Deucalion, the Greek Noah.. ) (c) In the sense that the plane is the genus of plane figures, and the solid of solids (for each one of the figures is either a particular plane or a particular solid); i.e., that which underlies the differentiae.

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(d) In the sense that in formulae the first component, which is stated as part of the essence, is the genus, and the qualities are said to be its differentiae. The term genus, then, is used in all these senses—(a) in respect of continuous generation of the same type; (b) in respect of the first mover of the same type as the things which it moves; (c) in the sense of material. For that to which the differentia or quality belongs is the substrate, which we call material.

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Things are called generically different whose immediate substrates are different and cannot be resolved one into the other or both into the same thing. E.g., form and matter are generically different, and all things which belong to different categories of being; for some of the things of which being is predicated denote the essence, others a quality, and others the various other things which have already been distinguished. For these also cannot be resolved either into each other or into any one thing.

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False means: (i) false as a thing ; (a) because it is not or cannot be substantiated; such are the statements that the diagonal of a square is commensurable, or that you are sitting. Of these one is false always, and the other sometimes; it is in these senses that these things are not facts.

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(b) Such things as really exist, but whose nature it is to seem either such as they are not, or like things which are unreal; e.g. chiaroscuro and dreams. For these are really something, but not that of which they create the impression. Things, then, are called false in these senses: either because they themselves are unreal, or because the impression derived from them is that of something unreal.

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(2.) A false statement is the statement of what is not, in so far as the statement is false. Hence every definition is untrue of anything other than that of which it is true; e.g., the definition of a circle is untrue of a triangle. Now in one sense there is only one definition of each thing, namely that of its essence; but in another sense there are many definitions,Here Aristotle is using the word λόγος not in the strict sense of definition but in the looser sense of a statement about something. since the thing itself, and the thing itself qualified (e.g. Socrates and cultured Socrates) are in a sense the same.

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But the false definition is not strictly a definition of anything. Hence it was foolish of AntisthenesThe Cynic; contemporary and renegade disciple of Socrates. He taught that definition, and even predication, are strictly speaking impossible. A simple entity can only be named; a complex entity can only be defined by naming its simple constituents. Cf. Aristot. Met. 8.3.7, 8; Plat. Theaet. 201d-202c, Plat. Soph. 251b, c. to insist that nothing can be described except by its proper definition: one predicate for one subject; from which it followed that contradiction is impossible, and falsehoodCf. Plat. Euthyd. 283e-284c, 286c, d. nearly so. But it is possible to describe everything not only by its own definition but by that of something else; quite falsely, and yet also in a sense truly—e.g., 8 may be described as double by the definition of 2.

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Such are the meanings of false in these cases. (3.) A false man is one who readily and deliberately makes such statements, for the sake of doing so and for no other reason; and one who induces such statements in others—just as we call things false which induce a false impression. Hence the proof in the HippiasPlat. Hipp. Min 365-375. that the same man is false and true is misleading;

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for it assumes (a) that the false man is he who is able to deceive, i.e. the man who knows and is intelligent; (b) that the man who is willingly bad is better. This false assumption is due to the induction; for when he says that the man who limps willingly is better than he who does so unwillingly, he means by limping pretending to limp. For if he is willingly lame, he is presumably worse in this case just as he is in the case of moral character.

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Accident <or attribute> means that which applies to something and is truly stated, but neither necessarily nor usually; as if, for example, while digging a hole for a plant one found a treasure. Then the finding of treasure is an accident to the man who is digging the hole; for the one thing is not a necessary consequence or sequel of the other, nor does one usually find treasure while planting.

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And a cultured man might be white; but since this does not happen necessarily or usually, we call it an accident. Thus since there are attributes and subjects, and some attributes apply to their subjects only at a certain place and time, any attribute which applies to a subject, but not because it was a particular subject or time or place, will be an accident.

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Nor is there any definite cause for an accident, but only a chance, i.e. indefinite, cause. It was by accident that X went to Aegina if he arrived there, not because he intended to go there but because he was carried out of his course by a storm, or captured by pirates.

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The accident has happened or exists, but in virtue not of itself but of something else; for it was the storm which was the cause of his coming to a place for which he was not sailing—i.e. Aegina.

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Accident has also another sense,i.e. property. namely, whatever belongs to each thing in virtue of itself, but is not in its essence; e.g. as having the sum of its angles equal to two right angles belongs to the triangle. Accidents of this kind may be eternal, but none of the former kind can be. There is an account of this elsewhere.The reference is probably to the Aristot. Analytica Posteriora 75a 18, 39-41.

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It is the principles and causes of the things which are that we are seeking; and clearly of the things which are qua being. There is a cause of health and physical fitness; and mathematics has principles and elements and causes; and in general every intellectual science or science which involves intellect deals with causes and principles, more or less exactly or simply considered.

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But all these sciences single out some existent thing or class, and concern themselves with that; not with Being unqualified, nor qua Being, nor do they give any account of the essence; but starting from it, some making it clear to perception, and others assuming it as a hypothesis, they demonstrate, more or less cogently, the essential attributes of the class with which they are dealing.

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Hence obviously there is no demonstration of substance or essence from this method of approach, but some other means of exhibiting it. And similarly they say nothing as to whether the class of objects with which they are concerned exists or not; because the demonstration of its essence and that of its existence belong to the same intellectual process.

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And since physical science also happens to deal with a genus of Being (for it deals with the sort of substance which contains in itself the principle of motion and rest), obviously it is neither a practical nor a productive science.

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For in the case of things produced the principle of motion (either mind or art or some kind of potency) is in the producer; and in the case of things done the will is the agent—for the thing done and the thing willed are the same. Thus if every intellectual activity is either practical or productive or speculative, physics will be a speculative science; but speculative about that kind of Being which can be moved, and about formulated substance for the most part only qua inseparable from matter.

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But we must not fail to observe how the essence and the formula exist, since without this our inquiry is ineffectual.

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Now of things defined, i.e. of essences, some apply in the sense that snub does, and some in the sense that concave does. The difference is that snub is a combination of form with matter; because the snub is a concave nose , whereas concavity is independent of sensible matter.

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Now if all physical terms are used in the same sense as snub—e.g. nose, eye, face, flesh, bone, and in general animal; leaf, root, bark, and in general vegetable (for not one of these has a definition without motion; the definition invariably includes matter)—it is clear how we should look for and define the essence in physical things, and why it is the province of the physicist to study even some aspects of the soul, so far as it is not independent of matter.

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It is obvious, then, from these considerations, that physics is a form of speculative science. And mathematics is also speculative; but it is not clear at present whether its objects are immutable and separable from matter; it is clear, however, that some branches of mathematics study their objects qua immutable and qua separable from matter. Obviously it is the province of a speculative science to discover whether a thing is eternal and immutable and separable from matter;

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not, however, of physics (since physics deals with mutable objects) nor of mathematics, but of a science prior to both. For physics deals with things which exist separately but are not immutable; and some branches of mathematics deal with things which are immutable, but presumably not separable, but present in matter; but the primary science treats of things which are both separable and immutable.

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Now all causes must be eternal, but these especially; since they are the causes of what is visible of things divine. Hence there will be three speculative philosophies: mathematics, physics, and theology— since it is obvious that if the divine is present anywhere, it is present in this kind of entity; and also the most honorable science must deal with the most honorable class of subject.

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The speculative sciences, then, are to be preferred to the other sciences, and theology to the other speculative sciences. One might indeed raise the question whether the primary philosophy is universal or deals with some one genus or entity; because even the mathematical sciences differ in this respect—geometry and astronomy deal with a particular kind of entity, whereas universal mathematics applies to all kinds alike.

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Then if there is not some other substance besides those which are naturally composed, physics will be the primary science; but if there is a substance which is immutable, the science which studies this will be prior to physics, and will be primary philosophy, and universal in this sense, that it is primary. And it will be the province of this science to study Being qua Being; what it is, and what the attributes are which belong to it qua Being.

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But since the simple term being is used in various senses, of which we saw that one was accidental , and another true (not-being being used in the sense of false); and since besides these there are the categories, e.g. the what, quality, quantity, place, time, and any other similar meanings; and further besides all these the potential and actual : since the term being has various senses, it must first be said of what is accidentally, that there can be no speculation about it.

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This is shown by the fact that no science, whether practical, productive or speculative, concerns itself with it. The man who produces a house does not produce all the attributes which are accidental to the house in its construction; for they are infinite in number. There is no reason why the house so produced should not be agreeable to some, injurious to others, and beneficial to others, and different perhaps from every other existing thing; but the act of building is productive of none of these results.

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In the same way the geometrician does not study the accidental attributes of his figures, nor whether a triangle is different from a triangle the sum of whose angles is equal to two right angles. And this accords with what we should reasonably expect, because accident is only, as it were, a sort of name. Hence in a way PlatoCf. Plat. Soph. 254a. was not far wrong in making sophistry deal with what is nonexistent;

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because the sophists discuss the accident more, perhaps, than any other people—whether cultured and grammatical,i.e. able to read and write. The sophistic argument is given by Alexander as follows: A is grammatical; therefore grammatical A=A. A is cultured; therefore cultured A=A. Therefore grammatical=cultured, and he who is grammatical must be cultured. But B, though grammatical, is not cultured. Therefore the grammatical is not the same as the cultured. and cultured Coriscus and Coriscus,If Coriscus is the same as cultured Coriscus, he is the same as cultured cultured Coriscus, and soad infinitum. Cf. Soph. Elench. 173a 34. are the same or different; and whether everything that is, but has not always been, has come into being, so that if a man who is cultured has become grammatical, he has also, being grammatical, become culturedIf A, being cultured, has become grammatical, then being cultured he is grammatical. Then being grammatical he is cultured. But he has not always, being grammatical, been cultured. So if that which is but has not always been must have come to be, then being grammatical he has become cultured; i.e., he must have been both grammatical before he was cultured and cultured before he was grammatical; which is absurd ( Ross).; and all other such discussions. Indeed it seems that the accidental is something closely akin to the nonexistent.

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This is clear too from such considerations as the following: of things which are in other senses there is generation and destruction, but of things which are accidentally there is not.i.e., the process of becoming or change takes place in the subject—the man , who is accidentally cultured, becomes grammatical, and when the process is complete the cultured is accidentally grammatical; but it does not become so. Nevertheless we must state further, so far as it is possible, with regard to the accidental, what its nature is and through what cause it exists. At the same time it will doubtless also appear why there is no science of it.

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Since, then, there are among existing things some which are invariable and of necessity (not necessity in the sense of compulsion,Cf. Aristot. Met. 5.5.2. but that by which we mean that it cannot be otherwise Aristot. Met. 5.5.3 ), and some which are not necessarily so, nor always, but usually: this is the principle and this the cause of the accidental. For whatever is neither always nor usually so, we call an accident.

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E.g., if in the dog-daysThe period from July 3 to August 11, during which the dog-star Sirius rises and sets with the sun. we have storm and cold, we call it an accident; but not if we have stifling and intense heat, because the latter always or usually comes at this time, but not the former. It is accidental for a man to be white (since this is neither always nor usually so), but it is not accidental for him to be an animal.

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It is by accident that a builder restores to health, because it is not a builder but a doctor who naturally does this; but the builder happened accidentally to be a doctor. A confectioner, aiming at producing enjoyment, may produce something health-giving; but not in virtue of his confectioner’s art. Hence, we say, it was accidental; and he produces it in a sense, but not in an unqualified sense.

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For there are potencies which produce other things, but there is no art or determinate potency of accidents, since the cause of things which exist or come to be by accident is also accidental.

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Hence, since not everything is or comes to be of necessity and always, but most things happen usually, the accidental must exist. E.g., the white man is neither always nor usually cultured; but since this sometimes happens, it must be regarded as accidental. Otherwise, everything must be regarded as of necessity.

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Therefore the cause of the accidental is the matter, which admits of variation from the usual.

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We must take this as our starting-point: Is everything either always or usually? This is surely impossible. Then besides these alternatives there is something else: the fortuitous and accidental. But again, are things usually so, but nothing always , or are there things which are eternal? These questions must be inquired into laterCf. Aristot. Met. 12.6-8.; but it is clear that there is no science of the accidental—because all scientific knowledge is of that which is always or usually so. How else indeed can one learn it or teach it to another? For a fact must be defined by being so always or usually; e.g., honey-water is usually beneficial in case of fever.

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But science will not be able to state the exception to the rule: when it is not beneficial—e.g. at the new moon; because that which happens at the new moon also happens either always or usually; but the accidental is contrary to this. We have now explained the nature and cause of the accidental, and that there is no science of it.

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It is obvious that there are principles and causes which are generable and destructible apart from the actual processes of generation and destructionOn the analogy of accidental events; see 2. 5.; for if this is not true, everything will be of necessity: that is, if there must necessarily be some cause, other than accidental, of that which is generated and destroyed. Will A be, or not? Yes, if B happens; otherwise not. And B will happen if C does.

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It is clear that in this way, as time is continually subtracted from a limited period, we shall come to the present. Accordingly So-and-so will die by disease or violence if he goes out; and this if he gets thirsty; and this if something else happens; and thus we shall come to what is the case now, or to something which has already happened. E.g. if he is thirsty; this will happen if he is eating pungent food, and this is either the case or not.

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Thus of necessity he will either die or not die. And similarly if one jumps over to the past, the principle is the same; for this—I mean that which has just happened—is already present in something. Everything, then, which is to be, will be of necessity; e.g., he who is alive must die—for some stage of the process has been reached already; e.g., the contraries are present in the same body—but whether by disease or violence is not yet determined; it depends upon whether so-and-so happens.

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Clearly, then, the series goes back to some starting-point, which does not go back to something else. This, therefore, will be the starting-point of the fortuitous, and nothing else is the cause of its generation. But to what sort of starting-point and cause this process of tracing back leads, whether to a material or final or moving cause, is a question for careful consideration.

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So much, then, for the accidental sense of being; we have defined it sufficiently. As for being qua truth, and not-being qua falsity, since they depend upon combination and separation, and taken together are concerned with the arrangement of the parts of a contradiction (since the true has affirmation when the subject and predicate are combined, and negation where they are divided; but the false has the contrary arrangement.

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How it happens that we combine or separate in thought is another question. By combining or separating in thought I mean thinking them not as a succession but as a unitysc., or not as a unity but as a succession (this is separating in thought).); for falsity and truth are not in things —the good, for example, being true, and the bad false—but in thought ; and with regard to simple concepts and essences there is no truth or falsity even in thought;

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—what points we must study in connection with being and not-being in this sense, we must consider later. But since the combination and separation exists in thought and not in things, and this sense of being is different from the proper senses (since thought attaches or detaches essence or quality or quantity or some other category), we may dismiss the accidental and real sensesi.e., the senses in which the verb to be is used to express an accidental or a true relation. of being.

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For the cause of the one is indeterminate and of the other an affection of thought; and both are connected with the remaining genus of being, and do not indicate any objective reality. Let us therefore dismiss them, and consider the causes and principles of Being itself qua Being. [We have made it clear in our distinction of the number of senses in which each term is used that being has several senses.]This sentence is almost certainly a later and clumsy addition to show the connection with the following book.

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The term being has several senses, which we have classified in our discussionAristot. Met. 5.7. of the number of senses in which terms are used. It denotes first the what of a thing, i.e. the individuality; and then the quality or quantity or any other such category. Now of all these senses which being has, the primary sense is clearly the what, which denotes the substance

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(because when we describe the quality of a particular thing we say that it is good or bad, and not five feet high or a man; but when we describe what it is, we say not that it is white or hot or five feet high, but that it is a man or a god), and all other things are said to be because they are either quantities or qualities or affections or some other such thing.

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Hence one might raise the question whether the terms to walk and to be well and to sit signify each of these things as being, or not; and similarly in the case of any other such terms; for not one of them by nature has an independent existence or can be separated from its substance. Rather, if anything it is the thing which walks or sits or is well that is existent.

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The reason why these things are more truly existent is because their subject is something definite; i.e. the substance and the individual, which is clearly implied in a designation of this kind, since apart from it we cannot speak of the good or sitting. Clearly then it is by reason of the substance that each of the things referred to exists.

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Hence that which is primarily, not in a qualified sense but absolutely, will be substance.

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Now primary has several meanings; but nevertheless substance is primary in all senses, both in definition and in knowledge and in time. For none of the other categories can exist separately, but substance alone;

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and it is primary also in definition, because in the formula of each thing the formula of substance must be inherent; and we assume that we know each particular thing most truly when we know what man or fire is— rather than its quality or quantity or position; because we know each of these points too when we know what the quantity or quality is.

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Indeed, the question which was raised long ago, is still and always will be, and which always baffles us—What is Being?—is in other words What is substance? Some say that it is oneThe Milesians and Eleatics.; others, more than one; some, finiteThe Pythagoreans and Empedocles.; others, infinite.Anaxagoras and the Atomists. And so for us too our chief and primary and practically our only concern is to investigate the nature of being in the sense of substance.

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Substance is thought to be present most obviously in bodies. Hence we call animals and plants and their parts substances, and also natural bodies, such as fire, water, earth, etc., and all things which are parts of these or composed of these, either of parts or them or of their totality; e.g. the visible universe and its parts, the stars and moon and sun.

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We must consider whether (a) these are the only substances, or (b) these and some others, or (c) some of these, or (d) some of these and some others, or (e) none of these, but certain others. SomeThe Pythagoreans. hold that the bounds of body—i.e. the surface, line, point and unit—are substances, and in a truer sense than body or the solid.

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Again, someThe pre-Socratics. believe that there is nothing of this kind besides sensible things, while others believe in eternal entities more numerous and more real than sensible things. Thus Plato posited the Forms and the objects of mathematics as two kinds of substance, and as a third the substance of sensible bodies;

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and SpeusippusPlato’s nephew and successor as the head of the Academy. assumed still more kinds of substances, starting with the One, and positing principles for each kind: one for numbers, another for magnitudes, and then another for the soul. In this way he multiplies the kinds of substance. SomeThe followers of Xenocrates, successor to Speusippus. again hold that the Forms and numbers have the same nature, and that other things—lines and planes—are dependent upon them; and soon back to the substance of the visible universe and sensible things.

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We must consider, then, with regard to these matters, which of the views expressed is right and which wrong; and what things are substances; and whether there are any substances besides the sensible substances, or not; and how sensible substances exist; and whether there is any separable substance (and if so, why and how) or no substance besides the sensible ones. We must first give a rough sketch of what substance is.

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The term substance is used, if not in more, at least in four principal cases; for both the essence and the universal and the genus are held to be the substance of the particular, and fourthly the substrate. The substrate is that of which the rest are predicated, while it is not itself predicated of anything else. Hence we must first determine its nature, for the primary substrate is considered to be in the truest sense substance.

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Now in one sense we call the matter the substrate; in another, the shape ; and in a third, the combination of the two. By matter I mean, for instance, bronze; by shape, the arrangement of the form; and by the combination of the two, the concrete thing: the statue. Thus if the form is prior to the matter and more truly existent, by the same argument it will also be prior to the combination.

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We have now stated in outline the nature of substance—that it is not that which is predicated of a subject, but that of which the other things are predicated. But we must not merely define it so, for it is not enough. Not only is the statement itself obscure, but also it makes matter substance; for if matter is not substance, it is beyond our power to say what else is.

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For when everything else is removed, clearly nothing but matter remains; because all the other things are affections, products and potencies of bodies, and length, breadth and depth are kinds of quantity, and not substances. For quantity is not a substance; rather the substance is that to which these affections primarily belong.

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But when we take away length and breadth and depth we can see no thing remaining, unless it be the something bounded by them; so that on this view matter must appear to be the only substance. By matter I mean that which in itself is neither a particular thing nor a quantity nor designated by any of the categories which define Being.

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For there is something of which each of these is predicated, whose being is different from that of each one of the categories; because all other things are predicated of substance, but this is predicated of matter. Thus the ultimate substrate is in itself neither a particular thing nor a quantity nor anything else. Nor indeed is it the negations of these; for the negations too will only apply to it accidentally.

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If we hold this view, it follows that matter is substance. But this is impossible; for it is accepted that separability and individuality belong especially to substance. Hence it would seem that the form and the combination of form and matter are more truly substance than matter is.

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The substance, then, which consists of both—I mean of matter and form—may be dismissed, since it is posterior and obvious. Matter too is in a sense evident. We must consider the third type, for this is the most perplexing.

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Now it is agreed that some sensible things are substances, and so we should begin our inquiry in connection with these.

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It is convenient to advance to the more intelligiblesc. by nature. All learning proceeds by induction from that which is intelligible to us (i.e., the complex facts and objects of our experience, which are bound up with sensation and therefore less intelligible in themselves), to that which is intelligible in itself (i.e., the simple universal principles of scientific knowledge).; for learning is always acquired in this way, by advancing through what is less intelligible by nature to what is more so. And just as in actions it is our task to start from the good of the individual and make absolute good good for the individual,Cf. Aristot. Ethics 1129b 5. so it is our task to start from what is more intelligible to oneself and make what is by nature intelligible intelligible to oneself.

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Now that which is intelligible and primary to individuals is often but slightly intelligible, and contains but little reality; but nevertheless, starting from that which is imperfectly intelligible but intelligible to oneself, we must try to understand the absolutely intelligible; advancing, as we have said, by means of these very things which are intelligible to us.

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Since we distinguished at the beginningAristot. Met. 7.3.1. the number of ways in which substance is defined, and since one of these appeared to be essence, we must investigate this.

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First, let us make certain linguistic statements about it.

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The essence of each thing is that which it is said to be per se. To be you is not to be cultured, because you are not of your own nature cultured. Your essence, then, is that which you are said to be

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of your own nature. But not even all of this is the essence; for the essence is not that which is said to be per se in the sense that whiteness is said to belong to a surface,Cf. Aristot. Met. 5.18.3, 4. because being a surface is not being white.

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Nor is the essence the combination of both, being a white surface. Why? Because the word itself is repeated. Hence the formula of the essence of each thing is that which defines the term but does not contain it. Thus if being a white surface is the same as being a smooth surface, white and smooth are one and the same.The statement that to be a white surface is the same as to be a smooth surface tells us nothing fresh about surface; it simply identifies white with smooth. Aristotle has in mind Democritus’s theory of color (that it is an impression conveyed to our eyes from the superficial texture of the object; Theophrastus, De Sensu 73-75); cf.Aristot. De Sensu 442b 11, Aristot. De Gen. et Corr. 316a 1.

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But since in the other categories too there are compounds with substance (because there is a substrate for each category, e.g. quality, quantity, time, place and motion), we must inquire whether there is a formula of the essence of each one of them; whether these compounds, e.g. white man, also have an essence.

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Let the compound be denoted by X.Literally cloak, but the word is chosen quite arbitrarily. Cf. Aristot. Met. 8.6.4. What is the essence of X?

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But this is not even a per se expression. We reply that there are two ways in which a definition can be not per se true of its subject: (a) by an addition, and (b) by an omission.

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In one case the definition is not per se true because the term which is being defined is combined with something else; as if, e.g., in defining whiteness one were to state the definition of a white man. In the other, because something else (which is not in the definition) is combined with the subject; as if, e.g., X were to denote white man, and X were defined as white. White man is white, but its essence is not to be white. But is to be X an essence at all?

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Surely not. The essence is an individual type; but when a subject has something distinct from it predicated of it, it is not an individual type. E.g., white man is not an individual type; that is, assuming that individuality belongs only to substances. Hence essence belongs to all things the account of which is a definition.

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We have a definition, not if the name and the account signify the same (for then all accounts would be definitions; because any account can have a name, so that even the Iliad will be a definition), but if the account is of something primary. Such are all statements which do not involve the predication of one thing of another.

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Hence essence will belong to nothing except species of a genus, but to these only; for in these the predicate is not considered to be related to the subject by participation or affection, nor as an accident. But of everything else as well, if it has a name, there will be a formula of what it means—that X belongs to Y; or instead of a simple formula one more exact—but no definition, nor essence.

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Or perhaps definition, like the what, has more than one sense. For the what in one sense means the substance and the individual, and in another each one of the categories: quantity, quality, etc.

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Just as is applies to everything, although not in the same way, but primarily to one thing and secondarily to others; so what it is applies in an unqualified sense to substance, and to other things in a qualified sense. For we might ask also what quality is, so that quality also is a what it is; not however without qualification, but just as in the case of not-being some say by a verbal quibble that not-being is—not in an unqualified sense, but is not-being—so too with quality.

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Now although we must also consider how we should express ourselves in each particular case, it is still more important to consider what the facts are. Hence now, since the language which we are using is clear, similarly essence also will belong primarily and simply to substance, and secondarily to other things as well; just as the what it is is not essence simply, but the essence of a quality or quantity.

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For it must be either by equivocation that we say that these things are , or by adding and subtracting qualifications, as we say that the unknowable is knownsc. to be unknowable.; since the truth is that we use the terms neither equivocally nor in the same sense, but just as we use the term medical in relation to one and the same thing; but not of one and the same thing, nor yet equivocally. The term medical is applied to a body and a function and an instrument, neither equivocally nor in one sense, but in relation to one thing.Cf. Aristot. Met. 4.2.2.

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However, in whichever way one chooses to speak of these things, it matters nothing; but this point is clear: that the primary and unqualified definition, and the essence, belong to substances. It is true that they belong equally to other things too, but not primarily . For if we assume this, it does not necessarily follow that there is a definition of anything which means the same as any formula; it must mean the same as a particular kind of formula, i.e. the formula of one thing—

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one not by continuity like the Iliad, or things which are arbitrarily combined, but in one of the proper senses of one. And one has the same variety of senses as being. Being means sometimes the individual thing, sometimes the quantity, sometimes the quality. Hence even white man will have a formula and definition; but in a different sense from the definition of whiteness and substance.

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The question arises: If one denies that a formula involving an added determinant is a definition, how can there be a definition of terms which are not simple but coupled? Because they can only be explained by adding a determinant.

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I mean, e.g., there is nose and concavity and snubness, the term compounded of the two, because the one is present in the other. Neither concavity nor snubness is an accidental, but a per se affection of the nose.Snubness is a per se affection of the nose, because it applies only to the nose and cannot be explained apart from it, but the same can hardly be said of concavity. Aristotle himself uses the word (κοιλότης) elsewhere in other connections. Nor are they attributes in the sense that white is of Callias or a man, because Callias is white and is by accident a man; but in the sense that male is an attribute of animal, and equality of quantity, and all other attributes which we say belong per se.

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That is, all things which involve the formula or name of the subject of the affection, and cannot be explained apart from it. Thus white can be explained apart from man, but not female apart from animal. Thus either these terms have no essence or definition, or else they have it in a different sense, as we have said.

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But there is also another difficulty about them. If snub nose is the same as concave nose, snub will be the same as concave. But if not, since it is impossible to speak of snub apart from the thing of which it is a per se affection (because snub means a concavity in the nose), either it is impossible to call the nose snub, or it will be a tautology, concave-nose nose because snub nose will equal concave-nose nose.

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Hence it is absurd that such terms as these should have an essence. Otherwise there will be an infinite regression; for in snub-nose nose there will be yet another nose. Clearly, then, there is definition of substance alone. If there were definition of the other categories also, it would have to involve an added determinant, as in the case of the qualitative; and of the odd, for this cannot be defined apart from number; nor can female apart from animal.

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By involving an added determinant I mean descriptions which involve a tautology, as in the above examples. Now if this is true, there will be no definition of compound expressions either; e.g., odd number. We fail to realize this because our terms are not used accurately. If on the other hand there are definitions of these too, either they are defined in a different way, or, as we have said, definition and essence must be used in more than one sense;

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thus in one sense there will be no definition of anything, and nothing will have an essence, except substances; and in another those other things will have a definition and essence. It is obvious, then, that the definition is the formula of the essence, and that the essence belongs either only to substances, or especially and primarily and simply.

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We must inquire whether the essence is the same as the particular thing, or different. This is useful for our inquiry about substance; because a particular thing is considered to be nothing other than its own substance, and the essence is called the substance of the thing.

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In accidental predications, indeed, the thing itself would seem to be different from its essence; e.g., white man is different from essence of white man. If it were the same, essence of man and essence of white man would be the same. For man and white man are the same, they say, and therefore essence of white man is the same as essence of man.

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But perhaps it is not necessarily true that the essence of accidental combinations is the same as that of the simple terms; because the extremes of the syllogism are not identical with the middle term in the same way.The argument consists of two syllogisms: White=essence of white man. Man=white man. Therefore man=essence of white man. But essence of man=man. Therefore essence of man=essence of white man. The conclusion is faulty because whereas the first identity is assumed to be absolute, the second is accidental. Perhaps it might be thought to follow that the accidental extremes are identical; e.g. essence of white and essence of cultured; but this is not admitted.Aristotle seems to mean that both essence of white man and essence of cultured man might be proved by the former syllogism to be identical in the same way with the middle term man, in which case it would seem that essence of white and essence of cultured are the same. There is, however, the same fallacy as before.

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But in per se expressions, is the thing necessarily the same as its essence, e.g., if there are substances which have no other substances or entities prior to them, such as some hold the Ideas to be?

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For if the Ideal Good is to be different from the essence of good, and the Ideal Animal and Being from the essence of animal and being, there will be other substances and entities and Ideas besides the ones which they describe; and prior to them, if essence is substance. And if they are separate from each other, there will be no knowledge of the Ideas, and the essences will not exist

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(by being separate I mean if neither the essence of good is present in the Ideal Good, nor being good in the essence of good); for it is when we know the essence of it that we have knowledge of a thing. And it is the same with other essences as with the essence of good; so that if the essence of good is not good, neither will the essence of being be, nor the essence of one be one.

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Either all essences exist alike, or none of them; and so if not even the essence of being is, neither will any other essence exist. Again that to which essentially good does not apply cannot be good. Hence the good must be one with the essence of good, the beautiful with the essence of beauty, and so with all terms which are not dependent upon something else, but self-subsistent and primary.The example of the Ideas as per se terms is used by Aristotle to show incidentally the fallacy of the Ideal theory: there can be no self-subsistent entity apart from the essence.

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For it is enough if this is so, even if they are not Forms; or perhaps rather even if they are. (At the same time it is clear also that if the Ideas are such as some hold, the substrate will not be substance; for the Ideas must be substances, but not involving a substrate, because if they did involve one they would exist in virtue of its participation in them.)This criticism is irrelevant to the point under discussion. It simply points out that the Ideal theory conflicts with received opinion (cf. Aristot. Met. 7.3.1).

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That each individual thing is one and the same with its essence, and not merely accidentally so, is apparent, not only from the foregoing considerations, but because to have knowledge of the individual is to have knowledge of its essence; so that by setting out examples it is evident that both must be identical.

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But as for the accidental term, e.g. cultured or white, since it has two meanings, it is not true to say that the term itself is the same as its essence; for both the accidental term and that of which it is an accident are white, so that in one sense the essence and the term itself are the same, and in another they are not, because the essence is not the same as the man or the white man, but it is the same as the affection.

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The absurdity <of separating a thing from its essence> will be apparent also if one supplies a name for each essence; for then there will be another essence besides the original one, e.g. the essence of horse will have a further essence. Yet why should not some things be identified with their essence from the outset,i.e. to avoid the infinite series implied in the last sentence. if essence is substance? Indeed not only are the thing and its essence one, but their formula is the same, as is clear from what we have just stated; for it is not by accident that the essence of one, and the one, are one.

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Moreover, if they are different, there will be an infinite series; for the essence of one and the one will both exist; so that in that case too the same principle will apply.i.e. since there is a distinct term essence of one besides one, there will be a third distinct term essence of essence of one; and so on as in the case of horse above. Clearly, then, in the case of primary and self-subsistent terms, the individual thing and its essence are one and the same.

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It is obvious that the sophistical objections to this thesis are met in the same way as the question whether Socrates is the same as the essence of Socrates; for there is no difference either in the grounds for asking the question or in the means of meeting it successfully. We have now explained in what sense the essence is, and in what sense it is not, the same as the individual thing.

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Of things which are generated, some are generated naturally, others artificially, and others spontaneously; but everything which is generated is generated by something and from something and becomes something. When I say becomes something I mean in any of the categories; it may come to be either a particular thing or of some quantity or quality or in some place.

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Natural generation is the generation of things whose generation is by nature.

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That from which they are generated is what we call matter; that by which, is something which exists naturally; and that which they become is a man or a plant or something else of this kind, which we call substance in the highest degree. All things which are generated naturally or artificially have matter; for it is possible for each one of them both to be and not to be, and this possibility is the matter in each individual thing.

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And in general both that from which and that in accordance with which they are generated, is nature; for the thing generated, e.g. plant or animal, has a nature. And that by which they are generated is the so-called formal nature, which has the same form as the thing generated (although it is in something else); for man begets man.

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Such is the generation of things which are naturally generated; the other kinds of generation are called productions. All productions proceed from either art or potency or thought.

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Some of them are also generated spontaneously and by chance in much the same way as things which are naturally generated; for sometimes even in the sphere of nature the same things are generated both from seed and without it.e.g. fish (Aristot. Hist. An. 569a 11) and insects (Aristot. Hist. An. 539a 24). We shall consider cases of this kind later.In Aristot. Met. 7.9. Things are generated artificially whose form is contained in the soul (by form I mean the essence of each thing, and its primary substance);

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for even contraries have in a sense the same form.The logical connection is: It is sufficient to say that the form of objects which are artificially produced is contained in the soul; for although artificial production can produce contrary effects, the form of the positive effect is the absence of the form of the negative effect, so that in a sense they have the same form. For the substance of the privation is the opposite substance; e.g., health is the substance of disease; for disease is the absence of health, and health is the formula and knowledge in the soul. Now the healthy subject is produced as the result of this reasoning: since health is so-and-so, if the subject is to be healthy, it must have such-and-such a quality, e.g. homogeneity; and if so, it must have heat.

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And the physician continues reasoning until he arrives at what he himself finally can do; then the process from this point onwards, i.e. the process towards health, is called production. Therefore it follows in a sense that health comes from health and a house from a house; that which has matter from that which has not (for the art of medicine or of building is the form of health or the house). By substance without matter I mean the essence.

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In generations and motions part of the process is called cogitation, and part production—that which proceeds from the starting-point and the form is cogitation, and that which proceeds from the conclusion of the cogitation is production. Each of the other intermediate measures is carried out in the same way. I mean, e.g., that if A is to be healthy, his physical condition will have to be made uniform. What, then, does being made uniform entail? So-and-so; and this will be achieved if he is made hot. What does this entail? So-and-so; now this is potentially present, and the thing is now in his power.

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The thing which produces, and from which the process of recovering health begins, is the form in the soul, if the process is artificial; if spontaneous, it is whatever is the starting-point of the production for the artificial producer; as in medical treatment the starting-point is, perhaps, the heating of the patient; and this the doctor produces by friction. Heat in the body, then, is either a part of health, or is followed (directly or through several intermediaries) by something similar which is a part of health. This is the ultimate thing, namely that produces, and in this sense is a part of, health—or of the house

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(in the form of stones)There is no real analogy between the casual relationship of heat to health and of stones to a house. The former is both material and efficient; the latter only material. Cf. Aristot. Met. 7.9.1. or of other things. Therefore, as we say, generation would be impossible if nothing were already existent. It is clear, then, that some part must necessarily pre-exist; because the matter is a part, since it is matter which pre-exists in the product and becomes something. But then is matter part of the formula? Well, we define bronze circles in both ways; we describe the matter as bronze, and the form as such-and-such a shape; and this shape is the proximate genus in which the circle is placed.

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The bronze circle, then, has its matter in its formula. Now as for that from which, as matter, things are generated, some things when they are generated are called not so-and-so, but made of so-and-so; e.g., a statue is not called stone, but made of stone. But the man who becomes healthy is not called after that from which he becomes healthy. This is because the generation proceeds from the privation and the substrate, which we call matter (e.g., both the man and the invalid become healthy),

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but it is more properly said to proceed from the privation; e.g., a man becomes healthy from being an invalid rather than from being a man. Hence a healthy person is not called an invalid, but a man, and a healthy man. But where the privation is obscure and has no name—e.g. in bronze the privation of any given shape, or in bricks and wood the privation of the shape of a house—the generation is considered to proceed from these materials, as in the former case from the invalid.

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Hence just as in the former case the subject is not called that from which it is generated, so in this case the statue is not called wood, but is called by a verbal change not wood, but wooden; not bronze, but made of bronze; not stone, but made of stone; and the house is called not bricks, but made of bricks. For if we consider the matter carefully, we should not even say without qualification that a statue is generated from wood, or a house from bricks; because that from which a thing is generated should not persist, but be changed. This, then, is why we speak in this way.

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Now since that which is generated is generated by something (by which I mean the starting-point of the process of generation), and from something (by which let us understand not the privation but the matter; for we have already distinguished the meanings of these), and becomes something (i.e. a sphere or circle or whatever else it may be); just as the craftsman does not produce the substrate, i.e. the bronze, so neither does he produce the sphere; except accidentally, inasmuch as the bronze sphere is a sphere, and he makes the former.

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For to make an individual thing is to make it out of the substrate in the fullest sense. I mean that to make the bronze round is not to make the round or the sphere, but something else; i.e. to produce this form in another medium. For if we make the form, we must make it out of something else; for this has been assumed. E.g., we make a bronze sphere; we do this in the sense that from A, i.e. bronze, we make B, i.e. a sphere.

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If, then, we make the spherical form itself, clearly we shall have to make it in the same way; and the processes of generation will continue to infinity.

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It is therefore obvious that the form (or whatever we should call the shape in the sensible thing) is not generated—generation does not apply to it— nor is the essence generated; for this is that which is induced in something else either by art or by nature or by potency.

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But we do cause a bronze sphere to be, for we produce it from bronze and a sphere; we induce the form into this particular matter, and the result is a bronze sphere. But if the essence of sphere in general is generated, something must be generated from something; for that which is generated will always have to be divisible, and be partly one thing and partly another; I mean partly matter and partly form.

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If then a sphere is the figure whose circumference is everywhere equidistant from the center, part of this will be the medium in which that which we produce will be contained, and part will be in that medium; and the whole will be the thing generated, as in the case of the bronze sphere. It is obvious, then, from what we have said, that the thing in the sense of form or essence is not generated, whereas the concrete whole which is called after it is generated; and that in everything that is generated matter is present, and one part is matter and the other form.

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Is there then some sphere besides the particular spheres, or some house besides the bricks? Surely no individual thing would ever have been generated if form had existed thus independently.If forms are self-subsistent substances, individual substances cannot be generated from them; for the individual contains the form, but one substance cannot contain another actually existing substance (Aristot. Met. 7.8.8). Form, however, is not a substance but a characteristic. Form means of such a kind; it is not a definite individual, but we produce or generate from the individual something of such a kind; and when it is generated it is an individual of such a kind.

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The whole individual, Callias or Socrates, corresponds to this bronze sphere, but man and animal correspond to bronze sphere in general.

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Obviously therefore the cause which consists of the Forms (in the sense in which some speak of them, assuming that there are certain entities besides particulars), in respect at least of generation and destruction, is useless; nor, for this reason at any rate, should they be regarded as self-subsistent substances.

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Indeed in some cases it is even obvious that that which generates is of the same kind as that which is generated—not however identical with it, nor numerically one with it, but formally one—e.g. in natural productions (for man begets man), unless something happens contrary to nature, as when a horse sires a mule. And even these cases are similar; for that which would be common to both horse and ass, the genus immediately above them, has no name; but it would probably be both, just as the mule is both.Normally the sire communicates his form to the offspring. In the case of a mule, the material element contributed by the dam, which is an ass, limits the effect of the formal element contributed bu the sire, which is a horse; but even so the form of the sire is generically the same as that of the offspring.

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Thus obviously there is no need to set up a form as a pattern (for we should have looked for Forms in these cases especially, since living things are in a special sense substances); the thing which generates is sufficient to produce, and to be the cause of the form in the matter. The completed whole, such-and-such a form induced in this flesh and these bones, is Callias or Socrates. And it is different from that which generated it, because the matter is different but identical in form, because the form is indivisible.

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The question might be raised why some things are generated both artificially and spontaneously—e.g. health—and others not; e.g. a house. The reason is that in some cases the matter—which is the starting-point of the process in the production and generation of artificial things, and in which some part of the result is already existent—is such that it can initiate its own motion, and in other cases it is not; and of the former kind some can initiate motion in a particular way, and some cannot. For many things can move themselves, but not in a particular way, e.g. so as to dance.

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It is impossible, then, for any things whose matter is of this kind (e.g. stones) to be moved in this particular way except by something else; but in that particular way it is possible. And it is so with fire.Stones can fall by themselves, but cannot by themselves build a house; fire can rise by itself, but cannot boil a kettle. For this reason some things cannot exist apart from the possessor of the art, and others can; because the motion can be initiated by those things which do not indeed possess the art, but can themselves be moved either by other things which do not possess the art, or by the motion from the part of the product which pre-exists in them.e.g., health can be produced as the result of the activity set up by heat in the body.

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It is clear also from what we have said that in a sense all artificial things are generated either from something which bears the same name (as is the case with natural objects) or from a part of themselves which bears the same name as themselves (e.g. a house from a house, inasmuch as it is generated by mind; for the art is the form), or from something which contains some part; that is if the generation is not accidental; for the direct and independent cause of the production is a part of the product.

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Heat in the motion produces heat in the body; and either this is health or a part of health, or a part of health or health accompanies it. And this is why heat is said to produce health, because it produces that of which health is a concomitant and consequence. Therefore as essence is the starting-point of everything in syllogisms (because syllogisms start from the what of a thing), so too generation proceeds from it.

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And it is the same with natural formations as it is with the products of art. For the seed produces just as do those things which function by art. It contains the form potentially, and that from which the seed comes has in some sense the same name as the product (for we must not expect that all should have the same name in the sense that man is produced by man—since woman is also produced by man); unless the product is a freak. This is why a mule is not produced by a mule.

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Those natural objects which are produced, like artificial objects, spontaneously, are those whose matter can also initiate for itself that motion which the seed initiates. Those whose matter cannot do this cannot be generated otherwise than by their proper parents.

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It is not only with reference to substance that our argument shows that the form is not generated; the same argument is common in its application to all the primary divisions, i.e. quantity, quality and the other categories.

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For just as the bronze sphere is generated, but not the sphere nor the bronze; and as in the case of bronze, if it is generated the form and matter are not (because they must always pre-exist), so it is too with the what and the quality and quantity and the other categories similarly; for it is not the quality that is generated, but the wood of that quality; nor is it the size, but the wood or animal of that size.

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But a peculiarity of substance may be gathered from this: that some other substance must pre-exist in actuality which produces it; e.g. an animal, if an animal is being generated; but a quality or quantity need not pre-exist otherwise than potentially.

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Since a definition is a formula, and every formula has parts; and since the formula is related to the thing in the same way as the part of the formula to the part of the thing, the questionThe questions discussed in chs. 10-12 arise out of the consideration of essence as definition. now arises: Must the formula of the parts be contained in the formula of the whole, or not? It seems clear that it is so in some cases, but not in others.

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The formula of the circle does not include that of the segments, but the formula of the syllable includes that of the letters. And yet the circle is divisible into its segments in just the same way as the syllable into its letters.

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Again, if the parts are prior to the whole, and the acute angle is part of the right angle, and the finger part of the animal, the acute angle will be prior to the right angle, and the finger to the man.

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But it is considered that the latter are prior; for in the formula the parts are explained from them; and the wholes are prior also in virtue of their ability to exist independently. The truth probably is that part has several meanings, one of which is that which measures in respect of quantity. However, let us dismiss this question and consider of what, in the sense of parts, substance consists.

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If then matter, form, and the combination of the two are distinct, and if both matter and form and their combination are substance, there is one sense in which even matter may be called part of a thing; and another in which it is not, but the only parts are those elements of which the formula of the form consists. E.g., flesh is not a part of concavity, because flesh is the matter in which concavity is induced; but it is a part of snubness. And bronze is part of the statue as a concrete whole, but not of the statue in the sense of form.

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We may speak of the form (or the thing as having a form) as an individual thing, but we may never so speak of that which is material by itself. This is why the formula of the circle does not contain that of the segments, whereas the formula of the syllable does contain that of the letters; for the letters are parts of the formula of the form; they are not matter; but the segments are parts in the sense of matter in which the form is induced. They approximate, however, more closely to the form than does the bronze when roundness is engendered in bronze.

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But there is a sense in which not even all the letters will be contained in the formula of the syllable; e.g. particular letters on waxi.e. written on a waxed tablet. or sounds in the air; for these too are part of the syllable in the sense that they are its sensible matter.

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For even if the line is divided and resolved into its halves, or if the man is resolved into bones and muscles and flesh, it does not follow that they are composed of these as parts of their essence, but as their matter; and these are parts of the concrete whole, but not of the form, or that to which the formula refers. Hence they are not in the formulae.

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Accordingly in some cases the formula will include the formula of such parts as the above, but in others it need not necessarily contain their formula, unless it is the formula of the concrete object. It is for this reason that some things are composed of parts in the sense of principles into which they can be resolved, while others are not.

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All things which are concrete combinations of form and matter (e.g. the snub or the bronze circle) can be resolved into form and matter, and the matter is a part of them; but such as are not concrete combinations with matter, but are without matter—whose formulae refer to the form only—cannot be resolved; either not at all, or at least not in this way.

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Thus these material components are principles and parts of the concrete objects, but they are neither parts nor principles of the form. For this reason the clay statue can be resolved into clay, and the sphere into bronze, and Callias into flesh and bones, and the circle too into segments, because it is something which is combined with matter. For we use the same name for the absolute circle and for the particular circle, since there is no special name for the particular circles.

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We have now stated the truth; nevertheless let us recapitulate and state it more clearly. All constituents which are parts of the formula, and into which the formula can be divided, are prior to their wholes—either all or some of them. But the formula of the right angle is not divisible into the formula of an acute angle, but vice versa; since in defining the acute angle we use the right angle, because the acute angle is less than a right angle.

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It is the same with the circle and the semicircle; for the semicircle is defined by means of the circle. And the finger is defined by means of the whole body; for a finger is a particular kind of part of a man. Thus such parts as are material, and into which the whole is resolved as into matter, are posterior to the whole; but such as are parts in the sense of parts of the formula and of the essence as expressed in the formula, are prior; either all or some of them.

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And since the soul of animals (which is the substance of the living creature) is their substance in accordance with the formula, and the form and essence of that particular kind of body (at least each part, if it is to be properly defined, will not be defined apart from its function; and this will not belong to it apart from perceptionWhich implies soul.); therefore the parts of the soul are prior, either all or some of them, to the concrete animal; and similarly in other individual cases.

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But the body and its parts are posterior to this substance, and it is not the substance, but the concrete whole, which is resolved into these parts as into matter. Therefore in one sense these parts are prior to the concrete whole, and in another not; for they cannot exist in separation. A finger cannot in every state be a part of a living animal; for the dead finger has only the name in common with the living one.

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Some parts are contemporary with the whole: such as are indispensable and in which the formula and the essence are primarily present; e.g. the heart or perhaps the brain,Cf. Aristot. Met. 5.1.1. for it does not matter which of them is of this nature. But man and horse and terms which are applied in this way to individuals, but universally, are not substance, but a kind of concrete whole composed of this particular formula and this particular matter regarded as universal. But individually Socrates is already composed of ultimate matter; and similarly in all other cases.

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A part, then, may be part of the form (by form I mean essence), or of the concrete whole composed of form and matter, or of the matter itself. But only the parts of the form are parts of the formula, and the formula refers to the universal; for circle is the same as essence of circle, and soul the same as essence of soul.

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But when we come to the concrete thing, e.g. this circle—which is a particular individual, either sensible or intelligible (by intelligible circles I mean those of mathematics,i.e., something very similar to the Platonic intermediates. Cf. Introduction. and by sensible those which are of bronze or wood)—of these individuals there is no definition;

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we apprehend them by intelligence or perception; and when they have passed from the sphere of actuality it is uncertain whether they exist or not, but they are always spoken of and apprehended by the universal formula. But the matter is in itself unknowable. Some matter is sensible and some intelligible; sensible, such as bronze and wood and all movable matter; intelligible, that which is present in sensible things not qua sensible, e.g. the objects of mathematics.See Aristot. Met. 13.2, 3.

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We have now discussed the case of the whole and part, and of prior and posterior. But we must answer the question, when we are asked which is prior—the right angle and circle and animal, or that into which they are resolved and of which they are composed, i.e. their parts—by saying that neither is absolutely prior.

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For if the soul also is the animal or living thing, or the soul of the individual is the individual, and being a circle is the circle, and being a right angle or the essence of the right angle is the right angle, then we must admit that the whole in one sense is posterior to the part in one sense: e.g. to the parts in the formula and the parts of a particular right angle

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(since both the material right angle of bronze and the right angle included by individual lines are posterior to their parts), but the immaterial angle is posterior to the parts in the formula, but prior to the parts in the individual. We must not give an unqualified answer. And if the soul is not the animal but something else, even so we must say that some wholes are prior and some are not, as has been stated.

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The question naturally presents itself, what sort of parts belong to the form and what sort belong not to it but to the concrete object. Yet if this is not plain it is impossible to define the particular; because the definition refers to the universal and the form. Therefore if it is not clear what kind of parts are material and what kind are not, the formula of the thing will not be clear either.

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In the case of things which can be seen to be induced in specifically different materials, as, e.g., a circle is in bronze and stone and wood, it seems clear that these things, the bronze and the stone, are in no sense part of the essential substance of the circle, because it is separable from them.

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As for things which are not visibly separable, there is no reason why the same should not apply to them; e.g., if all the circles that had ever been seen were bronze; for the bronze would be none the less no part of the form, but it is difficult to separate it in thought.

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For example, the form of man is always manifested in flesh and bones and elements of this kind; then are these actually parts of the form and formula, or are they not so, but matter, though since the form is not induced in other materials, we cannot separate it?

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Now since this seems to be possible, but it is not clear when, some thinkersThe Pythagoreans. are doubtful even in the case of the circle and the triangle, considering that it is not proper to define them by lines and continuous space, but that all these are to the circle or triangle as flesh or bone is to man, and bronze or stone to the statue; and they reduce everything to numbers, and say that the formula of line is the formula of 2.

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And of the exponents of the Forms, some make 2 the Ideal line, and some the form of the lineThe distinction seems to be that given in Aristot. Met. 8.3.1. Some held that the line, considered absolutely, is simply twoness; others that it is twoness in length. ; for they say that in some cases the form and that of which it is the form, e.g. 2 and the form of 2, are the same; but in the case of line this is no longer so.

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It follows, then, that there is one form of many things whose form is clearly different (a consequence which confronted the Pythagoreans tooCf. Aristot. Met. 1.5.17.), and that it is possible to make one supreme Form of everything, and not to regard the rest as forms. In this way, however, all things would be one.

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Now we have stated that the question of definitions involves some difficulty, and have shown why this is so. Hence to reduce everything in this way and to dispose of the matter is going too far; for some things are presumably a particular form in particular matter, or particular things in a particular state.

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And the analogy in the case of the living thing which the younger SocratesA disciple of the great Socrates; one of the speakers in the PoliticusPlat. Stat. and referred to in Plat. Theaet. 147c, Plat. Soph. 218b. used to state is not a good one; for it leads one away from the truth, and makes one suppose that it is possible for a man to exist without his parts, as a circle does without the bronze. But the case is not similar; for the animal is sensible and cannot be defined without motion, and hence not unless its parts are in some definite condition;

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for it is not the hand in any condition that is a part of a man, but only when it can perform its function, and so has life in it. Without life in it it is not a part.

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And with respect to mathematical objects, why are the formulae of the parts not parts of the formulae of the whole; e.g., why are the formulae of the semicircles not parts of the formula of the circle? for they are not sensible.

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Probably this makes no difference; because there will be matter even of some things which are not sensible. Indeed there will be matter in some sense in everything which is not essence or form considered independently, but a particular thing. Thus the semicircles will be parts not of the universal circle but of the particular circles, as we said beforeAristot. Met. 7.10.17.—for some matter is sensible, and some intelligible.

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It is clear also that the soul is the primary substance, and the body matter; and man or animal is the combination of both taken universally. And Socrates or Coriscus has a double sense, that is if the soul too can be called Socrates (for by Socrates some mean the soul and some the concrete person); but if Socrates means simply this soul and this body, the individual is composed similarly to the universal.

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Whether there is some other material component of these substances besides their matter, and whether we should look for some further substance in them, such as numbers or something of that kind, must be considered later.In Books 13 and 14. It is with a view to this that we are trying to determine the nature of sensible substances, since in a sense the study of sensible substances belongs to physics or secondary philosophy; for the physicist must know not only about the matter, but also about the substance according to the formula; this is even more essential.

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And in the case of definitions, in what sense the elements in the formula are parts of the definition, and why the definition is one formula (for the thing is clearly one, but in virtue of what is it one, seeing that it has parts?); this must be considered later.Aristot. Met. 8.6.

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We have stated, then, in a general account which covers all cases, what essence is, and how it is independent; and why the formula of the essence of some things contains the parts of the thing defined, while that of others does not; and we have shown that the material parts of a thing cannot be present in the formula of the substance (since they are not even parts of the substance in that sense, but of the concrete substance; and of this in one sense there is a formula, and in another sense there is not.

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There is no formula involving the matter, for this is indeterminate; but there is a formula in accordance with the primary substance, e.g., in the case of a man, the formula of the soul; because the substance is the indwelling form, of which and of the matter the so called concrete substance is composed. E.g., concavity is such a form, since from this and nose is derived snub nose and snubness—for nose will be present twice over in these expressions);

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but in the concrete substance, e.g. snub nose or Callias, matter will be present too.Chapters. 10-11; and cf. Aristot. Met. 7.4. We have stated also that the essence and the individual are in some cases the same, as in the case of the primary substances; e.g. crookedness and essence of crookedness, if this is primary.

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By primary I mean that which does not imply the presence of something in something else as a material substrate. But such things as are material or are compounded with matter are not the same as their essence; not even if they are accidentally one, e.g. Socrates and cultured; for these are only accidentally the same.

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Now let us first deal with definition, in so far as it has not been dealt with in the Analytics; for the problem stated thereAristot. An. Post. 92a 29. has a bearing upon our discussion of substance. The problem I mean is this: what constitutes the unity of the thing of which we say that the formula is a definition? E.g., in the case of man, two-footed animal; for let us take this as the formula of man.

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Why, then, is this a unity and not a plurality, animal and two-footed? For in the case of man and white we have a plurality when the latter does not refer to the former, but a unity when it does refer to it, and the subject, man, has an attribute; for then they become a unity and we have the white man.

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But in the case before us one term does not partake of the other; the genus is not considered to partake of its differentiae, for then the same thing would be partaking simultaneously of contraries, since the differentiae by which the genus is distinguished are contrary. And even if it does partake of them, the same argument applies, since the differentiae are many; e.g. terrestrial, two-footed, wingless.

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Why is it that these are a unity and not a plurality? Not because they are present in one genus, for in that case all the differentiae of the genus will form a unity. But all the elements in the definition must form a unity, because the definition is a kind of formula which is one and defines substance, so that it must be a formula of one particular thing; because the substance denotes one thing and an individual, as we say.

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We must firstThe other type of definition, that which states the constituent parts of a thing, is not discussed here. examine definitions which are reached by the process of division.

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For there is nothing else in the definition but the primary genus and the differentiae; the other genera consist of the primary genus together with the differentiae which are taken with it. E.g., the primary genus is animal; the next below it, two-footed animal; and again, two-footed wingless animal; and similarly also if the expression contains more terms still.

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In general it does not matter whether it contains many or few terms, nor, therefore, whether it contains few or two. Of the two one is differentia and the other genus; e.g., in two-footed animal animal is genus, and the other term differentia.

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If, then, the genus absolutely does not exist apart from the species which it includes, or if it exists, but only as matter (for speech is genus and matter, and the differentiae make the species, i.e. the letters, out of it), obviously the definition is the formula composed of the differentiae.

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But further we must also divide by the differentia of the differentia. E.g., having feet is a differentia of animal; then in turn we must discover the differentia of animal having feet qua having feet. Accordingly we should not say that of that which has feet one kind is winged and another wingless, (that is if we are to speak correctly; if we say this it will be through incapability), but only that one kind is cloven-footed and another not; because these are differentiae of foot, since cloven-footedness is a kind of footedness.

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And thus we tend always to progress until we come to the species which contain no differentiae. At this point there will be just as many species of foot as there are differentiae, and the kinds of animals having feet will be equal in number to the differentiae. Then, if this is so, obviously the ultimate differentia will be the substance and definition of the thing, since we need not state the same things more than once in definitions, because this is superfluous.

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However, it does happen; for when we say footed two-footed animal we have simply said animal having feet, having two feet. And if we divide this by its proper division, we shall be stating the same thing several times, as many times as there are differentiae.

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If, then, we keep on taking a differentia of a differentia, one of them, the last, will be the form and the substance. But if we proceed with reference to accidental qualities—e.g. if we divide that which has feet into white and black—there will be as many differentiae as there are divisions. It is therefore obvious that the definition is the formula derived from the differentiae, and strictly speaking from the last of them.

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This will be clear if we change the order of such definitions, e.g. that of man, saying two-footed footed animal; for footed is superfluous when we have already said two-footed. But there is no question of order in the substance; for how are we to think of one part as posterior and the other prior?

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With regard, then, to definitions by division, let this suffice as a preliminary statement of their nature.

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Since the subject of our inquiry is substance, let us return to it. Just as the substrate and the essence and the combination of these are called substance, so too is the universal. With two of these we have already dealt, i.e. with the essenceChs. 4-5.,10-12. and the substrateCh. 3.; of the latter we have said that it underlies in two senses—either being an individual thing (as the animal underlies its attributes), or as matter underlies the actuality.

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The universal also is thought by someThe Platonists. to be in the truest sense a cause and a principle. Let us therefore proceed to discuss this question too; for it seems impossible that any universal term can be substance.

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First, the substance of an individual is the substance which is peculiar to it and belongs to nothing else; whereas the universal is common; for by universal we mean that which by nature appertains to several things.

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Of what particular, then, will the universal be the substance? Either of all or of none. But it cannot be the substance of all; while, if it is to be the substance of one, the rest also will be that one; because things whose substance is one have also one essence and are themselves one.

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Again, substance means that which is not predicated of a subject, whereas the universal is always predicated of some subject.

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But perhaps although the universal cannot be substance in the sense that essence is, it can be present in the essence, as animal can be present in man and horse.

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Then clearly there is in some sense a formula of the universal. It makes no difference even if there is not a formula of everything that is in the substance; for the universal will be none the less the substance of something; e.g., man will be the substance of the man in whom it is present. Thus the same thing will happen againi.e., the argument in ch. 3 will apply to this case also.; e.g. animal will be the substance of that in which it is present as peculiar to it.

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Again, it is impossible and absurd that the individual or substance, if it is composed of anything, should be composed not of substances nor of the individual, but of a quality; for then non-substance or quality will be prior to substance or the individual. Which is impossible; for neither in formula nor in time nor in generation can the affections of substance be prior to the substance, since then they would be separable.

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Again, a substance will be present in Socrates, who is a substance; so that it will be the substance of two things. And in general it follows that if man and all terms used in this way are substance, none of the elements in the formula is the substance of anything, nor can it exist apart from the species or in anything else; I mean, e.g., that neither animal nor any other element of the formula can exist apart from the particular species.

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If we look at the question from this standpoint it is obvious that no universal attribute is substance; and it is also clear from the fact that none of the common predicates means so-and-so, but such and-such. Otherwise amongst many other awkward consequences we have the third man. See note on Aristot. Met. 1.9.3.

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Again, it is clear in this way too. Substance can not consist of substances actually present in it; for that which is actually two can never be actually one, whereas if it is potentially two it can be one. E.g., the double consists of two halves—that is, potentially; for the actualization separates the halves.

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Thus if substance is one, it cannot consist of substances present in it even in this sense, as Democritus rightly observes; he says that it is impossible for two to come from one, or one from two, because he identifies substance with the atoms.Cf. Aristot. De Caelo 303a 6, Aristot. De Gen. et Corr. 325a 35.

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Clearly then the same will also hold good in the case of number (assuming that number is a composition of units, as it is said to be by some); because either 2 is not 1, or there is not actually a unit in it.

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The consequence involves a difficulty; for if no substance can consist of universals, because they mean of such a kind, and not a particular thing; and if no substance can be actually composed of substances, every substance will be incomposite, and so there will be no formula of any substance.

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But in point of fact it is universally held, and has been previously stated,Aristot. Met. 7.5.5-7. that substance is the only or chief subject of definition; but on this showing there is no definition even of substance. Then there can be no definition of anything; or rather in a sense there can, and in a sense cannot. What this means will be clearer from what follows later.Aristot. Met. 7.15, Aristot. Met. 8.6.

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From these same considerations it is clear also what consequence follows for those who maintain that the Forms are substances and separable, and who at the same time make the species consist of the genus and the differentiae. If there are Forms, and if animal is present in the man and the horse, it is either numerically one and the same with them, or not.

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(In formula they are clearly one; for in each case the speaker will enunciate the same formula.) If, then, there is in some sense an Absolute Man, who is an individual and exists separately, then the constituents, e.g. animal and two-footed, must have an individual meaning and be separable and substances. Hence there must be an Absolute Animal too.

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(i) Then if the animal which is in the horse and the man is one and the same, as you are one and the same with yourself, how can the one which in things that exist separately be one, and why should not this animal also be separated from itself? Again, if it is to partake of two-footed and of many-footed, an impossibility follows; for contrary attributes will belong to it although it is one and individual.

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But if it does not, in what sense is it that one calls an animal two-footed or terrestrial? Perhaps the terms are combined and in contact or mixed. But all these expressions are absurd.

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(2) But there is a different animal in each species. Then there will be practically an infinity of things of which animal is the substance, since it is not in an accidental sense that man is derived from animal.

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Again, the Absolute Animal will be a plurality. For (a) the animal in each species will be the substance of that species, since the species is called after it and no other thing. Otherwise man would be derived from that other thing, which would be the genus of man. (b) Further, all the constituents of man will be Ideas. Then, since nothing can be the Idea of one thing and the substance of another (for this is impossible),

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each and every animal in the various species will be the Absolute Animal.

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Further, from what will these Forms be derived, and how can they be derived from the Absolute Animal? Or how can the animal, whose very essence is animal, exist apart from the Absolute Animal? And further, in the case of sensible things both these and still more absurd consequences follow. If, then, these consequences are impossible, clearly there are not Forms of sensible things in the sense in which some hold that there are.

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Since substance is of two kinds, the concrete thing and the formula (I mean that one kind of substance is the formula in combination with the matter, and the other is the formula in its full sense), substances in the former sense admit of destruction, for they also admit of generation. But the formula does not admit of destruction in the sense that it is ever being destroyed, since neither does it so admit of generation (for the essence of house is not generated, but only the essence of this house); formulae are , and are not, independently of generation and destruction; for it has been shownCf. Aristot. Met. 7.8.3. that no one either generates or creates them.

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For this reason also there is no definition or demonstration of particular sensible substances, because they contain matter whose nature is such that it can both exist and not exist. Hence all the individual instances of them are perishable.

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If, then, the demonstration and definition of necessary truths requires scientific knowledge, and if, just as knowledge cannot be sometimes knowledge and sometimes ignorance (it is opinion that is of this nature), so too demonstration and definition cannot vary (it is opinion that is concerned with that which can be otherwise than it is)— then clearly there can be neither definition nor demonstration of individual sensible substances.

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For (a) things which perish are obscure to those who have knowledge of them when they are removed from the sphere of their perception, and (b) even though their formulae are preserved in the soul, there will no longer be either definition or demonstration of them. Therefore in cases relating to definition, when we are trying to define any individual, we must not fail to realize that our definition may always be upset; because it is impossible to define these things.

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Nor, indeed, can any Idea be defined; for the Idea is an individual, as they say, and separable; and the formula must consist of words, and the man who is defining must not coin a word, because it would not be comprehensible. But the words which are in use are common to all the things which they denote; and so they must necessarily apply to something else as well. E.g., if a man were to define you, he would say that you are an animal which is lean or white or has some other attribute, which will apply to something else as well.

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And if it should be said that there is no reason why all the attributes separately should not belong to several things, and yet in combination belong to this alone, we must reply, (1.) that they also belong to both the elements; e.g., two-footed animal belongs both to animal and to two-footed (and in the case of eternal elements this is even necessarily so; since they are prior to the compound, and parts of it.

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Indeed they are also separable, if the term man is separable—for either neither can be separable, or both are so. If neither, the genus will not exist apart from the species, or if it is so to exist, so will the differentia); (2.) that animal and two-footed are prior in being to two-footed animal, and that which is prior to something else is not destroyed together with it.

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Again, if the Ideas are composed of Ideas (for constituents are less composite than that which they compose), still the elements of which the Idea is composed (e.g. animal and two-footed) will have to be predicated of many particulars. Otherwise, how can they be known? For there would be an Idea which cannot be predicated of more than one thing. But this is not considered possible; every Idea is thought to admit of participation.

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Thus, as we have said,The statement has only been implied in the preceding arguments. the impossibility of defining individuals is hard to realize when we are dealing with eternal entities, especially in the case of such as are unique, e.g. the sun and moon. For people go wrong not only by including in the definition attributes on whose removal it will still be sun—e.g., that which goes round the earth, or night-hidden (for they suppose that if it stops or becomes visiblesc. in the night. it will no longer be sun; but it is absurd that this should be so, since the sun denotes a definite substance)—they also mention attributes which may apply to something else; e.g., if another thing with those attributes comes into being, clearly it will be a sun. The formula, then, is general; but the sun was supposed to be an individual, like Cleon or Socrates.

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Why does not one of the exponents of the Ideas produce a definition of them? If they were to try, it would become obvious that what we have just said is true.

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It is obvious that even of those things which are thought to be substances the majority are potentialities; both the parts of living things (for none of them has a separate substantial existence; and when they are separated, although they still exist, they exist as matter), and earth, fire and air; for none of these is one thing —they are a mere aggregate before they are digested and some one thing is generated from them.

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It might be supposed very reasonably that the parts of living things and the corresponding parts of their vital principle are both, i.e. exist both actually and potentially, because they contain principles of motion derived from something in their joints; and hence some animalse.g. wasps, bees, tortoises (P. Nat. 467a 18, 468a 25). live even when they are divided. Nevertheless it is only potentially that all of them will exist when they are one and continuous by nature and not by force or concretion; for this sort of thing is malformation.i.e., it is only when they do not properly constitute a unity that parts can be said to exist actually.

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And since unity has the same variety of senses as being, and the substance of Unity is one, and things whose substance is numerically one are numerically one, evidently neither Unity nor Being can be the substance of things, just as neither being an element or principle can be the substance; but we ask what the principle is so that we may refer to something more intelligible.i.e., a thing is a principle in relation to something else which it explains; therefore a principle is less substantial than unity or being, which belong to a thing in itself.

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Now of these concepts Being and Unity are more nearly substance than are principle, element and cause; but not even the former are quite substance, since nothing else that is common is substance; for substance belongs to nothing except itself and that which contains it and of which it is the substance.

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Again, Unity cannot exist in many places at the same time, but that which is common is present in many things at the same time. Hence it is clear that no universal exists in separation apart from its particulars. The exponents of the Forms are partly right in their account when they make the Forms separate; that is, if the Forms are substances, but they are also partly wrong, since by Form they mean the one-over-many. i.e. universal; cf. Aristot. Met. 1.9.1.

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The reason for this is that they cannot explain what are the imperishable substances of this kind which exist besides particular sensible substances; so they make them the same in kind as perishable things (for these we know); i.e., they make Ideal Man and Ideal Horse, adding the word Ideal to the names of sensible things.

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However, I presume that even if we had never seen the stars, none the less there would be eternal substances besides those which we knew; and so in the present case even if we cannot apprehend what they are, still there must be eternal substances of some kind.

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It is clear, then, both that no universal term is substance and that no substance is composed of substances.

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As for what and what sort of thing we mean by substance, let us explain this by making, as it were, another fresh start. Perhaps in this way we shall also obtain some light upon that kind of substance which exists in separation from sensible substances. Since, then, substance is a kind of principle and cause, we had better pursue our inquiry from this point.

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Now when we ask why a thing is, it is always in the sense why does A belong to B?

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To ask why the cultured man is a cultured man is to ask either, as we have said, why the man is cultured, or something else. Now to ask why a thing is itself is no question; because when we ask the reason of a thing the fact must first be evident; e.g., that the moon suffers eclipse;

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and because it is itself is the one explanation and reason which applies to all questions such as why is man man? or why is the cultured person cultured? (unless one were to say that each thing is indivisible from itself, and that this is what being one really means); but this, besides being a general answer, is a summary one.The argument is: The question Why is the cultured man a cultured man? if it does not mean Why is the man cultured? can only mean Why is a thing itself? But when we ask a question the fact must be obvious; and since it is obvious that a thing is itself, because it is itself (or because each thing is indivisible from itself) is the one and only complete answer to all questions of this type. Since this answer (in either form) is clearly unsatisfactory, the question which it answers cannot be a proper question. We may, however, ask why a man is an animal of such-and-such a kind.

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It is clear, then, that we are not asking why he who is a man is a man; therefore we are asking why A, which is predicated of B, belongs to B. (The fact that A does belong to B must be evident, for if this is not so, the question is pointless.) E.g., Why does it thunder? means why is a noise produced in the clouds? for the true form of the question is one thing predicated in this way of another.

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Or again, why are these things, e.g. bricks and stones, a house? Clearly then we are inquiring for the cause (i.e., to speak abstractly, the essence); which is in the case of some things, e.g. house or bed, the end , and in others the prime mover—for this also is a cause. We look for the latter kind of cause in the case of generation and destruction, but for the former also in the case of existence.

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What we are now looking for is most obscure when one term is not predicated of another; e.g. when we inquire what man is; because the expression is a simple one not analyzed into subject and attributes. We must make the question articulate before we ask it; otherwise we get something which shares the nature of a pointless and of a definite question.

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Now since we must know that the fact actually exists, it is surely clear that the question is why is the matter so-and-so? e.g. why are these materials a house? Because the essence of house is present in them. And this matter, or the body containing this particular form, is man. Thus what we are seeking is the cause (i.e. the form) in virtue of which the matter is a definite thing; and this is the substance of the thing.

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Clearly then in the case of simple entitiesPure forms which contain no matter; in their case the method just described obviously will not apply. They can only be apprehended intuitively (cf. Aristot. Met. 9.10.). inquiry and explanation are impossible; in such cases there is a different mode of inquiry.

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Now since that which is composed of something in such a way that the whole is a unity; not as an aggregate is a unity, but as a syllable isThis sentence is not finished; the parenthesis which follows lasts until the end of the chapter.—the syllable is not the letters, nor is BA the same as B and A; nor is flesh fire and earth; because after dissolution the compounds, e.g. flesh or the syllable, no longer exist; but the letters exist, and so do fire and earth.

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Therefore the syllable is some particular thing; not merely the letters, vowel and consonant, but something else besides. And flesh is not merely fire and earth, or hot and cold, but something else besides.

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Since then this something else must be either an element or composed of elements, (a) if it is an element, the same argument applies again; for flesh will be composed of this and fire and earth, and again of another element, so that there will be an infinite regression. And (b) if it is composed of elements, clearly it is composed not of one (otherwise it will itself be that element) but of several; so that we shall use the same argument in this case as about the flesh or the syllable.

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It would seem, however, that this something else is something that is not an element, but is the cause that this matter is flesh and that matter a syllable, and similarly in other cases.

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And this is the substance of each thing, for it is the primary cause of its existence. And since, although some things are not substances, all substances are constituted in accordance with and by nature, substance would seem to be this nature, which is not an element but a principle.i.e. the formal cause. Cf. Aristot. Met. 5.4.4-6. An element is that which is present as matter in a thing, and into which the thing is divided; e.g., A and B are the elements of the syllable.

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We must now draw our conclusions from what has been said, and after summing up the result, bring our inquiry to a close. We have saidCf. Aristot. Met. 7.1. that the objects of our inquiry are the causes and principles and elements of substances. Now some substances are agreed upon by all; but about others certain thinkers have stated individual theories.

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Those about which there is agreement are natural substances: e.g. fire, earth, water, air and all the other simple bodies; next, plants and their parts, and animals and the parts of animals; and finally the sensible universe and its parts; and certain thinkers individually include as substances the Forms and the objects of mathematics.Cf. Aristot. Met. 7.2.

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And arguments show that there are yet other substances: the essence and the substrate.Cf. Aristot. Met. 7.3-4. Again, from another point of view, the genus is more nearly substance than the species, and the universal than the particularsCf. Aristot. Met. 7.13.; and there is a close connection between the universal and genus and the Ideas, for they are thought to be substance on the same grounds.Cf. Aristot. Met. 7.14.

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And since the essence is substance, and definition is the formula of the essence, we have therefore systematically examined definition and essential predication.Cf. Aristot. Met. 7.4-6, 12, 15. And since the definition is a formula, and the formula has parts, we have been compelled to investigate parts, and to discover what things are parts of the substance, and what are not; and whether the parts of the substance are also parts of the definition.Cf. Aristot. Met. 7.10, 11. Further, then, neither the universal nor the genus is substance.Cf. Aristot. Met. 7.13, 16.

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As for the Ideas and the objects of mathematics (for some say that these exist apart from sensible substances) we must consider them later.Books 13 and 14. But now let us proceed to discuss those substances which are generally accepted as such.

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Now these are the sensible substances, and all sensible substances contain matter.

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And the substrate is substance; in one sense matter (by matter I mean that which is not actually, but is potentially, an individual thing); and in another the formula and the specific shape (which is an individual thing and is theoretically separable); and thirdly there is the combination of the two, which alone admits of generation and destruction,Cf. Aristot. Met. 7.8. and is separable in an unqualified sense—for of substances in the sense of formula some are separableIn point of fact the only form which is absolutely separable is Mind or Reason. Cf. Aristot. Met. 12.7, 9. and some are not.

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That matter is also substance is evident; for in all opposite processes of change there is something that underlies those processes; e.g., if the change is of place , that which is now in one place and subsequently in another; and if the change is of magnitude , that which is now of such-and-such a size, and subsequently smaller or greater; and if the change is of quality , that which is now healthy and subsequently diseased.

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Similarly, if the change is in respect of being , there is something which is now in course of generation, and subsequently in course of destruction, and which is the underlying substrate, now as this individual thing, and subsequently as deprived of its individuality. In this last process of change the others are involved, but in either one or twoi.e., locomotion does not involve substantial change; alteration may or may not involve it (in Aristot. Met. 9.8.17 we find that it does not); increase or decrease does involve it. of the others it is not involved; for it does not necessarily follow that if a thing contains matter that admits of change of place, it also contains matter that is generable and destructible.e.g., the heavenly bodies, though imperishable, can move in space (Aristot. Met. 8.4.7, Aristot. Met. 12.2.4). The difference between absolute and qualified generation has been explained in the Physics.Aristot. Phys. 225a 12-20; cf. Aristot. De Gen. et Corr. 317a 17-31.

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Since substance in the sense of substrate or matter is admittedly substance, and this is potential substance, it remains to explain the nature of the actual substance of sensible things. Now DemocritusCf. Aristot. Met. 1.4.11. apparently assumes three differences in substance; for he says that the underlying body is one and the same in material, but differs in figure, i.e. shape; or inclination, i.e. position; or intercontact, i.e. arrangement.

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But evidently there are many differences; e.g. some things are defined by the way in which their materials are combined, as, for example, things which are unified by mixture, as honey-water; or by ligature, as a faggot; or by glue, as a book; or by clamping, as a chest; or by more than one of these methods. Other things are defined by their position, e.g. threshold and lintel (for these differ in being situated in a particular way); and others by place <or direction>, e.g. the winds; others by time, e.g. dinner and breakfast; and others by the attributes peculiar to sensible things, e.g. hardness and softness, density and rarity, dryness and humidity. Some are distinguished by some of these differences, and others by all of them; and in general some by excess and some by defect.

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Hence it is clear that is has the same number of senses; for a thing is a threshold because it is situated in a particular way, and to be a threshold means to be situated in this particular way, and to be ice means to be condensed in this particular way. Some things have their being defined in all these ways: by being partly mixed, partly blended, partly bound, partly condensed, and partly subjected to all the other different processes; as, for example, a hand or a foot.

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We must therefore comprehend the various kinds of differences—for these will be principles of being—i.e. the differences in degree, or in density and rarity, and in other such modifications, for they are all instances of excess and defect.

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And if anything differs in shape or in smoothness or roughness, all these are differences in straightness and curvature. For some things mixture will constitute being, and the opposite state not-being.

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From this it is evident that if substance is the cause of the existence of each thing, we must look among these differences for the cause of the being of each thing.

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No one of them, nor the combination of any two of them, is substance, but nevertheless each one of them contains something analogous to substance. And just as in the case of substances that which is predicated of the matter is the actuality itself, so in the other kinds of definition it is the nearest approximation to actuality. E.g., if we have to define a threshold, we shall call it a piece of wood or stone placed in such-and-such a way; and we should define a house as bricks and timber arranged in such-and-such a way;

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or again in some cases there is the final cause as well. And if we are defining ice, we shall describe it as water congealed or condensed in such-and-such a way; and a harmony is such-and-such a combination of high and low; and similarly in the other cases.

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From this it is evident that the actuality or formula is different in the case of different matter; for in some cases it is a combination, in others a mixture, and in others some other of the modes which we have described.

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Hence in defining the nature of a house, those who describe it as stones, bricks and wood, describe the potential house, since these things are its matter; those who describe it as a receptacle for containing goods and bodies, or something else to the same effect, describe its actuality; but those who combine these two definitions describe the third kind of substance, that which is composed of matter and form.

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For it would seem that the formula which involves the differentiae is that of the form and the actuality, while that which involves the constituent parts is rather that of the matter. The same is true of the kind of definitions which ArchytasA celebrated Pythagorean, contemporary with Plato. used to accept; for they are definitions of the combined matter and form. E.g., what is windlessness? Stillness in a large extent of air; for the air is the matter, and the stillness is the actuality and substance.

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What is a calm? Levelness of sea. The sea is the material substrate, and the levelness is the actuality or form.

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From the foregoing account it is clear what sensible substance is, and in what sense it exists; either as matter, or as form and actuality, or thirdly as the combination of the two.

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We must not fail to realize that sometimes it is doubtful whether a name denotes the composite substance or the actuality and the form—e.g. whether house denotes the composite thing, a covering made of bricks and stones arranged in such-and-such a way, or the actuality and form, a covering; and whether line means duality in length or dualityCf. Aristot. Met. 7.11.6.; and whether animal means a soul in a body or a soul; for the soul is the substance and actuality of some body.

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The term animal would be applicable to both cases; not as being defined by one formula, but as relating to one concept. These distinctions are of importance from another point of view, but unimportant for the investigation of sensible substance; because the essence belongs to the form and the actualization.

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Soul and essence of soul are the same, but man and essence of man are not, unless the soul is also to be called man; and although this is so in one sense, it is not so in another.

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It appears, then, upon inquiry into the matter,Cf. Plat. Theaet. 204aff. that a syllable is not derived from the phonetic elements plus combination, nor is a house bricks plus combination. And this is true; for the combination or mixture is not derived from the things of which it is a combination or mixture,

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nor, similarly, is any other of the differences. E.g., if the threshold is defined by its position, the position is not derived from the threshold, but rather vice versa. Nor, indeed, is man animal plus two-footed; there must be something which exists besides these, if they are matter; but it is neither an element nor derived from an element, but the substance; and those who offer the definition given above are omitting this and describing the matter.

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If, then, this something else is the cause of a man’s being, and this is his substance, they will not be stating his actual substance.

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Now the substance must be either eternal or perishable without ever being in process of perishing, and generated without ever being in process of generation. It has been clearly demonstrated elsewhereCf. Aristot. Met. 7.8. that no one generates or creates the form; it is the individual thing that is created, and the compound that is generated.

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But whether the substances of perishable things are separable or not is not yet at all clearCf. Aristot. Met. 8.1.6. n..; only it is clear that this is impossible in some cases, i.e. in the case of all things which cannot exist apart from the particular instances; e.g. house or implement.Cf. Aristot. Met. 7.8.6. Probably, then, neither these things themselves, nor anything else which is not naturally composed, are substances; for their nature is the only substance which one can assume in the case of perishable things.

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Hence the difficulty which perplexed the followers of AntisthenesCf. Aristot. Met. 5.29.4. and others similarly unlearned has a certain application; I mean the difficulty that it is impossible to define what a thing is (for the definition, they say, is a lengthy formula), but it is possible actually to teach others what a thing is like; e.g., we cannot say what silver is, but we can say that it is like tin.

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Hence there can be definition and formula of one kind of substance, i.e. the composite, whether it is sensible or intelligible; but not of its primary constituents, since the defining formula denotes something predicated of something, and this must be partly of the nature of matter and partly of the nature of form.

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It is also obvious that, if numbers are in any sense substances, they are such in this sense, and not, as someAristotle is referring to the Pythagoreans and Platonists, but seems as usual to misrepresent their views. His object in this section is to show that the relation of number to substance is only one of analogy. Cf. Aristot. Met. 13.6, 7, and see Introduction. describe them, aggregates of units. For (a) the definition is a kind of number, since it is divisible, and divisible into indivisible parts (for formulae are not infinite); and number is of this nature.

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And (b) just as when any element which composes the number is subtracted or added, it is no longer the same number but a different one, however small the subtraction or addition is; so neither the definition nor the essence will continue to exist if something is subtracted from or added to it. And (c) a number must be something in virtue of which it is a unity (whereas our opponents cannot say what makes it one); that is, if it is a unity.

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For either it is not a unity but a kind of aggregate, or if it is a unity, we must explain what makes a unity out of a plurality. And the definition is a unity; but similarly they cannot explain the definition either. This is a natural consequence, for the same reason applies to both, and substance is a unity in the way which we have explained, and not as some thinkers say: e.g. because it is a kind of unit or point; but each substance is a kind of actuality and nature.

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Also (d) just as a number does not admit of variation in degree, so neither does substance in the sense of form; if any substance does admit of this, it is substance in combination with matter.In Aristot. Categories 3b 33-4a 9 Aristotle does not allow this exception.

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Let this suffice as a detailed account of the generation and destruction of so-called substances, in what sense they are possible and in what sense they are not; and of the reference of things to number.

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As regards material substance, we must not fail to realize that even if all things are derived from the same primary cause, or from the same things as primary causesi.e. from prime matter or the four elements.; i.e. even if all things that are generated have the same matter for their first principle, nevertheless each thing has some matter peculiar to it; e.g., the sweet or the viscous is the proximate matter of mucus, and the bitter or some such thing is that of bile— although probably mucus and bile are derived from the same ultimate matter.

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The result is that there is more than one matter of the same thing, when one thing is the matter of the other; e.g., mucus is derived from the viscous; and from the sweet, if the viscous is derived from the sweet; and from bile, by the analysis of bile into its ultimate matter. For there are two senses in which X comes from Y; either because X will be found further on than Y in the process of development, or because X is produced when Y is analyzed into its original constituents.

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And different things can be generated by the moving cause when the matter is one and the same, e.g. a chest and a bed from wood. But some different things must necessarily have different matter; e.g., a saw cannot be generated from wood, nor does this lie in the power of the moving cause, for it cannot make a saw of wool or wood.

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If, then, it is possible to make the same thing from different matter, clearly the art, i.e. the moving principle, is the same; for if both the matter and the mover are different, so too is the product.

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So whenever we inquire what the cause is, since there are causes in several senses, we must state all the possible causes.

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E.g., what is the material cause of a man? The menses. What is the moving cause? The semen. What is the formal cause? The essence. What is the final cause? The end. (But perhaps both the latter are the same.) We must, however, state the most proximate causes. What is the matter? Not fire or earth, but the matter proper to man.

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Thus as regards generable natural substances we must proceed in this manner, if we are to proceed correctly; that is, if the causes are these and of this number, and it is necessary to know the causes. But in the case of substances which though natural are eternal the principle is different. For presumably some of them have no matter; or no matter of this kind, but only such as is spatially mobile.Cf. Aristot. Met. 8.1.8 n.

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Moreover, things which exist by nature but are not substances have no matter; their substrate is their substance. E.g., what is the cause of an eclipse; what is its matter? It has none; it is the moon which is affected. What is the moving cause which destroys the light? The earth. There is probably no final cause. The formal cause is the formula; but this is obscure unless it includes the efficient cause.

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E.g., what is an eclipse? A privation of light; and if we add caused by the earth’s intervention, this is the definition which includes the <efficient> cause. In the case of sleep it is not clear what it is that is proximately affected. Is it the animal? Yes; but in respect of what, and of what proximately? The heart, or some other part. Again, by what is it affected? Again, what is the affection which affects that part, and not the whole animal? A particular kind of immobility? Yes; but in virtue of what affection of the proximate subject is it this?

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Since some things both are and are not, without being liable to generation and destructionCf. Aristot. Met. 6.3.1, Aristot. Met. 7.8.3.—e.g. points,Cf. Aristot. Met. 3.5.8, 9. if they exist at all; and in general the forms and shapes of things (because white does not come to be, but the wood becomes white, since everything which comes into being comes from something and becomes something)—not all the contrariesi.e., we must distinguish contraries in the sense of contrary qualities from contraries in the sense of things characterized by contrary qualities. can be generated from each other. White is not generated from black in the same way as a white man is generated from a black man; nor does everything contain matter, but only such things as admit of generation and transformation into each other.

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And such things as, without undergoing a process of change, both are and are not, have no matter.

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There is a difficulty in the question how the matter of the individual is related to the contraries. E.g., if the body is potentially healthy, and the contrary of health is disease, is the body potentially both healthy and diseased? And is water potentially wine and vinegar? Probably in the one case it is the matter in respect of the positive state and form, and in the other case in respect of privation and degeneration which is contrary to its proper nature.

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There is also a difficulty as to why wine is not the matter of vinegar, nor potentially vinegar (though vinegar comes from it), and why the living man is not potentially dead. In point of fact they are not; their degeneration is accidental, and the actual matter of the living body becomes by degeneration the potentiality and matter of the dead body, and water the matter of vinegar; for the one becomes the other just as day becomes night.

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All things which change reciprocally in this way must return into the matter; e.g., if a living thing is generated from a dead one, it must first become the matter, and then a living thing; and vinegar must first become water, and then wine.

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With regard to the difficulty which we have describedAristot. Met. 7.12, Aristot. Met. 8.3.10, 11. in connection with definitions and numbers, what is the cause of the unification? In all things which have a plurality of parts, and which are not a total aggregate but a whole of some sort distinct from the parts, there is some cause ; inasmuch as even in bodies sometimes contact is the cause of their unity, and sometimes viscosity or some other such quality.

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But a definition is one account, not by connection, like the Iliad , but because it is a definition of one thing.

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What is it, then, that makes man one thing, and why does it make him one thing and not many, e.g. animal and two-footed, especially if, as some say, there is an Idea of animal and an Idea of two-footed?

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Why are not these Ideas man, and why should not man exist by participation, not in any man, but in two Ideas, those of animal and two-footed? And in general man will be not one, but two things—animal and two-footed. Evidently if we proceed in this way, as it is usual to define and explain, it will be impossible to answer and solve the difficulty.

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But if, as we maintain, man is part matter and part form—the matter being potentially, and the form actually man—, the point which we are investigating will no longer seem to be a difficulty. For this difficulty is just the same as we should have if the definition of XLiterally cloak; cf. Aristot. Met. 7.4.7 n. were round bronze; for this name would give a clue to the formula, so that the question becomes what is the cause of the unification of round and bronze?

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The difficulty is no longer apparent, because the one is matter and the other form. What then is it (apart from the active cause) which causes that which exists potentially to exist actually in things which admit of generation? There is no other cause of the potential sphere’s being an actual sphere; this was the essence of each.i.e., it was the essence of the potential sphere to become the actual sphere, and of the actual sphere to be generated from the potential sphere.

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Some matter is intelligible and some sensible, and part of the formula is always matter and part actuality; e.g., the circle is a plane figure.Even formulae contain matter in a sense (intelligible matter); i.e. the generic element in the species. Plane figure is the generic element of circle. But such thingThe highest genera, or categories. as have no matter, neither intelligible nor sensible, are ipso facto each one of them essentially something one; just as they are essentially something existent: an individual substance, a quality, or a quantity. Hence neither existent nor one is present in their definitions. And their essence is ipso facto something one, just as it is something existent.

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Hence also there is no other cause of the unity of any of these things, or of their existence; for each one of them is one and existent not because it is contained in the genus being or unity, nor because these genera exist separately apart from their particulars, but ipso facto.

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It is because of this difficulty that some thinkersThe Platonists. speak of participation, and raise the question of what is the cause of participation, and what participation means; and others speak of communion; e.g., LycophronA sophist, disciple of Gorgias. says that knowledge is a communion of the soul with knowing; and others call life a combination or connection of soul with body.

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The same argument, however, applies in every case; for being healthy will be the communion or connection or combination of soul and health; and being a bronze triangle a combination of bronze and triangle; and being white a combination of surface and whiteness. The reason for this is that people look for a unifying formula, and a difference, between potentiality and actuality.

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But, as we have said,Cf. sects. 4, 5. the proximate matter and the shape are one and the same; the one existing potentially, and the other actually. Therefore to ask the cause of their unity is like asking the cause of unity in general; for each individual thing is one, and the potential and the actual are in a sense one. Thus there is no cause other than whatever initiates the development from potentiality to actuality. And such things as have no matter are all, without qualification, essential unities.

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We have now dealt with Being in the primary sense, to which all the other categories of being are related; i.e. substance. For it is from the concept of substance that all the other modes of being take their meaning; both quantity and quality and all other such terms; for they will all involve the concept of substance, as we stated it in the beginning of our discussion.Aristot. Met. 7.1.

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And since the senses of being are analyzableCf. Aristot. Met. 6.2.1. not only into substance or quality or quantity, but also in accordance with potentiality and actuality and function, let us also gain a clear understanding about potentiality and actuality; and first about potentiality in the sense which is most proper to the word, but not most useful for our present purpose— for potentiality and actuality extend beyond the sphere of terms which only refer to motion.

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When we have discussed this sense of potentiality we will, in the course of our definitions of actuality,Chs. 6-10. explain the others also.

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We have made it plain elsewhereAristot. Met. 5.12. that potentiality and can have several senses.

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All senses which are merely equivocal may be dismissed; for some are used by analogy, as in geometry,Cf. Aristot. Met. 5.12.11. and we call things possible or impossible because they are or are not in some particular way. But the potentialities which conform to the same type are all principles, and derive their meaning from one primary sense of potency, which is the source of change in some other thing, or in the same thing qua other.

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One kind of potentiality is the power of being affected; the principle in the patient itself which initiates a passive change in it by the action of some other thing, or of itself qua other. Another is a positive state of impassivity in respect of deterioration or destruction by something else or by itself qua something else; i.e. by a transformatory principle—for all these definitions contain the formula of the primary sense of potentiality.

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Again, all these potentialities are so called either because they merely act or are acted upon in a particular way, or because they do so well . Hence in their formulae also the formulae of potentiality in the senses previously described are present in some degree.

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Clearly, then, in one sense the potentiality for acting and being acted upon is one (for a thing is capable both because it itself possesses the power of being acted upon, and also because something else has the power of being acted upon by it);

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and in another sense it is not; for it is partly in the patient (for it is because it contains a certain principle, and because even the matter is a kind of principle, that the patient is acted upon; i.e., one thing is acted upon by another: oily stuff is inflammable, and stuff which yields in a certain way is breakable, and similarly in other cases)—

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and partly in the agent; e.g. heat and the art of building: the former in that which produces heat, and the latter in that which builds. Hence in so far as it is a natural unity, nothing is acted upon by itself; because it is one, and not a separate thing.

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Incapacity and the incapable is the privation contrary to capacity in this sense; so that every capacity has a contrary incapacity for producing the same result in respect of the same subject.

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Privation has several sensesCf. Aristot. Met. 5.22.—it is applied (1.) to anything which does not possess a certain attribute; (2.) to that which would naturally possess it, but does not; either (a) in general, or (b) when it would naturally possess it; and either (1) in a particular way, e.g. entirely, or (2) in any way at all. And in some cases if things which would naturally possess some attribute lack it as the result of constraint, we say that they are deprived.

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Since some of these principles are inherent in inanimate things, and others in animate things and in the soul and in the rational part of the soul, it is clear that some of the potencies also will be irrational and some rational. Hence all arts, i.e. the productive sciences, are potencies; because they are principles of change in another thing, or in the artist himself qua other.

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Every rational potency admits equally of contrary results, but irrational potencies admit of one result only. E.g., heat can only produce heat, but medical science can produce disease and health. The reason of this is that science is a rational account, and the same account explains both the thing and its privation, though not in the same way; and in one sense it applies to both, and in another sense rather to the actual fact.

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Therefore such sciences must treat of contraries—essentially of the one, and non-essentially of the other; for the rational account also applies essentially to the one, but to the other in a kind of accidental way, since it is by negation and removal that it throws light on the contrary. For the contrary is the primary privation,Cf. Aristot. Met. 10.4.7. and this is the removal of that to which it is contrary.Literally of the other, i.e. the positive term.

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And since contrary attributes cannot be induced in the same subject, and science is a potency which depends upon the possession of a rational formula, and the soul contains a principle of motion, it follows that whereas the salutary can only produce health, and the calefactory only heat, and the frigorific only cold, the scientific man can produce both contrary results.

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For the rational account includes both, though not in the same way; and it is in the soul, which contains a principle of motion, and will therefore, by means of the same principle, set both processes in motion, by linking them with the same rational account. Hence things which have a rational potency produce results contrary to those of things whose potency is irrationalThe meaning of this awkward sentence is clearly shown in the latter part of 4.; for the results of the former are included under one principle, the rational account.

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It is evident also that whereas the power of merely producing (or suffering) a given effect is implied in the power of producing that effect well , the contrary is not always true; for that which produces an effect well must also produce it, but that which merely produces a given effect does not necessarily produce it well.

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There are some, e.g. the Megaric school,Founded by Euclides of Megara, an enthusiastic admirer of Socrates. The Megarics adopted the Eleatic system and developed it along dialectical lines. who say that a thing only has potency when it functions, and that when it is not functioning it has no potency. E.g., they say that a man who is not building cannot build, but only the man who is building, and at the moment when he is building; and similarly in the other cases.

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It is not difficult to see the absurd consequences of this theory. Obviously a man will not be a builder unless he is building, because to be a builder is to be capable of building; and the same will be true of the other arts.

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If, therefore, it is impossible to possess these arts without learning them at some time and having grasped them, and impossible not to possess them without having lost them at some time (through forgetfulness or some affection or the lapse of time; not, of course, through the destruction of the object of the art,i.e. the form of house. because it exists always), when the artist ceases to practice his art, he will not possess it;

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and if he immediately starts building again, how will he have re-acquired the art?

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The same is true of inanimate things. Neither the cold nor the hot nor the sweet nor in general any sensible thing will exist unless we are perceiving it (and so the result will be that they are affirming Protagoras’ theoryCf. IV. v., vi.). Indeed, nothing will have the faculty of sensation unless it is perceiving, i.e. actually employing the faculty.

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If, then, that is blind which has not sight, though it would naturally have it, and when it would naturally have it, and while it still exists, the same people will be blind many times a day; and deaf too.

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Further, if that which is deprived of its potency is incapable, that which is not happening will be incapable of happening; and he who says that that which is incapable of happening is or will be, will be in error, for this is what incapable meant.i.e., we have just said that that which is incapable is deprived of its potency—in this case, of its potency for happening.

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Thus these theories do away with both motion and generation; for that which is standing will always stand, and that which is sitting will always sit; because if it is sitting it will not get up, since it is impossible that anything which is incapable of getting up should get up.

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Since, then, we cannot maintain this, obviously potentiality and actuality are different. But these theories make potentiality and actuality identical; hence it is no small thing that they are trying to abolish.

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Thus it is possible that a thing may be capable of being and yet not be, and capable of not being and yet be; and similarly in the other categories that which is capable of walking may not walk, and that which is capable of not walking may walk.

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A thing is capable of doing something if there is nothing impossible in its having the actuality of that of which it is said to have the potentiality. I mean, e.g., that if a thing is capable of sitting and is not prevented from sitting, there is nothing impossible in its actually sitting; and similarly if it is capable of being moved or moving or standing or making to stand or being or becoming or not being or not becoming.

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The term actuality, with its implication of complete reality, has been extended from motions, to which it properly belongs, to other things; for it is agreed that actuality is properly motion.

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Hence people do not invest non-existent things with motion, although they do invest them with certain other predicates. E.g., they say that non-existent things are conceivable and desirable, but not that they are in motion. This is because, although these things do not exist actually, they will exist actually; for some non-existent things exist potentially; yet they do not exist, because they do not exist in complete reality.

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Now if, as we have said, that is possible which does not involve an impossibility, obviously it cannot be true to say that so-and-so is possible, but will not be, this view entirely loses sight of the instances of impossibility.If it is true to say that a thing which is possible will not be, anything may be possible, and nothing impossible. I mean, suppose that someone—i.e. the sort of man who does not take the impossible into account—were to say that it is possible to measure the diagonal of a square, but that it will not be measured, because there is nothing to prevent a thing which is capable of being or coming to be from neither being nor being likely ever to be.

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But from our premisses this necessarily follows: that if we are to assume that which is not, but is possible, to be or to have come to be, nothing impossible must be involved. But in this case something impossible will take place; for the measuring of the diagonal is impossible.

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The false is of course not the same as the impossible; for although it is false that you are now standing, it is not impossible.

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At the same time it is also clear that if B must be real if A is, then if it is possible for A to be real, it must also be possible for B to be real; for even if B is not necessarily possible, there is nothing to prevent its being possible. Let A, then, be possible. Then when A was possible, if A was assumed to be real, nothing impossible was involved; but B was necessarily real too. But ex hypothesi B was impossible. Let B be impossible.

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Then if B is impossible, A must also be impossible. But A was by definition possible. Therefore so is B.

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If, therefore, A is possible, B will also be possible; that is if their relation was such that if A is real, B must be real.

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Then if, A and B being thus related, B is not possible on this condition, A and B will not be related as we assumed; and if when A is possible B is necessarily possible, then if A is real B must be real too. For to say that B must be possible if A is possible means that if A is real at the time when and in the way in which it was assumed that it was possible for it to be real, then B must be real at that time and in that way.

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Since all potencies are either innate, like the senses, or acquired by practice, like flute-playing, or by study, as in the arts, some—such as are acquired by practice or a rational formula—we can only possess when we have first exercised themCf. Aristot. Met. 9.8.6, 7.; in the case of others which are not of this kind and which imply passivity, this is not necessary.

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Since anything which is possible is something possible at some time and in some way, and with any other qualifications which are necessarily included in the definition; and since some things can set up processes rationally and have rational potencies, while others are irrational and have irrational potencies; and since the former class can only belong to a living thing, whereas the latter can belong both to living and to inanimate things: it follows that as for potencies of the latter kind, when the agent and the patient meet in accordance with the potency in question, the one must act and the other be acted upon; but in the former kind of potency this is not necessary, for whereas each single potency of the latter kind is productive of a single effect, those of the former kind are productive of contrary effects,Cf. Aristot. Met. 9.2.4, 5. so that one potency will produce at the same time contrary effects.sc., if every potency must act automatically whenever agent and patient meet.

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But this is impossible. Therefore there must be some other deciding factor, by which I mean desire or conscious choice. For whichever of two things an animal desires decisively it will do, when it is in circumstances appropriate to the potency and meets with that which admits of being acted upon. Therefore everything which is rationally capable, when it desires something of which it has the capability, and in the circumstances in which it has the capability, must do that thing.

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Now it has the capability when that which admits of being acted upon is present and is in a certain state; otherwise it will not be able to act. (To add the qualification if nothing external prevents it is no longer necessary; because the agent has the capability in so far as it is a capability of acting; and this is not in all, but in certain circumstances, in which external hindrances will be excluded; for they are precluded by some of the positive qualifications in the definition.)

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Hence even if it wishes or desires to do two things or contrary things simultaneously, it will not do them, for it has not the capability to do them under these conditions, nor has it the capability of doing things simultaneously, since it will only do the things to which the capability applies and under the appropriate conditions.

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Since we have now dealt with the kind of potency which is related to motion, let us now discuss actuality; what it is, and what its qualities are. For as we continue our analysis it will also become clear with regard to the potential that we apply the name not only to that whose nature it is to move or be moved by something else, either without qualification or in some definite way, but also in other senses; and it is on this account that in the course of our inquiry we have discussed these as well.

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Actuality means the presence of the thing, not in the sense which we mean by potentially. We say that a thing is present potentially as Hermes is present in the wood, or the half-line in the whole, because it can be separated from it; and as we call even a man who is not studying a scholar if he is capable of studying. That which is present in the opposite sense to this is present actually.

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What we mean can be plainly seen in the particular cases by induction; we need not seek a definition for every term, but must comprehend the analogy: that as that which is actually building is to that which is capable of building, so is that which is awake to that which is asleep; and that which is seeing to that which has the eyes shut, but has the power of sight; and that which is differentiated out of matter to the matter; and the finished article to the raw material.

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Let actuality be defined by one member of this antithesis, and the potential by the other.

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But things are not all said to exist actually in the same sense, but only by analogy—as A is in B or to B, so is C in or to D; for the relation is either that of motion to potentiality, or that of substance to some particular matter.

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Infinity and void and other concepts of this kind are said to be potentially or actually in a different sense from the majority of existing things, e.g. that which sees, or walks, or is seen.

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For in these latter cases the predication may sometimes be truly made without qualification, since that which is seen is so called sometimes because it is seen and sometimes because it is capable of being seen; but the Infinite does not exist potentially in the sense that it will ever exist separately in actuality; it is separable only in knowledge. For the fact that the process of division never ceases makes this actuality exist potentially, but not separately.For Aristotle’s views about infinity and void see Aristot. Physics 3.4-8, 4.6-9 respectively.

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Since no action which has a limit is an end, but only a means to the end, as, e.g., the process of thinning; and since the parts of the body themselves, when one is thinning them, are in motion in the sense that they are not already that which it is the object of the motion to make them, this process is not an action, or at least not a complete one, since it is not an end; it is the process which includes the end that is an action.

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E.g., at the same time we see and have seen, understand and have understood, think and have thought; but we cannot at the same time learn and have learnt, or become healthy and be healthy. We are living well and have lived well, we are happy and have been happy, at the same time; otherwise the process would have had to cease at some time, like the thinning-process; but it has not ceased at the present moment; we both are living and have lived.

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Now of these processes we should call the one type motions, and the other actualizations.

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Every motion is incomplete—the processes of thinning, learning, walking, building—these are motions, and incomplete at that. For it is not the same thing which at the same time is walking and has walked, or is building and has built, or is becoming and has become, or is being moved and has been moved, but two different things; and that which is causing motion is different from that which has caused motion.

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But the same thing at the same time is seeing and has seen, is thinking and has thought. The latter kind of process, then, is what I mean by actualization, and the former what I mean by motion.

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What the actual is, then, and what it is like, may be regarded as demonstrated from these and similar considerations.

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We must, however, distinguish when a particular thing exists potentially, and when it does not; for it does not so exist at any and every time. E.g., is earth potentially a man? No, but rather when it has already become semen,This is inconsistent with Aristotle’s doctrine that the semen is the formal element in reproduction. Cf. Aristot. Met. 8.4.5, Aristot. Met. 6.9.5. and perhaps not even then; just as not everything can be healed by medicine, or even by chance, but there is some definite kind of thing which is capable of it, and this is that which is potentially healthy.

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The definition of that which as a result of thought comes, from existing potentially, to exist actually, is that, when it has been willed, if no external influence hinders it, it comes to pass; and the condition in the case of the patient, i.e. in the person who is being healed, is that nothing in him should hinder the process. Similarly a house exists potentially if there is nothing in X, the matter, to prevent it from becoming a house, i.e., if there is nothing which must be added or removed or changed; then X is potentially a house;

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and similarly in all other cases where the generative principle is external. And in all cases where the generative principle is contained in the thing itself, one thing is potentially another when, if nothing external hinders, it will of itself become the other. E.g., the semen is not yet potentially a man; for it must further undergo a change in some other medium.This is inconsistent with Aristotle’s doctrine that the semen is the formal element in reproduction. Cf. Aristot. Met. 8.4.5, Aristot. Met. 9.6.5. But when, by its own generative principle, it has already come to have the necessary attributes, in this state it is now potentially a man, whereas in the former state it has need of another principle;

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just as earth is not yet potentially a statue, because it must undergo a change before it becomes bronze.

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It seems that what we are describing is not a particular thing, but a definite material; e.g., a box is not wood, but wooden material,Cf. Aristot. Met. 7.7.10-12. and wood is not earth, but earthen material; and earth also is an illustration of our point if it is similarly not some other thing, but a definite material—it is always the latter term in this series which is, in the fullest sense, potentially something else.

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E.g., a box is not earth, nor earthen, but wooden; for it is this that is potentially a box, and this is the matter of the box—that is, wooden material in general is the matter of box in general, whereas the matter of a particular box is a particular piece of wood.

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If there is some primary stuff, which is not further called the material of some other thing, this is primary matter. E.g., if earth is made of air, and air is not fire, but made of fire, then fire is primary matter, not being an individual thing.

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For the subject or substrate is distinguishable into two kinds by either being or not being an individual thing. Take for example as the subject of the attributes man, or body or soul, and as an attribute cultured or white. Now the subject, when culture is induced in it, is called not culture but cultured, and the man is called not whiteness but white; nor is he called ambulation or motion, but walking or moving; just as we said that things are of a definite material.

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Thus where subject has this sense, the ultimate substrate is substance; but where it has not this sense, and the predicate is a form or individuality, the ultimate substrate is matter or material substance. It is quite proper that both matter and attributes should be described by a derivative predicate, since they are both indefinite.

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Thus it has now been stated when a thing should be said to exist potentially, and when it should not.

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Now since we have distinguishedAristot. Met. 5.11. the several senses of priority, it is obvious that actuality is prior to potentiality. By potentiality I mean not that which we have defined as a principle of change which is in something other than the thing changed, or in that same thing qua other, but in general any principle of motion or of rest; for nature also is in the same genus as potentiality, because it is a principle of motion, although not in some other thing, but in the thing itself qua itself.Cf. Aristot. Met. 5.4.1.

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To every potentiality of this kind actuality is prior, both in formula and in substance; in time it is sometimes prior and sometimes not.

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That actuality is prior in formula is evident; for it is because it can be actualized that the potential, in the primary sense, is potential, I mean, e.g., that the potentially constructive is that which can construct, the potentially seeing that which can see, and the potentially visible that which can be seen.

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The same principle holds in all other cases too, so that the formula and knowledge of the actual must precede the knowledge of the potential.

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In time it is prior in this sense: the actual is prior to the potential with which it is formally identical, but not to that with which it is identical numerically.

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What I mean is this: that the matter and the seed and the thing which is capable of seeing, which are potentially a man and corn and seeing, but are not yet so actually, are prior in time to the individual man and corn and seeing subject which already exist in actuality.

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But prior in time to these potential entities are other actual entities from which the former are generated; for the actually existent is always generated from the potentially existent by something which is actually existent—e.g., man by man, cultured by cultured—there is always some prime mover; and that which initiates motion exists already in actuality.

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We have saidAristot. Met. 7.7, 8. in our discussion of substance that everything which is generated is generated from something and by something; and by something formally identical with itself.

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Hence it seems impossible that a man can be a builder if he has never built, or a harpist if he has never played a harp; because he who learns to play the harp learns by playing it, and similarly in all other cases.

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This was the origin of the sophists’ quibble that a man who does not know a given science will be doing that which is the object of that science, because the learner does not know the science. But since something of that which is being generated is already generated, and something of that which is being moved as a whole is already moved (this is demonstrated in our discussion on MotionAristot. Physics, 6.6.), presumably the learner too must possess something of the science.

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At any rate from this argument it is clear that actuality is prior to potentiality in this sense too, i.e. in respect of generation and time.

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But it is also prior in substantiality; (a) because things which are posterior in generation are prior in form and substantiality; e.g., adult is prior to child, and man to semen, because the one already possesses the form, but the other does not;

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and (b) because everything which is generated moves towards a principle, i.e. its end . For the object of a thing is its principle; and generation has as its object the end . And the actuality is the end, and it is for the sake of this that the potentiality is acquired; for animals do not see in order that they may have sight, but have sight in order that they may see.

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Similarly men possess the art of building in order that they may build, and the power of speculation that they may speculate; they do not speculate in order that they may have the power of speculation—except those who are learning by practice; and they do not really speculate, but only in a limited sense, or about a subject about which they have no desire to speculate.

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Further, matter exists potentially, because it may attain to the form; but when it exists actually, it is then in the form. The same applies in all other cases, including those where the end is motion.

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Hence, just as teachers think that they have achieved their end when they have exhibited their pupil performing, so it is with nature. For if this is not so, it will be another case of Pauson’s HermesProbably a trick picture of some kind. So Pauson is said to have painted a picture of a horse galloping which when inverted showed the horse rolling on its back. Cf. Aelian, Var. Hist. 14.15; Lucian, Demosth. Enc. 24; Plut. Moralia, 396e; Pfuhl, Malerei und Zeichnung der Griechen, 763.; it will be impossible to say whether the knowledge is in the pupil or outside him, as in the case of the Hermes. For the activity is the end, and the actuality is the activity; hence the term actuality is derived from activity, and tends to have the meaning of complete reality.

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Now whereas in some cases the ultimate thing is the use of the faculty, as, e.g., in the case of sight seeing is the ultimate thing, and sight produces nothing else besides this; but in other cases something is produced, e.g. the art of building produces not only the act of building but a house; nevertheless in the one case the use of the faculty is the end, and in the other it is more truly the end than is the potentiality. For the act of building resides in the thing built; i.e., it comes to be and exists simultaneously with the house.

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Thus in all cases where the result is something other than the exercise of the faculty, the actuality resides in the thing produced; e.g. the act of building in the thing built, the act of weaving in the thing woven, and so on; and in general the motion resides in the thing moved. But where there is no other result besides the actualization, the actualization resides in the subject; e.g. seeing in the seer, and speculation in the speculator, and life in the soul

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(and hence also happiness, since happiness is a particular kind of life). Evidently, therefore, substance or form is actuality. Thus it is obvious by this argument that actuality is prior in substantiality to potentiality; and that in point of time, as we have said, one actuality presupposes another right back to that of the prime mover in each case.

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It is also prior in a deeper sense; because that which is eternal is prior in substantiality to that which is perishable, and nothing eternal is potential. The argument is as follows. Every potentiality is at the same time a potentiality for the opposite.Cf. 19. For whereas that which is incapable of happening cannot happen to anything, everything which is capable may fail to be actualized.

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Therefore that which is capable of being may both be and not be. Therefore the same thing is capable both of being and of not being. But that which is capable of not being may possibly not be; and that which may possibly not be is perishable; either absolutely, or in the particular sense in which it is said that it may possibly not be; that is, in respect either of place or of quantity or of quality. Absolutely means in respect of substance.

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Hence nothing which is absolutely imperishable is absolutely potential (although there is no reason why it should not be potential in some particular respect; e.g. of quality or place); therefore all imperishable things are actual. Nor can anything which is of necessity be potential; and yet these things are primary, for if they did not exist, nothing would exist. Nor can motion be potential, if there is any eternal motion. Nor, if there is anything eternally in motion, is it potentially in motion (except in respect of some starting-point or destination), and there is no reason why the matter of such a thing should not exist.

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Hence the sun and stars and the whole visible heaven are always active, and there is no fear that they will ever stop—a fear which the writerse.g. Empedocles; cf. Aristot. Met. 5.23.3 n. on physics entertain. Nor do the heavenly bodies tire in their activity; for motion does not imply for them, as it does for perishable things, the potentiality for the opposite, which makes the continuity of the motion distressing; this results when the substance is matter and potentiality, not actuality.

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Imperishable things are resembled in this respect by things which are always undergoing transformation, such as earth and fire; for the latter too are always active, since they have their motion independently and in themselves.Cf. Aristot. De Gen. et Corr. 337a 1-7. Other potentialities, according to the distinctions already made,Aristot. Met. 9.5.2. all admit of the opposite result; for that which is capable of causing motion in a certain way can also cause it not in that way; that is if it acts rationally.

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The same irrational potentialities can only produce opposite results by their presence or absence.

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Thus if there are any entities or substances such as the dialecticiansFor this description of the Platonists cf. Aristot. Met. 1.6.7. describe the Ideas to be, there must be something which has much more knowledge than absolute knowledge, and much more mobility than motion; for they will be in a truer sense actualities, whereas knowledge and motion will be their potentialities.This is a passing thrust at the Ideal theory. Absolute knowledge (the faculty of knowledge) will be a mere potentiality, and therefore substantially posterior to its actualization in particular instances. Thus it is obvious that actuality is prior both to potentiality and to every principle of change.

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That a good actuality is both better and more estimable than a good potentiality will be obvious from the following arguments. Everything of which we speak as capable is alike capable of contrary results; e.g., that which we call capable of being well is alike capable of being ill, and has both potentialities at once; for the same potentiality admits of health and disease, or of rest and motion, or of building and of pulling down, or of being built and of falling down.

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Thus the capacity for two contraries can belong to a thing at the same time, but the contraries cannot belong at the same time; i.e., the actualities, e.g. health and disease, cannot belong to a thing at the same time. Therefore one of them must be the good; but the potentiality may equally well be both or neither. Therefore the actuality is better.

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Also in the case of evils the end or actuality must be worse than the potentiality; for that which is capable is capable alike of both contraries.

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Clearly, then, evil does not exist apart from things ; for evil is by nature posterior to potentiality.The argument is presumably as follows (the fallacy, as pointed out by Bonitz, is indicated in parenthesis): That which has a separate substantial existence is actuality. Actuality is prior (substantially) to potentiality. Potentiality is prior to evil (in the moral scale. But since by evil Aristotle means the actualization of a potentiality for evil, potentiality is substantially posterior to evil). Therefore that which has a separate substantial existence is prior to evil; i.e., evil does not exist apart from particular instances of evil. The argument is directed against the Platonic Idea of evil (Plat. Rep. 476a); and the corollary which follows against the identification of Evil with one of the principles of the universe (Aristot. Met. 1.6.10, Aristot. Met. 12.10.6, Aristot. Met. 14.4.10, 11; cf. Plat. Laws 896e, Plat. Laws 898c). Nor is there in things which are original and eternal any evil or error, or anything which has been destroyed—for destruction is an evil.

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Geometrical constructions, too, are discovered by an actualization, because it is by dividing that we discover them. If the division were already done, they would be obvious; but as it is the division is only there potentially. Why is the sum of the interior angles of a triangle equal to two right angles? Because the angles about one point <in a straight line> are equal to two right angles. If the line parallel to the side had been already drawn, the answer would have been obvious at sight.The figure, construction and proof are as follows: ***

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Why is the angle in a semicircle always a right angle? If three lines are equal, the two forming the base, and the one set upright from the middle of the base, the answer is obvious to one who knows the former proposition.Aristotle implies a proof something after this fashion: FIGURE BAC is an angle in a semicircle. From D, the mid-point of the diameter BC, draw a perpendicular DE to meet the circumference at E. Join EB, EC.*** Thus it is evident that the potential constructions are discovered by being actualized. The reason for this is that the actualization is an act of thinking. Thus potentiality comes from actuality (and therefore it is by constructive action that we acquire knowledge). <But this is true only in the abstract>, for the individual actuality is posterior in generation to its potentiality.This whole passage (sects. 4, 5) should be compared with Aristot. Met. 9.8.3-7, where it logically belongs.

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The terms being and not-being are used not only with reference to the types of predication, and to the potentiality or actuality, or non-potentiality and non-actuality, of these types, but also (in the strictest senseThis appears to contradict Aristot. Met. 6.4.3. But it is just possible to interpret κυριώτατα(with Jaeger) as in the commonest sense. ) to denote truth and falsity. This depends, in the case of the objects, upon their being united or divided; so that he who thinks that what is divided is divided, or that what is united is united, is right; while he whose thought is contrary to the real condition of the objects is in error. Then when do what we call truth and falsity exist or not exist? We must consider what we mean by these terms.

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It is not because we are right in thinking that you are white that you are white; it is because you are white that we are right in saying so. Now if whereas some things are always united and cannot be divided, and others are always divided and cannot be united, others again admit of both contrary states, then to be is to be united, i.e. a unity; and not to be is to be not united, but a plurality.

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Therefore as regards the class of things which admit of both contrary states, the same opinion or the same statement comes to be false and true, and it is possible at one time to be right and at another wrong; but as regards things which cannot be otherwise the same opinion is not sometimes true and sometimes false, but the same opinions are always true or always false.

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But with regard to incomposite things, what is being or not-being, and truths or falsity? Such a thing is not composite, so as to be when it is united and not to be when it is divided, like the proposition that the wood is white, or the diagonal is incommensurable; nor will truth and falsity apply in the same way to these cases as to the previous ones.

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In point of fact, just as truth is not the same in these cases, so neither is being. Truth and falsity are as follows: contacti.e. direct and accurate apprehension. and assertion are truth (for assertion is not the same as affirmation), and ignorance is non-contact. I say ignorance, because it is impossible to be deceived with respect to what a thing is, except accidentallyi.e. we cannot be mistaken with regard to a simple term X. We either apprehend it or not. Mistake arises when we either predicate something wrongly of X, or analyze X wrongly.;

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and the same applies to incomposite substances, for it is impossible to be deceived about them. And they all exist actually, not potentially; otherwise they would be generated and destroyed; but as it is, Being itself is not generated (nor destroyed); if it were, it would be generated out of something. With respect, then, to all things which are essences and actual, there is no question of being mistaken, but only of thinking or not thinking them.

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Inquiry as to what they are takes the form of inquiring whether they are of such-and-such a nature or not.

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As for being in the sense of truth, and not-being in the sense of falsity, a unity is true if the terms are combined, and if they are not combined it is false. Again, if the unity exists, it exists in a particular way, and if it does not exist in that way, it does not exist at all.

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Truth means to think these objects, and there is no falsity or deception, but only ignorance—not, however, ignorance such as blindness is; for blindness is like a total absence of the power of thinking. And it is obvious that with regard to immovable things also, if one assumes that there are immovable things, there is no deception in respect of time.

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E.g., if we suppose that the triangle is immutable, we shall not suppose that it sometimes contains two right angles and sometimes does not, for this would imply that it changes; but we may suppose that one thing has a certain property and another has not; e.g., that no even number is a prime, or that some are primes and others are not. But about a single number we cannot be mistaken even in this way, for we can no longer suppose that one instance is of such a nature, and another not, but whether we are right or wrong, the fact is always the same.

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That one has several meanings has been already statedAristot. Met. 5.6. in our distinction of the various meanings of terms. But although it has a number of senses, the things which are primarily and essentially called one, and not in an accidental sense, may be summarized under four heads:

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(1.) That which is continuous, either absolutely or in particular that which is continuous by natural growth and not by contact or ligature; and of these things those are more strictly and in a prior sense one whose motion is more simple and indivisible.

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(2.) Of this kind in a still higher degree is that which is a whole and has a definite shape or form, particularly that which is such by nature and not by constraint (like things which are joined by glue or nails or by being tied together), but which contains in itself the cause of its continuity.

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A thing is of this kind if its motion is one and indivisible in respect of place and time; so that clearly if a thing has as its principle of motion the primary kind of motion (i.e. locomotion) in its primary form (i.e. circular locomotion), it is in the primary sense one spatial magnitude.This description applies to the celestial spheres.

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Some things, then, are one in this sense, qua continuous or whole; the other things which are one are those whose formula is one.

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Such are the things of which the concept is one, i.e. of which the concept is indivisible; and this is indivisible when the object is indivisible (3.) in form or (4.) in number. Now in number the individual is indivisible, and in form that which is indivisible in comprehension and knowledge; so that that which causes the unity of substances must be one in the primary sense.

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Such, then, in number are the meanings of one: the naturally continuous, the whole, the individual, and the universal. All these are one because they are indivisible; some in motion, and others in concept or formula. But we must recognize that the questions, What sort of things are called one? and What is essential unity, and what is the formula? must not be taken to be the same.

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One has these several meanings, and each thing to which some one of these senses applies will be one; but essential unity will have now one of these senses and now something else, which is still nearer to the term one, whereas they are nearer to its denotation . This is also true of element and cause, supposing that one had to explain them both by exhibiting concrete examples and by giving a definition of the term.

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There is a sense in which fire is an element (and no doubt so too is the indeterminateThe reference is undoubtedly to Anaximander. or some other similar thing, of its own nature), and there is a sense in which it is not; because to be fire and to be an element are not the same. It is as a concrete thing and as a stuff that fire is an element; but the term element denotes that it has this attribute: that something is made of it as a primary constituent.

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The same is true of cause or one and all other such terms.

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Hence to be one means to be indivisible (being essentially a particular thing, distinct and separate in place or form or thought), or to be whole and indivisible; but especially to be the first measure of each kind, and above all of quantity; for it is from this that it has been extended to the other categories.

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Measure is that by which quantity is known, and quantity qua quantity is known either by unity or by number, and all number is known by unity. Therefore all quantity qua quantity is known by unity, and that by which quantities are primarily known is absolute unity.

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Thus unity is the starting point of number qua number. Hence in other cases too measure means that by which each thing is primarily known, and the measure of each thing is a unit—in length, breadth, depth, weight and speed.

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(The terms weight and speed are common to both contraries, for each of them has a double meaning; e.g., weight applies to that which has the least amount of gravity and also to that which has excess of it, and speed to that which has the least amount of motion and also to that which has excess of it; for even the slow has some speed, and the light some weight.)

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In all these cases, then, the measure and starting-point is some indivisible unit (since even in the case of lines we treat the one-foot line as indivisible). For everywhere we require as our measure an indivisible unit; i.e., that which is simple either in quality or in quantity.

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Now where it seems impossible to take away or add, there the measure is exact. Hence the measure of number is most exact, for we posit the unit as in every way indivisible; and in all other cases we follow this example, for with the furlong or talent or in general with the greater measure an addition or subtraction would be less obvious than with a smaller one.

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Therefore the first thing from which, according to our perception, nothing can be subtracted is used by all men as their measure of wet and dry, weight and magnitude; and they think that they know the quantity only when they know it in terms of this measure. And they know motion too by simple motion and the most rapid, for this takes least time.

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Hence in astronomy a unit of this kind is the starting point and measure; for they assume that the motion of the heavens is uniform and the most rapid, and by it they judge the others. In music the measure is the quarter tone, because it is the smallest interval; and in language the letter. All these are examples of units in this sense—not in the sense that unity is something common to them all, but in the sense which we have described.

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The measure is not always numerically one, but sometimes more than one; e.g., there are two quarter tones, distinguished not by our hearing but by their theoretical ratiosi.e., the enharmonic (or quarter-tone proper) and the chromatic, which was 1/3 of a tone (Aristoxenus 1.21, 2.51). There was also the δίεσις ἡμιολία, which was 3/8 of a tone.; and the articulate sounds by which we measure speech are more than one; and the diagonal of a square is measured by two quantities,The meaning seems to be that the diameter consists of two parts, one equal to the side, and the other representing its excess over the side; the two parts being incommensurate are measured by different units (Ross). καὶ ἡ πλευρά must, I think, be a gloss. and so are all magnitudes of this kind. Thus unity is the measure of all things, because we learn of what the substance is composed by dividing it, in respect of either quantity or form.

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Hence unity is indivisible, because that which is primary in each class of things is indivisible. But not every unit is indivisible in the same sense—e.g. the foot and the arithmetical unit; but the latter is absolutely indivisible, and the former must be classed as indivisible with respect to our power of perception, as we have already stated; since presumably everything which is continuous is divisible.

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The measure is always akin to the thing measured. The measure of magnitude is magnitude, and in particular the measure of length is a length; of breadth, a breadth; of sounds, a sound; of weight, a weight; of units, a unit; for this is the view that we must take, and not that the measure of numbers is a number. The latter, indeed, would necessarily be true, if the analogy held good; but the supposition is not analogous—it is as though one were to suppose that the measure of units is units, and not a unit; for number is a plurality of units.

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We also speak of knowledge or sense perception as a measure of things for the same reason, because through them we come to know something; whereas really they are measured themselves rather than measure other things. But our experience is as though someone else measured us, and we learned our height by noticing to what extent he applied his foot-rule to us.

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Protagoras says that man is the measure of all things, meaning, as it were, the scholar or the man of perception; and these because they possess, the one knowledge, and the other perception, which we hold to be the measures of objects. Thus, while appearing to say something exceptional, he is really saying nothing.What Protagoras really meant was (apparently) that appearances are true relatively to the percipient. Cf. Aristot. Met. 4.4.27, and see Burnet, Greek Philosophy (Part I. Thales to Plato), 92.

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Obviously, then, unity in the strictest sense, if we make our definition in accordance with the meaning of the term, is a measure; particularly of quantity, and secondarily of quality. Some things will be of this kind if they are indivisible in quantity, and others if in quality. Therefore that which is one is indivisible, either absolutely or qua one.

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We must inquire, with regard to the substance and nature of unity, in which sense it exists. This is the same question which we approached in our discussion of difficultiesAristot. Met. 3.4.24-27.: what unity is, and what view we are to take of it; whether that unity itself is a kind of substance—as first the Pythagoreans, and later Plato, both maintain—or whether rather some nature underlies it, and we should give a more intelligible account of it, and more after the manner of the physicists; for of them oneEmpedocles. holds that the One is Love, anotherAnaximenes. Air, and anotherAnaximander. the Indeterminate.

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Now if no universal can be a substance (as we have stated in our discussionAristot. Met. 7.13. of substance and being), and being itself cannot be a substance in the sense of one thing existing alongside the many (since it is common to them), but only as a predicate, then clearly neither can unity be a substance; because being and unity are the most universal of all predicates.

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Therefore (a) genera are not certain entities and substances separate from other things; and (b) unity cannot be a genus, for the same reasons that being and substance cannot.Cf. Aristot. Met. 3.3.7.

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Further, the nature of unity must be the same for all categories.

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Now being and unity have the same number of meanings; so that since in the category of qualities unity is something definite, i.e. some definite entity, and similarly in the category of quantity, clearly we must also inquire in general what unity is, just as in the case of being; since it is not enough to say that its nature is simply unity or being.

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But in the sphere of colors unity is a color, e.g. white; that is if all the other colors are apparently derived from white and black, and black is a privation of white, as darkness is of light. Thus if all existing things were colors, all existing things would be a number; but of what?

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Clearly of colors. And unity would be some one color, e.g. white. Similarly if all existing things were tunes, there would be a number—of quarter-tones; but their substance would not be a number; and unity would be something whose substance is not unity but a quarter-tone. Similarly in the case of sounds, existing things would be a number of letters, and unity would be a vowel;

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and if existing things were right-lined figures, they would be a number of figures, and unity would be a triangle. And the same principle holds for all other genera. Therefore if in the categories of passivity and quality and quantity and motion there is in every category a number and a unity, and if the number is of particular things and the unity is a particular unity, and its substance is not unity, then the same must be true in the case of substances, because the same is true in all cases.

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It is obvious, then, that in every genus one is a definite entity, and that in no case is its nature merely unity; but as in the sphere of colors the One-itself which we have to seek is one color, so too in the sphere of substance the One-itself is one substance.

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And that in a sense unity means the same as being is clear (a) from the fact that it has a meaning corresponding to each of the categories, and is contained in none of them—e.g., it is contained neither in substance nor in quality, but is related to them exactly as being is; (b) from the fact that in one man nothing more is predicated than in manCf. Aristot. Met. 4.2.6-8.(just as Being too does not exist apart from some thing or quality or quantity); and (c) because to be one is to be a particular thing.

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One and Many are opposed in several ways. Unity and Plurality are opposed as being indivisible and divisible; for that which is divided or divisible is called a plurality, and that which is indivisible or undivided is called one. Then since opposition is of four kinds, and one of the present pairs of opposites is used in a privative sense, they must be contraries, and neither contradictories nor relative terms.

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Unity is described and explained by its contrary—the indivisible by the divisible—because plurality, i.e. the divisible, is more easily perceptible than the indivisible; and so in formula plurality is prior to the indivisible, on account of our powers of perception.

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To Unity belong (as we showed by tabulation in our distinction of the contrariesCf. Aristot. Met. 4.2.9.) Identity, Similarity and Equality; and to Plurality belong Otherness, Dissimilarity and Inequality.

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IdentityOr the same. Cf. Aristot. Met. 5.9. has several meanings. (a) Sometimes we speak of it in respect of number. (b) We call a thing the same if it is one both in formula and in number, e.g., you are one with yourself both in form and in matter; and again (c) if the formula of the primary substance is one, e.g., equal straight lines are the same, and equal quadrilaterals with equal angles, and there are many more examples; but in these equality means unity.

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Things are similarOr like. Cf. Aristot. Met. 5.9.5.(a) if, while not being the same absolutely or indistinguishable in respect of their concrete substance, they are identical in form; e.g the larger square is similar to the smaller, and unequal straight lines are similar. These are similar, but not absolutely the same. (b) If, having the same form, and being capable of difference in degree, they have no difference of degree.

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(c) If things have an attribute which is the same and one in form—e.g. white—in different degrees, we say that they are similar because their form is one. (d) If the respects in which they are the same are more than those in which they differ, either in general or as regards their more prominent qualities; e.g., tin is similar to silver, as being white; and gold to fire, as being yellow or flame-colored.

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Thus it is obvious that OtherCf. Aristot. Met. 5.9.4. and Unlike also have several meanings. (a) In one sense other is used in the sense opposite to the same; thus everything in relation to every other thing is either the same or other. (b) In another sense things are other unless both their matter and their formula are one; thus you are other than your neighbor. (c) The third sense is that which is found in mathematics.sc. as opposed to same in sense (a); 3 above. Therefore everything in relation to everything else is called either other or the same; that is, in the case of things of which unity and being are predicated;

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for other is not the contradictory of the same, and so it is not predicated of non-existent things (they are called not the same), but it is predicated of all things which exist; for whatever is by nature existent and one is either one or not one with something else.

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Other and same, then, are opposed in this way; but differenceCf. Aristot. Met. 5.9.4. is distinct from otherness.

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For that which is other than something need not be other in a particular respect, since everything which is existent is either other or the same. But that which is different from something is different in some particular respect, so that that in which they differ must be the same sort of thing; i.e. the same genus or species.

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For everything which is different differs either in genus or in species—in genus, such things as have not common matter and cannot be generated into or out of each other, e.g. things which belong to different categories; and in species, such things as are of the same genus (genus meaning that which is predicated of both the different things alike in respect of their substance).

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The contrariesCf. Aristot. Met. 5.10. are different, and contrariety is a kind of difference. That this is rightly premissed is made clear by induction; for the contraries are obviously all different, since they are not merely other, but some are other in genus, and others are in the same line of predication, and so are in the same genus and the same in genus. We have distinguished elsewhereAristot. Met. 5.28.4. what sort of things are the same or other in genus.

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Since things which differ can differ from one another in a greater or less degree, there is a certain maximum difference, and this I call contrariety. That it is the maximum difference is shown by induction. For whereas things which differ in genus have no means of passing into each other, and are more widely distant, and are not comparable, in the case of things which differ in species the contraries are the extremes from which generation takes place;

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and the greatest distance is that which is between the extremes, and therefore also between the contraries. But in every class the greatest thing is complete. For (a) that is greatest which cannot be exceeded, and (b) that is complete outside which nothing proper to it can be found. For complete difference implies an end, just as all other things are called complete because they imply an end.

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And there is nothing beyond the end; for in everything the end is the last thing, and forms the boundary. Thus there is nothing beyond the end, and that which is complete lacks nothing.

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From this argument, then, it is clear that contrariety is maximum difference; and since we speak of contraries in various senses, the sense of completeness will vary in accordance with the sense of contrariety which applies to the contraries.

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This being so, evidently one thing cannot have more than one contrary (since there can be nothing more extreme than the extreme, nor can there be more than two extremes of one interval); and in general this is evident, if contrariety is difference, and difference (and therefore complete difference) is between two things.

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The other definitions of contraries must also be true, for (1.) complete difference is the maximum difference; since (a) we can find nothing beyond it, whether things differ in genus or in species (for we have shown that difference in relation to things outside the genus is impossible; this is the maximum difference between them); and (b) the things which differ most in the same genus are contraries; for complete difference is the maximum difference between these.

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(2.) The things which differ most in the same receptive material are contraries; for contraries have the same matter. (3.) The most different things which come under the same faculty are contraries; for one science treats of one class of things, in which complete difference is the greatest.

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Positive state and Privation constitute primary contrariety—not every form of privation (for it has several senses), but any form which is complete. All other contraries must be so called with respect to these; some because they possess these, others because they produce them or are productive of them, and others because they are acquisitions or losses of these or other contraries.

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Now if the types of opposition are contradiction, privation, contrariety and relation, and of these the primary type is contradiction, and an intermediate is impossible in contradiction but possible between contraries, obviously contradiction is not the same as contrariety; and privation is a form of contradiction;

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for it is either that which is totally incapable of possessing some attribute,This is not a proper example of privation. Cf. Aristot. Met. 5.22. or that which would naturally possess some attribute but does not, that suffers privation—either absolutely or in some specified way. Here we already have several meanings, which we have distinguished elsewhere. Thus privation is a kind of contradiction or incapacity which is determinate or associated with the receptive material.

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This is why though there is no intermediate in contradiction there is one in some kinds of privation. For everything is either equal or not equal, but not everything is either equal or unequal; if it is, it is only so in the case of a material which admits of equality. If, then, processes of material generation start from the contraries, and proceed either from the form and the possession of the form, or from some privation of the form or shape, clearly all contrariety must be a form of privation, although presumably not all privation is contrariety.

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This is because that which suffers privation may suffer it in several senses; for it is only the extremes from which changes proceed that are contraries.

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This can also be shown by induction. Every contrariety involves privation as one of its contraries, but not always in the same way: inequality involves the privation of equality, dissimilarity that of similarity, evil that of goodness.

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And the differences are as we have stated: one case is, if a thing is merely deprived; another, if it is deprived at a certain time or in a certain part—e.g. at a certain age or in the important part—or entirely. Hence in some cases there is an intermediate (there are men who are neither good nor bad), and in others there is not—a thing must be either odd or even.

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Again, some have a determinate subject, and others have not. Thus it is evident that one of a pair of contraries always has a privative sense; but it is enough if this is true of the primary or generic contraries, e.g. unity and plurality; for the others can be reduced to them.

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Since one thing has one contrary, it might be asked in what sense unity is opposed to plurality, and the equal to the great and to the small. For if we always use the word whether in an antithesis—e.g., whether it is white or black, or whether it is white or not (but we do not ask whether it is a man or white, unless we are proceeding upon some assumption, and asking, for instance, whether it was Cleon who came or Socrates.

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This is not a necessary disjunction in any class of things, but is derived from the use in the case of opposites—for it is only opposites that cannot be true at the same time—and we have this same use here in the question which of the two came? for if both alternatives were possible, the question would be absurd; but even so the question falls into an antithesis: that of one or many—i.e., whether both came, or one)—

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if, then, the question whether is always concerned with opposites, and we can ask whether it is greater or smaller, or equal, what is the nature of the antithesis between equal and greater or smaller? It is contrary neither to one only, nor to both: for (a) it is no more contrary to the greater than to the smaller; (b) equal is contrary to unequal, and thus it will be contrary to more than one thing;

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(c) if unequal means the same as both greater and smaller at the same time, equal must still be opposed to them both: This difficulty supports the theoryHeld by the Platonists. Cf. Aristot. Met. 14.1.4, 5. that the unequal is a duality. But the result is that one thing is contrary to two; which is impossible.

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Further, it is apparent that equal is intermediate between great and small, but it is not apparent that any contrariety is intermediate, nor can it be, by definition; for it could not be complete if it were the intermediate of something, but rather it always has something intermediate between itself and the other extreme.

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It remains, then, that it is opposed either as negation or as privation. Now it cannot be so opposed to one of the two, for it is no more opposed to the great than to the small.

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Therefore it is a privative negation of both. For this reason we say whether with reference to both, and not to one of the two—e.g., whether it is greater or equal, or whether it is equal or smaller; there are always three alternatives. But it is not a necessary privation; for not everything is equal which is not greater or smaller, but only things which would naturally have these attributes.

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The equal, then, is that which is neither great nor small, but would naturally be either great or small; and it is opposed to both as a privative negation, and therefore is intermediate between them. And that which is neither good nor bad is opposed to both, but it has no name (for each of these terms has several meanings, and there is no one material which is receptive of both); that which is neither white nor black is better entitled to a name,

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although even this has no single name, but the colors of which this negation is privatively predicated are to a certain extent limited; for it must be either grey or buff or something similar.

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Therefore those persons are wrong in their criticism who imagine that all terms are used analogously, so that that which is neither a shoe nor a hand will be intermediate between shoe and hand, because that which is neither good nor bad is intermediate between good and bad—as though there must be an intermediate in all cases; but this does not necessarily follow.

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For the one is a joint negation of opposites where there is an intermediate and a natural interval; but in the other case there is no question of difference, since the joint negation applies to things which are in different genera, and therefore the substrate is not one.Cf. Aristot. Met. 10.3.8

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A similar question might be raised about one and many. For if many is absolutely opposed to one, certain impossibilities result. (1) One will be few; for many is also opposed to few.

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(2) Two will be many; since twofold is manifold, and twofold is derived from two. Therefore one will be few; for in what relation can two be many if not in relation to one, which must therefore be few? for there can be nothing less. (3) If much and little are in plurality what long and short are in length, and if whatever is much is also many,

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and many is much (unless indeed there is a difference in the case of a plastic continuumi.e., a fluid, which cannot be described as many. ), few will be a plurality. Therefore one will be a plurality, if it is few; and this necessarily follows if two is many. Presumably, however, although many in a sense means much, there is a distinction; e.g., water is called much but not many.

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To all things, however, which are divisible the term many is applicable: in one sense, if there is a plurality which involves excess either absolutely or relatively (and similarly few is a plurality involving defect); and in another in the sense of number, in which case it is opposed to one only. For we say one or many just as if we were to say one and ones, or white thing and white things, or were to compare the things measured with the measure.

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Multiples, too, are spoken of in this way; for every number is many, because it consists of ones, and because every number is measurable by one; and also as being the opposite of one, and not of few. In this sense even two is many; but as a plurality involving excess either relatively or absolutely it is not many, but the first plurality. Two is, however, absolutely few; because it is the first plurality involving defect

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(hence AnaxagorasCf. Aristot. Met. 1.3.9. was not right in leaving the subject by saying all things were together, infinite both in multitude and in smallness; instead of in smallness he should have said in fewness,sc. and then the absurdity of his view would have been apparent, for, etc. Aristotle assumes the Anaxagoras meant smallness (μικρότης) to be the opposite of multitude (πλῆθος); but he meant just what he said—that the particles of which things consist are infinitely many and infinitely small. See Bowman in Classical Review 30, 42-44. for things cannot be infinite in fewness), since fewness is constituted not by one, as some hold, but by two.

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In the sphere of numbers one is opposed to many as the measure to the measurable, i.e., as relative terms are opposed which are not of their own nature relative. We have distinguished elsewhereAristot. Met. 5.15.8, 9. that things are called relative in two senses—either as being contraries, or as knowledge is related to the knowable, A being related to B because B is described in relation to A.

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There is no reason why one should not be fewer than something, e.g. two; for if it is fewer it is not therefore few. Plurality is, as it were, a genus of number, since number is a plurality measurable by one. And in a sense one and number are opposed; not, however, as being contrary, but as we have said some relative terms to be; for it is qua measure and measurable that they are opposed.

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(Hence not everything which is one is a number—e.g., a thing which is indivisible.) But although the relation between knowledge and the knowable is said to be similar to this, it turns out not to be similar. For it would seem that knowledge is a measure, and the knowable that which is measurable by it; but it happens that whereas all knowledge is knowable, the knowable is not always knowledge, because in a way knowledge is measured by the knowable.Cf. Aristot. Met. 10.1.19.

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Plurality is contrary neither to the few (whose real contrary is the many, as an excessive plurality to an exceeded plurality) nor in all senses to one; but they are contrary in one sense (as has been said) as being the one divisible and the other indivisible; and in another as being relative (just as knowledge is relative to the knowable) if plurality is a number and one is the measure.

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Since there can be, and in some cases is, an intermediate between contraries, intermediates must be composed of contraries; for all intermediates are in the same genus as the things between which they are intermediate.

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By intermediates we mean those things into which that which changes must first change. E.g., if we change from the highest string to the lowest by the smallest gradations we shall first come to the intermediate notes; and in the case of colors if we change from white to black we shall come to red and grey before we come to black; and similarly in other cases.

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But change from one genus into another is impossible except accidentally; e.g., from color to shape. Therefore intermediates must be in the same genus as one another and as the things between which they are intermediate.

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But all intermediates are between certain opposites, for it is only from these per se that change is possible.

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Hence there can be no intermediate between things which are not opposites; for then there would be change also between things which are not opposites. Of things which are opposites, contradiction has no intermediate term (for contradiction means this: an antithesis one term of which must apply to any given thing, and which contains no intermediate term); of the remaining types of opposites some are relative, others privative, and others contrary.

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Those relative opposites which are not contrary have no intermediate. The reason for this is that they are not in the same genus— for what is intermediate between knowledge and the knowable?—but between great and small there is an intermediate. Now since intermediates are in the same genus, as has been shown, and are between contraries, they must be composed of those contraries. For the contraries must either belong to a genus or not. And if there is a genus in such a way

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that it is something prior to the contraries, then the differentiae which constitute the contrary species (for species consist of genus and differentiae) will be contraries in a prior sense.

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E.g., if white and black are contraries, and the one is a penetrativeThis is Plato’s definition. Cf. Plat. Tim. 67d, e. and the other a compressive color, these differentiae, penetrative and compressive, are prior, and so are opposed to each other in a prior sense.

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But it is the species which have contrary differentiae that are more truly contraries; the other, i.e. intermediate, species will consist of genus and differentiae. E.g., all colors which are intermediate between white and black should be described by their genus (i.e. color) and by certain differentiae.

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But these differentiae will not be the primary contraries; otherwise every thing will be either white or black. Therefore they will be different from the primary contraries. Therefore they will be intermediate between them, and the primary differentiae will be the penetrative and the compressive. Thus we must first investigate the contraries which are not contained in a genus, and discover of what their intermediates are composed.

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For things which are in the same genus must either be composed of differentiae which are not compounded with the genus, or be incomposite. Contraries are not compounded with one another, and are therefore first principles; but intermediates are either all incomposite or none of them. Now from the contraries something is generated in such a way that change will reach it before reaching the contraries themselves (for there must be something which is less in degree than one contrary and greater than the other). Therefore this also will be intermediate between the contraries.

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Hence all the other intermediates must be composite; for that which is greater in degree than one contrary and less than the other is in some sense a compound of the contraries of which it is said to be greater in degree than one and less than the other. And since there is nothing else homogeneous which is prior to the contraries, all intermediates must be composed of contraries.

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Therefore all the lower terms, both contraries and intermediates, must be composed of the primary contraries. Thus it is clear that intermediates are all in the same genus, and are between contraries, and are all composed of contraries.

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That which is other in species than something else is other in respect of something and that something must apply to both. E.g., if an animal is other in species than something else, they must both be animals. Hence things which are other in species must be in the same genus. The sort of thing I mean by genus is that in virtue of which two things are both called the same one thing; and which is not accidentally differentiated, whether regarded as matter or otherwise.

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For not only must the common quality belong to both, e.g., that they are both animals, but the very animality of each must be different; e.g., in one case it must be equinity and in the other humanity. Hence the common quality must for one be other in species than that which it is for the other. They must be, then, of their very nature, the one this kind of animal, and the other that ; e.g., the one a horse and the other a man.

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Therefore this difference must be otherness of genus (I say otherness of genus because by difference of genus I mean an otherness which makes the genus itself other); this, then, will be a form of contrariety. This is obvious by induction.Aristotle does not use induction to prove his point; indeed he does not prove it at all. For all differentiation is by opposites, and we have shownIn ch. 4. that contraries are in the same genus, because contrariety was shown to be complete difference. But difference in species is always difference from something in respect of something; therefore this is the same thing, i.e. the genus, for both.

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(Hence too all contraries which differ in species but not in genus are in the same line of predication,Or category. and are other than each other in the highest degree; for their difference is complete, and they cannot come into existence simultaneously.) Hence the difference is a form of contrariety.

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To be other in species, then, means this: to be in the same genus and involve contrariety, while being indivisible

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(and the same in species applies to all things which do not involve contrariety, while being indivisible); for it is in the course of differentiation and in the intermediate terms that contrariety appears, before we come to the indivisibles.i.e., indivisible species and individuals.

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Thus it is evident that in relation to what is called genus no species is either the same or other in species (and this is as it should be, for the matter is disclosed by negation, and the genus is the matter of that of which it is predicated as genus; not in the sense in which we speak of the genus or clan of the Heraclidae,Cf. Aristot. Met. 5.28.1. but as we speak of a genus in nature); nor yet in relation to things which are not in the same genus. From the latter it will differ in genus, but in species from things which are in the same genus. For the difference of things which differ in species must be a contrariety; and this belongs only to things which are in the same genus.

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The question might be raised as to why woman does not differ in species from man, seeing that female is contrary to male, and difference is contrariety; and why a female and a male animal are not other in species, although this difference belongs to animal per se, and not as whiteness or blackness does; male and female belong to it qua animal.

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This problem is practically the same as why does one kind of contrariety (e.g. footed and winged) make things other in species, while another (e.g. whiteness and blackness) does not? The answer may be that in the one case the attributes are peculiar to the genus, and in the other they are less so; and since one element is formula and the other matter, contrarieties in the formula produce difference in species, but contrarieties in the concrete whole do not.

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Hence the whiteness or blackness of a man does not produce this, nor is there any specific difference between a white man and a black man; not even if one term is assigned to each. For we are now regarding man as matter, and matter does not produce difference; and for this reason, too, individual men are not species of man, although the flesh and bones of which this and that man consist are different. The concrete whole is other, but not other in species, because there is no contrariety in the formula, and this is the ultimate indivisible species.

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But Callias is definition and matter. Then so too is white man, because it is the individual, Callias, who is white. Hence man is only white accidentally. Again, a bronze circle and a wooden one do not differ in species; and a bronze triangle and a wooden circle differ in species not because of their matter, but because there is contrariety in their formulae.

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But does not matter, when it is other in a particular way, make things other in species? Probably there is a sense in which it does. Otherwise why is this particular horse other in species than this particular man, although the definitions involve matter? Surely it is because there is contrariety in the definition, for so there also is in white man and black horse; and it is a contrariety in species, but not because one is white and the other black; for even if they had both been white, they would still be other in species.

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Male and female are attributes peculiar to the animal, but not in virtue of its substance; they ar material or physical. Hence the same semen may, as the result of some modification, become either female or male.

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We have now stated what to be other in species means, and why some things differ in species and others do not.

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Since contraries are other in form,It appears that in this chapter (apart from 5, which may be a later addition) the terms εἶδος and γένος are used in a non-technical sense. Cf. Ross on Aristot. Met. 1058b 28. and the perishable and imperishable are contraries (for privation is a definite incapacity), the perishable must be other in kind than the imperishable. But so far we have spoken only of the universal terms; and so it might appear to be unnecessary that anything perishable and imperishable should be other in form, just as in the case of white and black.

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For the same thing may be both at the same time, if it is a universal (e.g, man may be both white and black); and it may still be both if it is a particular, for the same person may be white and black, although not at the same time. Yet white is contrary to black. But although some contraries

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(e.g. those which we have just mentioned, and many others) can belong to certain things accidentally, others cannot; and this applies to the perishable and the imperishable. Nothing is accidentally perishable; for that which is accidental may not be applicable; but perishability is an attribute which applies necessarily when it is applicable at all. Otherwise one and the same thing will be imperishable as well as perishable, if it is possible for perishability not to apply to it.

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Thus perishability must be either the substance or in the substance of every perishable thing. The same argument also applies to the imperishable; for both perishability and imperishability are attributes which are necessarily applicable. Hence the characteristics in respect of which and in direct consequence of which one thing is perishable and another imperishable are opposed; and therefore they must be other in kind.

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Thus it is obvious that there cannot be Forms such as some thinkers maintain; for then there would be both a perishable and an imperishable man. i.e., the individual man is perishable and the Idea of man imperishable; and these must be other in kind (γένει non-technical). But the Platonists hold that the Idea is the same in species as the particular. This is impossible if it is other in genus (γένει technical). Yet the Forms are said to be the same in species as the particulars, and not merely to share a common predicate with them; but things which are other in genus differ more widely than things which are other in species.

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That wisdom is a science of first principles is clear from our Introductory remarks,Aristot. Met. 1.3-10. in which we of raised objections to the statements of other thinkers about the first principles. It might be asked, however, whether we should regard Wisdom as one science or as more than one.Cf. Aristot. Met. 3.1.5, Aristot. Met. 3.2.1-10. If as one, it may be objected that the objects of one science are always contraries; but the first principles are not contraries. And if it is not one, what sort of sciences are we to suppose them to be?

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Again, is it the province of one science, or of more than one, to study the principles of demonstration?Cf. Aristot. Met. 3.1.5, , Aristot. Met. 3.2.10-15, where the problem takes a slightly different form. If of one, why of it rather than of any other? And if of more than one, of what sort are we to suppose them to be?

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Again, are we to suppose that Wisdom deals with all substances or not?Cf. Aristot. Met. 3.1.6, Aristot. Met. 3.2.15-17. If not with all, it is hard to lay down with what kind it does deal; while if there is one science of them all, it is not clear how the same science can deal with more than one subject.

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Again, is this science concerned only with substances, or with attributes as well?Cf. Aristot. Met. 3.1.8-10, Aristot. Met. 3.2.18-19. For if it is a demonstration of attributes, it is not concerned with substances; and if there is a separate science of each, what is each of these sciences, and which of them is Wisdom? qua demonstrative, the science of attributes appears to be Wisdom; but qua concerned with that which is primary, the science of substances.

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Nor must we suppose that the science which we are seeking is concerned with the causes described in the Physics.Aristot. Physics 2.3. It is not concerned with the final cause; for this is the Good, and this belongs to the sphere of action and to things which are in motion; and it is this which first causes motion (for the end is of this nature); but there is no Prime Mover in the sphere of immovable things.

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And in general it is a difficult question whether the science which we are now seeking is concerned with sensible substances, or not with sensible substances, but with some other kind.Cf. Aristot. Met. 3.1.7, Aristot. Met.3.2.20-30. If with another kind, it must be concerned either with the Forms or with mathematical objects. Now clearly the Forms do not exist. (But nevertheless, even if we posit them, it is a difficult question as to why the same rule does not apply to the other things of which there are Forms as applies to the objects of mathematics.

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I mean that they posit the objects of mathematics as intermediate between the Forms and sensible things, as a third class besides the Forms and the things of our world; but there is no third manThis phrase has no technical sense here; cf. Aristot. Met. 1.9.4. or horse besides the Ideal one and the particulars. If on the other hand it is not as they make out, what sort of objects are we to suppose to be the concern of the mathematician? Not surely the things of our world; for none of these is of the kind which the mathematical sciences investigate.)

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Nor indeed is the science which we are now seeking concerned with the objects of mathematics; for none of them can exist separately. But it does not deal with sensible substances either; for they are perishable.

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In general the question might be raised, to what science it pertains to discuss the problems concerned with the matteri.e., intelligible matter (cf. Aristot. Met. 7.10.18). This problem is not raised in Book 3. of mathematical objects.

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It is not the province of physics, because the whole business of the physicist is with things which contain in themselves a principle of motion and rest; nor yet of the science which inquires into demonstration and

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scientific knowledge, for it is simply this sort of thing which forms the subject of its inquiry. It remains, therefore, that it is the science which we have set ourselves to find that treats of these subjects.

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One might consider the question whether we should regard the science which we are now seeking as dealing with the principles which by some are called elements.Cf. Aristot. Met. 3.1.10, Aristot. Met. 3.3. But everyone assumes that these are present in composite things; and it would seem rather that the science which we are seeking must be concerned with universals, since every formula and every science is of universals and not of ultimate species; so that in this case it must deal with the primary genera.

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These would be Being and Unity; for these, if any, might best be supposed to embrace all existing things, and to be most of the nature of first principles, because they are by nature primary; for if they are destroyed, everything else is destroyed with them, since everything exists and is one.

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But inasmuch as, if Being and Unity are to be regarded as genera, they must be predicable of their differentiae, whereas no genus is predicable of any of its differentiae, from this point of view it would seem that they should be regarded neither as genera nor as principles.

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Further, since the more simple is more nearly a principle than the less simple, and the ultimate subdivisions of the genus are more simple than the genera (because they are indivisible), and the genera are divided into a number of different species, it would seem that species are more nearly a principle than genera.

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On the other hand, inasmuch as species are destroyed together with their genera, it seems more likely that the genera are principles; because that which involves the destruction of something else is a principle. These and other similar points are those which cause us perplexity.

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Again, ought we to assume the existence of something else besides particular things, or are they the objects of the science which we are seeking?Cf. Aristot. Met. 3.1.11, Aristot. Met. 3.4.1-8. It is true that they are infinite in number; but then the things which exist besides particulars are genera or species, and neither of these is the object of the science which we are now seeking. We have explained Aristot. Met. 11.1.11-13 why this is impossible.

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Indeed, in general it is a difficult question whether we should suppose that there is some substance which exists separately besides sensible substances (i.e. the substances of our world), or that the latter constitute reality, and that it is with them that Wisdom is concerned. It seems that we are looking for some other kind of substance, and that this is the object of our undertaking: I mean, to see whether there is anything which exists separately and independently, and does not appertain to any sensible thing.

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But again, if there is another kind of substance besides sensible substances, to what kind of sensible things are we to suppose that it corresponds? Why should we suppose that it corresponds to men or horses rather than to other animals, or even to inanimate objects in general? And yet to manufacture a set of eternal substances equal in number to those which are sensible and perishable would seem to fall outside the bounds of plausibility.

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Yet if the principle which we are now seeking does not exist in separation from bodies, what can we suppose it to be if not matter? Yes, but matter does not exist actually, but only potentially. It might seem rather that a more appropriate principle would be form or shape; but this is perishableForms which are induced in matter are perishable, although not subject to the process of destruction; they are at one time and are not at another (cf. Aristot. Met. 7.15.1). The only pure form (i.e., the only form which is independent of matter in any and every sense) is the prime mover (Aristot. Met. 12.7).; and so in general there is no eternal substance which exists separately and independently.

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But this is absurd, because it seems natural that there should be a substance and principle of this kind, and it is sought for as existing by nearly all the most enlightened thinkers. For how can there be any order in the universe if there is not something eternal and separate and permanent?

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Again, if there is a substance and principle of such a nature as that which we are now seeking, and if it is one for all things, i.e. the same for both eternal and perishable things, it is a difficult question as to why, when the principle is the same, some of the things which come under that principle are eternal, and others not; for this is paradoxical.Cf. Aristot. Met. 3.1.12, Aristot. Met. 3.4.11-23.

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But if there is one principle of perishable things, and another of eternal things, if the principle of perishable things is also eternal, we shall still have the same difficulty; because if the principle is eternal, why are not the things which come under that principle eternal? And if it is perishable, it must have another principle behind it, and that principle must have another behind it; and the process will go on to infinity.

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On the other hand, if we posit the principles which seem most unchangeable, Being and Unity,Cf. Aristot. Met. 3.1.13, Aristot. Met. 3.4.24-34.(a) unless each of them denotes a particular thing and a substance, how can they be separate and independent? but the eternal and primary principles for which we are looking are of this nature.

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(b) If, however, each of them denotes a particular thing and a substance, then all existing things are substances; for Being is predicated of everything, and Unity also of some things.

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But that all things are substances is false. (c) As for those who maintain that Unity is the first principle and a substance, and who generate number from Unity and matter as their first product, and assert that it is a substance, how can their theory be true? How are we to conceive of 2 and each of the other numbers thus composed, as one? On this point they give no explanation; nor is it easy to give one.

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But if we posit lines or the things derived from them (I mean surfaces in the primary sensei.e., intelligible surfaces, etc.) as principles,Cf. Aristot. Met. 3.1.15, Aristot. Met. 3.5. these at least are not separately existing substances, but sections and divisions, the former of surfaces and the latter of bodies (and points are sections and divisions of lines); and further they are limits of these same things. All these things are integral parts of something else, and not one of them exists separately.

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Further, how are we to suppose that there is a substance of unity or a point? for in the case of every substancesc. which is liable to generation or destruction. there is a process of

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generation, but in the case of the point there is not; for the point is a division.

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It is a perplexing fact also that whereas every science treats of universals and types, substance is not a universal thing, but rather a particular and separable thing; so that if there is a science that deals with first principles, how can we suppose that substance is a first principle?Cf. Aristot. Met. 3.1.14, Aristot. Met. 3.6.7-9.

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Again, is there anything besides the concrete whole (I mean the matter and the form in combination) or not?This section belongs to the problem discussed in 1-5 above. If not, all things in the nature of matter are perishable; but if there is something, it must be the form or shape. It is hard to determine in what cases this is possible and in what it is not; for in some cases, e.g. that of a house, the form clearly does not exist in separation.

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Again, are the first principles formally or numerically the same?Cf. Aristot. Met. 3.1.12, Aristot. Met. 3.4.8-10. If they are numerically one, all things will be the same.

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Since the science of the philosopher is concerned with Being qua Being universally,This chapter corresponds to Aristot. Met. 4.1, 2, with which it should be compared. and not with some part of it, and since the term Being has several meanings and is not used only in one sense, if it is merely equivocal and has no common significance it cannot fall under one science (for there is no one class in things of this kind); but if it has a common significance it must fall under one science.

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Now it would seem that it is used in the sense which we have described, like medical and healthy, for we use each of these terms in several senses; and each is used in this way because it has a reference, one to the science of medicine, and another to health, and another to something else; but each refers always to the same concept. A diagnosis and a scalpel are both called medical, because the one proceeds from medical science and the other is useful to it.

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The same is true of healthy; one thing is so called because it is indicative, and another because it is productive, of health; and the same applies to all other cases. Now it is in this same way that everything which exists is said to be ; each thing is said to be because it is a modification or permanent or temporary state or motion or some other such affection of Being qua Being.

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And since everything that is can be referred to some one common concept, each of the contrarieties too can be referred to the primary differentiae and contrarieties of Being—whether the primary differentiae of Being are plurality and unity, or similarity and dissimilarity, or something else; for we may take them as already discussed.Cf. Aristot. Met. 4.2.9 n.

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It makes no difference whether that which is is referred to Being or Unity; for even if they are not the same but different, they are in any case convertible, since that which is one also in a sense is , and that which is is one.

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Now since the study of contraries pertains to one and the same science, and each contrary is so called in virtue of privation (although indeed one might wonder in what sense they can be called contraries in virtue of privation when they admit of a middle term—e.g. unjust and just), in all such cases we must regard the privation as being not of the whole definition but of the ultimate species. E.g., if the just man is one who is obedient to the laws in virtue of some volitional state, the unjust man will not be entirely deprived of the whole definition, but will be one who is in some respect deficient in obedience to the laws; and it is in this respect that the privation of justice will apply to him (and the same holds good in all other cases).

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And just as the mathematician makes a study of abstractions (for in his investigations he first abstracts everything that is sensible, such as weight and lightness, hardness and its contrary, and also heat and cold and all other sensible contrarieties, leaving only quantity and continuity—sometimes in one, sometimes in two and sometimes in three dimensions—and their affections qua quantitative and continuous, and does not study them with respect to any other thing; and in some cases investigates the relative positions of things and the properties of these, and in others their commensurability or incommensurability, and in others their ratios; yet nevertheless we hold that there is one and the same science of all these things, viz. geometry), so it is the same with regard to Being.

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For the study of its attributes in so far as it is Being, and of its contrarietiesi.e., identity, otherness, etc. qua Being, belongs to no other science than Philosophy; for to physics one would assign the study of things not qua Being but qua participating in motion, while dialectics and sophistry deal with the attributes of existing things, but not of things qua Being, nor do they treat of Being itself in so far as it is Being.

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Therefore it remains that the philosopher is the man who studies the things which we have described, in so far as they are Being. And since everything that is , although the term has several meanings, is so described in virtue of some one common concept, and the same is true of the contraries (since they can be referred to the primary contrarieties and differences of Being), and since things of this kind can fall under one science, the difficulty which we stated at the beginningAristot. Met. 11.1.1. may be regarded as solvedAlso the problem stated in ch. i. 3.—I mean the problem as to how there can be one science of several things which are different in genus.

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Since even the mathematician uses the common axioms only in a particular application, it will be the province of Primary Philosophy to study the principles of these as well.This chapter corresponds to Aristot. Met. 4.3.1-6, and answers the problem stated in Aristot. Met. 11.1.2.

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That when equals are taken from equals the remainders are equal is an axiom common to all quantities; but mathematics isolates a particular part of its proper subject matter and studies it separately; e.g. lines or angles or numbers or some other kind of quantity, but not qua Being, but only in so far as each of them is continuous in one, two or three dimensions. But philosophy does not investigate particular things in so far as each of them has some definite attribute, but studies that which is , in so far as each particular thing is .

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The same applies to the science of physics as to mathematics, for physics studies the attributes and first principles of things qua in motion, and not qua Being; but Primary Science, as we have said, deals with these things only in so far as the subjects which underlie them are existent, and not in respect of anything else. Hence we should regard both physics and mathematics as subdivisions of Wisdom.

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There is a principle in existing things about which we cannot make a mistakeThis chapter corresponds to Aristot. Met. 4.3.7-4.31.; of which, on the contrary, we must always realize the truth—viz. that the same thing cannot at one and the same time be and not be, nor admit of any other similar pair of opposites. Of such axioms although there is a proof ad hominem, there is no absolute proof;

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because there is no principle more convincing than the axiom itself on which to base an argument, whereas there must be such a principle if there is to be absolute proof.

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But he who wants to convince an opponent who makes opposite statements that he is wrong must obtain from him an admission which shall be identical with the proposition that the same thing cannot at one and the same time be and not be, but shall seem not to be identical with it. This is the only method of proof which can be used against one who maintains that opposite statements can be truly made about the same subject.

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Now those who intend to join in discussion must understand one another to some extent; for without this how can there be any common discussion between them? Therefore each of the terms which they use must be intelligible and signify something; not several things, but one only; or if it signifies more than one thing, it must be made clear to which of these the term is applied.

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Now he who says that A is and is not denies what he asserts, and therefore denies that the term signifies what it does signify. But this is impossible. Therefore if to be so-and-so has a definite meaning, the opposite statement about the same subject cannot be true.

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Again, if the term has a definite significance and this is truly stated, it must of necessity be so.sect. 6=Aristot. Met. 4.4.14-16. But that which of necessity is can never not be. Hence opposite statements about the same subject cannot be true.

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Again, if the assertion is no more true than the negation, it will be no more true to say A is man than to say A is not man. With this section cf. Aristot. Met. 4.4.26-30.

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But it would also be admitted that it is more or at least not less true to say that a man is not a horse than to say that he is not a man; and therefore, since it was assumed that opposite statements are equally true, it will be true to say that the same person is also a horse. It follows therefore, that the same person is a man and a horse, or any other animal.

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Thus, although there is no absolute proof of these axioms, there is an ad hominem proof where one’s opponent makes these assumptions.sect. 8=Aristot. Met. 4.3.10. Perhaps even Heraclitus himself, if he had been questioned on these lines, would have been compelled to admit that opposite statements can never be true of the same subjects; as it is, he adopted this theory through ignorance of what his doctrine implied.

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In general,sect. 9-11=Aristot. Met. 4.4.31. if what he says is true, not even this statement itself (I mean that the same thing can at one and the same time be and not be) will be true;

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because just as, when they are separated, the affirmation is no more true than the negation, so in the same way, if the complex statement is taken as a single affirmation, the negation will be just as true as the whole statement regarded as an affirmation.

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And further, if nothing can be truly affirmed, then this very statement—that there is no such thing as a true affirmation—will be false. But if there is such a thing, the contentions of those who raise objections of this kind and utterly destroy rational discourse may be considered to be refuted.Cf. Aristot. Met. 4.8.4, 5.

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Very similar to the views which we have just mentioned is the dictum of ProtagorasThis chapter forms a summary of Aristot. Met. 4.5-8. sect. 1-3=Aristot. Met. 4.5.1-5.; for he said that man is the measure of all things, by which he meant simply that each individual’s impressions are positively true.

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But if this is so, it follows that the same thing is and is not, and is bad and good, and that all the other implications of opposite statements are true; because often a given thing seems beautiful to one set of people and ugly to another, and that which seems to each individual is the measure.

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This difficulty will be solved if we consider the origin of the assumption. It seems probable that it arose in some cases from the doctrine of the natural philosophers, and in others from the fact that everyone does not form the same opinion about the same things, but to some a given thing seems sweet and to others the contrary.

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For that nothing comes from what is not, but everything from what is, is a doctrine common to nearly all natural philosophers.With sect. 4, 5 cf. Aristot. Met. 4.5.6. Since, then, a thing does not become white which was before completely white and in no respect not-white, that which becomes white must come from what was not-white. Hence according to this theory there would be generation from what is not, unless the same thing were originally white and not-white.

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However, it is not hard to solve this difficulty. We have explained in the PhysicsAristot. Physics 1.7-9. in what sense things which are generated are generated from what is not, and in what sense from what is.

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But to attach equal importance to the opinions and impressions of opposing parties is foolish, because clearly one side or the other must be wrong.sect. 5-7=Aristot. Met. 4.5.23-27.

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This is evident from what happens in the sphere of sensation; for the same thing never seems to some people sweet and to others to the contrary unless one of the parties has the organ of sense which distinguishes the said flavors injured or impaired. Such being the case, the one party should be taken as the measure, and the other not.

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And I hold the same in the case of good and bad, and of beautiful and ugly, and of all other such qualities. For to maintain this viewi.e., that the same thing has contrary qualities. is just the same as to maintain that what appears to us when we press the finger below the eye and make a thing seem two instead of one must be two because it appears to be so, and then afterwards that it must be one; because if we do not interfere with our sight that which is one appears to be one.

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And in general it is absurd to form our opinion of the truth from the appearances of things in this world of ours which are subject to change and never remain in the same statesect. 8, 9 (first half)=Aristot. Met. 4.5.21, 22.; for it is by reference to those things which are always the same state and undergo no change that we should prosecute our search for truth.

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Of this kind are the heavenly bodies; for these do not appear to be now of one nature and subsequently of another, but are manifestly always the same and have no change of any kind.

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Again, if there is motion there is also something which is moved; and everything is moved from something and into something. Therefore that which is moved must be in that from which it is to be moved, and must also not be in it; and must be moved into so-and-so and must also come to be in it; but the contradictory statements cannot be true at the same time, as our opponents allege.

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And if the things of our world are in a state of continuous flux and motion in respect of quantity, and we assume this although it is not true, why should they not be constant in respect of quality?Cf. Aristot. Met. 4.5.20, 21. It appears that not the least reason why our opponents predicate opposite statements of the same thing is that they start with the assumption that quantity is not constant in the case of bodies; hence they say that the same thing is and is not six feet long.

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But essence depends upon quality, and this is of a determinate, whereas quantity is of an indeterminate nature.

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Again, when the doctor orders them to adopt some article of diet, why do they adopt it?Cf. Aristot. Met. 4.4.39-42. For on their view it is no more true that a thing is bread than that it is not; and therefore it would make no difference whether they ate it or not. But as it is, they adopt a particular food as though they knew the truth about it and it were the food prescribed;

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yet they ought not to do so if there were no fixed and permanent nature in sensible things and everything were always in a state of motion and flux.

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Again, if we are always changing and never remain the same, is it any wonder that to us, as to the diseased, things never appear the same?With this section cf. Aristot. Met. 4.5.7-14.

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For to the diseased, since they are not in the same physical condition as when they were well, sensible qualities do not appear to be the same; although this does not mean that the sensible things themselves partake of any change, but that they cause different, and not the same, sensations in the diseased. Doubtless the same must be true if the change which we have referred to takes place in us.

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If, however, we do not change but remain always the same, there must be something permanent.

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As for those who raise the aforesaid difficulties on dialectical grounds,With this section cf. Aristot. Met. 4.5.3, 4, Aristot. Met. 4.6.1-3. it is not easy to find a solution which will convince them unless they grant some assumption for which they no longer require an explanation; for every argument and proof is possible only in this way. If they grant no assumption, they destroy discussion and reasoning in general.

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Thus there is no arguing with people of this kind; but in the case of those who are perplexed by the traditional difficulties it is easy to meet and refute the causes of their perplexity. This is evident from what has been already said.

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Thus from these considerations it is obvious that opposite statements cannot be true of the same thing at one time; nor can contrary statements, since every contrariety involves privation. This is clear if we reduce the formulae of contraries to their first principles.Cf. Aristot. Met. 4.6.10, 11.

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Similarly no middle term can be predicated of one and the same thing of which one of the contraries is predicated.Cf. Aristot. Met. 4.7 where, however, the point which is proved is that there can be no intermediate between contradictories.

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If, when the subject is white, we say that it is neither white nor black, we shall be in error; for it follows that it is and is not white, because the first of the two terms in the complex statement will be true of the subject, and this is the contradictory of white.

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Thus we cannot be right in holding the views either of HeraclitusCf. Aristot. Met. 11.5.8 or of Anaxagoras.Cf. Aristot. Met. 4.7.8-8.5

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If we could, it would follow that contraries are predicable of the same subject; for when heAnaxagoras. What he really meant was that even the sweetest things contain some bitter particles. Cf. Anaxagoras Fr. 11 (Diels); Burnet, E.G.P. 129. says that in everything there is a part of everything, he means that nothing is sweet any more than it is bitter, and similarly with any of the other pairs of contraries; that is, if everything is present in everything not merely potentially but actually and in differentiation.

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Similarly all statements cannot be false, nor all true. Among many other difficulties which might be adduced as involved by this supposition there is the objection that if all statements were false, not even this proposition itself would be true; while if they were all true it would not be false to say that they are all false.

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Every science inquires for certain principles and causes with respect to every knowable thing which comes within its scopeThis chapter corresponds to Aristot. Met. 6.1; cf. also Aristot. Met. 4.3.1-6 and ch. 4 above. It also answers the problem stated in ch. 1.2.; e.g., the sciences of medicine and physical culture do this, and so does each of the other productive and mathematical sciences. Each one of these marks out for itself some class of objects, and concerns itself with this as with something existent and real, but not qua real; it is another science distinct from these which does this.

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Each of the said sciences arrives in some way at the essence in a particular class of things, and then tries to prove the rest more or less exactly. Some arrive at the essence through sense-perception, and some by hypothesis; hence it is obvious from such a process of induction that there is no demonstration of the reality or essence.

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Now since there is a science of nature, clearly it must be different from both practical and productive science. In a productive science the source of motion is in the producer and not in the thing produced, and is either an art or some other kind of potency; and similarly in a practical science the motion is not in the thing acted upon but rather in the agent.

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But the science of the natural philosopher is concerned with things which contain in themselves a source of motion. From this it is clear that natural science must be neither practical nor productive, but speculative; since it must fall under one of these classes.

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And since every science must have some knowledge of the essence and must use it as a starting-point, we must be careful to observe how the natural philosopher should define, and how he should regard the formula of essence—whether in the same way as the term snub, or rather as the term concave.

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For of these the formula of snub is stated in conjunction with the matter of the object, whereas that of concave is stated apart from the matter; since snubness is only found in the nose, which is therefore included in the formula, for the snub is a concave nose . Thus it is obvious that the formula of flesh and eye and the other parts of the body must always be stated in conjunction with their matter.

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Since there is a science of Being qua Being and separately existent, we must inquire whether this should be regarded as identical with natural science or rather as a distinct branch of knowledge. Physics deals with things which contain a source of motion in themselves, and mathematics is speculative and is a science which deals with permanent things, but not with things which can exist separately.

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Hence there is a science distinct from both of these, which deals with that which exists separately and is immovable; that is, if there really is a substance of this kind—I mean separately existent and immovable—as we shall endeavor to prove.Aristot. Met. 12.6, 7. And if there is an entity of this kind in the world of reality, here surely must be the Divine, and this must be the first and most fundamental principle.

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Evidently, then, there are three kinds of speculative science: physics, mathematics, and theology. The highest class of science is the speculative, and of the speculative sciences themselves the highest is the last named, because it deals with the most important side of reality; and each science is reckoned higher or lower in accordance with the object of its study.

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The question might be raised as to whether the science of Being qua Being should be regarded as universal or not.

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Each of the mathematical sciences deals with some one class of things which is determinate, but universal mathematics is common to all alike. If, then, natural substances are the first of existing things, physics will be the first of the sciences; but if there is some other nature and substance which exists separately and is immovable, then the science which treats of it must be different from and prior to physics, and universal because of its priority.

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Since the term Being in its unqualified sense is used with several meanings, of which one is accidental Being, we must first consider Being in this sense.Sections 1-9 of this chapter correspond to Aristot. Met. 6.2-4. Clearly none of the traditional sciences concerns itself with the accidental; the science of building does not consider what will happen to the occupants of the house, e.g. whether they will find it unpleasant or the contrary to live in; nor does the science of weaving or of shoemaking or of confectionery.

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Each of these sciences considers only what is proper to it, i.e. its particular end. As for the question whether the cultured is also the lettered, or the quibbleThis is a different form of the quibble in Aristot. Met. 6.2.4. Here the fallacy obviously consists in the wrong application of the word ἅμα(at once or at the same time). that the man who is cultured, when he has become lettered, will be both at once although he was not before; but that which is but was not always so must have come to be; therefore he must have become at the same time cultured and lettered

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—none of the recognized sciences considers this, except sophistry. This is the only science which concerns itself with the accidental, and hence Plato was not far wrong in sayingPlat. Sop. 254a. that the sophist spends his time in the study of unreality. But that it is not even possible for there to be a science of the accidental will be apparent if we try to see what the accidental really is.

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Of some things we say that they are so always and of necessity (necessity having the sense not of compulsion, but that which we use in logical demonstrationCf. Aristot. Met. 6.2.6.), and of others that they are so usually, but of others that they are so neither usually nor always and of necessity, but fortuitously. E.g., there might be a frost at midsummer, although this comes about neither always and of necessity nor usually; but it might happen sometimes.

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The accidental, then, is that which comes about, but not always nor of necessity nor usually. Thus we have now stated what the accidental is; and it is obvious why there can be no science of such a thing, because every science has as its object that which is so always or usually, and the accidental falls under neither of these descriptions.

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Clearly there can be no causes and principles of the accidental such as there are of that which is per se; otherwise everything would be of necessity. For if A is when B is, and B is when C is, and C is not fortuitously but of necessity, then that of which C was the cause will also be of necessity, and so on down to the last causatum , as it is called.

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(But this was assumed to be accidental.) Therefore everything will be of necessity, and the element of chance, i.e. the possibility of a thing’s either happening or not, is entirely banished from the world of events. Even if we suppose the cause not to exist already but to be coming to be, the result will be the same; for everything will come to be of necessity.

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The eclipse tomorrow will come about if A does, and A will if B does, and B if C does; and in this way if we keep on subtracting time from the finite time between now and to-morrow, we shall at some point arrive at the present existing condition. Therefore since this exists, everything subsequent to it will happen of necessity, and so everything happens of necessity.

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As for what is in the sense of what is true or what is accidental , the former depends upon a combination in thought, and is an affection of thought (hence we do not look for the principles of Being in this sense, but only for those of objective and separable Being) the latter is not necessary but indeterminate (I mean the accidental); and of such a thing the causes are indefinite and cannot be reduced to a system.

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Teleology is found in events which come about in the course of nature or as a result of thought.This section is taken from Aristot. Physics 2.5, 6. It is chance <or luck> when one of these comes about by accident; for a thing may be a cause, just as it may exist, either per se or accidentally. Chance is an accidental cause of normally purposive teleological events.

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Hence chance and thought have the same sphere of action, for there is no purpose without thought. Causes from which chance results may come about are indeterminate; hence chance is inscrutable to human calculation, and is a cause only accidentally, but in the strictest sense is a cause of nothing.

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It is good or bad luck when the result is good or bad, and good or bad fortune when the result is on a large scale.

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Since nothing accidental is prior to that which is per se, neither are accidental causes prior. Therefore if chance or spontaneity is the cause of the universe, mind and nature are prior causes.The argument is stated more fully and clearly in Aristot. Physics 2.6ff.. Chance produces indirectly the effects produced directly by mind; and spontaneity is similarly related to nature. But the indirect cause presupposes the direct. The argument is directed against the Atomists. Cf. Aristot. Phys. 196a 24, Simplicius 327.24, Cicero De Nat. Deor. 1.66 (nulla cogente natura, sed concursu quodam fortuito).

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A thing may exist only actually or potentially, or actually and potentially; it may be a substance or a quantity or one of the other categories. There is no motionThe discussion of motion in this chapter consists of extracts from Aristot. Physics 3.1-3. apart from things, for change is always in accordance with the categories of Beingi.e., change is substantial (generation and destruction); quantitative (increase and decrease); qualitative (alteration); spatial (locomotion). Cf. Aristot. Met. 11.12.1, 2.; and there is nothing which is common to these and in no one category. Each category belongs to all its members in two ways—e.g. substance, for this is sometimes the form of the thing and sometimes its privation;

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and as regards quality there is white and black; and as regards quantity, complete and incomplete; and as regards spatial motion there is up and down or light and heavy—so that there are as many forms of motion and change as there are of Being.This is inaccurate; see previous note.

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Now since every kind of thing is divided into the potential and the real, I call the actualization of the potential as such,What Aristotle means by this is explained more clearly in the following sections, which may be summarized thus. The material substrate, e.g. bricks, etc., which is potentially a house, may be regarded (a) as potential material; in this sense it is actualized as bricks before building begins; (b) as potentially a house; in this sense when it is actualized it is no longer buildable but built, i.e., it is no longer potential; (c) as potentially buildable into a house. In this sense its actualization is conterminous with the process of building, and is incomplete (sect.11), and should not be described as ἐντελέχεια or complete reality. But Aristotle often uses this term as synonymous with the vaguer ἐνέργεια. motion.

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That this is a true statement will be clear from what follows. When the buildable in the sense in which we call it such exists actually, it is being built; and this is the process of building. The same is true of the processes of learning, healing, walking, jumping, ageing, maturing. Motion results when the complete reality itself exists, and neither sooner nor later.

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The complete reality, then, of that which exists potentially, when it is completely real and actual, not qua itself but qua movable, is motion. By qua I mean this. The bronze is potentially a statue; but nevertheless the complete reality of the bronze qua bronze is not motion. To be bronze is not the same as to be a particular potentiality; since if it were absolutely the same by definition the complete reality of the bronze would be a kind of motion; but it is not the same.

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(This is obvious in the case of contraries; for the potentiality for health and the potentiality for illness are not the same—for if they were, health and illness would be the same too—but the substrate which becomes healthy or ill, whether it is moisture or blood, is one and the same.) And since it is not the same, just as color and visible are not the same, it is the complete reality of the potential qua potential that is motion.

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It is evident that it is this, and that motion results when the complete reality itself exists, and neither sooner nor later. For everything may sometimes be actual, and sometimes not; e.g. the buildable qua buildable; and the actualization of the buildable qua buildable is the act of building.

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For the actualization is either this—the act of building—or a house. But when the house exists, it will no longer be buildable; the buildable is that which is being built. Hence the actualization must be the act of building, and the act of building is a kind of motion. The same argument applies to the other kinds of motion.

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That this account is correct is clear from what the other authorities say about motion, and from the fact that it is not easy to define it otherwise. For one thing, it could not be placed in any other class; this is clear from the fact that some peoplePythagoreans and Platonists. Cf. Aristot. Met. 1.5.6, Plat. Soph. 256d. identify it with otherness and inequality and not-being, none of which is necessarily moved;

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moreover change is no more into these or out of them than into or out of their opposites.The criticism implied is: If motion is identified with otherness, inequality, etc., then these concepts must be either (a) subjects of motion, which is absurd, or (b) termini of motion, in which case the same must be true of their contraries, since motion is between contraries. The reason for placing motion in this class is that it is considered to be indeterminate, and the principles in one of the columns of contraries are indeterminate, being privative; for none of them is a determinate thing or quality or any of the other categories.

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The reason for considering motion to be indeterminate is that it cannot be associated either with the potentiality or with the actuality of things; for neither that which is potentially nor that which is actually of a certain size is necessarily moved.

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And motion is considered to be a kind of actualization, but incompleteCf. note on sect. 2 (end) above, and Aristot. Met. 9.6.7-10.; the reason of this is that the potential, of which it is the actualization, is incomplete.

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Thus it is difficult to comprehend what motion is; for we must associate it either with privation or with potentiality or with absolute actuality; and apparently none of these is possible.

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There remains, then, the account which we have given; that it is an actuality, and an actuality of the kind which we have described, which is hard to visualize but capable of existing.

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That motion is in the movable is evident; for it is the complete realization of the movable by that which is capable of causing motion, and the actualization of that which is capable of causing motion is identical with that of the movable.

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For it must be a complete realization of them both; since a thing is capable of moving because it has the potentiality, but it moves only when it is active; but it is upon the movable that it is capable of acting. Thus the actuality of both alike is one; just as there is the same interval from one to two as from two to one, and the hill up and the hill down are one, although their being is not one; the case of the mover and the thing moved is similar.

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This chapter consists of extracts from Aristot. Physics 3.4, 5, 7.The infinite is either (a) that which cannot be traversed because it is not its nature to be traversed (just as sound is by nature invisible); or (b) that which admits of an endless traverse; or (c) scarcely admits of traverse; or (d) which, though it would naturally admit of traverse or limit, does not do so. Further, it may be infinite in respect of addition or of subtraction or of both.

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That the infinite should be a separate independent entity,The Pythagorean and Platonic view. and yet imperceptible, is impossible.

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For if it is neither magnitude nor plurality, but infinity itself is the essence of it, and not merely an accident, it must be indivisible; because that which is divisible is either magnitude or plurality. And if it is indivisible it cannot be infinite, except in the same way as sound is invisible. But this is not what people mean by infinite; and it is not the infinite in this sense that we are investigating, but the infinite in the sense of the untraversable.

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Again, how can the infinite exist independently unless number and magnitude, of which infinity is an attribute, also exist independently?Aristotle has argued that they do not in Aristot. Met. 1.9.16-25. And further, if the infinite is accidental, it cannot, qua infinite, be an element of things; just as the invisible is not an element of speech, although sound is invisible. It is clear also that the infinite cannot exist actually.

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Otherwise any part of it which we might take would be infinite; for infinity and the infinite are the same, if the infinite is substance and is not predicated of a subject. Therefore it is either indivisible, or if it is partible, the parts into which it is divisible are infinite. But the same thing cannot be many infinites; for just as a part of air is air, so a part of the infinite will be infinite, if the infinite is a substance and principle.

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Therefore it is impartible and indivisible. But this is impossible of the actually infinite, because it must be some quantity. Therefore infinity is an accidental attribute. But if so, as we have said, it cannot be it that is a principle, but that of which it is an accident: airAccording to Anaximenes; cf. Theophrastus, Phys. Opin. Fr. 2 (Ritter and Preller 26). or the even. According to the Pythagoreans. Cf. Aristot. Met. 1.5.5. n

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The foregoing inquiry is general; but what follows will show that the infinite does not exist in sensible things.

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If the definition of a body is that which is bounded by surfaces, then no body, whether sensible or intelligible, can be infinite nor can there be any separate and infinite number, since number or that which involves number is numerable. This is clearly shown by the following concrete argument. The infinite can neither be composite nor simple. For (a) it cannot be a composite body if the elements are limited in numberThis is proved in Aristot. Physics 1.6.;

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for the contraries must be equal, and no one of them must be infinite; for if the potency of one of the two corporeal elements is in any way inferior, the finite element will be destroyed by the infinite. And every element cannot be infinite, because body is that which has extension in all directions, and the infinite is that which is extended without limit; so that if the infinite is corporeal it will be infinite in all directions.sc. and so no other body can exist beside it.

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Nor (b) can the infinite be any simple body; neither, as someAnaximander. It seems, however, that by ἄπειρον he meant indeterminate or undifferentiated, although he no doubt regarded this principle as infinite as well. Cf. notes on Aristot. Met. 1.7.3, Aristot. Met. 12.2.3. hold, something which is apart from the elements and from which they suppose the elements to be generated (for there is no such body apart from the elements; everything can be resolved into that of which it consists, but we do not see things resolved into anything apart from the simple bodies), nor fire nor any other element.

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Apart from the question of how any of them could be infinite, the All, even if it is finite, cannot be or become any one of the elements, as Heraclitus saysCf. Hereclitus Fr. 20-22 (Bywater). all things at certain times become fire. The same argument applies as to the One which the physicists posit besides the elements; for all change proceeds from the contrary, e.g. from hot to cold.The argument seems to be: Since all change is from contrary to contrary, and it is impossible that either (a) one of the elements should be contrary to the rest, or (b) one material principle should be contrary to all four elements, it follows that no one element, and similarly that no one material principle apart from the elements, can be the ultimate material principle of the universe.

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Again, a sensible body is in some region, and the region of the whole and of the part (e.g. of the earth) is the same.i.e., the region of the universe which is proper to a given element is proper also to any part of that element. The proper region of earth is the center, of fire the circumference of the universe. Cf. Aristot. De Caelo 1.2. Therefore if the infinite body is homogeneous, it will be immovable or will always be in motionRoss is evidently right in taking this to refer to the rest or motion of the parts. An infinite body cannot move as a whole, because there is no space outside it.; but this is impossible, for why should there be rest or motion below rather than above or in any other region? E.g., if there were a clod, in what region would it move or be at rest?

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The region proper to the body which is homogeneous with the clod is infinite. Then will the clod occupy the whole of that region? How can it? Then what of its rest or motion? It will either rest everywhere—in which case it cannot move—or move everywhere; in which case it cannot rest.If earth is an infinite body, its region must be infinite. But the infinite has no center (cf. sect. 13). Therefore a clod, which cannot occupy the whole region proper to earth, will have no region proper to itself to which it can move or in which it can rest. And if the whole is not alike throughout, the regions proper to its parts are unlike also; and (a) the body of the whole is not one, except in virtue of contact; (b) the parts will be either finite or infinite in kind.

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Finite they cannot be, for then those of one kind would be infinitesc. in quantity. If the universe is infinite in quantity, and the elements are limited in kind, some of the elements (or at least one) must be infinite in quantity. But this is impossible, just as it is impossible that all the elements should be infinite in quantity. Cf. sect. 7 above and those of another would not (if the whole is infinite); e.g., fire or water would be infinite. But such a condition would involve the destruction of the contraries. But if the parts are infinitesc. in kind or number. and simple, the regions proper to them are infinite and the elements will be infinite. And since this is impossible,Cf. sect. 6 n. the regions are finiteCf. sect. 14 n. and the whole must be finite.

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In general, there cannot be an infinite body and a place for bodies if every body which is sensible has either weight or lightness; for it will have to move either towards the center or upwards, and the infinite—either the whole or the half—cannot do either; for how can you divide it? How can the infinite be part up and part down, or part extreme and part center?

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Further, every sensible body is in some place, and of place there are six kinds,i.e., above and below, before and behind, right and left (Aristot. Phys. 205b 31). but these cannot exist in an infinite body. In general, if an infinite place is impossible, so is an infinite body; because that which is in a place is somewhere, and this means either up or down or one of the other kinds of place, and each of these is a limit.

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The infinite is not the same in the sense that it is one nature whether it applies to magnitude or to motion or to time; the posterior is derived from the prior sense, e.g. motion is called infinite in virtue of the magnitude involved when a thing is moved or changed or increased, and time is so called on account of motion.Cf. Aristot. Met. 5.13.5.

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That which changes either changes accidentally, as when the cultured walks; or is said to change in general because something in it changes, as in the case of things which change in their parts; the body becomes healthy because the eye does.

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But there is something which is moved directly per se, i.e. the essentially movable. The same applies to that which moves, for it moves sometimes accidentally, sometimes partially, and sometimes per se. There is something that moves directly, and something that is moved; and also a time in which, and something from which, and something into which it is moved. But the forms and modifications and place into which moving things are moved are immovable; e.g. knowledge and warmth. It is not warmth that is motion, but the process of warming.

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Non-accidental change is not found in all things, but only between contraries and intermediates and contradictories. We can convince ourselves of this by means of induction. That which changes changes either from positive into positive, or from negative into negative, or from positive into negative, or from negative into positive.

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By positive I mean that which is denoted by an affirmation. Thus there must be three forms of change; for that which is from negative into negative is not change, because they are neither contraries nor contradictories, since they entail no opposition. The change from the negative into its contradictory positive is generation—absolute change absolute generation, and qualified change qualified generation; and the change from the positive to the negative is destruction—absolute change absolute destruction, and qualified change qualified destruction.The change from positive to positive is omitted here (but cf. sect. 7). Aristotle no doubt intended to use it as an example of non-substantial change, e.g. from poor man to rich man; but since this can be regarded as change from poor man to not-poor man, or not-rich man to rich man, he includes it as a qualified type of substantial change.

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Now if what is not has several meanings, and neither that which implies a combination or separation of terms,i.e., falsity. Cf. Aristot. Met. 9.10.1. nor that which relates to potentiality and is opposed to unqualified Being, admits of motion (not-white or not-good, however, admits of motion accidentally, because not-white may be a man; but that which is not so-and-so in an absolute sense does not admit of it at all), then what is not cannot be moved. If this is so, generation cannot be motion; for it is what is not that is generated.

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For even if the generation is in the highest degree accidental, still it is true to say that not-being is predicable of that which is generated absolutely. And the argument applies similarly to rest. Thus not only do these difficult conclusions follow, but also that everything which is moved is in a place, whereas what is not is not in a place; for then it would be somewhere. Nor is destruction motion; for the contrary of motion is motion or rest, but the contrary of destruction is generation.

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And since every motion is a kind of change, and the three kinds of change are those which we have described,sect. 3. and of these those which relate to generation and destruction are not motions, and these are the changes between contradictories, the change from positive to positive must alone be motion. The subjects are either contraries or intermediates (for privative terms may also be regarded as contraries) and are denoted by a positive term—e.g. naked or toothless or black.

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Now since the categories are distinguished as substance, quality, place, activity or passivity, relation and quantity,Aristotle generally distinguishes eight categories (originally ten, but he seems to have abandoned κεῖσθαιposition and ἔχεινstate at an early date); here he omits time as being relative to motion (it is that by which motion can be numerically estimated; cf. Aristot. Met. 12.6.2, Aristot. Phys. 219b 1) and therefore neither the subject nor the terminus of motion. Cf. Ross ad loc. there must be three kinds of motion, in respect of quality, quantity and place. There is no motionThere is, however, change in respect of substance (generation and destruction), but this is between contradictories and is not motion in the strict sense. Cf. Aristot. Met. 11.11.6, and sect. 4 below. The distinction between motion and change is not always maintained. in respect of substance, because substance has no contrary; nor of the relative, because it is possible that when one of two related things changes the relation to it of the other thing, even though the thing itself does not change, may become untrue; therefore the motion of these related things is accidental.

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Nor is there motion of the agent or patient, or of the mover and the thing moved, because there is no motion of motion nor no generation of generation, nor in general is there change of change. There are two ways in which there might be motion of motion: (1) Motion might be the subject of motion, as, e.g., a man is moved because he changes from white to black; in this way motion might be heated or cooled or might change its place or increase.

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But this is impossible, because the change is not a subject. Or (2) some other subject might change from change to some other form of existence, as, e.g., a man changes from sickness to health. But this is also impossible except accidentally.

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Every motion is a change from one thing into something else; and the same is true of generation and destruction, except that these are changes into opposites in one sense,sc. contradictories. while the other, i.e. motion, is a change into opposites in another sense.sc. contraries. Hence a thing changes at the same time from health to sickness, and from this change itself into another.

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Now clearly if it has fallen ill it will be already changed (for it cannot remain at rest) into that other change, whatever it may be; and further this cannot be, in any given case, any chance change; and it also must be from something into something else. Therefore it will be the opposite change, viz. becoming healthy. But this is so accidentally; just as there is change from recollecting to forgetting because the subject changes, now in the direction of knowledge and now in that of ignorance.

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Further, we shall have an infinite series if there is to be change of change and becoming of becoming, because if the latter of two becomings comes to be from the former, the former must come to be too. E.g., if simple becoming was once coming to be, that which comes to be something was also once coming to be. Therefore that which simply comes to be was not yet, but there was already something coming to be coming to be something.

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But this too was at one time coming to be, and therefore it was not at that time coming to be something. But in infinite series there is no first term, and therefore in this series the first term cannot exist, nor can any subsequent term. Therefore nothing can be either generated or moved or changed.

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Further, the same thing which admits of motion admits also of the contrary motion and of rest, and that which admits of generation admits also of destruction.

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Therefore that which comes to be, when it has come to be coming to be, is then in course of perishingsc. which is absurd.; for it does not perish as soon as it is coming to be coming to be, nor afterwards, because that which is perishing must exist .That which comes to be must cease to be, and it can cease to be only when it exists. Therefore if that which comes to be comes to be coming to be, it must cease to be when it is coming to be; before this it does not exist, but is only coming to be coming to be, and after this it is not that which comes to be but that which has come to be.

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Further, there must be some matter underlying that which is coming to be or changing. What then will it be? What is it that becomes motion or generation in the same way as it is body or soul that undergoes change? And moreover what is that which is the terminus of the motion? For that which we are considering must be a motion or generation of A from B into C.

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How then can these conditions be fulfilled? There can be no learning of learning, and therefore there can be no generation of generation.

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Since there is no motion of substance or of the relative or of activity and passivity, it remains that there is motion in respect of quality, quantity and place; for each of these admits of contrariety. By quality I mean not that which is in the substance (for indeed even the differentia is a quality), but the passive quality in virtue of which a thing is said to be acted upon or to be immune from being acted upon.Cf. Aristot. Met. 5.14.

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The immovable is either that which is wholly incapable of being moved, or that which is scarcely moved in the course of a long time or is slow in starting, or that which would naturally be moved but cannot be moved at the time when and from the place whence and in the way in which it would naturally be moved. This last is the only kind of immovable thing which I recognize as being at rest; for rest is contrary to motion, and so must be a privation of that which admits of motion.

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Things are together in place which are in the primary sensei.e., when they occupy one place to the exclusion of anything else. Cf. Aristot. Phys. 209a 33-b 1. in one place, and separate which are in different places. Contrary in place is that which is at a maximum distance in a straight line.I have transferred this sentence from the end of the section, where it is placed in the text, on the ground that it fits more naturally here. I suspect that it, like the displaced portion of sect. 13, was originally a marginal note which was later inserted in the body of the text, but in the wrong position. Things are said to be in contact whose extremes are together in place. An intermediate is that at which a changing thing which changes continuously in accordance with its nature naturally arrives before it arrives at the extreme into which it is changing. Since all change takes place between opposites, and these are either contraries or contradictories, and contradictories have no middle term, clearly it is to the sphere of contraries that the intermediate belongs.I have followed Prantl’s suggestion in transferring this sentence from the end of sect. 13.

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Successive is that which comes after the beginning (the order being determined by position or form or in some other way) and has nothing of the same class between itself and that which it succeeds; e.g. lines in the case of a line, and units in that of a unit, and a house in the case of a house (but there is nothing to prevent something else from coming between). For that which is successive is a thing which is successive and posterior to some other thing. 1 is not successive to 2, nor is the new mooni.e., the first day of the month. to the second day of the month.

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Contiguous is that which is successive and in contact. The continuous is a species of the contiguous.

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I call two things continuous when their respective boundaries, by which they are kept together in contact, become one and the same; hence clearly the continuous belongs to the sphere of things whose nature it is to become one by contiguity.

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Clearly successive is the most ultimate term; for the successive need not be in contact, but contact implies succession; and if there is continuity there is contact, but if there is contact there is not necessarily continuity;

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and where there is no contact there is no coalescence. Therefore a point is not the same as a unit; for points admit of contact, whereas units do not, but only of succession; and between points there is something intermediate, but between units there is not.

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Our inquiry is concerned with substance; for it is the principles and causes of substances that we are investigating. Indeed if the universe is to be regarded as a whole, substance is its first part; and if it is to be regarded as a succession,Cf. Aristot. Met. 12.10.14, Aristot. Met. 14.3.9. even so substance is first, then quality, then quantity. Moreover, the latter hardly exist at all in the full sense, but are merely qualifications and affections of Being. Otherwise not-white and not-straight would also exist; at any rate we say that they too are, e.g., it is not white.

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Further, none of the other categories is separately existent. Even the ancients in effect testify to this, for it was of substance that they sought the principles and elements and causes. Present-day thinkersPlatonists. tend to regard universals as substance, because genera are universal, and they hold that these are more truly principles and substances because they approach the question theoretically; but the ancients identified substance with particular things, e.g. fire and earth, and not with body in general.

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Now there are three kinds of substance. One is sensible (and may be either eternali.e., the celestial bodies. or perishable; the latter, e.g. plants and animals, is universally recognized); of this we must apprehend the elements, whether they are one or many.

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Another is immutable , which certain thinkers hold to exist separately; some dividing it into two classes, others combining the Forms and the objects of mathematics into a single class, and others recognizing only the objects of mathematics as of this nature.These three views were held respectively by Plato, Xenocrates and Speusippus. Cf. Aristot. Met. 7.2.3, 4; Aristot. Met. 13.1.4, and see Introduction. The first two kinds of substance come within the scope of physics, since they involve motion; the last belongs to some other science, if there is no principle common to all three.

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Sensible substance is liable to change. Now if change proceeds from opposites or intermediates—not however from all opposites (for speech is not white), but only from the contraryCf. Aristot. Met. 10.7.—then there must be something underlying which changes into the opposite contrary; for the contrariesi.e., contrary qualities. Cf. Aristot. Met. 8.5.1. do not change.

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Further, something persists, whereas the contrary does not persist. Therefore besides the contraries there is some third thing, the matter . Now if change is of four kinds, in respect either of substance or of quality or of quantity or of place, and if change of substance is generation or destruction in the simple sense, and change of quantity is increase or decrease, and change of affection is alteration, and change of place is locomotion, then changes must be in each case into the corresponding contrary state.

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It must be the matter, then, which admits of both contraries, that changes. And since that which is is twofold, everything changes from that which is potentially to that which is actually; e.g. from potentially white to actually white. The same applies to increase and decrease. Hence not only may there be generation accidentally from that which is not, but also everything is generated from that which is, but is potentially and is not actually.

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And this is the one of Anaxagoras; for his all things were together,Anaxagoras Fr. 1 (Diels). and the mixture of Empedocles and Anaximander and the doctrine of Democritus would be better expressed as all things were together potentially, but not actually. In this passage I follow Ross’s punctuation and interpretation, which seem to me to be certainly right. Anaxagoras’s undifferentiated infinity of homoeomerous particles (although contrasted with the unifying principle of Mind, cf. Aristot. Met. 1.8.14) can be regarded as in a sense a unity. Again, μῖγμα(as Ross points out) in its Aristotelian sense of complete fusion is a fair description of Anaximander’s indeterminate. The general meaning of the passage is that in each of the systems referred to the material principle in its elemental state should have been described as existing only potentially.

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Hence these thinkers must have had some conception of matter. All things which change have matter, but different things have different kinds; and of eternal things such as are not generable but are movable by locomotion have matter; matter, however, which admits not of generation, but of motion from one place to another.Cf. Aristot. Met. 12.1.3, Aristot. Met. 8.1.7, 8.

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One might raise the question from what sort of not-being generation takes place; for not-being has three senses.(1) the negation of a category, (2) falsity, (3) unrealized potentiality. Cf. Aristot. Met. 14.2.10. If a thing exists through a potentiality, nevertheless it is not through a potentiality for any chance thing; different things are derived from different things.

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Nor is it satisfactory to say that all things were together, for they differ in their matter, since otherwise why did they become an infinity and not one? For Mind is one; so that if matter is also one, only that could have come to be in actuality whose matter existed potentially. The causes and principles, then, are three; two being the pair of contraries, of which one is the formula or form and the other the privation, and the third being the matter.This classification is found in Aristot. Physics 1.6, 7, but is foreign to the main treatise of the Metaphysics. See Introduction.

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We must next observeSee Introduction. that neither matter nor form (I mean in the proximate sense) is generated. All change is of some subject by some agent into some object. The agent is the immediate mover; the subject is the matter; and the object is the form. Thus the process will go on to infinity if not only the bronze comes to be round, but also roundness or bronze comes to be; there must, then, be some stopping-point.

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We must next observe that every substance is generated from something which has the same name (substances including not only natural but all other products). Things are generated either by art or by nature or by chance or spontaneously. Art is a generative principle in something else; nature is a generative principle in the subject itselfIn natural reproduction the generative principle is obviously in the parent. But the offspring is in a sense a part of the parent, and so Aristotle identifies the two.(for man begets man); the other causes are privations of these.Cf. Aristot. Met. 11.8.12 n.

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There are three kinds of substance: (1.) matter, which exists individually in virtue of being apparentAristotle is contrasting proximate with primary matter. Fire, the primary matter of a man, is a simple undifferentiated element which cannot be perceived as such, and has no individuality. The head, and the other parts of the body, considered merely as in contact and not as forming an organic unity, are the proximate matter of a man; they are perceptible and individual. Flesh (in general) represents the matter in an intermediate stage.(for everything which is characterized by contact and so not by coalescence is matter and substrate; e.g. fire, flesh and head; these are all matter, and the last is the matter of a substance in the strictest sense); (2.) the naturei.e., form.(existing individually)—i.e. a kind of positive state which is the terminus of motion; and (3.) the particular combination of these, e.g. Socrates or Callias. In some cases the individuality does not exist apart from the composite substance (e.g., the form of a house does not exist separately, except as the art of building;

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nor are these forms liable to generation and destruction; there is a distinct sense in which house and health and every artificial product, considered in the abstract, do or do not existi.e., in the mind of the architect or doctor.); if it does so at all, it does so in the case of natural objects. Hence Plato was not far wrong in sayingSee Introduction. that there are as many Forms as there are kinds of natural objects; that is if there are Forms distinct from the things of our world.

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Moving causes are causes in the sense of pre-existent things, but formal causes coexist with their effects. For it is when the man becomes healthy that health exists, and the shape of the bronze sphere comes into being simultaneously with the bronze sphere.

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Whether any form remains also afterwards is another question. In some cases there is nothing to prevent this, e.g. the soul may be of this nature (not all of it, but the intelligent part; for presumably all of it cannot be). Clearly then there is no need on these grounds for the Ideas to exist; for man begets man, the individual begetting the particular person. And the same is true of the arts, for the art of medicine is the formula of health.

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In one sense the causes and principles are different for different things; but in another, if one speaks generally and analogically, they are the same for all. For the question might be raised whether the principles and elements of substances and of relations are the same or different; and similarly with respect to each of the other categories. But it is absurd that they should be the same for all; for then relations and substance would have the same constituents.

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What then can their common constituent be? For there is nothing common to and yet distinct from substance and the other predicable categories, yet the element is prior to that of which it is an element. Moreover substance is not an element of relations, nor is any of the latter an element of substance. Further, how can all the categories have the same elements?

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For no element can be the same as that which is composed of elements; e.g., neither B nor A can be the same as BA (nor indeed can any of the intelligibles,Unity and Being are called intelligibles as being the most universal predicates and as contrasted with particulars, which are sensible. e.g. Unity or Being, be an element; for these apply in every case, even to composite things); hence no element can be either substance or relation. But it must be one or the other. Therefore the categories have not all the same elements.

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The truth is that, as we say, in one sense all things have the same elements and in another they have not. E.g., the elements of sensible bodies are, let us say, (1) as form, the hot, and in another sense the cold, which is the corresponding privation; as matter, that which directly and of its own nature is potentially hot or cold. And not only these are substances, but so are (2) the compoundsThis apparently refers to the elements; fire and air are hot matter, water and earth cold matter. of which they are principles, and (3) any unity which is generated from hot and cold, e.g. flesh or bone; for the product of hot and cold must be distinct from them.

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These things, then, have the same elements and principles, although specifically different things have specifically different elements; we cannot, however, say that all things have the same elements in this sense, but only by analogy: i.e., one might say that there are three principles, form, privation and matter.

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But each of these is different in respect of each class of things, e.g., in the case of color they are white, black, surface; or again there is light, darkness and air, of which day and night are composed. And since not only things which are inherent in an object are its causes, but also certain external things, e.g. the moving cause, clearly principle and element are not the same; but both are causes. Principles are divided into these two kinds, and that which moves a thing or brings it to rest is a kind of principle and substance.

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Thus analogically there are three elements and four causes or principles; but they are different in different cases, and the proximate moving cause is different in different cases. Health, disease, body; and the moving cause is the art of medicine. Form, a particular kind of disorder, bricks; and the moving cause is the art of building.

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And since in the sphere of natural objects the moving cause of man is man, while in the sphere of objects of thought the moving cause is the form or its contrary, in one sense there are three causes and in another four. For in a sense the art of medicine is health, and the art of building is the form of a house, and man begets man; but besides these there is that which as first of all things moves all things.For the first time the ultimate efficient cause is distinguished from the proximate. Aristotle is leading up to the description of the Prime Mover which occupies the latter half of the book.

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Now since some things can exist in separation and others cannot, it is the former that are substances. And therefore all things have the same causes, because without substance there can be no affections and motions. Next we shall seeSee Introduction. that these causes are probably soul and body, or mind, appetite and body.Aristotle is thinking of animals and human beings, which are substances in the truest sense. Again, there is another sense in which by analogy the principles are the same viz. actuality and potentiality; but these are different for different things, and apply to them in different ways.

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For in some cases the same thing exists now actually and now potentially; e.g. wine or flesh or man (actuality and potentiality also fall under the causes as already described; for the form exists actually if it is separable, and so does the compound of form and matter, and the privation, e.g. darkness or disease; and the matter exists potentially, for it is this which has the potentiality of becoming bothi.e., of acquiring either of the contrary qualities distinguished by the form and the privation;

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but the distinction in virtue of actuality and potentiality applies in a different sense to cases where the matter of cause and effect is not the same, in some of which the form is not the same but different. E.g., the cause of a man is (i) his elements: fire and earth as matter, and the particular form; (2) some external formal cause, viz. his father; and besides these (3) the sun and the ecliptic,The sun, moving in the ecliptic, approaches nearer to the earth in summer, causing generation, and recedes farther from the earth in winter, causing destruction. Cf. Aristot. Met. 12.6.10 n., Aristot. De Gen. et Corr. 336a 32. which are neither matter nor form nor privation nor identical in form with him, but cause motion.

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Further, we must observe that some causes can be stated universally, but others cannot.

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The proximate principles of all things are the proximate actual individual and another individual which exists potentially.i.e., the proximate efficient cause and proximate matter. Therefore the proximate principles are not universal. For it is the particular that is the principle of particulars; man in general is the principle of man in general, but there is no such person as man, whereas Peleus is the principle of Achilles and your father of you, and this particular B of this particular BA; but B in general is the principle of BA regarded absolutely.

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Again, even if the causes of substances are universal, still, as has been said,Aristot. Met. 12.4.6. different things, i.e. things which are not in the same genus, as colors, sounds, substances and quantity, have different causes and elements, except in an analogical sense; and the causes of things which are in the same species are different, not in species, but because the causes of individuals are different: your matter and form and moving cause being different from mine, although in their universal formula they are the same.

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As for the question what are the principles or elements of substances and relations and qualities, whether they are the same or different, it is evident that when the terms principle and element are used with several meanings they are the same for everything; but when the meanings are distinguished, they are not the same but different; except that in a certain sense they are the same for all. In a certain sense they are the same or analogous, because (a) everything has matter, form, privation and a moving cause; (b) the causes of substances may be regarded as the causes of all things, since if substances are destroyed everything is destroyed; and further (c) that which is first in complete realityi.e., the prime mover. is the cause of all things.

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In another sense, however, proximate causes are different; there are as many proximate causes as there are contraries which are predicated neither as genera nor with a variety of meaningsi.e., individual forms and privations of individual things.; and further the particular material causes are different. Thus we have stated what the principles of sensible things are, and how many they are, and in what sense they are the same and in what sense different.

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Since we have seenAristot. Met. 12.1.3, 4. that there are three kinds of substance, two of which are natural and one immutable, we must now discuss the last named and show that there must be some substance which is eternal and immutable. Substances are the primary reality, and if they are all perishable, everything is perishable. But motion cannot be either generated or destroyed, for it always existedCf. Aristot. Physics 8.1-3; nor can time, because there can be no priority or posteriority if there is no time.The argument seems to be: If we assume that time was generated, it follows that before that there was no time; but the very term before implies time. The same applies to the destruction of time.

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Hence as time is continuous, so too is motion; for time is either identical with motion or an affection of it.Cf. Aristot. Met. 11.12.1 n. But there is no continuous motion except that which is spatial, of spatial motion only that which is circular.These statements are proved inAristot. Physics 8.8, 9.

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But even if we are to suppose that there is something which is kinetic and productive although it does not actually move or produce, there will not necessarily be motion; for that which has a potentiality may not actualize it.

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Thus it will not help matters if we posit eternal substances, as do the exponents of the Forms, unless there is in them some principle which can cause change.As there is not, according to Aristotle; cf. Aristot. Met. 1.7.4. And even this is not enough, nor is it enough if there is another substance besides the Forms; for unless it actually functions there will not be motion.

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And it will still not be enough even if it does function, if its essence is potentiality; for there will not be eternal motion, since that which exists potentially may not exist. Therefore there must be a principle of this kind whose essence is actuality. Furthermore these substancesAristotle is now thinking not only of the prime mover (God or Mind) but also of the movers of the celestial spheres. Cf. Aristot. Met. 12.8.14. must be immaterial; for they must be eternal if anything is. Therefore they are actuality.

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There is a difficulty, however; for it seems that everything which actually functions has a potentiality, whereas not everything which has a potentiality actually functions; so that potentiality is prior. But if this is so, there need be no reality; for everything may be capable of existing, but not yet existent.

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Yet if we accept the statements of the cosmologists who generate everything from Night,Cf. Hes. WD 17, Hes. Th. 116ff. or the doctrine of the physicists that all things were together,Cf. Aristot. Met. 12.2.3. we have the same impossibility; for how can there be motion if there is no actual cause? Wood will not move itself—carpentry must act upon it; nor will the menses or the earth move themselves—the seeds must act upon the earth, and the semen on the menses.

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Hence some, e.g. LeucippusCf. Aristot. Met. 1.4.12, Aristot. De Caelo 300b 8, and see Burnet, E.G.P. 178. and Plato,Cf. Plat. Tim. 30a, and sect. 8 below. posit an eternal actuality, for they say that there is always motion; but why there is, and what it is, they do not say; nor, if it moves in this or that particular way, what the cause is. For nothing is moved at haphazard, but in every case there must be some reason present; as in point of fact things are moved in one way by nature, and in another by force or mind or some other agent. And further, what kind of motion is primary? For this is an extremely important point.

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Again, Plato at least cannot even explain what it is that he sometimes thinks to be the source of motion, i.e., that which moves itself; for according to him the soul is posterior to motion and coeval with the sensible universe.Aristotle refers to Plato’s rather inconsistent account in Plat. Tim. 30-34. Now to suppose that potentiality is prior to actuality is in one sense right and in another wrong; we have explainedThe reference is probably to 5 above, but cf. Aristot. Met. 9.8. the distinction.

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But that actuality is prior is testified by Anaxagoras (since mind is actuality), and by Empedocles with his theory of Love and Strife, and by those who hold that motion is eternal, e.g. Leucippus.

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Therefore Chaos or Night did not endure for an unlimited time, but the same things have always existed, either passing through a cycle or in accordance with some other principle—that is, if actuality is prior to potentiality.

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Now if there is a regular cycle, there must be somethingThe sphere of the fixed stars, Aristot. Met. 12.8.9; cf. Aristot. De Gen. et Corr. 336a 23ff. which remains always active in the same way; but if there is to be generation and destruction, there must be something elseThe sun, which has its own yearly orbit in the ecliptic, and a daily rotation round the earth, which is explained most economically with reference to the rotation of the sphere of the fixed stars. Cf. Aristot. Met. 12.5.3 n., Aristot. De Gen. et Corr. 336a 23ff. which is always active in two different ways. Therefore this must be active in one way independently, and in the other in virtue of something else, i.e. either of some third active principle or of the first.

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It must, then, be in virtue of the first; for this is in turn the cause both of the third and of the second. Therefore the first is preferable, since it was the cause of perpetual regular motion, and something else was the cause of variety; and obviously both together make up the cause of perpetual variety. Now this is just what actually characterizes motions; therefore why need we seek any further principles?

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Since (a) this is a possible explanation, and (b) if it is not true, we shall have to regard everything as coming from Night Aristot. Met. 12.6.6 and all things together and not-being,Aristot. Met. 12.2.2, 3. these difficulties may be considered to be solved. There is something which is eternally moved with an unceasing motion, and that circular motion. This is evident not merely in theory, but in fact. Therefore the ultimate heaven must be eternal. Then there is also something which moves it.

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And since that which is moved while it moves is intermediate, there is something which moves without being moved; something eternal which is both substance and actuality.

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Now it moves in the following manner. The object of desire and the object of thought move without being moved. The primary objects of desire and thought are the same. For it is the apparent good that is the object of appetite, and the real good that is the object of the rational will.This shows that desire in general (of which appetite and will are the irrational and rational aspects) has as its object the good. Desire is the result of opinion rather than opinion that of desire; it is the act of thinking that is the starting-point.

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Now thought is moved by the intelligible, and one of the series of contrariesAristotle himself recognizes two series, lists or columns of contraries, similar to those of the Pythagoreans (Aristot. Met. 1.5.6). One, the positive, contains being, unity, substance, etc.; the other is negative and contains not-being, plurality, non-substance, etc. The negative terms are intelligible only in reference to the positive. Cf. Aristot. Met. 4.2.21. is essentially intelligible. In this series substance stands first, and of substance that which is simple and exists actually. (The one and the simple are not the same; for one signifies a measure,Cf Aristot. Met. 5.6.17. whereas simple means that the subject itself is in a certain state.)

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But the Good, and that which is in itself desirable, are also in the same series; and that which is first in a class is always best or analogous to the best.

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That the final cause may apply to immovable things is shown by the distinction of its meanings. For the final cause is not only the good for something, but also the good which is the end of some action. In the latter sense it applies to immovable things, although in the former it does not; and it causes motion as being an object of love, whereas all other things cause motion because they are themselves in motion.

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Now if a thing is moved, it can be otherwise than it is. Therefore if the actuality of the heaven is primary locomotion, then in so far as the heaven is moved, in this respect at least it is possible for it to be otherwise; i.e. in respect of place, even if not of substantiality. But since there is something—X—which moves while being itself unmoved, existing actually, X cannot be otherwise in any respect.

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For the primary kind of change is locomotion,Proved in Aristot. Physics 8.7. and of locomotion circular locomotion Aristot. Physics 8.9 ; and this is the motion which X induces. Thus X is necessarily existent; and qua necessary it is good, and is in this sense a first principle.The argument is: X (the prime mover), since it imparts the primary motion, cannot be liable to motion (or change) of any kind. Therefore it exists of necessity, and must be good (cf. Aristot. Met. 5.5.6); and it is qua good, i.e., the object of desire, that X is a first principle. For the necessary has all these meanings: that which is by constraint because it is contrary to impulse; and that without which excellence is impossible; and that which cannot be otherwise, but is absolutely necessary.Cf. Aristot. Met. 5.5

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Such, then, is the first principle upon which depend the sensible universe and the world of nature.

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And its life is like the best which we temporarily enjoy. It must be in that state always (which for us is impossible), since its actuality is also pleasure.For the relation of pleasure to actuality or activity see Aristot. Nic. Eth. 10.4.(And for this reason waking, sensation and thinking are most pleasant, and hopes and memories are pleasant because of them.) Now thinking in itself is concerned with that which is in itself best, and thinking in the highest sense with that which is in the highest sense best.Since the prime mover is pure actuality, and has or rather is the highest form of life, Aristotle identifies it with the highest activity—pure thinking.

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And thought thinks itself through participation in the object of thought; for it becomes an object of thought by the act of apprehension and thinking, so that thought and the object of thought are the same, because that which is receptive of the object of thought, i.e. essence, is thought. And it actually functions when it possesses this object.In actualization the subject and object of thought (like those of perception, Aristot. De Anima 3.2.) are identical. Hence it is actuality rather than potentiality that is held to be the divine possession of rational thought, and its active contemplation is that which is most pleasant and best.

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If, then, the happiness which God always enjoys is as great as that which we enjoy sometimes, it is marvellous; and if it is greater, this is still more marvellous. Nevertheless it is so. Moreover, life belongs to God. For the actuality of thought is life, and God is that actuality; and the essential actuality of God is life most good and eternal. We hold, then, that God is a living being, eternal, most good; and therefore life and a continuous eternal existence belong to God; for that is what God is.

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Those who suppose, as do the Pythagoreans and Speusippus,The view is referred to again in Aristot. Met. 12.10.6, Aristot. Met. 14.4.2, 3, Aristot. Met. 14.5.1. that perfect beauty and goodness do

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not exist in the beginning (on the ground that whereas the first beginnings of plants and animals are causes, it is in the products of these that beauty and perfection are found) are mistaken in their views.

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For seed comes from prior creatures which are perfect, and that which is first is not the seed but the perfect creature. E.g., one might say that prior to the seed is the man—not he who is produced from the seed, but another man from whom the seed comes.Cf. Aristot. Met. 9.8.4, 5.

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Thus it is evident from the foregoing account that there is some substance which is eternal and immovable and separate from sensible things; and it has also been shown that this substance can have no magnitude, but is impartible and indivisible (for it causes motion for infinite time, and nothing finite has an infinite potentialityCf.Aristot. Physics 266a24-b6.; and therefore since every magnitude is either finite or infinite, it cannot have finite magnitude,

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and it cannot have infinite magnitude because there is no such thing at all); and moreover that it is impassive and unalterable; for all the other kinds of motion are posterior to spatial motion. Thus it is clear why this substance has these attributes.

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We must not disregard the question whether we should hold that there is one substance of this kind or more than one, and if more than one, how many; we must review the pronouncements of other thinkers and show that with regard to the number of the substances they have said nothing that can be clearly stated.

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The theory of the Ideas contains no peculiar treatment of the question; for the exponents of the theory call the Ideas numbers, and speak of the numbers now as though they were unlimited and now as though they were limited by the number 10Cf. Aristot. Met. 13.8.17, 20. This was a Pythagorean survival, cf. Vol. I. Introduction. xvi.; but as for why there should be just so many numbers, there is no explanation given with demonstrative accuracy.

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We, however, must discuss the question on the basis of the assumptions and distinctions which we have already made.

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The first principle and primary reality is immovable, both essentially and accidentally, but it excites the primary form of motion, which is one and eternal.

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Now since that which is moved must be moved by something, and the prime mover must be essentially immovable, and eternal motion must be excited by something eternal, and one motion by some one thing; and since we can see that besides the simple spatial motion of the universei.e., the (apparent) diurnal revolution of the heavens.(which we hold to be excited by the primary immovable substance) there are other spatial motions—those of the planets—which are eternal (because a body which moves in a circle is eternal and is never at rest—this has been proved in our physical treatisesAristot. Physics 8.8, 9, Aristot. De Caelo 1.2, 2.3-8.); then each of these spatial motions must also be excited by a substance which is essentially immovable and eternal.

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For the nature of the heavenly bodies is eternal, being a kind of substance; and that which moves is eternal and prior to the moved; and that which is prior to a substance must be a substance. It is therefore clear that there must be an equal number of substances, in nature eternal, essentially immovable, and without magnitude; for the reason already stated.Aristot. Met. 12.7.12, 13.

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Thus it is clear that the movers are substances, and that one of them is first and another second and so on in the same order as the spatial motions of the heavenly bodies.

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As regards the number of these motions, we have now reached a question which must be investigated by the aid of that branch of mathematical science which is most akin to philosophy, i.e. astronomy; for this has as its object a substance which is sensible but eternal, whereas the other mathematical sciences, e.g. arithmetic and geometry, do not deal with any substance. That there are more spatial motions than there are bodies which move in space is obvious to those who have even a moderate grasp of the subject, since each of the non-fixed stars has more than one spatial motion.

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As to how many these spatial motions actually are we shall now, to give some idea of the subject, quote what some of the mathematicians say, in order that there may be some definite number for the mind to grasp; but for the rest we must partly investigate for ourselves and partly learn from other investigators, and if those who apply themselves to these matters come to some conclusion which clashes with what we have just stated, we must appreciate both views, but follow the more accurate.

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EudoxusOf Cnidus (circa 408 -355 B.C.). He was a pupil of Plato, and a distinguished mathematician. held that the motion of the sun and moon involves in either case three spheres,For a full discussion of the theories of Eudoxus and Callipus see Dreyer, Planetary Systems 87-114; Heath,Aristarchus of <placeName key="perseus,Samos City">Samos</placeName>190-224. of which the outermost is that of the fixed stars,Not identical with that of the fixed stars, but having the same motion. the second revolves in the circle which bisects the zodiac,i.e., revolves with its equator in the ecliptic. and the third revolves in a circle which is inclined across the breadth of the zodiaci.e., has the plane of its equator inclined to the plane of the ecliptic. This sphere carries the sun (or moon) fixed to a point in its equator.; but the circle in which the moon moves is inclined at a greater angle than that in which the sun moves.

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And he held that the motion of the planets involved in each case four spheres; and that of these the first and second are the sameNot the same, but having the same motion. as before (for the sphere of the fixed stars is that which carries round all the other spheres, and the sphere next in order, which has its motion in the circle which bisects the zodiac, is common to all the planets); the third sphere of all the planets has its poles in the circle which bisects the zodiac; and the fourth sphere moves in the circle inclined to the equator of the third. In the case of the third sphere, while the other planets have their own peculiar poles, those of Venus and Mercury are the same.

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Callippusof Cyzicus (fl. 380 B.C.). Simplicius says (Simplicius 493.5-8) that he corrected and elaborated Eudoxus’s theory with Aristotle’s help while on a visit to him at Athens. assumed the same arrangement of the spheres as did Eudoxus (that is, with respect to the order of their intervals), but as regards their number, whereas he assigned to Jupiter and Saturn the same number of spheres as Eudoxus, he considered that two further spheres should be added both for the sun and for the moon, if the phenomena are to be accounted for, and one for each of the other planets.

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But if all the spheres in combination are to account for the phenomena, there must be for each of the other planets other spheres, one less in number than those already mentioned, which counteract these and restore to the same position the first sphere of the star which in each case is next in order below.Aristotle is trying to establish a mechanical relation between the spheres, which Eudoxus and Callipus did not attempt to do. In this way only can the combination of forces produce the motion of the planets.

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Therefore since the forces by which the planets themselves are moved are 8 for Jupiter and Saturn, and 25 for the others, and since of these the only ones which do not need to be counteracted are those by which the lowest planetThe moon. is moved, the counteracting spheres for the first two planets will be 6, and those of the remaining four will be 16; and the total number of spheres, both those which move the planets and those which counteract these, will be 55.

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If we do not invest the moon and the sun with the additional motions which we have mentioned,In sect. 11. there will be 47 (?)Either Aristotle has made a slip in his calculations, or we should read ἐννέα(Sosigenes) for ἑπτά; this would give 49, which appears to be the correct total. For alternative explanations of an error in calculation see Ross ad loc. spheres in all.

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This, then, may be taken to be the number of the spheres; and thus it is reasonable to suppose that there are as many immovable substances and principles,i.e., the movers of the spheres.—the statement of logical necessity may be left to more competent thinkers.

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If there can be no spatial motion which is not conducive to the motion of a star, and if moreover every entity and every substance which is impassive and has in itself attained to the highest good should be regarded as an end, then there can be no other entity besides these,See previous note. and the number of the substances must be as we have said. For if there are other substances, they must move something, since they are the end of spatial motion.

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But there can be no other spatial motions besides those already mentioned. This is a reasonable inference from a general consideration of spatial motion. For if everything which moves exists for the sake of that which is moved, and every motion for the sake of something which is moved, no motion can exist for the sake of itself or of some other motion, but all motions must exist for the sake of the stars.

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For if we are to suppose that one motion is for the sake of another, the latter too must be for the sake of something else; and since the series cannot be infinite, the end of every motion must be one of the divine bodies which are moved through the heavens.

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It is evident that there is only one heaven.This paragraph seems to belong to an earlier period of Aristotle’s thought. At any rate the argument that plurality involves matter is inconsistent with the view that there are 55 immaterial movers. For if there is to be a plurality of heavens (as there is of men), the principle of each must be one in kind but many in number.

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But all things which are many in number have matter (for one and the same definition applies to many individuals, e.g. that of man; but Socrates is oneThe definition or form is one and universal; it is the combination of form with matter that constitutes an individual. Thus a plurality of individuals is caused by the combination of the same form with different matter.), but the primary essence has no matter, because it is complete reality. Therefore the prime mover, which is immovable, is one both in formula and in number; and therefore so also is that which is eternally and continuously in motion. Therefore there is only one heaven.

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A tradition has been handed down by the ancient thinkers of very early times, and bequeathed to posterity in the form of a myth, to the effect that these heavenly bodies are gods,This statement is not literally true. The planets do not seem to have been associated with the gods of popular mythology until the fourth century B.C. (see Burnet, E.G.P. p. 23 n.). But Aristotle’s general meaning seems to be that the gods were identified with the primary natural forces; and this is substantially true. and that the Divine pervades the whole of nature.

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The rest of their tradition has been added later in a mythological form to influence the vulgar and as a constitutional and utilitarian expedientCf. Aristot. Met. 2.3.1.; they say that these gods are human in shape or are like certain other animals,e.g. the Egyptian deities. Zoomorphism in Greek religion is a doubtful quantity. and make other statements consequent upon and similar to those which we have mentioned.

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Now if we separate these statements and accept only the first, that they supposed the primary substances to be gods, we must regard it as an inspired saying and reflect that whereas every art and philosophy has probably been repeatedly developed to the utmost and has perished again, these beliefs of theirs have been preserved as a relic of former knowledge. To this extent only, then, are the views of our forefathers and of the earliest thinkers intelligible to us.

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The subject of Mind involves certain difficulties. Mind is held to be of all phenomena the most supernatural; but the question of how we must regard it if it is to be of this nature involves certain difficulties. If Mind thinks nothing, where is its dignity? It is in just the same state as a man who is asleep. If it thinks, but something else determines its thinking, then since that which is its essence is not thinking but potentiality,i.e., if its thinking is determined by something else, Mind is only a potentiality, and not (as described in Aristot. Met. 12.7.1-9) the highest actuality. it cannot be the best reality; because it derives its excellence from the act of thinking.

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Again, whether its essence is thought or thinking, what does it think? It must think either itself or something else; and if something else, then it must think either the same thing always, or different things at different times. Then does it make any difference, or not, whether it thinks that which is good or thinks at random?

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Surely it would be absurd for it to think about some subjects. Clearly, then, it thinks that which is most divine and estimable, and does not change; for the change would be for the worse, and anything of this kind would immediately imply some sort of motion. Therefore if Mind is not thinking but a potentiality, (a) it is reasonable to suppose that the continuity of its thinking is laboriousCf. Aristot. Met. 9.8.18.; (b) clearly there must be something else which is more excellent than Mind; i.e. the object of thought;

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for both thought and the act of thinking will belong even to the thinker of the worst thoughts.If Mind is a potentiality, since a potentiality is of contraries, Mind may think that which is worst. Therefore if this is to be avoided (as it is, since it is better not to see some things than to see them), thinking cannot be the supreme good. Therefore Mind thinks itself, if it is that which is best; and its thinking is a thinking of thinking.

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Yet it seems that knowledge and perception and opinion and understanding are always of something else, and only incidentally of themselves.

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And further, if to think is not the same as to be thought, in respect of which does goodness belong to thought? for the act of thinking and the object of thought have not the same essence. The answer is that in some cases the knowledge is the object. In the productive sciences, if we disregard the matter, the substance, i.e. the essence, is the object; but in the speculative sciences the formula or the act of thinking is the object. Therefore since thought and the object of thought are not different in the case of things which contain no matter, they will be the same, and the act of thinking will be one with the object of thought.

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There still remains the question whether the object of thought is composite; for if so, thought would change in passing from one part of the whole to another. The answer is that everything which contains no matter is indivisible. Just as the human mind, or rather the mind of composite beings,i.e., beings composed of matter as well as form. Such beings are contrasted with the divine Mind, which is pure form. is in a certain space of timeThe meaning of this sentence is shown by the definition of Happiness in Aristot. Nic. Eth. 1098a 16-20. It takes the human mind a lifetime of the highest intellectual activity of which it is capable to attain to happiness; but the divine Mind is always happy. Cf. Aristot. Met. 12.7.9.(for it does not possess the good at this or at that moment, but in the course of a certain whole period it attains to the supreme good, which is other than itself), so is absolute self-thought throughout all eternity.

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We must also consider in which sense the nature of the universe contains the good or the supreme good; whether as something separate and independent, or as the orderly arrangement of its parts.

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Probably in both senses, as an army does; for the efficiency of an army consists partly in the order and partly in the general; but chiefly in the latter, because he does not depend upon the order, but the order depends upon him. All things, both fishes and birds and plants, are ordered together in some way, but not in the same way; and the system is not such that there is no relation between one thing and another; there is a definite connection.

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Everything is ordered together to one end; but the arrangement is like that in a household, where the free persons have the least liberty to act at random, and have all or most of their actions preordained for them, whereas the slaves and animals have little common responsibility and act for the most part at random; for the nature of each class is a principle such as we have described.The free persons correspond to the heavenly bodies, whose movements are fixed by necessity; the servile class to human beings. Each class acts in accordance with its nature, a principle which produces obedience to duty in the higher creatures, caprice in the lower ( Ross).

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I mean, for example, that everything must at least come to dissolution; and similarly there are other respects in which everything contributes to the good of the whole.

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We must not fail to observe how many impossibilities and absurdities are involved by other theories, and what views the more enlightened thinkers hold, and what views entail the fewest difficulties.

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All thinkers maintain that all things come from contraries; but they are wrong both in saying all thingsBecause there is an eternal substance, which is not derived from contraries (Aristot. Met. 12.6.1). and in saying that they come from contraries,Things are derived from a substrate as well (Aristot. Met. 12.2.1). nor do they explain how things in which the contraries really are present come from the contraries; for the contraries cannot act upon each other. For us, however, this problem is satisfactorily solved by the fact that there is a third factor. Other thinkers make one of the two contraries matter; e.g., this is done by thoseSee on Aristot. Met. 14.1.4. who make the Unequal matter for the Equal, or the Many matter for the One.

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But this also is disposed of in the same way; for the one matter of two contraries is contrary to nothing. Further, on their view everything except Unity itself will partake of evil; for the BadThe Bad was identified with the unequal; cf. Aristot. Met. 1.6.10. is itself one of the elements. The other schoolSee Aristot. Met. 12.7.10 does not even regard the Good and the Bad as principles; yet the Good is in the truest sense a principle in all things. The former school is right in holding that the Good is a principle, but they do not explain how it is a principle— whether as an end or as a moving cause or as form.

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Empedocles theory is also absurd, for he identifies the Good with Love.Cf. Aristot. Met. 1.4.3. This is a principle both as causing motion (since it combines) and as matter (since it is part of the mixture).Empedocles Fr. 17 (Diels), 18-20. Now even if it so happens that the same thing is a principle both as matter and as causing motion, still the essence of the two principles is not the same. In which respect, then, is Love a principle? And it is also absurd that Strife should be imperishable; strife is the very essence of evil.Cf. Aristot. Met. 9.9.3.

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Anaxagoras makes the Good a principle as causing motion; for Mind moves things, but moves them for some end, and therefore there must be some other GoodMotion presupposes a final cause, which was not what Anaxagoras meant by Mind. Cf. Aristot. Met. 1.7.5.—unless it is as we say; for on our view the art of medicine is in a sense health.Aristotle identifies the efficient cause, in a sense, with the final cause. Cf. Aristot. Met. 7.9.3. It is absurd also not to provide a contrary for the Good, i.e. for Mind.In Aristot. Met. 1.6.10 Aristotle describes Anaxagoras as a recognizing contrary principles of good and evil. Moreover, on Aristotle’s own showing, evil cannot be a principle (Aristot. Met. 9.9.3). But all those who recognize the contraries fail to make use of the contraries, unless we systematize their theories.

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And none of them explains why some things are perishable and others imperishable; for they make all existing things come from the same first principles.Cf. Aristot. Met. 3.4.11-20. Again, someCf. Aristot. Met. 12.2.2, 3. make existing things come from not-being, while others,The Eleatics. Cf. Aristot. Met. 1.5.10-13. to avoid this necessity, make all things one. Again, no one explains why there must always be generation, and what the cause of generation is.

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Moreover, those who posit two principles must admit another superior principle,i.e., an efficient cause. and so must the exponents of the Forms; for what made or makes particulars participate in the Forms? And on all other views it follows necessarily that there must be something which is contrary to Wisdom or supreme knowledge, but on ours it does not. For there is no contrary to that which is primary,

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since all contraries involve matter, and that which has matter exists potentially; and the ignorance which is contrary to Wisdom would tend towards the contrary of the object of Wisdom; but that which is primary has no contrary.

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Further, if there is to be nothing else besides sensible things, there will be no first principle, no order, no generation, and no celestial motions, but every principle will be based upon another,If there is nothing but what is sensible or potential, there can be no prime mover (which is actuality) to excite motion in the universe, and no teleology in causation. For the cosmologists on causation see Aristot. Met. 3.3.11-13. as in the accounts of all the cosmologists and physicists.

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And if the Forms or numbers are to exist, they will be causes of nothing; or if not of nothing, at least not of motion.

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Further, how can extension, i.e. a continuum, be produced from that which is unextended? Number cannot, either as a moving or as a formal cause, produce a continuum. Moreover, no contrary can be essentially productive and kinetic, for then it would be possible for it not to exist;

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and further, the act of production would in any case be posterior to the potentiality. Therefore the world of reality is not eternal. But there are real objects which are eternal. Therefore one of these premisses must be rejected. We have described how this may be done.By assuming an eternal actual mover (Aristot. Met. 12.6.4).

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Further, in virtue of what the numbers, or soul and body, or in general the form and the object, are one, no one attempts to explain; nor is it possible to do so except on our theory, that it is the moving cause that makes them one.Cf.Aristot. Met. 8.6.

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As for thoseSpeusippus and his followers; cf. Aristot. Met. 7.2.4, Aristot. Met. 14.3.8. who maintain that mathematical number is the primary reality, and so go on generating one substance after another and finding different principles for each one, they make the substance of the universe incoherent (for one substance in no way affects another by its existence or non-existence) and give us a great many governing principles. But the world must not be governed badly:

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The rule of many is not good; let one be the ruler.Hom. Il.2.204.

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We have already explained what the substance of sensible things is, dealing in our treatise on physicsThe reference is presumably to Aristot. Physics 1. with the material substrate, and subsequently with substance as actuality.In Books 7-9.

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Now since we are inquiring whether there is or is not some immutable and eternal substance besides sensible substances, and if there is, what it is, we must first examine the statements of other thinkers, so that if they have been mistaken in any respect, we may not be liable to the same mistakes; and if there is any view which is common to them and us, we may not feel any private self-irritation on this score. For we must be content if we state some points better than they have done, and others no worse.

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There are two views on this subject. Some say that mathematical objects, i.e. numbers and lines, are substances; and others again that the Ideas are substances.

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Now since someThis was the orthodox Platonist view; cf. Aristot. Met. 1.6.4. recognize these as two classes— the Ideas and the mathematical numbers—and othersXenocrates and his followers. regard both as having one nature, and yet othersThe Pythagoreans and Speusippus. hold that only the mathematical substances are substances, we must first consider the mathematical objects, without imputing to them any other characteristic—e.g. by asking whether they are really Ideas or not, or whether they are principles and substances of existing things or not—and merely inquire whether as mathematical objects they exist or not, and if they do, in what sense; then after this we must separately consider the Ideas themselves, simply and in so far as the accepted procedure requires; for most of the arguments have been made familiar already by the criticisms of other thinkers.

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And further, the greater part of our discussion must bear directly upon this second question—viz. when we are considering whether the substances and first principles of existing things are numbers and Ideas; for after we have dealt with the Ideas there remains this third question.

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Now if the objects of mathematics exist, they must be either in sensible things, as some hold; or separate from them (there are some also who hold this view); or if they are neither the one nor the other, either they do not exist at all, or they exist in some other way. Thus the point which we shall have to discuss is concerned not with their existence, but with the mode of their existence.

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That the objects of mathematics cannot be in sensible things, and that moreover the theory that they are is a fabrication, has been observed already in our discussion of difficultiesCf. Aristot. Met. 3.2.23-30. —the reasons being (a) that two solids cannot occupy the same space, and (b) that on this same theory all other potentialities and characteristics would exist in sensible things, and none of them would exist separately. This, then, has been already stated;

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but in addition to this it is clearly impossible on this theory for any body to be divided. For it must be divided in a plane, and the plane in a line, and the line at a point; and therefore if the point is indivisible, so is the line, and so on.

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For what difference does it make whether entities of this kind are sensible objects, or while not being the objects themselves, are yet present in them? the consequence will be the same, for either they must be divided when the sensible objects are divided, or else not even the sensible objects can be divided.

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Nor again can entities of this kind exist separately.

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For if besides sensible solids there are to be other solids which are separate from them and prior to sensible solids, clearly besides sensible planes there must be other separate planes, and so too with points and lines; for the same argument applies. And if these exist, again besides the planes, lines and points of the mathematical solid, there must be others which are separate;

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for the incomposite is prior to the composite, and if prior to sensible bodies there are other non-sensible bodies, then by the same argument the planes which exist independently must be prior to those which are present in the immovable solids. Therefore there will be planes and lines distinct from those which coexist with the separately-existent solids; for the latter coexist with the mathematical solids, but the former are prior to the mathematical solids.

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Again, in these planes there will be lines, and by the same argument there must be other lines prior to these; and prior to the points which are in the prior lines there must be other points, although there will be no other points prior to these.

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Now the accumulation becomes absurd; because whereas we get only one class of solids besides sensible solids, we get three classes of planes besides sensible planes—those which exist separately from sensible planes, those which exist in the mathematical solids, and those which exist separately from those in the mathematical solids—four classes of lines, and five of points;

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with which of these, then, will the mathematical sciences deal? Not, surely, with the planes, lines and points in the immovable solid; for knowledge is always concerned with that which is prior. And the same argument applies to numbers; for there will be other units besides each class of points, and besides each class of existing things, first the sensible and then the intelligible; so that there will be an infinite number of kinds of mathematical numbers.

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Again, there are the problems which we enumerated in our discussion of difficultiesAristot. Met. 3.2.23-27.: how can they be solved? For the objects of astronomy will similarly be distinct from sensible things, and so will those of geometry; but how can a heaven and its parts (or anything else which has motion) exist apart from the sensible heaven? And similarly the objects of optics and of harmonics will be distinct, for there will be sound and sight apart from the sensible and particular objects.

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Hence clearly the other senses and objects of sense will exist separately; for why should one class of objects do so rather than another? And if this is so, animals too will exist separately, inasmuch as the senses will.

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Again, there are certain general mathematical theorems which are not restricted to these substances.

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Here, then, we shall have yet another kind of substance intermediate between and distinct from the Ideas and the intermediates, which is neither number nor points nor spatial magnitude nor time. And if this is impossible, clearly it is also impossible that the aforesaid substances should exist separately from sensible objects.

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In general, consequences result which are contrary both to the truth and to received opinion if we thus posit the objects of mathematics as definite separately-existent entities. For if they exist in this way, they must be prior to sensible spatial magnitudes, whereas in truth they must be posterior to them; for the incomplete spatial magnitude is in point of generation prior, but in point of substantiality posterior, as the inanimate is to the animate.

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Again, in virtue of what can we possibly regard mathematical magnitudes as one? Things in this world of ours may be reasonably supposed to be one in virtue of soul or part of the soul, or some other influence; apart from this they are a plurality and are disintegrated. But inasmuch as the former are divisible and quantitative, what is the cause of their unity and cohesion?

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Again, the ways in which the objects of mathematics are generated prove our point;

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for they are generated first in the dimension of length, then in that of breadth, and finally in that of depth, whereupon the process is complete. Thus if that which is posterior in generationi.e., in the natural order of development. Thus generation (γένεσις) is used in two different senses in this argument, which therefore becomes invalid (Bonitz). is prior in substantiality, body will be prior to plane and line, and in this sense it will also be more truly complete and whole, because it can become animate; whereas how could a line or plane be animate? The supposition is beyond our powers of apprehension.

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Further, body is a kind of substance, since it already in some sense possesses completeness; but in what sense are lines substances? Neither as being a kind of form or shape, as perhaps the soul is, nor as being matter, like the body; for it does not appear that anything can be composed either of lines or of planes or of points,

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whereas if they were a kind of material substance it would be apparent that things can be so composed. Let it be granted that they are prior in formula; yet not everything which is prior in formula is also prior in substantiality. Things are prior in substantiality which when separated have a superior power of existence; things are prior in formula from whose formulae the formulae of other things are compounded. And these characteristics are not indissociable.

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For if attributes, such as moving or white, do not exist apart from their substances, white will be prior in formula to white man, but not in substantiality; for it cannot exist in separation, but always exists conjointly with the concrete whole—by which I mean white man.

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Thus it is obvious that neither is the result of abstraction prior, nor the result of adding a determinant posterior—for the expression white man is the result of adding a determinant to white.

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Thus we have sufficiently shown (a) that the objects of mathematics are not more substantial than corporeal objects; (b) that they are not prior in point of existence to sensible things, but only in formula; and (c) that they cannot in any way exist in separation.

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And since we have seensect. 1-3 above. that they cannot exist in sensible things, it is clear that either they do not exist at all, or they exist only in a certain way, and therefore not absolutely; for exist has several senses.

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The general propositions in mathematics are not concerned with objects which exist separately apart from magnitudes and numbers; they are concerned with magnitudes and numbers, but not with them as possessing magnitude or being divisible. It is clearly possible that in the same way propositions and logical proofs may apply to sensible magnitudes; not qua sensible, but qua having certain characteristics.

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For just as there can be many propositions about things merely qua movable, without any reference to the essential nature of each one or to their attributes, and it does not necessarily follow from this either that there is something movable which exists in separation from sensible things or that there is a distinct movable nature in sensible things; so too there will be propositions and sciences which apply to movable things, not qua movable but qua corporeal only; and again qua planes only and qua lines only, and qua divisible, and qua indivisible but having position, and qua indivisible only.

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Therefore since it is true to say in a general sense not only that things which are separable but that things which are inseparable exist, e.g., that movable things exist, it is also true to say in a general sense that mathematical objects exist, and in such a form as mathematicians describe them.

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And just as it is true to say generally of the other sciences that they deal with a particular subject—not with that which is accidental to it (e.g. not with white if the healthy is white, and the subject of the science is the healthy), but with that which is the subject of the particular science; with the healthy if it treats of things qua healthy, and with man if qua man—so this is also true of geometry. If the things of which it treats are accidentally sensible although it does not treat of them qua sensible, it does not follow that the mathematical sciences treat of sensible things—nor, on the other hand, that they treat of other things which exist independently apart from these.

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Many attributes are essential properties of things as possessing a particular characteristic; e.g., there are attributes peculiar to an animal qua female or qua male, although there is no such thing as female or male in separation from animals. Hence there are also attributes which are peculiar to things merely qua lines or planes.

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And in proportion as the things which we are considering are prior in formula and simpler, they admit of greater exactness; for simplicity implies exactness. Hence we find greater exactness where there is no magnitude, and the greatest exactness where there is no motion; or if motion is involved, where it is primary, because this is the simplest kind; and the simplest kind of primary motion is uniform motion.Aristot. Met. 12.7.6.

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The same principle applies to both harmonics and optics, for neither of these sciences studies objects qua sight or qua sound, but qua lines and numbersOptics studies lines and harmonics numbers because these sciences are subordinate to geometry and arithmetic (Aristot. An. Post. 75b 15).; yet the latter are affections peculiar to the former. The same is also true of mechanics.

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Thus if we regard objects independently of their attributes and investigate any aspect of them as so regarded, we shall not be guilty of any error on this account, any more than when we draw a diagram on the ground and say that a line is a foot long when it is not; because the error is not in the premisses.Cf. Aristot. Met. 14.2.9, 10. The best way to conduct an investigation in every case is to take that which does not exist in separation and consider it separately; which is just what the arithmetician or the geometrician does.

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For man, qua man, is one indivisible thing; and the arithmetician assumes man to be one indivisible thing, and then considers whether there is any attribute of man qua indivisible. And the geometrician considers man neither qua man nor qua indivisible, but qua something solid. For clearly the attributes which would have belonged to man even if man were somehow not indivisible can belong to man irrespectively of his humanity or indivisibility.

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Hence for this reason the geometricians are right in what they maintain, and treat of what really exists; i.e., the objects of geometry really exist. For things can exist in two ways, either in complete reality or as matter.i.e., potentially.

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And since goodness is distinct from beauty (for it is always in actions that goodness is present, whereas beauty is also in immovable things), theyCf. Aristot. Met. 3.2.4. are in error who assert that the mathematical sciences tell us nothing about beauty or goodness;

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for they describe and manifest these qualities in the highest degree, since it does not follow, because they manifest the effects and principles of beauty and goodness without naming them, that they do not treat of these qualities. The main species of beauty are orderly arrangement, proportion, and definiteness; and these are especially manifested by the mathematical sciences.

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And inasmuch as it is evident that these (I mean, e.g., orderly arrangement and definiteness) are causes of many things, obviously they must also to some extent treat of the cause in this sense, i.e. the cause in the sense of the Beautiful. But we shall deal with this subject more explicitly elsewhere.There is no obvious fulfilment of this promise.

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As regards the objects of mathematics, then, the foregoing account may be taken as sufficient to show that they exist, and in what sense they exist, and in what sense they are prior and in what they are not. But as regards the Ideas we must first consider the actual theory in relation to the Idea, without connecting it in any way with the nature of numbers, but approaching it in the form in which it was originally propounded by the first exponentsIt seems quite obvious that Aristotle intends this vague phrase to refer to Plato. Cf. Aristot. Met. 1.6.1-3, with which the following sections 2-5 should be compared. On the whole subject see Introduction. of the Ideas.

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The theory of Forms occurred to those who enunciated it because they were convinced as to the true nature of reality by the doctrine of Heraclitus, that all sensible things are always in a state of flux; so that if there is to be any knowledge or thought about anything, there must be certain other entities, besides sensible ones, which persist. For there can be no knowledge of that which is in flux.

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Now Socrates devoted his attention to the moral virtues, and was the first to seek a general definition of these (for of the Physicists Democritus gained only a superficial grasp of the subjectCf. Aristot. Phys. 194a 20, Aristot. De Part. Anim. 642a 24. and defined, after a fashion, the hot and the cold; while the PythagoreansCf. Aristot. Met. 1.5.2, 16. at an earlier date had arrived at definitions of some few things—whose formulae they connected with numbers—e.g., what opportunity is, or justice or marriage); and he naturally inquired into the essence of things;

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for he was trying to reason logically, and the starting-point of all logical reasoning is the essence. At that time there was as yet no such proficiency in Dialectic that men could study contraries independently of the essence, and consider whether both contraries come under the same science.

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There are two innovationsThis is perhaps too strong a word. What Aristotle means is that Socrates was the first thinker who attached importance to general definitions and systematically used arguments from analogy in order to arrive at them. The Greeks as a whole were only too readily impressed by analogy; Socrates merely developed an already prevalent tendency. For an example of his method see the reference at Aristot. Met. 5.29.5 n. which, may fairly be ascribed to Socrates: inductive reasoning and general definition. Both of these are associated with the starting-point of scientific knowledge.

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But whereas Socrates regarded neither universals nor definitions as existing in separation, the Idealists gave them a separate existence, and to these universals and definitions of existing things they gave the name of Ideas.Cf. Introduction.

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Hence on their view it followed by virtually the same argument that there are Ideas of all terms which are predicated universallyWith sect. 6-13 cf. Aristot. Met. 1.9.1-8, which are almost verbally the same. See Introduction.; and the result was very nearly the same as if a man who wishes to count a number of things were to suppose that he could not do so when they are few, and yet were to try to count them when he has added to them. For it is hardly an exaggeration to say that there are more Forms than there are particular sensible things (in seeking for whose causes these thinkers were led on from particulars to Ideas); because corresponding to each thing there is a synonymous entity, apart from the substances (and in the case of non-substantial things there is a One over the Many) both in our everyday world and in the realm of eternal entities.

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Again, not one of the ways in which it is attempted to prove that the Forms exist demonstrates their point; from some of them no necessary conclusion follows, and from others it follows that there are Form of things of which they hold that there are no Forms.

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For according to the arguments from the sciences, there will be Forms of all things of which there are sciences; and according to the One-over-Many argument, of negations too; and according to the argument that we have some conception of what has perished there will be Forms of perishable things, because we have a mental picture of these things. Further, of the most exact arguments some establish Ideas of relations, of which the Idealists deny that there is a separate genus, and others state the Third Man.

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And in general the arguments for the Forms do away with things which are more important to the exponents of the Forms than the existence of the Ideas; for they imply that it is not the Dyad that is primary, but Number; and that the relative is prior to number, and therefore to the absolute; and all the other conclusions in respect of which certain persons by following up the views held about the Forms have gone against the principles of the theory.

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Again, according to the assumption by which they hold that the Ideas exist, there will be Forms not only of substances but of many other things (since the concept is one not only in the case of substances but in the case of non-substantial things as well; and there can be sciences not only of substances but also of other things; and there are a thousand other similar consequences);

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but it follows necessarily from the views generally held about them that if the Forms are participated in, there can only be Ideas of substances, because they are not participated in accidentally; things can only participate in a Form in so far as it is not predicated of a subject.

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I mean, e.g., that if a thing participates in absolute doubleness, it participates also in something eternal, but only accidentally; because it is an accident of doubleness to be eternal. Thus the Ideas will be substance. But the same terms denote substance in the sensible as in the Ideal world; otherwise what meaning will there be in saying that something exists besides the particulars, i.e. the unity comprising their multiplicity?

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If the form of the Ideas and of the things which participate in them is the same, they will have something in common (for why should duality mean one and the same thing in the case of perishable 2’s and the 2’s which are many but eternal, and not in the case of absolute duality and a particular 2?). But if the form is not the same, they will simply be homonyms; just as though one were to call both Callias and a piece of wood man, without remarking any property common to them.

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sect. 14, 15 have no counterpart in Book 1.And if we profess that in all other respects the common definitions apply to the Forms, e.g. that plane figure and the other parts of the definition apply to the Ideal circle, only that we must also state of what the Form is a Form, we must beware lest this is a quite meaningless statement.The suggestion is that the definition of an Ideal circle is the same as that of a particular circle, except that it must have added to it the statement of what particular the Idea is an Idea.

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For to what element of the definition must the addition be made? to center, or plane or all of them? For all the elements in the essence of an Idea are Ideas; e.g. animal and two-footed. sc. in the definition or essence of Ideal man. Further, it is obvious that being an Idea, just like plane, must be a definite characteristic which belongs as genus to all its species.i.e., being an idea will be a characteristic common to all ideas, and so must be itself an Idea.

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This chapter corresponds almost verbally to Aristot. Met. 1.9.9-15. Cf. note on Aristot. Met. 13.4.6.Above all we might examine the question what on earth the Ideas contribute to sensible things, whether eternal or subject to generation and decay; for they are not the cause of any motion or change in them.

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Moreover they are no help towards the knowledge of other things (for they are not the substance of particulars, otherwise they would be in particulars) or to their existence (since they are not present in the things which participate in them. If they were, they might perhaps seem to be causes, in the sense in which the admixture of white causes a thing to be white.

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But this theory, which was stated first by Anaxagoras and later by Eudoxus in his discussion of difficulties, and by others also, is very readily refuted; for it is easy to adduce plenty of impossibilities against such a view). Again, other things are not in any accepted sense derived from the Forms.

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To say that the Forms are patterns, and that other things participate in them, is to use empty phrases and poetical metaphors; for what is it that fashions things on the model of the Ideas? Besides, anything may both be and come to be without being imitated from something else; thus a man may become like Socrates whether Socrates exists or not,

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and even if Socrates were eternal, clearly the case would be the same. Also there will be several patterns (and therefore Forms) of the same thing; e.g., animal and two-footed will be patterns of man, and so too will the Idea of man.

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Further, the Forms will be patterns not only of sensible things but of Ideas; e.g. the genus will be the pattern of its species; hence the same thing will be pattern and copy. Further, it would seem impossible for the substance and that of which it is the substance to exist in separation; then how can the Ideas, if they are the substances of things, exist in separation from them?

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In thePhaedoPlat. Phaedo 100d. this statement is made: that the Forms are causes both of being and of generation. Yet assuming that the Forms exist, still there is no generation unless there is something to impart motion; and many other things are generated (e.g. house and ring) of which the Idealists say that there are no Forms.

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Thus it is clearly possible that those things of which they say that there are Ideas may also exist and be generated through the same kind of causes as those of the things which we have just mentioned, and not because of the Forms. Indeed, as regards the Ideas, we can collect against them plenty of evidence similar to that which we have now considered; not only by the foregoing methods, but by means of more abstract and exact reasoning.

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Now that we have dealt with the problems concerning the Ideas, we had better re-investigate the problems connected with numbers that follow from the theory that numbers are separate substances and primary causes of existing things. Now if number is a kind of entity, and has nothing else as its substance, but only number itself, as some maintain; then either (a) there must be some one part of number which is primary, and some other part next in succession, and so on, each part being specifically differentThis statement bears two meanings, which Aristotle confuses: (i) There must be more than one number-series, each series being different in kind from every other series; (2) All numbers are different in kind, and inaddible. Confusion (or textual inaccuracy) is further suggested by the fact that Aristotle offers no alternative statement of the nature of number in general, such as we should expect from his language. In any case the classification is arbitrary and incomplete.—

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and this applies directly to units, and any given unit is inaddible to any other given unit; or (b) theyThe units. are all directly successive, and any units can be added to any other units, as is held of mathematical number; for in mathematical number no one unit differs in any way from another.

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Or (c) some units must be addible and others not. E.g., 2 is first after 1, and then 3, and so on with the other numbers; and the units in each number are addible, e.g. the units in the firsti.e., Ideal or natural.2 are addible to one another, and those in the first 3 to one another, and so on in the case of the other numbers; but the units in the Ideal 2 are inaddible to those in the Ideal 3;

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and similarly in the case of the other successive numbers. Hence whereas mathematical number is counted thus: after 1, 2 (which consists of another 1 added to the former) and 3 (which consists of another 1 added to these two) and the other numbers in the same way, Ideal number is counted like this: after 1, a distinct 2 not including the original 1; and a 3 not including the 2, and the rest of the numbers similarly.

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Or (d) one kind of number must be such as we first described, and another or such as the mathematicians maintain, and that which we have last described must be a third kind.

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Again, these numbers must exist either in separation from things, or not in separation, but in sensible things (not, however, in the way which we first considered,In Aristot. Met. 13.2.1-3. but in the sense that sensible things are composed of numbers which are present in themThe Pythagorean number-atomist view; See Introduction.)—either some of them and not others, or all of them.i.e., either all numbers are material elements of things, or some are and others are not.

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These are of necessity the only ways in which the numbers can exist. Now of those who say that unity is the beginning and substance and element of all things, and that number is derived from it and something else, almost everyone has described number in one of these ways (except that no one has maintained that all units are inaddibleCf. sect. 2.);

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and this is natural enough, because there can be no other way apart from those which we have mentioned. Some hold that both kinds of number exist, that which involves priority and posteriority being identical with the Ideas, and mathematical number being distinct from Ideas and sensible things, and both kinds being separable from sensible thingsCf. Aristot. Met. 1.6.4.; others hold that mathematical number alone exists,Cf. Aristot. Met. 12.10.14. being the primary reality and separate from sensible things.

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The Pythagoreans also believe in one kind of number—the mathematical; only they maintain that it is not separate, but that sensible substances are composed of it. For they construct the whole universe of numbers, but not of numbers consisting of abstract units; they suppose the units to be extended—but as for how the first extended unit was formed they appear to be at a loss.Cf. Aristot. Met. 13.8.9, 10, Aristot. Met. 14.3.15, Aristot. Met. 14.5.7, and see Introduction.

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Another thinker holds that primary or Ideal number alone exists; and someCf. 10ff., Aristot. Met. 13.1.4. identify this with mathematical number.

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The same applies in the case of lines, planes and solids.

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SomePlato. distinguish mathematical objects from those which come after the Ideasi.e., the (semi-)Ideal lines, planes, etc. Cf. Aristot. Met. 1.9.30.; and of those who treat the subject in a different manner someSpeusippus; cf. sect. 7 above. speak of the mathematical objects and in a mathematical way—viz. those who do not regard the Ideas as numbers, nor indeed hold that the Ideas exist—and othersXenocrates. For his belief in indivisible lines see Ritter and Preller 362. Aristotle ascribes the doctrine to Plato in Aristot. Met. 1.9.25. speak of the mathematical objects, but not in a mathematical way; for they deny that every spatial magnitude is divisible into extended magnitudes, or that any two given units make 2.

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But all who hold that Unity is an element and principle of existing things regard numbers as consisting of abstract units, except the Pythagoreans; and they regard number as having spatial magnitude, as has been previously stated.sect. 8.

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It is clear from the foregoing account (1.) in how many ways it is possible to speak of numbers, and that all the ways have been described. They are all impossible, but doubtless somesc. the view of Xenocrates (cf. Aristot. Met. 13.8.8). are more so than others.

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First, then, we must inquire whether the limits are addible or inaddible; and if inaddible, in which of the two ways which we have distinguished.Aristot. Met. 13.6.2, 3. For it is possible either (a) that any one unit is inaddible to any other, or (b) that the units in the Ideal 2 are inaddible to those in the Ideal 3, and thus that the units in each Ideal number are inaddible to those in the other Ideal numbers.

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Now if all units are addible and do not differ in kind, we get one type of number only, the mathematical, and the Ideas cannot be the numbers thus produced;

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for how can we regard the Idea of Man or Animal, or any other Form, as a number? There is one Idea of each kind of thing: e.g. one of Humanity and another one of Animality; but the numbers which are similar and do not differ in kind are infinitely many, so that this is no more the Idea of Man than any other 3 is. But if the Ideas are not numbers, they cannot exist at all;

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for from what principles can the Ideas be derived? Number is derived from Unity and the indeterminate dyad, and the principles and elements are said to be the principles and elements of number, and the Ideas cannot be placed either as prior or as posterior to numbers.Since the only principles which Plato recognizes are Unity and the Dyad, which are numerical (Aristotle insists on regarding them as a kind of 1 and 2), and therefore clearly principles of number; and the Ideas can only be derived from these principles if they (the Ideas) are (a) numbers (which has been proved impossible) or (b) prior or posterior to numbers (i.e., causes or effects of numbers, which they cannot be if they are composed of a different kind of units); then the Ideas are not derived from any principle at all, and therefore do not exist.

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But if the units are inaddible in the sense that any one unit is inaddible to any other, the number so composed can be neither mathematical number (since mathematical number consists of units which do not differ, and the facts demonstrated of it fit in with this character) nor Ideal number. For on this view 2 will not be the first number generated from Unity and the indeterminate dyad, and then the other numbers in succession, as theyThe Platonists. say 2, 3, because the units in the primary 2 are generated at the same time,This was the orthodox Platonist view of the generation of ideal numbers; or at least Aristotle is intending to describe the orthodox view. Plato should not have regarded the Ideal numbers as composed of units at all, and there is no real reason to suppose that he did (see Introduction). But Aristotle infers from the fact that the Ideal 2 is the first number generated (and then the other Ideal numbers in the natural order) that the units of the Ideal 2 are generated simultaneously, and then goes on to show that this is incompatible with the theory of inaddible units. whether, as the originator of the theory held, from unequalsi.e., the Great-and-Small, which Aristotle wrongly understands as two unequal things. It is practically certain that Plato used the term (as he did that of Indeterminate Dyad) to describe indeterminate quantity. See Introduction.(coming into being when these were equalized), or otherwise—

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since if we regard the one unit as prior to the other,This is a necessary implication of the theory of inaddible units (cf. Aristot. Met. 13.6.1, 2). it will be prior also to the 2 which is composed of them; because whenever one thing is prior and another posterior, their compound will be prior to the latter and posterior to the former.So the order of generation will be: (i) Unity (ungenerated); (2) first unit in 2; (3) second unit in 2; and the Ideal 2 will come between (2) and (3).

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Further, since the Ideal 1 is first, and then comes a particular 1 which is first of the other 1’s but second after the Ideal 1, and then a third 1 which is next

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after the second but third after the first 1, it follows that the units will be prior to the numbers after which they are called; e.g., there will be a third unit in 2 before 3 exists, and a fourth and fifth in 3 before these numbers exist.This is a corollary to the previous argument, and depends upon an identification of ones (including the Ideal One or Unity) with units.

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It is true that nobody has represented the units of numbers as inaddible in this way; but according to the principles held by these thinkers even this view is quite reasonable, although in actual fact it is untenable.

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For assuming that there is a first unit or first 1,i.e., the Ideal One. it is reasonable that the units should be prior and posterior; and similarly in the case of 2’s, if there is a first 2. For it is reasonable and indeed necessary that after the first there should be a second; and if a second, a third; and so on with the rest in sequence.

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But the two statements, that there is after 1 a first and a second unit, and that there is a first 2, are incompatible. These thinkers, however, recognize a first unit and first 1, but not a second and third; and they recognize a first 2, but not a second and third.

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It is also evident that if all units are inaddible, there cannot be an Ideal 2 and 3, and similarly with the other numbers;

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for whether the units are indistinguishable or each is different in kind from every other, numbers must be produced by addition; e.g. 2 by adding 1 to another 1, and 3 by adding another 1 to the 2, and 4 similarly.This is of course not true of the natural numbers.

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This being so, numbers cannot be generated as these thinkers try to generate them, from Unity and the dyad; because 2 becomes a part of 3,i.e., 3 is produced by adding 1 to 2. and 3 of 4, and the same applies to the following numbers.

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But according to them 4 was generated from the first 2 and the indeterminate dyad, thus consisting of two 2’s apart from the Ideal 2.Cf. sect. 18. Otherwise 4 will consist of the Ideal 2 and another 2 added to it, and the Ideal 2 will consist of the Ideal 1 and another 1; and if this is so the other element cannot be the indeterminate dyad, because it produces one unit and not a definite 2.The general argument is: Numbers are produced by addition; but this is incompatible with the belief in the Indeterminate Dyad as a generative principle, because, being duplicative, it cannot produce single units.

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Again, how can there be other 3’s and 2’s besides the Ideal numbers 3 and 2, and in what way can they be composed of prior and posterior units? All these theories are absurd and fictitious, and there can be no primary 2 and Ideal 3. Yet there must be, if we are to regard Unity and the indeterminate dyad as elements.i.e., if numbers are not generated by addition, there must be Ideal (or natural) numbers.

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But if the consequences are impossible, the principles cannot be of this nature.

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If, then, any one unit differs in kind from any other, these and other similar consequences necessarily follow. If, on the other hand, while the units in different numbers are different, those which are in the same number are alone indistinguishable from one another, even so the consequences which follow are no less difficult.

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For example, in the Ideal number 10 there are ten units, and 10 is composed both of these and of two 5’s. Now since the Ideal 10 is not a chance number,I think Ross’s interpretation of this passage must be right. The Ideal 10 is a unique number, and the numbers contained in it must be ideal and unique; therefore the two 5’s must be specifically different, and so must their units—which contradicts the view under discussion. and is not composed of chance 5’s, any more than of chance units, the units in this number 10 must be different;

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for if they are not different, the 5’s of which the 10 is composed will not be different; but since these are different, the units must be different too. Now if the units are different, will there or will there not be other 5’s in this 10, and not only the two? If there are not, the thing is absurdi.e., it is only reasonable to suppose that other 5’s might be made up out of different combinations of the units.; whereas if there are, what sort of 10 will be composed of them? for there is no other 10 in 10 besides the 10 itself:

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Again, it must also be true that 4 is not composed of chance 2’s. For according to them the indeterminate dyad, receiving the determinate dyad, made two dyads; for it was capable of duplicating that which it received.Cf. Introduction.

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Again, how is it possible that 2 can be a definite entity existing besides the two units, and 3 besides the three units? Either by participation of the one in the other, as white man exists besides white and man, because it partakes of these concepts; or when the one is a differentia of the other, as man exists besides animal and two-footed.

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Again, some things are one by contact, others by mixture, and others by position; but none of these alternatives can possibly apply to the units of which 2 and 3 consist. Just as two men do not constitute any one thing distinct from both of them, so it must be with the units.

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The fact that the units are indivisible will make no difference; because points are indivisible also, but nevertheless a pair of points is not anything distinct from the two single points.

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Moreover we must not fail to realize this: that on this theory it follows that 2’s are prior and posterior, and the other numbers similarly.

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Let it be granted that the 2’s in 4 are contemporaneous; yet they are prior to those in 8, and just as the <determinate> 2 produced the 2’s in 4, soIn each case the other factor is the indeterminate dyad (cf. sect. 18). they produced the 4’s in 8. Hence if the original 2 is an Idea, these 2’s will also be Ideas of a sort.

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And the same argument applies to the units, because the units in the original 2 produce the four units in 4; and so all the units become Ideas, and an Idea will be composed of Ideas. Hence clearly those things also of which these things are Ideas will be composite; e.g., one might say that animals are composed of animals, if there are Ideas of animals.

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In general, to regard units as different in any way whatsoever is absurd and fictitious (by fictitious I mean dragged in to support a hypothesis). For we can see that one unit differs from another neither in quantity nor in quality; and a number must be either equal or unequal—this applies to all numbers, but especially to numbers consisting of abstract units.

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Thus if a number is neither more nor less, it is equal; and things which are equal and entirely without difference we assume, in the sphere of number, to be identical. Otherwise even the 2’s in the Ideal 10 will be different, although they are equal; for if anyone maintains that they are not different, what reason will he be able to allege?

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Again, if every unit plus another unit makes 2, a unit from the Ideal 2 plus one from the Ideal 3 will make 2—a 2 composed of different unitsWhich conflicts with the view under discussion.; will this be prior or posterior to 3? It rather seems that it must be prior, because one of the units is contemporaneous with 3, and the other with 2.The implication seems to be, as Ross says, that the Platonists will refuse to admit that there is a number between 2 and 3.

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We assume that in general 1 and 1, whether the things are equal or unequal, make 2; e.g. good and bad, or man and horse; but the supporters of this theory say that not even two units make 2.

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If the number of the Ideal 3 is not greater than that of the Ideal 2, it is strange; and if it is greater, then clearly there is a number in it equal to the 2, so that this number is not different from the Ideal 2.

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But this is impossible, if there is a first and second number.i.e., if numbers are specifically different. Cf. Aristot. Met. 13.6.1. Nor will the Ideas be numbers. For on this particular point they are right who claim that the units must be different if there are to be Ideas, as has been already stated.sect. 2-4 above. For the form is unique; but if the units are undifferentiated, the 2’s and 3’s will be undifferentiated.

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Hence they have to say that when we count like this, l, 2, we do not add to the already existing number; for if we do, (a) number will not be generated from the indeterminate dyad, and (b) a number cannot be an Idea; because one Idea will pre-exist in another, and all the Forms will be parts of one Form.i.e., the biggest number.

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Thus in relation to their hypothesis they are right, but absolutely they are wrong, for their view is very destructive, inasmuch as they will say that this point presents a difficulty: whether, when we count and say 1, 2, 3, we count by addition or by enumerating distinct portions.This is Apelt’s interpretation of κατὰ μερίδας. For this sense of the word he quotes Plut. Mor. 644c. The meaning then is: If you count by addition, you regard number as exhibited only in concrete instances; if you treat each number as a distinct portion (i.e. generated separately), you admit another kind of number besides the mathematical. Aristotle says that number can be regarded in both ways. But we do both; and therefore it is ridiculous to refer this point to so great a difference in essence.

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First of all it would be well to define the differentia of a number; and of a unit, if it has a differentia. Now units must differ either in quantity or in quality; and clearly neither of these alternatives can be true. But units may differ, as number does, in quantity. But if units also differed in quantity, number would differ from number, although equal in number of units.

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Again, are the first units greater or smaller, and do the later units increase in size, or the opposite? All these suggestions are absurd. Nor can units differ in quality; for no modification can ever be applicable to them, because these thinkers hold that even in numbers quality is a later attribute than quantity.Numbers have quality as being prime or composite, plane or solid (i.e., products of two or three factors); but these qualities are clearly incidental to quantity. Cf. Aristot. Met. 5.14.2.

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Further, the units cannot derive quality either from unity or from the dyad; because unity has no quality, and the dyad produces quantity, because its nature causes things to be many. If, then, the units differ in some other way, they should most certainly state this at the outset, and explain, if possible, with regard to the differentia of the unit, why it must exist; or failing this, what differentia they mean.

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Clearly, then, if the Ideas are numbers, the units cannot all be addible, nor can they all be inaddible in either sense. Nor again is the theory sound which certain other thinkersCf. Aristot. Met. 13.1.4. hold concerning numbers.

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These are they who do not believe in Ideas, either absolutely or as being a kind of numbers, but believe that the objects of mathematics exist, and that the numbers are the first of existing things, and that their principle is Unity itself. For it is absurd that if, as they say, there is a 1 which is first of the 1’s,i.e., Speusippus recognized unity or the One as a formal principle, but admitted no other ideal numbers. Aristotle argues that this is inconsistent. there should not be a 2 first of the 2’s, nor a 3 of the 3’s; for the same principle applies to all cases.

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Now if this is the truth with regard to number, and we posit only mathematical number as existing, Unity is not a principle. For the Unity which is of this nature must differ from the other units; and if so, then there must be some 2 which is first of the 2’s; and similarly with the other numbers in succession.

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But if Unity is a principle, then the truth about numbers must rather be as Plato used to maintain; there must be a first 2 and first 3, and the numbers cannot be addible to each other. But then again, if we assume this, many impossibilities result, as has been already stated.Aristot. Met. 13.7.1-8.3. Moreover, the truth must lie one way or the other; so that if neither view is sound, number cannot have a separate abstract existence.

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From these considerations it is also clear that the third alternativeCf. Aristot. Met. 13.6.7.—that Ideal number and mathematical number are the same—is the worst; for two errors have to be combined to make one theory. (1.) Mathematical number cannot be of this nature, but the propounder of this view has to spin it out by making peculiar assumptions; (2.) his theory must admit all the difficulties which confront those who speak of Ideal number.

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The Pythagorean view in one way contains fewer difficulties than the view described above, but in another way it contains further difficulties peculiar to itself. By not regarding number as separable, it disposes of many of the impossibilities; but that bodies should be composed of numbers, and that these numbers should be mathematical, is impossible.See Introduction.

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For (a) it is not true to speak of indivisible magnitudesThis is proved in Aristot. De Gen. et. Corr. 315b 24-317a 17.; (b) assuming that this view is perfectly true, still units at any rate have no magnitude; and how can a magnitude be composed of indivisible parts? Moreover arithmetical number consists of abstract units. But the Pythagoreans identify number with existing things; at least they apply mathematical propositions to bodies as though they consisted of those numbers.See Introduction.

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Thus if number, if it is a self-subsistent reality, must be regarded in one of the ways described above, and if it cannot be regarded in any of these ways, clearly number has no such nature as is invented for it by those who treat it as separable.

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Again, does each unit come from the Great and the Small, when they are equalizedCf. Aristot. Met. 13.7.5 n. Aristotle is obviously referring to the two units in the Ideal 2.; or does one come from the Small and another from the Great? If the latter, each thing is not composed of all the elements, nor are the units undifferentiated; for one contains the Great, and the other the Small, which is by nature contrary to the Great.

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Again, what of the units in the Ideal 3? because there is one over. But no doubt it is for this reason that in an odd number they make the Ideal One the middle unit.Cf. DieIs, Vorsokratiker 270. 18. If on the other hand each of the units comes from both Great and Small, when they are equalized, how can the Ideal 2 be a single entity composed of the Great and Small? How will it differ from one of its units? Again, the unit is prior to the 2; because when the unit disappears the 2 disappears.

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Therefore the unit must be the Idea of an Idea, since it is prior to an Idea, and must have been generated before it. From what, then? for the indeterminate dyad, as we have seen,Aristot. Met. 13.7.18. causes duality.

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Again, number must be either infinite or finite (for they make number separable, so that one of these alternatives must be true).The point seems to be that if number is self-subsistent it must be actually finite or infinite. Aristotle himself holds that number is infinite only potentially; i.e., however high you can count, you can always count higher.

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Now it is obvious that it cannot be infinite, because infinite number is neither odd nor even, and numbers are always generated either from odd or from even number. By one process, when 1 is added to an even number, we get an odd number; by another, when 1 is multiplied by 2, we get ascending powers of 2; and by another, when powers of 2 are multiplied by odd numbers, we get the remaining even numbers.

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Again, if every Idea is an Idea of something, and the numbers are Ideas, infinite number will also be an Idea of something, either sensible or otherwise. This, however, is impossible, both logicallyi.e., as implying an actual infinite. and on their own assumption,i.e., as inconsistent with the conception of an Idea as a determining principle. since they regard the Ideas as they do.

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If, on the other hand, number is finite, what is its limit? In reply to this we must not only assert the fact, but give the reason.

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Now if number only goes up to 10, as some hold,Cf. Aristot. Met. 12.8.2. The Platonists derived this view from the Pythagoreans; see Introduction. in the first place the Forms will soon run short. For example, if 3 is the Idea of Man, what number will be the Idea of Horse? Each number up to 10 is an Idea; the Idea of Horse, then, must be one of the numbers in this series, for they are substances or Ideas.

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But the fact remains that they will run short, because the different types of animals will outnumber them. At the same time it is clear that if in this way the Ideal 3 is the Idea of Man, so will the other 3’s be also (for the 3’s in the same numbersRobin is probably right in taking this to mean that the 3 which is in the ideal 4 is like the 3 which is in the 4 which is in a higher ideal number, and so on (La Theorie platonicienne des Idees et des Nombres d’apres Aristote, p. 352). are similar), so that there will be an infinite number of men; and if each 3 is an Idea, each man will be an Idea of Man; or if not, they will still be men.

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And if the smaller number is part of the greater, when it is composed of the addible units contained in the same number, then if the Ideal 4 is the Idea of something, e.g. horse or white, then man will be part of horse, if man is 2. It is absurd also that there should be an Idea of 10 and not of 11, nor of the following numbers.

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Again, some things exist and come into being of which there are no FormsCf. Aristot. Met. 13.4.7, 8; Aristot. Met. 1.9.2, 3.; why, then, are there not Forms of these too? It follows that the Forms are not the causes of things.

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Again, it is absurd that number up to 10 should be more really existent, and a Form, than 10 itself; although the former is not generated as a unity, whereas the latter is. However, they try to make out that the series up to 10 is a complete number;

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at least they generate the derivatives, e.g. the void, proportion, the odd, etc., from within the decad. Some, such as motion, rest, good and evil, they assign to the first principles; the rest to numbers.From the Dyad were derived void (Theophrastus, Met. 312.18-313.3) and motion (cf. Aristot. Met. 1.9.29, Aristot. Met. 11.9.8). Rest would naturally be derived from unity. For good and evil see Aristot. Met. 1.6.10. Proportion alone of the derivatives here mentioned appears to be derived from number. As Syrianus says, the three types of proportion can be illustrated by numbers from within the decad—arithmetical 1. 2. 3, geometrical 1. 2. 4, harmonic 2. 3. 6.

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Hence they identify the odd with Unity; because if oddness depended on 3, how could 5 be odd?sc. because (on their theory) 3 is not contained in 5. Thus oddness had to be referred to not a number but a principle—unity.

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Again, they hold that spatial magnitudes and the like have a certain limit; e.g. the first or indivisible line, then the 2, and so on; these too extending up to 10.The indivisible line or point was connected with 1, the line with 2, the plane with 3 and the solid with 4 (Aristot. Met. 14.3.9); and 1+2+3+4=10.

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Again, if number is separable, the question might be raised whether Unity is prior, or 3 or 2.

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Now if we regard number as composite, Unity is prior; but if we regard the universal or form as prior, number is prior, because each unit is a material part of number, while number is the form of the units. And there is a sense in which the right angle is prior to the acute angle—since it is definite and is involved in the definition of the acute angle—and another sense in which the acute angle is prior, because it is a part of the other, i.e., the right angle is divided into acute angles.

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Thus regarded as matter the acute angle and element and unit are prior; but with respect to form and substance in the sense of formula, the right angle, and the whole composed of matter and form, is prior. For the concrete whole is nearer to the form or subject of the definition, although in generation it is posterior.Cf. Aristot. Met. 7.10, 11.

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In what sense, then, is the One a first principle? Because, they say, it is indivisible.

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But the universal and the part or element are also indivisible. Yes, but they are prior in a different sense; the one in formula and the other in time. In which sense, then, is the One a first principle? for, as we have just said, both the right angle seems to be prior to the acute angle, and the latter prior to the former; and each of them is one.

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Accordingly the Platonists make the One a first principle in both senses. But this is impossible; for in one sense it is the One qua form or essence, and in the other the One qua part or matter, that is primary. There is a sense in which both number and unit are one; they are so in truth potentially—that is, if a number is not an aggregate but a unity consisting of units distinct from those of other numbers, as the Platonists hold—

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but each of the twoAristotle takes the number two as an example, but the principle is of course universal. In a sense both number and unit are one; but if the number exists as an actual unity, the unit can only exist potentially. units is not one in complete reality. The cause of the error which befell the Platonists was that they were pursuing their inquiry from two points of view—that of mathematics and that of general definition—at the same time. Hence as a result of the former they conceived of the One or first principle as a point, for the unit is a point without position. (Thus they too, just like certain others,

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represented existing things as composed of that which is smallest.)Perhaps the Atomists; but cf. Aristot. Met. 1.8.3, 4. We get, then, that the unit is the material element of numbers, and at the same time is prior to the number 2; and again we get that it is posterior to 2 regarded as a whole or unity or form. On the other hand, through looking for the universal, they were led to speak of the unity predicated of a given number as a part in the formal sense also. But these two characteristics cannot belong simultaneously to the same thing.

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And if Unity itself must only be without positionIf the text is sound (and no convincing emendation has been suggested), it seems best to understand ἄθετον in a rather wider sense than the semi-technical one put forward by Ross. Without position = not localized, i.e. abstract. Unity as a principle has no concrete instance.(for it differs only in that it is a principle) and 2 is divisible whereas the unit is not, the unit will be more nearly akin to Unity itself; and if this is so, Unity itself will also be more nearly akin to the unit than to 2. Hence each of the units in 2 will be prior to 2. But this they deny; at least they make out that 2 is generated first.Cf. Aristot. Met. 13.7.5. Further, if 2 itself and 3 itself are each one thing, both together make 2. From what, then, does this 2 come?

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Since there is no contact in numbers, but units which have nothing between them—e.g. those in 2 or 3—are successive, the question might be raised whether or not they are successive to Unity itself, and whether of the numbers which succeed it 2 or one of the units in 2 is prior.

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We find similar difficulties in the case of the genera posterior to numberCf. Aristot. Met. 13.6.10.—the line, plane and solid. Some derive these from the species of the Great and Small; viz. lines from the Long and Short, planes from the Broad and Narrow, and solids from the Deep and Shallow. These are species of the Great and Small.

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As for the geometrical first principle which corresponds to the arithmetical One, different Platonists propound different views.Cf. Aristot. Met. 3.4.34, Aristot. Met. 14.3.9. In these too we can see innumerable impossibilities, fictions and contradictions of all reasonable probability. For (a) we get that the geometrical forms are unconnected with each other, unless their principles also are so associated that the Broad and Narrow is also Long and Short; and if this is so, the plane will be a line and the solid a plane.

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Moreover, how can angles and figures, etc., be explained? And (b) the same result follows as in the case of number; for these concepts are modifications of magnitude, but magnitude is not generated from them, any more than a line is generated from the Straight and Crooked, or solids from the Smooth and Rough.

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Common to all these Platonic theories is the same problem which presents itself in the case of species of a genus when we posit universals—viz. whether it is the Ideal animal that is present in the particular animal, or some other animal distinct from the Ideal animal. This question will cause no difficulty if the universal is not separable; but if, as the Platonists say, Unity and the numbers exist separately, then it is not easy to solve (if we should apply the phrase not easy to what is impossible).

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For when we think of the one in 2, or in number generally, are we thinking of an Idea or of something else?

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These thinkers, then, generate geometrical magnitudes from this sort of material principle, but othersThe reference is probably to Speusippus; Plato and Xenocrates did not believe in points (Aristot. Met. 1.9.25, Aristot. Met. 13.5.10 n). generate them from the point (they regard the point not as a unity but as similar to Unity) and another material principle which is not plurality but is similar to it; yet in the case of these principles none the less we get the same difficulties.

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For if the matter is one, line, plane and solid will be the same; because the product of the same elements must be one and the same. If on the other hand there is more than one kind of matter—one of the line, another of the plane, and another of the solid—either the kinds are associated with each other, or they are not. Thus the same result will follow in this case also; for either the plane will not contain a line, or it will be a line.

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Further, no attempt is made to explain how number can be generated from unity and plurality; but howsoever they account for this, they have to meet the same difficulties as those who generate number from unity and the indeterminate dyad. The one school generates number not from a particular plurality but from that which is universally predicated; the other from a particular plurality, but the first; for they hold that the dyad is the first plurality.Aristotle again identifies the indeterminate dyad with the number 2.

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Thus there is practically no difference between the two views; the same difficulties will be involved with regard to mixture, position, blending, generation and the other similar modes of combination.sc. of the elements of number.

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We might very well ask the further question: if each unit is one, of what it is composed; for clearly each unit is not absolute unity. It must be generated from absolute unity and either plurality or a part of plurality.

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Now we cannot hold that the unit is a plurality, because the unit is indivisible; but the view that it is derived from a part of plurality involves many further difficulties, because (a) each part must be indivisible; otherwise it will be a plurality and the unit will be divisible, and unity and plurality will not be its elements, because each unit will not be generated from pluralitysc. but from an indivisible part of plurality—which is not a plurality but a unity. and unity.

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(b) The exponent of this theory merely introduces another number; because plurality is a number of indivisible parts.i.e., to say that number is derived from plurality is to say that number is derived from number—which explains nothing.

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Again, we must inquire from the exponent of this theory whether the numbersc. which plurality has been shown to be. is infinite or finite.

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There was, it appears, a finite plurality from which, in combination with Unity, the finite units were generated; and absolute plurality is different from finite plurality. What sort of plurality is it, then, that is, in combination with unity, an element of number?

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We might ask a similar question with regard to the point, i.e. the element out of which they create spatial magnitudes.

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This is surely not the one and only point. At least we may ask from what each of the other points comes; it is not, certainly, from some interval and the Ideal point. Moreover, the parts of the interval cannot be indivisible parts, any more than the parts of the plurality of which the units are composed; because although number is composed of indivisible parts, spatial magnitudes are not.

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All these and other similar considerations make it clear that number and spatial magnitudes cannot exist separately. Further, the fact that the leading authoritiesAlexander preferred the reading πρώτους, interpreting it in this sense; and I do not see why he should not be followed. Ross objects that πρῶτος is used in the chronological sense in 16., but this is really no argument. For a much more serious (although different) inconsistency in the use of terms cf. Aristot. Met. 12.3.1. disagree about numbers indicates that it is the misrepresentation of the facts themselves that produces this confusion in their views.

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ThoseSpeusippus and his followers. who recognize only the objects of mathematics as existing besides sensible things, abandoned Ideal number and posited mathematical number because they perceived the difficulty and artificiality of the Ideal theory. Others,Xenocrates and his followers. wishing to maintain both Forms and numbers, but not seeing how, if one posits theseUnity and the indeterminate dyad; for the difficulty see Aristot. Met. 13.7.3, 4. as first principles, mathematical number can exist besides Ideal number, identified Ideal with mathematical number,—but only in theory, since actually mathematical number is done away with, because the hypotheses which they state are peculiar to them and not mathematical.Cf. Aristot. Met. 13.6.10.

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And hePlato. who first assumed that there are Ideas, and that the Ideas are numbers, and that the objects of mathematics exist, naturally separated them. Thus it happens that all are right in some respect, but not altogether right; even they themselves admit as much by not agreeing but contradicting each other. The reason of this is that their assumptions and first principles are wrong;

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and it is difficult to propound a correct theory from faulty premisses: as Epicharmus says, no sooner is it said than it is seen to be wrong. Epicharmus, Fr. 14, Diels.

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We have now examined and analyzed the questions concerning numbers to a sufficient extent; for although one who is already convinced might be still more convinced by a fuller treatment, he who is not convinced would be brought no nearer to conviction.

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As for the first principles and causes and elements, the views expressed by those who discuss only sensible substance either have been described in the PhysicsAristot. Physics 1.4-6. or have no place in our present inquiry; but the views of those who assert that there are other substances besides sensible ones call for investigation next after those which we have just discussed.

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Since, then, some thinkers hold that the Ideas and numbers are such substances, and that their elements are the elements and principles of reality, we must inquire what it is that they hold, and in what sense they hold it.

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ThoseThe Pythagoreans and Speusippus. who posit only numbers, and mathematical numbers at that, may be considered laterAristot. Met. 14.2.21, Aristot. Met. 14.3.2-8, 15, 16.; but as for those who speak of the Ideas, we can observe at the same time their way of thinking and the difficulties which befall them. For they not only treat the Ideas as universal substances, but also as separable and particular.

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(That this is impossible has been already shownAristot. Met. 3.6.7-9. by a consideration of the difficulties involved.) The reason why those who hold substances to be universal combined these two views was that they did not identify substances with sensible things. They considered that the particulars in the sensible world are in a state of flux, and that none of them persists, but that the universal exists besides them and is something distinct from them.

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This theory, as we have said in an earlier passage,Aristot. Met. 13.4, and cf. Aristot. Met. 1.6. was initiated by Socrates as a result of his definitions, but he did not separate universals from particulars; and he was right in not separating them. This is evident from the facts; for without the universal we cannot acquire knowledge, and the separation of the universal is the cause of the difficulties which we find in the Ideal theory.

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Others,The Platonists. regarding it as necessary, if there are to be any substances besides those which are sensible and transitory, that they should be separable, and having no other substances, assigned separate existence to those which are universally predicated; thus it followed that universals and particulars are practically the same kind of thing. This in itself would be one difficulty in the view which we have just described.See Introduction.

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Let us now mention a point which presents some difficulty both to those who hold the Ideal theory and to those who do not. It has been stated already, at the beginning of our treatise, among the problems.Cf. Aristot. Met. 3.4.8-10, Aristot. Met. 3.6.7-9. If we do not suppose substances to be separate, that is in the way in which particular things are said to be separate, we shall do away with substance in the sense in which we wish to maintain it; but if we suppose substances to be separable, how are we to regard their elements and principles?

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If they are particular and not universal, there will be as many real things as there are elements, and the elements will not be knowable. For let us suppose that the syllables in speech are substances, and that their letters are the elements of substances. Then there must be only one BA, and only one of each of the other syllables; that is, if they are not universal and identical in form, but each is numerically one and an individual, and not a member of a class bearing a common name.

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(Moreover, the Platonists assume that each Ideal entity is unique.) Now if this is true of the syllables, it is also true of their letters. Hence there will not be more than one A, nor more than one of any of the other letters,This is, as a matter of fact, the assumption upon which the whole argument rests; Aristotle is arguing in a circle. on the same argument by which in the case of the syllable there cannot be more than one instance of the same syllable. But if this is so, there will be no other things besides the letters, but only the letters.

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Nor again will the elements be knowable; for they will not be universal, and knowledge is of the universal. This can be seen by reference to proofs and definitions; for there is no logical conclusion that a given triangle has its angles equal to two right angles unless every triangle has its angles equal to two right angles, or that a given man is an animal unless every man is an animal.

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On the other hand, if the first principles are universal, either the substances composed of them will be universal too, or there will be a non-substance prior to substance; because the universal is not substance, and the element or first principle is universal; and the element or first principle is prior to that of which it is an element or first principle.

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All this naturally follows when they compose the Ideas of elements and assert that besides the substances which have the same form there are also Ideas each of which is a separate entity.

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But if, as in the case of the phonetic elements, there is no reason why there should not be many A’s and B’s, and no A itself or B itself apart from these many, then on this basis there may be any number of similar syllables.

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The doctrine that all knowledge is of the universal, and hence that the principles of existing things must also be universal and not separate substances, presents the greatest difficulty of all that we have discussed; there is, however, a sense in which this statement is true, although there is another in which it is not true.

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Knowledge, like the verb to know, has two senses, of which one is potential and the other actual. The potentiality being, as matter, universal and indefinite, has a universal and indefinite object; but the actuality is definite and has a definite object, because it is particular and deals with the particular.

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It is only accidentally that sight sees universal color, because the particular color which it sees is color; and the particular A which the grammarian studies is an A. For if the first principles must be universal, that which is derived from them must also be universal, as in the case of logical proofsBecause ἀπόδειξις (logical or syllogistic proof) must be in the first figure (Aristot. An. Post. 1.14), and in that figure universal premises always give a universal conclusion. (Ross.); and if this is so there will be nothing which has a separate existence; i.e. no substance. But it is clear that although in one sense knowledge is universal, in another it is not.

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With regard to this kind of substance,i.e., the Platonic Ideas or numbers, which they regarded as unchangeable substances. There is, however, no definite transition to a fresh subject at this point. The criticisms of the Ideas or numbers as substances, and of the Platonic first principles, have not been grouped systematically in Books 13 and 14. Indeed there is so little distinction in subject matter between the two books that in some Mss. 14 was made to begin at 13.9.10. (Syrianus ad loc.). See Introduction. then, let the foregoing account suffice. All thinkers make the first principles contraries; as in the realm of natural objects, so too in respect of the unchangeable substances.

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Now if nothing can be prior to the first principle of all things, that first principle cannot be first principle if it is an attribute of something else. This would be as absurd as to say that white is the first principle, not qua anything else but qua white, and yet that it is predicable of a subject, and is white because it is an attribute of something else; because the latter will be prior to it.

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Moreover, all things are generated from contraries as from a substrate, and therefore contraries must most certainly have a substrate. Therefore all contraries are predicated of a subject, and none of them exists separately. But there is no contrary to substance; not only is this apparent, but it is borne out by reasoned consideration.Cf. Aristot. Categories 3b 24-27 Thus none of the contraries is strictly a first principle; the first principle is something different.

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But the Platonists treat one of the contraries as matter, some opposing the unequal to Unity (on the ground that the former is of the nature of plurality) and others plurality.

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For according to some,Plato; cf. Aristot. Met. 13.7.5. numbers are generated from the unequal dyad of the Great and Small; and according to another,Probably Speusippus. from plurality; but in both cases they are generated by the essence of unity. For he who speaks of the unequal and Unity as elements, and describes the unequal as a dyad composed of Great and Small, speaks of the unequal, i.e. the Great and Small, as being one; and does not draw the distinction that they are one in formula but not in number.This shows clearly that by the Great-and Small Plato meant a single principle, i.e., indeterminate quantity. Aristotle admits this here because he is contrasting the Great-and Small with the One; but elsewhere he prefers to regard the Platonic material principle as a duality. See Introduction.

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Again, they state the first principles, which they call elements, badly; some say that the Great and the Small, together with Unity (making 3Cf. previous note. in all), are the elements of numbers; the two former as matter, and Unity as form. Others speak of the Many and Few, because the Great and the Small are in their nature more suited to be the principles of magnitude; and others use the more general term which covers these—the exceeding and the exceeded.

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But none of these variations makes any appreciable difference with respect to some of the consequences of the theory; they only affect the abstract difficulties, which these thinkers escape because the proofs which they themselves employ are abstract.

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There is, however, this exception: if the exceeding and the exceeded are the first principles, and not the Great and the Small, on the same principle number should be derived from the elements before 2 is derived; for as the exceeding and the exceeded is more universal than the Great and Small, so number is more universal than 2. But in point of fact they assert the one and not the other.

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Others oppose the different or other to Unity; and others contrast Plurality and Unity.

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Now if, as they maintain, existing things are derived from contraries, and if there is either no contrary to unity, or if there is to be any contrary it is plurality; and if the unequal is contrary to the equal, and the different to the same, and the other to the thing itself then those who oppose unity to plurality have the best claim to credibility—but even their theory is inadequate, because then unity will be few. For plurality is opposed to paucity, and many to few.

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That unity denotes a measureCf. Aristot. Met. 5.6.17, 18, Aristot. Met. 10.1.8, 21. is obvious. And in every case there is something else which underlies it; e.g., in the scale there is the quarter-tone; in spatial magnitude the inch or foot or some similar thing; and in rhythms the foot or syllable. Similarly in the case of gravity there is some definite weight. Unity is predicated of all things in the same way; of qualities as a quality, and of quantities as a quantity.

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(The measure is indivisible, in the former case in kind, and in the latter to our senses.) This shows that unity is not any independent substance. And this is reasonable; because unity denotes a measure of some plurality, and number denotes a measured plurality and a plurality of measures. (Hence too it stands to reason that unity is not a number; for the measure is not measures, but the measure and unity are starting-points.)

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The measure must always be something which applies to all alike; e.g., if the things are horses, the measure is a horse; if they are men, the measure is a man; and if they are man, horse and god, the measure will presumably be an animate being, and the number of them animate beings.

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If the things are man, white and walking, there will scarcely be a number of them, because they all belong to a subject which is one and the same in number; however, their number will be a number of genera, or some other such appellation.

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ThoseCf. sect. 5. who regard the unequal as a unity, and the dyad as an indeterminate compound of great and small, hold theories which are very far from being probable or possible. For these terms represent affections and attributes, rather than substrates, of numbers and magnitudes—many and few applying to number, and great and small to magnitude— just as odd and even, smooth and rough, straight and crooked, are attributes.

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Further, in addition to this error, great and small and all other such terms must be relative. And the relative is of all the categories in the least degree a definite entity or substance; it is posterior to quality and quantity. The relative is an affection of quantity, as we have said, and not its matter; since there is something else distinct which is the matter both of the relative in general and of its parts and kinds.

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There is nothing great or small, many or few, or in general relative, which is many or few, great or small, or relative to something else without having a distinct nature of its own. That the relative is in the lowest degree a substance and a real thing is shown by the fact that of it aloneCf. Aristot. Met. 11.12.1. There Aristotle refers to seven categories, but here he omits activity and passivity as being virtually identical with motion. there is neither generation nor destruction nor change in the sense that in respect of quantity there is increase and decrease, in respect of quality, alteration, in respect of place, locomotion, and in respect of substance, absolute generation and destruction.

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There is no real change in respect of the relative; for without any change in itself, one term will be now greater, now smaller or equal, as the other term undergoes quantitative change. Moreover, the matter of every thing, and therefore of substance, must be that which is potentially of that nature; but the relative is neither potentially substance nor actually.

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It is absurd, then, or rather impossible, to represent non-substance as an element of substance and prior to it; for all the other categories are posterior to substance. And further, the elements are not predicated of those things of which they are elements; yet many and few are predicated, both separately and together, of number; and long and short are predicated of the line, and the Plane is both broad and narrow.

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If, then, there is a plurality of which one term, viz. few, is always predicable, e.g. 2 (for if 2 is many, 1 will be fewCf. Aristot. Met. 10.6.1-3.), then there will be an absolute many; e.g., 10 will be many (if there is nothing more than 10Cf. Aristot. Met. 13.8.17.), or 10,000. How, then, in this light, can number be derived from Few and Many? Either both ought to be predicated of it, or neither; but according to this view only one or the other is predicated.

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But we must inquire in general whether eternal things can be composed of elements. If so, they will have matter; for everything which consists of elements is composite.

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Assuming, then, that that which consists of anything, whether it has always existed or it came into being, must come into being <if at all> out of that of which it consists; and that everything comes to be that which it comes to be out of that which is it potentially (for it could not have come to be out of that which was not potentially such, nor could it have consisted of it); and that the potential can either be actualized or not; then however everlasting number or anything else which has matter may be, it would be possible for it not to exist, just as that which is any number of years old is as capable of not existing as that which is one day old. And if this is so, that which has existed for so long a time that there is no limit to it may also not exist.

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Therefore things which contain matter cannot be eternal, that is, if that which is capable of not existing is not eternal, as we have had occasion to say elsewhere.Aristot. Met. 9.8.15-17, Aristot. De Caelo 1.12. Now if what we have just been saying—that no substance is eternal unless it is actuality—is true universally, and the elements are the matter of substance, an eternal substance can have no elements of which, as inherent in it, it consists.

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There are some who, while making the element which acts conjointly with unity the indeterminate dyad, object to the unequal, quite reasonably, on the score of the difficulties which it involves. But they are rid only of those difficultiesCf. Aristot. Met. 14.1.14-17. which necessarily attend the theory of those who make the unequal, i.e. the relative, an element; all the difficulties which are independent of this view must apply to their theories also, whether it is Ideal or mathematical number that they construct out of these elements.

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There are many causes for their resorting to these explanations, the chief being that they visualized the problem in an archaic form. They supposed that all existing things would be one, absolute Being, unless they encountered and refuted Parmenides’ dictum:

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It will ne’er be proved that things which are not, are,Parmenides Fr. 7 (Diels).

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i.e., that they must show that that which is not, is; for only so—of that which is, and of something else—could existing things be composed, if they are more than one.Cf. Plat. Soph. 237a, 241d, 256e.

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However, (i) in the first place, if being has several meanings (for sometimes it means substance, sometimes quality, sometimes quantity, and so on with the other categories), what sort of unity will all the things that are constitute, if not-being is not to be? Will it be the substances that are one, or the affections (and similarly with the other categories), or all the categories together? in which case the this and the such and the so great, and all the other categories which denote some sense of Being, will be one.

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But it is absurd, or rather impossible, that the introduction of one thing should account for the fact that what is sometimes means so-and-so, sometimes such-and-such, sometimes of such-and-such a size, sometimes in such-and-such a place.

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(2) Of what sort of not-being and Being do real things consist? Not-being, too, has several senses, inasmuch as Being has; and not-man means not so-and-so, whereas not straight means not such-and-such, and not five feet long means not of such-and-such a size. What sort of Being and not-being, then, make existing things a plurality?

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This thinker means by the not-being which together with Being makes existing things a plurality, falsity and everything of this naturePlat. Soph. 237a, 240; but Aristotle’s statement assumes too much.; and for this reason also it was saidPresumably by some Platonist. that we must assume something which is false, just as geometricians assume that a line is a foot long when it is not.

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But this cannot be so; for (a) the geometricians do not assume anything that is false (since the proposition is not part of the logical inferencei.e., the validity of a geometrical proof does not depend upon the accuracy of the figure.), and (b) existing things are not generated from or resolved into not-being in this sense. But not only has not-being in its various cases as many meanings as there are categories, but moreover the false and the potential are called not-being; and it is from the latter that generation takes place—man comes to be from that which is not man but is potentially man, and white from that which is not white but is potentially white; no matter whether one thing is generated or many.

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Clearly the point at issue is how being in the sense of the substances is many; for the things that are generated are numbers and lines and bodies. It is absurd to inquire how Being as substance is many, and not how qualities or quantities are many.

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Surely the indeterminate dyad or the Great and Small is no reason why there should be two whites or many colors or flavors or shapes; for then these too would be numbers and units. But if the Platonists had pursued this inquiry, they would have perceived the cause of plurality in substances as well; for the causeMatter, according to Aristotle; and there is matter, or something analogous to it, in every category. Cf. Aristot. Met. 12.5. is the same, or analogous.

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This deviation of theirs was the reason why in seeking the opposite of Being and unity, from which in combination with Being and unity existing things are derived, they posited the relative (i.e. the unequal), which is neither the contrary nor the negation of Being and unity, but is a single characteristic of existing things, just like substance or quality. They should have investigated this question also; how it is that relations are many, and not one.

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As it is, they inquire how it is that there are many units besides the primary unity, but not how there are many unequal things besides the Unequal. Yet they employ in their arguments and speak of Great and Small, Many and Few (of which numbers are composed), Long and Short (of which the line is composed), Broad and Narrow (of which the plane is composed), Deep and Shallow (of which solids are composed); and they mention still further kinds of relation.Cf. Aristot. Met. 14.1.6, 18, Aristot. Met. 1.9.23. Now what is the cause of plurality in these relations?

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We must, then, as I say, presuppose in the case of each thing that which is it potentially. The authorPlato. of this theory further explained what it is that is potentially a particular thing or substance, but is not per se existent—that it is the relative (he might as well have said quality); which is neither potentially unity or Being, nor a negation of unity or Being, but just a particular kind of Being.

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And it was still more necessary, as we have said,sect. 11. that, if he was inquiring how it is that things are many, he should not confine his inquiry to things in the same category, and ask how it is that substances or qualities are many, but that he should ask how it is that things in general are many; for some things are substances, some affections, and some relations.

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Now in the case of the other categories there is an additional difficulty in discovering how they are many. For it may be said that since they are not separable, it is because the substrate becomes or is many that qualities and quantities are many; yet there must be some matter for each class of entities, only it cannot be separable from substances.

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In the case of particular substances, however, it is explicable how the particular thing can be many, if we do not regard a thing both as a particular substance and as a certain characteristic.This, according to Aristotle, is how the Platonists regard the Ideas. See Introduction. The real difficulty which arises from these considerations is how substances are actually many and not one.

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Again, even if a particular thing and a quantity are not the same, it is not explained how and why existing things are many, but only how quantities are many;

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for all number denotes quantity, and the unit, if it does not mean a measure, means that which is quantitatively indivisible. If, then, quantity and substance are different, it is not explained whence or how substance is many; but if they are the same, he who holds this has to face many logical contradictions.

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One might fasten also upon the question with respect to numbers, whence we should derive the belief that they exist.

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For onePlato and his orthodox followers. who posits Ideas, numbers supply a kind of cause for existing things; that is if each of the numbers is a kind of Idea, and the Idea is, in some way or other, the cause of existence for other things; for let us grant them this assumption.

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But as for himSpeusippus. who does not hold this belief, because he can see the difficulties inherent in the Ideal theory (and so has not this reason for positing numbers), and yet posits mathematical number, what grounds have we for believing his statement that there is a number of this kind, and what good is this number to other things? He who maintains its existence does not claim that it is the cause of anything, but regards it as an independent entity; nor can we observe it to be the cause of anything; for the theorems of the arithmeticians will all apply equally well to sensible things, as we have said.Aristot. Met. 13.3.1.

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Those, then, who posit the Ideas and identify them with numbers, by their assumption (in accordance with their method of abstracting each general term from its several concrete examples) that every general term is a unity, make some attempt to explain why number exists.I have followed Ross’s text and interpretation of this sentence. For the meaning cf. Aristot. Met. 14.2.20. Since, however, their arguments are neither necessarily true nor indeed possible, there is no justification on this ground for maintaining the existence of number.

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The Pythagoreans, on the other hand, observing that many attributes of numbers apply to sensible bodies, assumed that real things are numbers; not that numbers exist separately, but that real things are composed of numbers.See Introduction. But why? Because the attributes of numbers are to be found in a musical scale, in the heavens, and in many other connections.Cf. Aristot. Met. 14.6.5.

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As for those who hold that mathematical number alone exists,Cf. Aristot. Met. 14.2.21. they cannot allege anything of this kindi.e., that things are composed of numbers. consistently with their hypotheses; what they did say was that the sciences could not have sensible things as their objects. But we maintain that they can; as we have said before. And clearly the objects of mathematics do not exist in separation; for if they did their attributes would not be present in corporeal things.

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Thus in this respect the Pythagoreans are immune from criticism; but in so far as they construct natural bodies, which have lightness and weight, out of numbers which have no weight or lightness, they appear to be treating of another universe and other bodies, not of sensible ones.See Introduction.

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But those who treat number as separable assume that it exists and is separable because the axioms will not apply to sensible objects; whereas the statements of mathematics are true and appeal to the soul.The statements of mathematics appeal so strongly to our intelligence that they must be true; therefore if they are not true of sensible things, there must be some class of objects of which they are true. The same applies to mathematical extended magnitudes.

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It is clear, then, both that the contrary theoryThe Pythagorean theory, which maintains that numbers not only are present in sensible things but actually compose them, is in itself an argument against the Speusippean view, which in separating numbers from sensible things has to face the question why sensible things exhibit numerical attributes. can make out a case for the contrary view, and that those who hold this theory must find a solution for the difficulty which was recently raisedsect. 3.—why it is that while numbers are in no way present in sensible things, their attributes are present in sensible things.

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There are someProbably Pythagoreans. Cf. Aristot. Met. 7.2.2, Aristot. Met. 3.5.3. who think that, because the point is the limit and extreme of the line, and the line of the plane, and the plane of the solid, there must be entities of this kind.

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We must, then, examine this argument also, and see whether it is not exceptionally weak. For (1.) extremes are not substances; rather all such things are merely limits. Even walking, and motion in general, has some limit; so on the view which we are criticizing this will be an individual thing, and a kind of substance. But this is absurd. And moreover (2.) even if they are substances, they will all be substances of particular sensible things, since it was to these that the argument applied. Why, then, should they be separable?

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Again, we may, if we are not unduly acquiescent, further object with regard to all number and mathematical objects that they contribute nothing to each other, the prior to the posterior. For if number does not exist, none the less spatial magnitudes will exist for those who maintain that only the objects of mathematics exist; and if the latter do not exist, the soul and sensible bodies will exist.That the criticism is directed against Speusippus is clear from Aristot. Met. 7.2.4. Cf. Aristot. Met. 12.10.14.

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But it does not appear, to judge from the observed facts, that the natural system lacks cohesion, like a poorly constructed drama. ThoseXenocrates (that the reference is not to Plato is clear from sect. 11). who posit the Ideas escape this difficulty, because they construct spatial magnitudes out of matter and a number—2 in the case of lines, and 3, presumably, in that of planes, and 4 in that of solids; or out of other numbers, for it makes no difference.

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But are we to regard these magnitudes as Ideas, or what is their mode of existence? and what contribution do they make to reality? They contribute nothing; just as the objects of mathematics contribute nothing. Moreover, no mathematical theorem applies to them, unless one chooses to interfere with the principles of mathematics and invent peculiar theoriese.g. that of indivisible lines. of one’s own. But it is not difficult to take any chance hypotheses and enlarge upon them and draw out a long string of conclusions.

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These thinkers, then, are quite wrong in thus striving to connect the objects of mathematics with the Ideas. But those who first recognized two kinds of number, the Ideal and the mathematical as well, neither have explained nor can explain in any way how mathematical number will exist and of what it will be composed; for they make it intermediate between Ideal and sensible number.

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For if it is composed of the Great and Small, it will be the same as the former, i.e. Ideal, number. But of what other Great and Small can it be composed? for Plato makes spatial magnitudes out of a Great and Small.This interpretation (Ross’s second alternative, reading τίνος for τινος) seems to be the most satisfactory. For the objection cf. Aristot. Met. 3.4.34. And if he speaks of some other component, he will be maintaining too many elements; while if some one thing is the first principle of each kind of number, unity will be something common to these several kinds.

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We must inquire how it is that unity is these many things, when at the same time number, according to him, cannot be derived otherwise than from unity and an indeterminate dyad.The argument may be summarized thus. If mathematical number cannot be derived from the Great-and-Small or a species of the Great-and-Small, either it has a different material principle (which is not economical) or its formal principle is in some sense distinct from that of the Ideal numbers. But this implies that unity is a kind of plurality, and number or plurality can only be referred to the dyad or material principle.

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All these views are irrational; they conflict both with one another and with sound logic, and it seems that in them we have a case of Simonides’ long storyThe exact reference is uncertain, but Aristotle probably means Simonides of Ceos. Cf. Simonides Fr. 189 (Bergk).; for men have recourse to the long story, such as slaves tell, when they have nothing satisfactory to say.

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The very elements too, the Great and Small, seem to protest at being dragged in; for they cannot possibly generate numbers except rising powers of 2.Assuming that the Great-and-Small, or indeterminate dyad, is duplicative (Aristot. Met. 13.7.18).

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It is absurd also, or rather it is one of the impossibilities of this theory, to introduce generation of things which are eternal.

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There is no reason to doubt whether the Pythagoreans do or do not introduce it; for they clearly state that when the One had been constituted—whether out of planes or superficies or seed or out of something that they cannot explain—immediately the nearest part of the Infinite began to be drawn in and limited by the Limit.Cf. Aristot. Physics 3.4, Aristot. Physics 4.6, and Burnet, E.G.P. sect. 53.

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However, since they are here explaining the construction of the universe and meaning to speak in terms of physics, although we may somewhat criticize their physical theories, it is only fair to exempt them from the present inquiry; for it is the first principles in unchangeable things that we are investigating, and therefore we have to consider the generation of this kind of numbers.

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TheyThe Platonists. say that there is no generation of odd numbers,This statement was probably symbolical. They described the odd numbers as ungenerated because they likened them to the One, the principle of pure form (Ross ad loc.). which clearly implies that there is generation of even ones; and some hold that the even is constructed first out of unequals—the Great and Small—when they are equalized.Cf. Aristot. Met. 13.7.5. Therefore the inequality must apply to them before they are equalized. If they had always been equalized they would not have been unequal before; for there is nothing prior to that which has always been.

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Hence evidently it is not for the sake of a logical theory that they introduce the generation of numbers

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A difficulty, and a discredit to those who make light of the difficulty, arises out of the question how the elements and first principles are related to the the Good and the Beautiful. The difficulty is this: whether any of the elements is such as we mean when weAristotle speaks as a Platonist. See Introduction. speak of the Good or the Supreme Good, or whether on the contrary these are later in generation than the elements.

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It would seem that there is an agreement between the mythologists and some present-day thinkers,The Pythagoreans and Speusippus; cf. Aristot. Met. 12.7.10. who deny that there is such an element, and say that it was only after some evolution in the natural order of things that both the Good and the Beautiful appeared. They do this to avoid a real difficulty which confronts those who hold, as some do, that unity is a first principle.

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This difficulty arises not from ascribing goodness to the first principle as an attribute, but from treating unity as a principle, and a principle in the sense of an element, and then deriving number from unity. The early poets agree with this view in so far as they assert that it was not the original forces—such as Night, Heaven, Chaos or Ocean—but Zeus who was king and ruler.

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It was, however, on the ground of the changing of the rulers of the world that the poets were led to state these theories; because those of them who compromise by not describing everything in mythological language—e.g. PherecydesOf Syros (circa 600-525 B.C.). He made Zeus one of the three primary beings (Diels,Vorsokratiker201, 202). and certain others—make the primary generator the Supreme Good; and so do the Magi,The Zoroastrian priestly caste. and some of the later philosophers such as Empedocles and Anaxagoras: the one making Love an element,Cf. Aristot. Met. 3.1.13. and the other making Mind a first principle.Cf. Aristot. Met. 1.3.16.

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And of those who hold that unchangeable substances exist, somePlato; cf. Aristot. Met. 1.6.10. identify absolute unity with absolute goodness; but they considered that the essence of goodness was primarily unity.

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This, then, is the problem: which of these two views we should hold.

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Now it is remarkable if that which is primary and eternal and supremely self-sufficient does not possess this very quality, viz. self-sufficiency and immunity, in a primary degree and as something good. Moreover, it is imperishable and self-sufficient for no other reason than because it is good. Hence it is probably true to say that the first principle is of this nature.

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But to say that this principle is unity, or if not that, that it is an element, and an element of numbers, is impossible; for this involves a serious difficulty, to avoid which some thinkersSpeusippus and his followers; cf. sect. 3. have abandoned the theory (viz. those who agree that unity is a first principle and element, but of mathematical number). For on this view all units become identical with some good, and we get a great abundance of goods.If unity is goodness, and every unit is a kind of unity, every unit must be a kind of goodness—which is absurd.

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Further, if the Forms are numbers, all Forms become identical with some good. Again, let us assume that there are Ideas of anything that we choose. If there are Ideas only of goods, the Ideas will not be substancesBecause they are Ideas not of substances but of qualities.; and if there are Ideas of substances also, all animals and plants, and all things that participate in the Ideas, will be goods.Because the Ideas are goods.

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Not only do these absurdities follow, but it also follows that the contrary element, whether it is plurality or the unequal, i.e. the Great and Small, is absolute badness. Hence one thinkerSpeusippus. avoided associating the Good with unity, on the ground that since generation proceeds from contraries, the nature of plurality would then necessarily be bad.

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OthersPlato and Xenocrates. hold that inequality is the nature of the bad. It follows, then, that all things partake of the Bad except one—absolute unity; and that numbers partake of it in a more unmitigated form than do spatial magnitudesAs being more directly derived from the first principles. Cf. Aristot. Met. 1.9.23 n.; and that the Bad is the province for the activity of the Good, and partakes of and tends towards that which is destructive of the Good; for a contrary is destructive of its contrary.

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And if, as we said,Aristot. Met. 14.1.17. the matter of each thing is that which is it potentially—e.g., the matter of actual fire is that which is potentially fire—then the Bad will be simply the potentially Good.

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Thus all these objections follow because (1.) they make every principle an element; (2.) they make contraries principles; (3.) they make unity a principle; and (4.) they make numbers the primary substances, and separable, and Forms.

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If, then, it is impossible both not to include the Good among the first principles, and to include it in this way, it is clear that the first principles are not being rightly represented, nor are the primary substances. Nor is a certain thinkerEvidently Speusippus; cf. Aristot. Met. 14.4.3. right in his assumption when he likens the principles of the universe to that of animals and plants, on the ground that the more perfect forms are always produced from those which are indeterminate and imperfect, and is led by this to assert that this is true also of the ultimate principles; so that not even unity itself is a real thing.Speusippus argued that since all things are originally imperfect, unity, which is the first principle, must be imperfect, and therefore distinct from the good. Aristotle objects that the imperfect does not really exist, and so Speusippus deprives his first principle of reality.

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He is wrong; for even in the natural world the principles from which these things are derived are perfect and complete—for it is man that begets man; the seed does not come first.Cf. Aristot. Met. 9.8.5. It is absurd also to generate space simultaneously with the mathematical solids (for space is peculiar to particular things, which is why they are separable in space, whereas the objects of mathematics have no position) and to say that they must be somewhere, and yet not explain what their spatial position is.

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Those who assert that reality is derived from elements, and that numbers are the primary realities, ought to have first distinguished the senses in which one thing is derived from another, and then explained in what way number is derived from the first principles. Is it by mixture? But (a) not everything admits of mixturee.g. to admit of mixture a thing must first have a separate existence, and the Great-and-Small, which is an affection or quality of number (Aristot. Met. 14.1.14) cannot exist separately.; (b) the result of mixture is something different; and unity will not be separable,sc. when it has once been mixed. Cf. Aristot. De Gen. et Corr. 327b 21-26. nor will it be a distinct entity, as they intend it to be.

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Is it by composition, as we hold of the syllable? But (a) this necessarily implies position; (b) in thinking of unity and plurality we shall think of them separately. This, then, is what number will be—a unit plus plurality, or unity plus the Unequal.

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And since a thing is derived from elements either as inherent or as not inherent in it, in which way is number so derived? Derivation from inherent elements is only possible for things which admit of generation.And numbers are supposed to be eternal. Cf. Aristot. Met. 14.2.1-3. Is it derived as from seed?

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But nothing can be emitted from that which is indivisible.i.e., unity, being indivisible, cannot contribute the formal principle of generation in the way that the male parent contributes it. Is it derived from a contrary which does not persist? But all things which derive their being in this way derive it also from something else which does persist. Since, therefore, one thinkerSpeusippus: Plato. Cf. Aristot. Met. 14.1.5. regards unity as contrary to plurality, and another (treating it as the Equal) as contrary to the Unequal, number must be derived as from contraries.

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Hence there is something else which persists from which, together with one contrary, number is or has been derived.The objection is directed against the Platonist treatment of the principles as contraries (cf. Aristot. Met. 14.4.12), and may be illustrated by Aristot. Met. 12.1.5-2.2. Plurality, as the contrary of unity, is privation, not matter; the Platonists should have derived numbers from unity and some other principle which is truly material.

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Further, why on earth is it that whereas all other things which are derived from contraries or have contraries perish, even if the contrary is exhausted in producing them,Because it may be regarded as still potentially present. number does not perish? Of this no explanation is given; yet whether it is inherent or not, a contrary is destructive; e.g., Strife destroys the mixture.According to Empedocles Fr. 17 (Diels). It should not, however, do this; because the mixture is not its contrary.

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Nor is it in any way defined in which sense numbers are the causes of substances and of Being; whether as bounds,The theories criticized from this point onwards to Aristot. Met. 14.6.11 are primarily Pythagorean. See Introduction. e.g. as points are the bounds of spatial magnitudes,e.g. the line by 2 points, the triangle (the simplest plane figure) by 3, the tetrahedron (the simplest solid figure) by 4. and as EurytusDisciple of Philolaus; he flourished in the early fourth century B.C. determined which number belongs to which thing—e.g. this number to man, and this to horse—by using pebbles to copy the shape of natural objects, like those who arrange numbers in the form of geometrical figures, the triangle and the square.cf. Burnet, E.G.P. sect. 47.

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Or is it because harmony is a ratio of numbers, and so too is man and everything else? But in what sense are attributes—white, and sweet, and hot—numbers?This is an objection to the view that numbers are causes as bounds. And clearly numbers are not the essence of things, nor are they causes of the form; for the ratioOr formula. is the essence, and numberIn the sense of a number of material particles. is matter.

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E.g. the essence of flesh or bone is number only in the sense that it is three parts of fire and two of earth.Cf. Empedocles Fr. 96 (Diels). And the number, whatever it is, is always a number of something; of particles of fire or earth, or of units. But the essence is the proportion of one quantity to another in the mixture; i.e. no longer a number, but a ratio of the mixture of numbers, either of corporeal particles or of any other kind. Thus number is not an efficient cause—neither number in general, nor that which consists of abstract units—nor is it the matter, nor the formula or form of things. Nor again is it a final cause.

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The question might also be raised as to what the good is which things derive from numbers because their mixture can be expressed by a number, either one which is easily calculable,i.e., a simple ratio. or an odd number.It is hard to see exactly what this means. If the terms of a ratio are rational, one of them must be odd. Alexander says a ratio like 1 : 3 is meant. Oddness was associated with goodness (cf. Aristot. Met. 1.5.6). For in point of fact honey-water is no more wholesome if it is mixed in the proportion three times threeApparently the Pythagoreans meant by this three parts of water to three of honey. Aristotle goes on to criticize this way of expressing ratios.; it would be more beneficial mixed in no particular proportion, provided that it be diluted, than mixed in an arithmetical proportion, but strong.

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Again, the ratios of mixtures are expressed by the relation of numbers, and not simply by numbers; e.g., it is 3 : 2, not 3 X 2Cf. previous note.; for in products of multiplication the units must belong to the same genus. Thus the product of 1 x 2 x 3 must be measurable by 1, and the product of 4 X 5 x 7 by 4. Therefore all products which contain the same factor must be measurable by that factor. Hence the number of fire cannot be 2 X 5 X 3 X 7 if the number of water is 2 x 3.sc. because if so, a particle of fire would simply equal 35 particles of water.

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If all things must share in number, it must follow that many things are the same; i.e., that the same number belongs both to this thing and to something else. Is number, then, a cause; i.e., is it because of number that the object exists? Or is this not conclusive? E.g., there is a certain number of the sun’s motions, and again of the moon’s,5 in each case, according to Aristotle; cf. Aristot. Met. 12.7.9, 11. and indeed of the life and maturity of every animate thing. What reason, then, is there why some of these numbers should not be squares and others cubes, some equal and others double?

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There is no reason; all things must fall within this range of numbers if, as was assumed, all things share in number, and different things may fall under the same number. Hence if certain things happened to have the same number, on the Pythagorean view they would be the same as one another, because they would have the same form of number; e.g., sun and moon would be the same.Cf. previous note.

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But why are these numbers causes? There are seven vowels,In the Greek alphabet. seven strings to the scale,In the old heptachord; cf. note on Aristot. Met. 5.11.4. seven Pleiads; most animals (though not allCf. Aristot. Hist. An. 576a 6.) lose their teeth in the seventh year; and there were seven heroes who attacked Thebes. Is it, then, because the number 7 is such as it is that there were seven heroes, or that the Pleiads consist of seven stars? Surely there were seven heroes because of the seven gates, or for some other reason, and the Pleiads are seven because we count them so; just as we count the Bear as 12, whereas others count more stars in both.

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Indeed, they assert also that Ξ, Ψ and Ζ are concords,According to Alexander ζ was connected with the fourth, ξ with the fifth, and ψ with the octave. and that because there are three concords, there are three double consonants. They ignore the fact that there might be thousands of double consonants—because there might be one symbol for ΓΡ. But if they say that each of these letters is double any of the others, whereas no other is,θ, φ , and χ are aspirated, not double, consonants. and that the reason is that there are three regionsPalate, lips, and teeth. of the mouth, and that one consonant is combined with σ in each region, it is for this reason that there are only three double consonants, and not because there are three concords—because there are really more than three; but there cannot be more than three double consonants.

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Thus these thinkers are like the ancient Homeric scholars, who see minor similarities but overlook important ones.

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Some say that there are many correspondences of this kind; e.g., the middle notesi.e., the μέση(fourth) and παραμέση(fifth), whose ratios can be expressed as 8 : 6, 9 : 6. of the octave are respectively 8 and 9, and the epic hexameter has seventeen syllables, which equals the sum of these two; and the line scans in the first half with nine syllables, and in the second with eight.i.e., a dactylic hexameter whose sixth foot is always a spondee or trochee has nine syllables in the first three feet and eight in the last three. For τὸ δεξιόν meaning the first part of a metrical system see Bassett,Journal of Classical Philology 11.458-460.

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And they point out that the interval from α to ω in the alphabet is equal to that from the lowest note of a flute to the highest, whose number is equal to that of the whole system of the universe.Alexander suggests that the number 24 may have been made up of the 12 signs of the zodiac, the 8 spheres (fixed stars, five planets, sun and moon) and 4 elements. We must realize that no one would find any difficulty either in discovering or in stating such correspondences as these in the realm of eternal things, since they occur even among perishable things.

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As for the celebrated characteristics of number, and their contraries, and in general the mathematical properties, in the sense that some describe them and make them out to be causes of the natural world, it would seem that if we examine them along these lines, they disappear; for not one of them is a cause in any of the senses which we distinguished with until respect to the first Principles.Cf. Aristot. Met. 1.3.1, Aristot. Met. 5.1, 2.

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There is a sense, however, in which these thinkers make it clear that goodness is predicable of numbers, and that the odd, the straight, the equal-by-equal,i.e., square. and the powersProbably their power of being represented as regular figures; e.g. the triangularity of 3 or 6. of certain numbers, belong to the series of the Beautiful.Cf. Aristot. Met. 1.5.6. For the seasons are connected with a certain kind of numberi.e., 4.; and the other examples which they adduce from mathematical theorems all have the same force.

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Hence they would seem to be mere coincidences, for they are accidental; but all the examples are appropriate to each other, and they are one by analogy. For there is analogy between all the categories of Being—as straight is in length, so is level in breadth, perhaps odd in number, and white in color.

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Again, it is not the Ideal numbers that are the causes of harmonic relations, etc. (for Ideal numbers, even when they are equal, differ in kind, since their units also differ in kind)Aristotle has argued (Aristot. Met. 13.6-8.) that if the Ideal numbers differ in kind, their units must differ in kind. Hence even equal numbers, being composed of different units, must be different in kind. In point of fact, since each ideal number is unique, no two of them could be equal.; so on this ground at least we need not posit Forms.

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Such, then, are the consequences of the theory, and even more might be adduced. But the mere fact that the Platonists find so much trouble with regard to the generation of Ideal numbers, and can in no way build up a system, would seem to be a proof that the objects of mathematics are not separable from sensible things, as some maintain, and that the first principles are not those which these thinkers assume.

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This pointer pattern extracts book and section.

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This pointer pattern extracts book.

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Between Housecraft (the art of governing a Household or Home) and Statecraft (the art of governing a Nation) there are differences corresponding to those between the two kinds of community over which they severally preside. There is, however, this further difference: that whereas the government of a nation is in many hands, a household has but a single ruler.

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Now some arts are divided into two separate branches, one concerned with the making of an object—for example a lyre or a flute—and the other with its use when made. Statecraft on the other hand shows us how to build up a nation from its beginning, as well as how to order rightly a nation that already exists; from which we infer that Housecraft also tells us first how to acquire a household and then how to conduct its affairs.

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By a Nation we mean an assemblage of houses, lands, and property sufficient to enable the inhabitants to lead a civilized life. This is proved by the fact that when such a life is no longer possible for them, the tie itself which unites them is dissolved. Moreover, it is with such a life in view that the association is originally formed; and the object for which a thing exists and has come into being is in fact the very essence of that particular thing.

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From this definition of a Nation, it is evident that the art of Housecraft is older than that of Statecraft, since the Household, which it creates, is older; being a component part of the Nation created by Statecraft.

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Accordingly we must consider the nature of Housecraft, and what the Household, which it creates, actually is.

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The component parts of a household are (l) human beings, and (2) goods and chattels. And as households are no exception to the rule that the nature of a thing is first studied in its barest and simplest form, we will follow Hesiod and begin by postulatingHomestead first, and a woman; a plough-ox hardy to furrow. For the steading takes precedence among our physical necessities, and the woman among our free associates. It is, therefore, one of the tasks of Homecraft to set in order the relation between man and woman; in other words, to see that it is what it ought to be.

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Of occupations attendant on our goods and chattels, those come first which are natural. Among these precedence is given to the one which cultivates the land; those like mining, which extract wealth from it, take the second place. Agriculture is the most honest of all such occupations; seeing that the wealth it brings is not derived from other men. Herein it is distinguished from trade and the wage-earning employments, which acquire wealth from others by their consent; and from war, which wrings it from them perforce. It is also a natural occupation; since by Nature’s appointment all creatures receive sustenance from their mother, and mankind like the rest from their common mother the earth.

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And besides all this, agriculture contributes notably to the making of a manly character; because, unlike the mechanical arts, it does not cripple and weaken the bodies of those engaged in it, but inures them to exposure and toil and invigorates them to face the perils of war. For the farmer’s possessions, unlike those of other men, lie outside the city’s defences.

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When we turn our attention to the human part of the household, it is the woman who makes the first claim upon it; 〈for the natural comes first, as we have said,〉 and nothing is more natural than the tie between female and male. For we have elsewhere laid down the premissCf. Aristot. Pol. 1.1. that Nature is intent on multiplying severally her types; and this is true of every animal in particular. Neither the female, however, can effect this without the male, nor the male without the female; whence the union of the sexes has of necessity arisen.

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Now among the lower animals, this union is irrational in character; it exists merely for the purpose of procreation, and lasts only so long as the parents are occupied in producing their brood. In tame animals, on the other hand, and those which possess a greater share of intelligence, it has assumed a more complex form; for in their case we see more examples of mutual help, goodwill, and co-operation.

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It is, however, in the human species that this complexity is most marked; since the co-operation between woman and man aims not merely at existence, but at a happy existence. Nor do mankind beget children merely to pay the service they owe to Nature, but also that they may themselves receive a benefit; for the toil they undergo while they are strong and their offspring is still weak is repaid by that offspring when it in turn is grown strong and the parents by reason of age are weak.

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At the same time Nature, by this cycle of changes, fulfills her purpose of perpetuating existence; preserving the type when she is unable to preserve the individual.Cf. Aristot. De Gen. An. 731b. And so with this purpose in view Divine Providence has fashioned the nature of man and of woman for their partnership. For they are distinguished from each other by the possession of faculties not adapted in every case to the same tasks, but in some cases for opposite ones, though contributing to the same end. For Providence made man stronger and woman weaker, so that he in virtue of his manly prowess may be more ready to defend the home, and she, by reason of her timid nature, more ready to keep watch over it; and while he brings in fresh supplies from without, she may keep safe what lies within. In handicrafts again, woman was given a sedentary patience, though denied stamina for endurance of exposure; while man, though inferior to her in quiet employments, is endowed with vigor for every active occupation. In the production of children both share alike; but each makes a different contribution to their upbringing. It is the mother who nurtures, and the father who educates.

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We begin then with the rules that should govern a man’s treatment of his wife. And the first of these forbids him to do her wrong; for if he observes this, he is not likely himself to suffer wrong at her hands. As the Pythagoreans declare, even the common rule or custom of mankind thus ordains, forbidding all wrong to a wife as stringently as though she were a suppliant whom one has raised from the hearthstone. And a man does wrong to his wife when he associates with other women.

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As regards the intercourse of marriage, wives should neither importune their husbands, nor be restless in their absence; but a man should accustom his wife to be content whether he is at home or away. Good also is the advice of Hesiod: Take thee a maiden to wife, and teach her ways of discretion. Hes. WD 699 For differences of ways and habits are little conducive to affection.

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As regards adornment: it is not well that souls should approach one another in borrowed plumes, nor is it well in the case of bodies. Intercourse which depends 〈for its charm〉 upon outward adornment differs in no respect from that of figures on the stage in their conventional attire.

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Of property, the first and most indispensable kind is that which is also best and most amenable to Housecraft; and this is the human chattel. Our first step therefore must be to procure good slaves. Of slaves there are two kinds; those in positions of trust, and the laborers. And since it is matter of experience that the character of the young can be moulded by training, when we require to charge slaves with tasks befitting the free, we have not only to procure the slaves, but to bring them up 〈for the trust〉.

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In our intercourse with slaves we must neither suffer them to be insolent nor treat them with cruelty. A share of honor should be given to those who are doing more of a freeman’s work, and abundance of food to those who are laboring with their hands. And whereas the use of wine renders even free men insolent, so that in many countries they too refrain from it—as, for instance, the Carthaginians do when they are on campaign—it follows that we must either deny wine to slaves altogether, or reserve it for rare occasions.

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We may apportion to our slaves (1) work, (2) chastisement, and (3) food. If men are given food, but no chastisement nor any work, they become insolent. If they are made to work, and are chastised, but stinted of their food, such treatment is oppressive, and saps their strength. The remaining alternative, therefore, is to give them work, and a sufficiency of food. Unless we pay men, we cannot control them; and food is a slave’s pay.

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Slaves, again, are no exception to the rule that men become worse when better conduct is not followed by better treatment, but virtue and vice remain alike unrewarded.

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Accordingly we must keep watch over our workers, suiting our dispensations and indulgences to their desert; whether it be food or clothing, leisure or chastisement that we are apportioning. Both in theory and in practice we must take for our model a physician’s freedom in prescribing his medicines; observing at the same time that food differs from medicine in that it requires to be constantly administered.

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The best laborers will be furnished by those races of mankind which are neither wholly spiritless nor yet overbold. Each extreme has its vice; the spiritless cannot endure hard labor, and the high-spirited will not readily brook control.

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Every slave should have before his eyes a definite goal or term of his labor. To set the prize of freedom before him is both just and expedient; since having a prize to work for, and a time defined for its attainment, he will put his heart into his labors. We should, moreover, take hostages 〈for our slaves’ fidelity〉 by allowing them to beget children; and avoid the practice of purchasing many slaves of the same nationality, as men avoid doing in towns. We should also keep festivals and give treats, more on the slaves account than on that of the freemen; since the free have a fuller share in those enjoyments for the sake of which these institutions exist.

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There are four qualities which the head of a household must possess in dealing with his property. Firstly, he must have the faculty of acquiring, and secondly that of preserving what he has acquired; otherwise there is no more benefit in acquiring than in baling with a colander, or in the proverbial wine-jar with a hole in the bottom. Thirdly and fourthly, he must know how to improve his property, and how to make use of it; since these are the ends for which the powers of acquisition and of preservation are sought.

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Everything we possess should be duly classified ; and the amount of our productive property exceed that of the unproductive. Produce should be so employed that we do not risk all our possessions at once. For the safe keeping of our property, we shall do well to adopt the Persian and Laconian systems. Athenian housecraft has, however, some advantages. The Athenian buys immediately with the produce of his sales, and the smaller households keep no idle deposits in store.

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Under the Persian system, the master himself undertook the entire disposition and supervision of the household, following the practice which Dion used to remark in Dionysius. No one, indeed, takes the same care of another’s property as of his own; so that, as far as is possible, each man ought to attend to his affairs in person. We may commend also a pair of sayings, one attributed to a Persian and the other to a Libyan. The former on being asked what best conditions a horse, repliedHis master’s eye.Cf. Xen. Ec. 12. The Libyan, when asked what kind of manure is best, answeredThe master’s footprints.

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The master and mistress should, therefore, give personal supervision, each to his or her special department of the household work. In small households, an occasional inspection will suffice; in estates managed through stewards, inspections must be frequent. For in stewardship as in other matters there can be no good copy without a good example; and if the master and mistress do not attend diligently to their estate, their deputies will certainly not do so.

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Moreover, as such habits are both commendable for moral reasons and also conducive to good management, the master and mistress will do well to rise earlier than their servants and to retire later; to treat their home as a city, and never leave it unguarded; nor ever, by night or by day, to postpone a task which ought to be done. Rising before daylight is also to be commended; it is a healthy habit, and gives more time for the management of the household as well as for liberal studies.

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We have remarked that on small holdings the Athenian method of disposing of the produce is advantageous. On large estates, after the amount for the year’s or the month’s outlay has been set apart, it should be handed to the overseers; and so also with implements, whether for daily or for occasional use. In addition, an inspection of implements and stores should be made periodically, so that remainders and deficiencies may alike be noted.

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In constructing a homestead, we have to provide for the stock which it is to shelter, and for its health and well-being. Providing for the stock involves questions such as these: What type of building is best for the storage of crops and of clothing? How are we to store the dry crops, and how the moist ones? Of the other stock, how is the living to be housed, and how the dead? and what accommodation are we to make for slaves and free, for women and men, for foreigners and fellow-citizens? For well-being and health, again, the homestead should be airy in summer, and sunny in winter.

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A homestead possessing these qualities would be longer than it is deep; and its main front would face the south. On large estates, moreover, it seems worth while to instal as porter a man incapable of other work, to keep his eye on what passes in and out. That implements may be ready for use, the Laconian practice should be followed. Each should be kept in its own place; thus it will always be to hand, and not require seeking.

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Right administration of a household demands in the first place familiarity with the sphere of one’s actionOr,the localities wherein we work.; in the second Place, good natural endowments; and in the third, an uprights and industrious way of life. For the lack of any one of these qualifications will involve many a failure in the task one takes in hand.

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Of such administrations there are four main types, under which all others may be classified. We have the administration of a king; of the governors under him; of a free state; and of a private citizen.

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Of these, that of a king is the most extensive, yet at the same time the simplest. A governor’s office is also very extensive, but divided into a great variety of departments. The administration of a free state is again very varied, but it is the easiest to conduct; while that, of a private individual presents the like variety, but within limits which are narrowest of all. For the most part, all four will of necessity cover the same ground; we will, however, take them in turn, and see what is especially characteristic of each.

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Taking first the royal administration, we see that while theoretically its power is unlimited, it is in practice concerned with four departments, namely currency, exports, imports, and expenditure.

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Taking these severally, I assign to that of currency the seasonable regulation of prices; to imports and exports, the profitable disposition, at any given time, of the dues received from provincial governors; and to expenditure, the reduction of outgoings as occasion may serve, and the question of meeting expenses by currency or by commodities.

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The second kind of administration, that of the governor, is concerned with six different classes of revenue; those, namely, arising from agriculture, from the special products of the country, from markets, from taxes, from cattle, and from other sources.

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Taking these in turn, the first and most important of them is revenue from agriculture, which some call tithe and some produce-tax.Boeckh translates ἐκφόριονGrundsteuer. But how then does it differ from τῶν κατὰ γῆν τελῶν below? The second is that from special products; in one place gold, in another silver, in another copper, and so on. Third in importance is revenue from markets, and fourth that which arises from taxes on land and on sales. In the fifth place we have revenue from cattle, called tithe or first-fruits; and in the sixth, revenue from other sources, which we term poll-tax, or tax on industry.

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Of our third kind of administration, that of a free state, the most important revenue is that arising from the special products of the country. Next follows revenue from markets and occupations; and finally that from every-day transactions.Or (understanding λειτουργιῶν)regular public services.

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Fourthly and lastly, we must consider the administration of a private citizen. It is difficult to reduce this to rules owing to the necessary variety of its aims; yet it is the most limited of the four, because both revenues and expenses are 〈comparatively〉 small. Taking its revenues in turn, the chief are those from agriculture; next in importance, those from other every-day occupations; while third comes interest on money. Apart from all these, there is a matter common to all kinds of administration which is best considered at this particular point, and deserves more than cursory attention. This is the importance of keeping expenditure within the limits of revenue.

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Having thus enumerated the divisions of our subject, we must next consider whether the province or the free state with which we are concerned is able to produce all the forms of revenue we have just detailed or at least the chief of them; 〈and this being known〉 must make the best use of what we have. Next we must inquire what kinds of revenue, at present wholly lacking, are yet potentially existent; what kinds, though now small, may with care be increased, and how far certain items of present expenditure may without prejudice to the commonwealth be diminished.

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Having spoken thus of administrations and their various departments, we have further proceeded to collect such instances as we deemed noteworthy of the means adopted by certain statesmen in times past for the replenishment of the treasury, and also of their skill in administration. These anecdotes 〈which follow〉, seemed to us by no means lacking in utility; being capable from time to time of application by others to the business they themselves have in hand.

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Cypselus of Corinth had made a vow that if he became master of the city, he would offer to Zeus the entire property of the Corinthians. Accordingly he commanded them to make a return of their possessions; which done, he took from each a tenth part, and told them to employ the remainder in trading. A year later, he repeated the process. And so in ten years’ time it came to pass that Cypselus received the entire amount which he had dedicated; while the Corinthians on their part had replaced all that they had paid him.

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Lygdamis of Naxos, after driving into exile a party of the inhabitants, found that no one would give him a fair price for their property. He therefore sold it to the exiled owners. The exiles had left behind them a number of works of art destined for temple offerings, which lay in certain workshops in an unfinished condition. These Lygdamis proceeded to sell to the exiles and whoso else would buy them; allowing each purchaser to have his name engraved on the offering.

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The people of Byzantium, being in need of funds, sold such dedicated lands as belonged to the State; those under crops, for a term of years, and those uncultivated, in perpetuity. In like manner they sold lands appropriated to religious celebrations or ancestral cults, not excepting those that were on private estatesSee Lys. 7, the seventh Speech of the Athenian orator Lysias.; for the owners of the surrounding land were ready to give a high price for them. To the dispossessed celebrants 〈they assigned〉 such other public lands surrounding the gymnasium, the agora, or the harbor, as belonged to the State. Moreover they claimed as public property all open spaces where anything was sold, together with the sea-fisheries, the traffic in salt, and the trade of professional conjurors, soothsayers, charm-sellers, and the like; exacting from all these one-third of their gains. The right of changing money they sold to a single bank, whose proprietor was given a monopoly of the sale and purchase of coin, protected under penalty of confiscation.

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And whereas previously the rights of citizenship were by law confined to those whose parents were both citizens, lack of funds, induced them to offer citizenship to him who had one citizen parent on payment of the sum of thirty minae.A mina of silver (1 lb. 5 oz. avoirdupois) was coined into 100 drachmae, each being an artisan’s ordinary daily wage.

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On another occasion, when food and funds were both scarce, they called home all vessels that were trading in the Pontus. On the merchants protesting, they were at length allowed to trade on payment of a tithe of their profits. This tax of 10 per cent was also extended to purchases of every kind.

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It happened that certain aliens residing in the city had lent money on the security of citizens’ property. As these aliens did not possess the right of holding such property, the people offered to recognize the title of anyone who chose to pay into the treasury one third of the amount secured.

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Hippias of Athens offered for sale upper stories that projected over the public streets,Cf. Goethe,Warheit und Dichtung, Book I.In Frankfurt, as in several ancient cities, those who had erected wooden buildings had sought to obtain more room by allowing the first and higher floors to overhang in the street. . . . At last a law was carried that in all entirely new houses the first floor alone should project; above that, the wall should be perpendicular. The poet’s father, wishing to rebuild his house without sacrifice of floor-space, underpinned the upper stories and renewed the building piecemeal from below. Cf. also 14. together with flights of steps, railings, and doors that opened outwards. The owners of the buildings bought them, and in this way a large sum of money was collected.

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He also called inLit.rendered invalid. the existing currency, promising to pay the holders at a fixed rate. But when they came to receive the new mintage, he reissued the old coins.

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Those who were expecting to equip a war-vessel or preside over a tribe or train a chorus or undertake the expense of some other public service of the kind, he allowed, if they chose, to commute the service for a moderate sum, and to be enrolled on the list of those who had performed it.

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Moreover, whenever a citizen died, the priestess of the temple of Athena on the AcropolisThis was the public treasury, like the Temple of Saturnus at Rome. was to receive one quart measure of barley, one of wheat, and a silver obolus.1/6 of the drachma. See 3 above. And when a child was born, the father paid the same dues.

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The Athenian colonists at Potidaea, being in need of funds for the war, agreed that all should make a return of their property for assessment of tax. But instead of each returning the entire amount to his own parish, properties were to be assessed separately, each in its own locality, so that the poor might propose a reduced assessment; while those without any 〈landed〉 property were assessed at two minae a head. On these assessments each man paid the State the full amount of the war-tax.

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The city of Antissa had been accustomed to celebrate the festival of Dionysus with great magnificence. Year by yearOrAll through the year. great provision was made for the occasion, and costly sacrifices were prepared. Now one year the city found itself in need of funds; and shortly before the festival, on the proposal of a citizen named Sosipolis, the people after vowing that they would next year offer to Dionysus a double amount, collected all that had been provided and sold it. In this way they realized a large sum of money to meet their necessity.

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On one occasion the people of Lampsacus were expecting to be attacked by a large fleet of triremes.War-ships, each propelled by some 174 rowers ranked in three tiers. The price of barley meal being then four drachmae for a bushel and a half, they instructed the retailers to sell it at six drachmae. Oil, which was at three drachmae for six pints, was to be sold at four drachmae and a half, and wine and other commodities at a proportionate increase. In this way the retailer got the original price, while the State took the addition and filled its treasury.

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The people of Heraclea, being about to dispatch a fleet of forty ships against the lords of Bosporus, were at a loss for the necessary funds. They therefore bought up all the merchants’ stock of corn and oil and wine and other marketable commodities, agreeing to pay at a future date. The merchants were well satisfied that they had disposed of their cargoes without breaking bulk; and the people, advancing two months’ pay to their armament, sent along with it a fleet of merchant-vessels laden with the commodities, every ship being in charge of a public official. When the expedition reached its goal, the men purchased from these officials all they needed. In this way, the money was collected before the leaders again paid their men; so that the same payment sufficed until the expedition returned home.

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When the Samians entreated the Lacedaemonians for money to enable them to return to their country, the Lacedaemonians passed a resolution that they and their servants and their beasts of burden should go without food for one day; and that the expense each one thus saved should be given to the Samians.

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The people of Chalcedon had a large number of mercenary troops in their city, to whom they could not pay the wages they owed. Accordingly they made proclamation that anyone, either citizen or alien, who had right of reprisal against any city or individual, and wished to exercise it, should have his name entered on a list. A large number of names was enrolled, and the people thus obtained a specious pretext for exercising reprisal upon ships that were passing on their way to the Pontus. They accordingly arrested the ships and fixed a period within which they would consider any claims that might be made in respect of them. Having now a large fund in hand, they paid off the mercenaries, and set up a tribunal to decide the claims; and those whose goods had been unjustly seized were compensated out of the revenues of the state.

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At Cyzicus, civil strife broke out between the democratic and oligarchic parties. The former proved victorious, and the rich citizens were placed under arrest. But as the city owed money to its troops, a resolution was passed that the lives of those under arrest should be spared, and that they should be allowed to depart into exile on paying a sum of money to the state.

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At Chios there was a law that all debts should be entered on a public register. Being in need of funds, the people resolved that debtors should pay their debts into the treasury, and that the state should meet the creditors’ interest out of its revenues until its former prosperity returned.

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Mausolus lord of Caria received from the King of PersiaProbably Artaxerxes II. who reigned 405-359 B.C. a demand for tribute. Therefore he summoned the wealthiest men in his dominion, and told them that the King was asking for the tribute, and he had not the means of paying it. Men whom he had previously suborned at once came forward and declared what each was ready to contribute. With this example before them, they who were wealthier than these, partly in shame and partly in alarm, promised and paid much larger sums than the others.

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Being again in lack of funds, Mausolus summoned a public meeting of the people of Mylassa and told them that the King of Persia was preparing to attack him; and that Mylassa his capital city was unfortified. He therefore bade the citizens contribute each as liberally as he could, saying that what they now paid in would afford security to the rest of their possessions. By these means he obtained large contributions. But though he kept the money, he declared that heaven, for the present, forbade the building of the walls.

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Condalus, who was a lieutenant-governor under Mausolus, whenever on his progress through the country he was presented with a sheep, a pig, or a calf, had a record made of the donor’s name and of the date. He then bade the man take the beast home and keep it until he should again pass that way. After what he considered a sufficient interval, he would demand the beast together with such profits as he reckoned it had produced. All trees, too, which projected over the king’s highway, or fell thereon, he sold as profits accruing to the State.

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When one of his soldiers died, he charged a drachma for the right of passing the body through the gates. This was not only a source of revenue, but a check on the commanders, who were thus prevented from falsifying the date of the man’s death.

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Noticing that the Lycians were fond of wearing their hair long, Condalus proclaimed that a dispatch had arrived from the King ordering him to send hair to make forelocks for his horses; and that Mausolus had therefore instructed him to shave their heads. However, if they would pay him a fixed sum per head, he would send to Greece for hair. They were glad to comply with his demand, and a large sum was collected, the number of those taxed being great.

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Aristoteles of Rhodes,Mentioned by Proclus in his commentary on the Timaeus of Plato. A coin of Phocaea is extant bearing the name. when governor of Phocaea, found himself in need of funds. Noticing that there were at Phocaea two opposing parties, he held a secret conference with one of them, at which he declared that the other party was offering him money if he would favor their pretensions; that he, however, preferred to receive from those now before him, and to entrust to them the administration of the city. On hearing this, they immediately contributed the money he asked, and gave it him. Thereupon he told the other party what he had received from them; and they in turn promised him at least an equal amount. Having thus taken the money of both factions, he effected a reconciliation between them.

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He also observed that there were many law-suits pending between the citizens, and that they had grave and long-standing plaints against one another which had arisen in course of war. He therefore appointed a tribunal, and made proclamation that all who failed to appear before it within a stated period should lose the right to a legal decision of their outstanding claims. Then, by taking into his own hands the court-fees for a number of suits, and also those appeal-cases which involved penalties, and receiving [through others] money from both sides, he obtained altogether a very considerable sum.

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The people of Clazomenae, suffering from dearth of grain and scarcity of funds, passed a resolution that any private citizens who had stores of oil should lend it to the State at interest; this being a produce which their land bears in abundance. The loan arranged, they hired vessels and sent them to the depots whence they obtained their grain, 〈and bought a consignment〉 on security of the value of the oil.

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The same people, owing their mercenaries twenty talents of pay and being unable to find it, were giving the leaders of the troop four talents of interest each year. But failing to reduce the capital debt, and committed to this fruitless drain on their revenue, they struck an iron coinage of twenty talents, bearing the face-value of the silver. This they distributed proportionately among the wealthiest citizens, and received from them silver to the same amount. Through this expedient, the private citizens possessed a currency which was good for their daily needs, and the state was relieved of its debt. Next, they proceeded to pay interest out of revenue to those who had advanced the silver; and little by little distributed repayment among them, recalling at the same time the currency of iron.Plut. Lycurgus speaks of an iron currency at Sparta, and Seneca De beneficiis of a leather one. These, not being exchangeable abroad, threw the nation upon its own resources and prevented the import of luxuries.

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The people of Selybria had a law, passed in time of famine, which forbade the export of grain. On one occasion, however, they were in need of funds; and as they possessed large stores of grain, they passed a resolution that citizens should deliver up their corn to the state at the regular fixed price, each retaining for himself a year’s supply. They then granted right of export to any who desired it, fixing what they deemed a suitable price.

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At Abydos civil strife had caused the land to remain uncultivated; while the resident aliens, to whom the city was already indebted, refused to make any further advances. A resolution was accordingly passed that anyone who would might lend money to enable the farmers to cultivate their land, on the understanding that the lender had the first claim on its produce; others taking from what was then left.

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The people of Ephesus, being in need of funds, passed a law forbidding their women to wear gold, and ordering them to lend the State what gold they had in their possession.

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They also offered to any citizen who was willing to pay a fixed sum the right of having his name inscribed on a certain pillar of their templeThis temple, dedicated to Artemis, was restored with great magnificence after its destruction by fire in 356 B.C. For its fame see Acts 19. Portions of the sculptured pillars are to be seen in the British Museum. as the donor thereof.

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Dionysius of Syracuse, being desirous of collecting funds, called a public assembly, and declared that Demeter had appeared to him, and bade him convey all the women’s ornaments into her temple. That he himself had done so with the ornaments of his own household; and the others must now follow his example, and thereby avoid any visitation of the goddess’s anger. Anyone who failed to comply would, he declared, be guilty of sacrilege. Through fear of the goddess as well as of the despot, all the citizens brought in whatever they had. Then Dionysius, after sacrificing to the goddess, removed the ornaments to his own treasury as a loan which he had borrowed from her. As time went on, the women again appeared with precious ornaments. Dionysius thereupon issued a decree that any woman who desired to wear gold should make an offering of a fixed amount in the temple.

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Intending to build a fleet of triremes, Dionysius knew that he should require funds for the purpose. He therefore called an assembly and declared that a certain city was offered to him by traitors, and he needed money to pay them. The citizens therefore must contribute two staters apiece.The stater was a Persian gold coin worth 20 drachmae. (See 3.) The money was paid; but after two or three days, Dionysius, pretending that the plot had failed, thanked the citizens and returned to each his contribution. In this way he won the confidence of the citizens; so that when he again asked for money, they contributed in the expectation that they would receive it back. But this time he kept it for building the fleet.

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On another occasion being in straits for silver he minted a coinage of tin, and summoning a public assembly, spoke at length in its favor. The citizens perforce voted that everyone should regard as silver, and not as tin, whatever he received.

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Again being in need of funds, he requested the citizens to contribute. On their declaring that they had not the wherewithal, he brought out the furnishings of his palace and offered them for sale, pretending to be compelled through lack of money. At the sale, he had a list made of the articles and their purchasers; and when they had all paid, he commanded every one to bring back the article he had bought.

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Finding that because of his imposts the citizens were ceasing to rear sheep and cattle, he made proclamation that he needed no more money until a certain 〈date〉; so that those who now became possessed of any stock would not be liable to taxation. A large number of citizens lost no time in acquiring a quantity of sheep and cattle, on the understanding that they would be free of impost. But Dionysius, when he thought the fitting time was come, had them all valued and imposed a tax. The citizens were angry at being thus deceived, and proceeded to kill and sell their beasts. On Dionysius’s making a decree that only such beasts should be slain as were needed each day, the owners retorted by offering their animals as sacrifices; whereupon the despot forbade the sacrifice of female beasts.

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Once more funds were lacking, and Dionysius ordered a list to be made for him of all houses whose heirs were orphan. Having obtained a complete list, he made use of the orphans’ property until each should come of age.

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After the capture of Rhegium, he summoned a meeting of the citizens, and told them why he had a good right to sell them as slaves. If, however, they would pay him the expenses of the war and three minaeSee 3. a head besides, he would release them. The people of Rhegium brought forth all their hoards; the poor borrowed from the wealthier and from the foreigners resident in the city; and so the amount demanded was paid. But though he received this money from them, none the less he sold them all for slaves, having succeeded 〈by his trick〉 in bringing to light the hoarded goods which they had previously concealed.

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On another occasion he had borrowed money from the citizens, promising to repay it. On their demanding its return, he bade each bring him, under pain of death, whatever silver he possessed. This silver when brought he coined into drachmae each bearing the face value of two: with these he repaid the 〈previous〉 debt and also what had just been brought in.

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He also made a raid on Tyrrhenia with a hundred ships, and rifled the temple of Leucothea of a large amount of gold and silver, besides a quantity of works of art. But being aware that his sailors too had taken much plunder, he made proclamation that each should bring him, under pain of death, one-half of what he had; the remainder of their takings they might keep. On the understanding that if they brought in half their plunder they would retain the rest in security, they obeyed. But when Dionysius had got the treasure into his hands, he commanded them to bring him the other half as well.

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The people of Mende used to meet the expenses of administration from harbor and other duties, but refrained from collecting the imposts on land and on houses. They kept, however, a register of the owners, and when the state was in need of funds, they collected the arrears. Meanwhile the owners had the advantage of trafficking with their whole property undiminished by any payment of percentages.

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The same city being at war with Olynthus and needing funds, passed a resolution that all the slaves they possessed, with the exception of one male and one female apiece, should be sold on behalf of the State, which was thus enabled to raise a loan from private citizens.Or:that citizens should sell to the state what slaves they possessed . . . as the equivalent of a loan from private persons to the city 〈of the slaves’ value〉.

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Callistratus, when in Macedonia, caused the harbor-dues, which were usually sold for twenty talents, to produce twice as much. For noticing that only the wealthier men were accustomed to buy them because the sureties for the twenty talents were obliged to show talent for talent, he issued a proclamation that anyone might buy the dues on furnishing securities for one-third of the amount, or as much more as could be procured in each case.

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Timotheus of Athens during his campaign against Olynthus was short of silver, and issued to his men a copper coinage instead. On their complaining, he told them that all the merchants and retailers would accept it in lieu of silver. But the merchants he instructed to buy in turn with the copper they received such produce of the land as was for sale, as well as any booty brought to them; such copper as remained on their hands he would exchange for silver.

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During the campaign of CorcyraApparently in 375 B.C. See the end of Xenophon’s fifth Book ofHellenicaXen. Hell. 5. this same Timotheus was reduced to sore straits. His men demanded their pay; refused to obey his orders; and declared they would desert to the enemy. Accordingly he summoned a meeting and told them that the stormy weather was delaying the arrival of the silver he expected; meanwhile, as he had on hand such abundance of provisions, he would charge them nothing for the three months’ ration of grain already advanced. The men, unable to believe that Timotheus would have sacrificed so large a sum to them unless he was in truth expecting the money, made no further claim for pay until he had completed his dispositions.

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At the siege of Samos,In 366 B.C. Timotheus sold the crops and other country property to the besieged Samians themselves, and thus obtained plenty of money to pay his men. But finding the camp was short of provisions owing to the arrival of reinforcements, he forbade the sale of milled corn, or of any measure less than 1 1/2 bushels of corn or 8 1/2 gallons of wine or oil. Accordingly the officers bought supplies wholesale and issued them to their men; the reinforcements thenceforth brought their own provisions, and sold any surplus on their departure. In this way the needs of the soldiers were satisfactorily met.

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Didales the Persian was able to provide for the daily needs of his mercenaries from the enemy’s country; but had no coined money to give them. When their pay became due, and they demanded it, he had recourse to the following trick. He called a meeting, and told the men that he had plenty of money, but that it was stored in a certain fortress, which he named. He then broke up his encampment and marched in that direction. On reaching the neighborhood of the fortress, he himself went on ahead, and entering the place seized all the silver vessels in the temples. He then loaded his mules in such a way that this plate was exposed, thus suggesting that silver formed the entire load; and so continued his march. The soldiers, beholding the plate and supposing that they convoyed a full load of silver, were cheered by the expectation of their pay. They were informed however by Didales that they would have to take it to Amisus to be coined—a journey of many days, and in the winter season. And during all this time, he continued to employ the army without giving it more than its necessary rations.

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Moreover, all the craftsmen in the army, and the hucksters who traded with the soldiers by barter, were under his personal control, and enjoyed a complete monopoly.

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When Taos,Called Tachos (Ταχώς) by Xenophon and Plutarch. Perhaps that form should be restored here. (Bonitz and Susemihl.) The name recurs in 37. king of Egypt, needed funds for an expedition he was making, Chabrias of Athens advised him to inform the priests that to save expense it was necessary to suppress some of the temples together with the majority of the attendant priests. On hearing this, each priesthood, being anxious to retain their own temple, offered him money from their private possessions 〈as well as from the temple funds〉. When the king had thus received money from them all, Chabrias bade him tell the priests to spend on the temple-service and on their own maintenance one-tenth of what they formerly spent, and lend him the remainder until he had made peace with the King 〈of Persia〉.

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Moreover, each inhabitant was to contribute a stated proportion of his household and personal possessions; and when grain was sold, buyer and seller were each to contribute, apart from the price, one obol per artabeThe artabe was a Persian measure containing nearly 50 quarts. The obol was 1/6 of a drachma of silver.; while a tax of one tenth was to be imposed on profits arising from ships and workshops and other sources of gain.

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Again, when Taos was on the point of setting out from Egypt, Chabrias advised him to make requisition of all uncoined gold and silver in the possession of the inhabitants; and when most of them complied, he bade the king make use of the bullion, and refer the lenders to the governors of his provinces for compensation out of the taxes.

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Iphicrates of Athens provided Cotys with money for a force which he had collected in the following manner. He bade him order 〈each〉 of his subjects to sow for him a piece of land bearing 4 1/2 bushels. A large quantity of grain was thus gathered, from the price of which, when brought to the depots on the coast, the king obtained as much money as he wanted.

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Cotys of Thrace asked the people of Peirinthus for a loan to enable him to raise an army. On their refusing, he begged them at any rate to let him have some of their citizens to garrison certain fortresses, and release for active service the men who were there on duty. They readily complied, thinking thus to obtain control of the fortresses. But Cotys placed in custody the men they sent, and told the citizens that they might have them back when they had sent him the amount of the loan he desired.

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Mentor of Rhodes, after taking Hermias prisoner and seizing his fortresses, left in their various districts the officials appointed by him. By this means he restored their confidence, so that they all took again to themselves the property they had hidden or had sent secretly out of the country. Then Mentor arrested them and stripped them of all they had.

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Memnon of Rhodes, on making himself master of Lampsacus, found he was in need of funds. He therefore assessed upon the wealthiest inhabitants a quantity of silver, telling them that they should recover it from the other citizens. But when the other citizens made their contributions, Memnon said they must lend him this money also, fixing a certain date for its repayment.

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Again being in need of funds, he asked for a contribution, to be recovered, as he said, from the city revenues. The citizens complied, thinking that they would speedily reimburse themselves. But when the revenue payments came in, he declared that he must have these also, and would repay the lenders subsequently with interest.

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His mercenary troops he requested to forgo six days’ pay and rations each year, on the plea that on those days they were neither on garrison duty nor on the march nor did they incur any expense. (He referred to the days omitted from alternate months.As the moon’s cycle is completed in 29 1/2 days, it was customary to alternatehollow months of 29 days with thefull months of 30 days. Memnon paid his men by the month, but deducted a day’s pay everyhollow month.)

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Moreover, being accustomed previously to issue his men’s rations of corn on the second day of the month, in the first month he postponed the distribution for three days, and in the second month for five; proceeding in this fashion until at length it took place on the last day of the month.

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Charidemus of Oreus, being in occupation of certain fortress-towns in Aeolis, and threatened with an attack by Artabazus,For the circumstances, and a (hostile) account of this commander’s adventures, see Demosthenes,Against AristocratesDem. 23. was in need of money to pay his troops. After their first contributions, the inhabitants declared they had no more to give. Charidemus then issued a proclamation to the town he deemed wealthiest, bidding the inhabitants send away to another fortress all the coin and valuables they possessed, under convoy which he would provide. He himself openly set the example with his own goods, and prevailed on them to comply. But when he had conducted them a little way out of the town, he made an inventory of their goods, took all he wanted, and led them home again.

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He had also issued a proclamation in the cities he governed forbidding anyone to keep arms in his house, under pain of a stated fine. At first, however, he took no care to enforce it, nor did he make any inquisition; so that the people treated his proclamation as nugatory, and made no attempt to get rid of what arms each possessed. Then Charidemus unexpectedly ordered a search to be made from house to house, and exacted the penalty from those who were found in possession of arms.

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A Macedonian named Philoxenus, who was governor of Caria, being in need of funds proclaimed that he intended to celebrate the festival of Dionysus. The wealthiest inhabitants were selected to provide the choruses, and were informed what they were expected to furnish. Noticing their disinclination, Philoxenus sent to them privately and asked what they would give to be relieved of the duty. They told him they were prepared to pay a much larger sum than they expected to spend 〈on the choruses〉 in order to avoid the trouble and the interruption of their business. Philoxenus accepted their offers, and proceeded to enrol a second levy. These also paid; and at last he received what he desired from each company.

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Euaises the Syrian, when governor of Egypt, received information that the local governors were meditating rebellion. He therefore summoned them to the palace and proceeded to hang them all, sending word to their relations that they were in prison. These accordingly made offers, each on behalf of his own kinsman, seeking by payment to secure their release. Euaises agreed to accept a certain sum for each, and when it had been paid returned to the relations the dead body.

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While Cleomenes of Alexandria was governor of Egypt,Cf. Dem. 56:Cleomenes . . . from the time that he received the government, has done immense mischief to your state, and still more to the rest of Greece, by buying up corn for resale and keeping it at his own price ( Kennedy’s translation). at a time when there was some scarcity in the land, but elsewhere a grievous famine, he forbade the export of grain. On the local governors representing that if there were no export of grain they would be unable to pay in their taxes, he allowed the export, but laid a heavy duty on the corn. By this means he obtained a large amount of duty from a small amount of export, and at the same time deprived the officials of their excuse.

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When Cleomenes was making a progress by water through the province where the crocodile is worshipped, one of his servants was carried off. Accordingly, summoning the priests, he told them that he intended to retaliate on the crocodiles for this unprovoked aggression; and gave orders for a battue. The priests, to save the credit of their god, collected all the gold they could, and succeeded in putting an end to the pursuit.

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King Alexander had given Cleomenes command to establish a town near the island of Pharus, and to transfer thither the market hitherto held at Canopus. Sailing therefore to Canopus he informed the priests and the men of property there that he was come to remove them. The priests and residents thereupon contributed money to induce him to leave their market where it was. He took what they offered, and departed; but afterwards returned, when all was ready to build the town, and proceeded to demand an excessive sum; which represented, he said, the difference the change of site would make to him. They however declared themselves unable to pay it, and were accordingly removed.

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On another occasion he sent an agent to make a certain purchase for him. Learning that the agent had made a good bargain, but intended to charge him a high price, he proceeded to inform the man’s associates that he had been told he had purchased the goods at an excessive price, and that therefore he did not intend to recognize the transaction; denouncing at the same time with feigned anger the fellow’s stupidity. They on hearing this asked him not to believe what was said against the agent until he himself arrived and rendered his account. On the man’s arrival, his associates told him what Cleomenes had said. He, desirous of winning their approval as well as that of Cleomenes, debited the latter with the actual price he had given.

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At a time when the price of grain in Egypt was ten drachmae 〈a measure〉 ,If the measure intended is the Attic medimnos , it is 1 1/2 bushels. The Persian artabe may however be meant, which was equal to 1 medimnos and 1/16th. In either case the price is very high compared with 3 drachmae per medimnos, the price at Athens in 390 B.C. Yet Polybius 9.44 says that at Rome during the war with Hannibal (210) corn was sold for fifteen drachmae per medimnos. As a contrast cf. what the same author says of the fertility of Gallia Cisalpina, where in time of peace this same measure of wheat was sold for four obols, and of barley for two. See note on 25. Cleomenes sent for the growers and asked them at what price they would contract to supply him with their produce. On their quoting a price lower than what they were charging the merchants, he offered them the full price they were accustomed to receive from others; and taking over the entire supply, sold it at a fixed rate of thirty-two drachmae 〈for the same measure〉.

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He also sent for the priests, and told them that the expenditure on the temples was very unevenly distributed in the country; and that some of these, together with the majority of the attendant priests, must accordingly be suppressed. The priests, supposing him to be in earnest, and wishing each to secure the continuance of his own temple and office, gave him money individually from their private possessions as well as collectively from the temple funds.Cf. 25.

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Antimenes of Rhodes, who was appointed by Alexander superintendent of highways in the province of Babylon, adopted the following means of raising funds. An ancient law of the country imposed a tax of one-tenth on all imports; but this had fallen into total abeyance. Antimenes kept a watch for all governors and soldiers whose arrival was expected, and upon the many ambassadors and craftsmen who were invited to the city, but brought with them others who dwelt there unofficially; and also upon the multitude of presents that were brought 〈to these persons〉 , on which he exacted the legal tax of a tenth.

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Another expedient was this. He invited the owners of any slaves in the camp to register them at whatever value they desired, undertaking at the same time to pay him eight drachmae a year. If the slave ran away, the owner was to recover the registered value. Many slaves were thus registered, and a large sum of money was paid 〈in premiums〉. And when a slave ran away, Antimenes instructed the governor of the 〈province〉 where the camp lay either to recover the man or to pay his master his value.

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Ophellas of Olynthus appointed an officer to superintend the revenues of the Province of Athribis. The local governors came to him, and told him they were willing to pay a much larger amount in taxes; but asked him to remove the present superintendent. Ophellas inquired if they were really able to pay what they promised; and on their assuring him that they were, left the superintendent in office and instructed him to demand from them the amount of tax which they themselves had assessed. And so, without being chargeable either with discountenancing the officer he had appointed, or with taxing the governors beyond their own estimate, he obtained from the latter many times his previous revenue.

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Pythocles the Athenian recommended his fellow-countrymen that the State should take over from private citizens the lead obtained from the mines of LauriumThese silver mines were state property; but mining rights therein were let to private citizens. Lead and silver were found in the same ore and had to be separated. The weight of the lead is not specified: it may have been a talent of 80 lbs. See Boeckh, Staatshaushaltung der Athener; and Xen. Ways. at the price of two drachmae 〈per talent〉 which they were asking, and should itself sell it at the fixed price of six drachmae.

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Chabrias had levied crews for a hundred and twenty ships to serve King Taos.See 25. Finding that Taos needed only sixty ships, he gave the crews of the superfluous sixty their choice between providing those who were to serve with two months’ rations, and themselves taking their place. Desiring to remain at their business, they gave what he demanded.

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Antimenes bade the governors of the provinces replenish, in accordance with the law of the country, the magazines along the royal highways. Whenever an army passed through the country or any other body of men unaccompanied by the king, he sent an officer to sell them the contents of the magazines.

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Cleomenes, as the beginning of the month approached when his soldiers’ allowance became due, deliberately sailed away down the river; and not till the month was advanced did he return and distribute the allowance. For the coming month, he omitted the distribution altogether until the following month began. Thus the men were quieted by the recent distribution, and Cleomenes, passing over a month each year, docked his troops of a month’s pay.σιταρχία (corn allowance) and μισθός (pay) here seem to be identified; possibly because in a land where grain was readily purchasable the former was given in money. Cf. 23, 29.

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Stabelbius, king of the Mysians, lacking pay to give his troops, summoned a meeting of the officers, and declared that he no longer needed the private soldiers, but only the officers. When he required troops, he would entrust a sum of money to each officer and send him to collect mercenaries; but that meanwhile he preferred to give the officers the pay he would otherwise have to give the men. Accordingly he bade each dismiss the men who were on his own muster-roll. The officers, scenting a source of gain for themselves, dismissed their men, as they were bidden. Shortly afterwards, Stabelbius called them together and informed them that a conductor without his chorus and an officer without his men were alike useless; wherefore let them depart from his country.

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When Dionysius was making a tour of the temples, wherever he saw a gold or silver table set, he bade them fill a cupin honor of the good spirit,Cf. Cic. De natura deorum 3.3.4 and Athenaeus Deipnosophistae 15.693. and then had the table carried away. Wherever, again, he saw a precious bowl set before one of the images, he would order its removal, with the words I accept it. He also stripped the images of their golden raiment and garlands, and declaring he would give them lighter and more fragrant wear, arrayed them in robes of white 〈linen〉 and garlands of white socks.

- - - From 7eb4ee8652734af1cf0f572ced6889e1ccd8fd90 Mon Sep 17 00:00:00 2001 From: lcerrato Date: Mon, 13 May 2024 15:59:19 -0400 Subject: [PATCH 4/6] (grc_conversation) tlg0086 translation work continues #1399 --- data/tlg0086/tlg034/__cts__.xml | 10 +- .../tlg034/tlg0086.tlg034.perseus-eng1.xml | 2188 ++++------------- .../tlg034/tlg0086.tlg034.perseus-eng2.xml | 538 ++++ manifest.txt | 21 + 4 files changed, 1060 insertions(+), 1697 deletions(-) create mode 100644 data/tlg0086/tlg034/tlg0086.tlg034.perseus-eng2.xml diff --git a/data/tlg0086/tlg034/__cts__.xml b/data/tlg0086/tlg034/__cts__.xml index 770dd4d24..476843005 100644 --- a/data/tlg0086/tlg034/__cts__.xml +++ b/data/tlg0086/tlg034/__cts__.xml @@ -8,11 +8,15 @@ Aristotle. Aristotelis Opera, Vol. 11. Bekker, Immanuel, editor. Oxford: Oxford University Press, 1837. + + Poetics + Aristotle. The Poetics. "Longinus," On the sublime. Demetrius, On Style. Fyfe, William Hamilton, translator. London: William Heinemann Ltd.; Cambridge, MA: Harvard University Press, 1939 (printing). + + + Ars Poetica (Arabic) -Arisṭūṭālīs: Fann al-šiʿr, maʿa l-tarǧamah al-ʿarabīyah - al-qadīmah wa-šurūḥ al-Fārābī wa-Ibn Sīnā wa-Ibn Rušd. ed. ʿAbd al-Raḥmān - Badawī. Cairo, Maktabat al-nahḍah al-miṣrīyah, 1953. +Arisṭūṭālīs: Fann al-šiʿr, maʿa l-tarǧamah al-ʿarabīyah al-qadīmah wa-šurūḥ al-Fārābī wa-Ibn Sīnā wa-Ibn Rušd. ed. ʿAbd al-Raḥmān Badawī. Cairo, Maktabat al-nahḍah al-miṣrīyah, 1953. diff --git a/data/tlg0086/tlg034/tlg0086.tlg034.perseus-eng1.xml b/data/tlg0086/tlg034/tlg0086.tlg034.perseus-eng1.xml index 70aa7ca47..e4977a92f 100644 --- a/data/tlg0086/tlg034/tlg0086.tlg034.perseus-eng1.xml +++ b/data/tlg0086/tlg034/tlg0086.tlg034.perseus-eng1.xml @@ -1,17 +1,12 @@ - - - -%PersProse; -]> - - - + + + + - Poetics (English). Machine readable text + Poetics Aristotle - + William Hamilton Fyfe Perseus Project, Tufts University Gregory Crane @@ -23,1716 +18,521 @@ The Annenberg CPB/Project - About 146Kb + Trustees of Tufts University Medford, MA - Perseus Project - - - Text was scanned at St. Olaf Spring, 1992. - + Perseus Digital Library Project + Perseus 2.0 + tlg0086.tlg034.perseus-eng2.xml + + Available under a Creative Commons Attribution-ShareAlike 4.0 International License + + + Aristotle - Aristotle in 23 Volumes, Vol. 23, translated by W.H. Fyfe. + Aristotle, The Poetics. "Longinus," On the sublime. Demetrius, On Style + William Hamilton Fyfe - Cambridge, MA, Harvard University Press; London, William - Heinemann Ltd. - 1932 + William Heinemann Ltd. + London + Harvard University Press + Cambridge, MA + 1939 + + + Loeb Classical Library + + HathiTrust - + + + - - + + + +

This pointer pattern extracts chapter and subchapter.

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This pointer pattern extracts chapter.

+ + - English - Greek + English + Greek + - - May, 1993 - - wpm - (n/a) - - Tagged in conformance with Prose.e dtd. - - - July 27, 1993 - - em - (n/a) - - Put Bekker line 1 milestone tags at the beginning of each section so that the - incoming list creator would work. Changed RREFDECL. - - - 1/1999 - - lmc - (n/a) - - Corrected two typos in 1449a. - - - 5/27/09 - - RS - (n/a) - - -$Log: aristot.poet_eng.xml,v $ -Revision 1.3 2010-12-14 16:47:30 lcerrato -fixed three typos based on user report - -Revision 1.2 2010/06/16 19:18:48 rsingh04 -cleaned up bad place tags in a few texts and cleaned up the document format - -Revision 1.1 2009/10/09 19:49:17 rsingh04 -more reorganizing of texts module by collection + EpiDoc and CTS conversion and general header review. + fixed three typos based on user report + cleaned up bad place tags in a few texts and cleaned up the document format + more reorganizing of texts module by collection + began reorganizing texts module by collection. created separate work directory in texts module to keep hopper files separate from in progress files + fixed typo + fixed cvs log keyword + edited entity tags CEH + fixed bibl errors - zr + added cvs log keyword + Corrected two typos in 1449a. + Put Bekker line 1 milestone tags at the beginning of each section so that the incoming list creator would work. Changed RREFDECL. + Tagged in conformance with Prose.e dtd. + Text was scanned at St. Olaf Spring, 1992. + + -Revision 1.1 2009/10/08 19:12:40 rsingh04 -began reorganizing texts module by collection. created separate work directory in texts module to keep hopper files separate from in progress files + + +
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+LetThe text here printed is based on Vahlen’s third edition(Leipzig, 1885), and the chief deviations from it are noted at the foot of each page. The prime source of all existing texts of the Poetics is the eleventh century Paris manuscript, No. 1741, designated as Ac. To the manuscripts of the Renaissance few, except Dr. Margoliouth, now assign any independent value, but they contain useful suggestions for the correction of obvious errors and defects in Ac. These are here designated “copies.”V. stands for Vahlen’s third edition, and By. for the late Professor Ingram Bywater, who has earned the gratitude and admiration of all students of the Poetics by his services both to the text and to its interpretation. Then there is the Arabic transcript. Translated in the eleventh century from a Syriac translation made in the eighth century, it appears to make little sense, but sometimes gives dim visions of the readings of a manuscript three centuries older but not necessarily better than Ac, readings which confirm some of the improvements introduced into Renaissance texts. us here deal with Poetry, its essence and its several species, with the characteristic function of each species and the way in which plots must be constructed if the poem is to be a success; and also with the number and character of the constituent parts of a poem, and similarly with all other matters proper to this same inquiry; and let us, as nature directs, begin first with first principles.

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Epic poetry, then, and the poetry of tragic drama, and, moreover, comedy and dithyrambic poetry, and most flute-playing and harp-playing, these, speaking generally, may all be said to be representations of life.The explanation of μίμησις, as Aristotle uses the word, demands a treatise; all that a footnote can say is this:—Life presents to the artist the phenomena of sense, which the artist re-presents in his own medium, giving coherence, designing a pattern. That this is true not only of drama and fiction but also of instrumental music (most flute-playing and harp-playing) was more obvious to a Greek than to us, since Greek instrumental music was more definitely imitative. The technical display of the virtuoso Plato describes as a beastly noise. Since μίμησις in this sense and μιμητής and the verb μιμεῖσθαι have a wider scope than any one English word, it is necessary to use more than one word in translation, e.g. μιμητής is what we call an artist; and for μίμησις where representation would be clumsy we may use the word art; the adjective must be imitative, since representative has other meanings.

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But they differ one from another in three ways: either in using means generically differenti.e., means that can be divided into separate categories. or in representing different objects or in representing objects not in the same way but in a different manner.

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For just as by the use both of color and form people represent many objects, making likenesses of them—some having a knowledge of art and some working empirically—and just as others use the human voice; so is it also in the arts which we have mentioned, they all make their representations in rhythm and language and tune, using these means either separately or in combination.

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For tune and rhythm alone are employed in flute-playing and harp-playing and in any other arts which have a similar function, as, for example, pipe-playing.

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Rhythm alone without tune is employed by dancers in their representations, for by means of rhythmical gestures they represent both character and experiences and actions.πάθη καὶ πράξεις cover the whole field of life, what men do (πράξεις) and what men experience (πάθη). Since πάθη means also emotions and that sense may be present here, but as a technical term in this treatise πάθος is a calamity or tragic incident, something that happens to the hero.

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But the art which employs words either in bare prose or in metres, either in one kind of metre or combining several, happens up to the present day to have no name.

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For we can find no common term to apply to the mimes of Sophron and XenarchusSophron and Xenarchus, said to he father and son, lived in Syracuse, the elder a contemporary of Euripides. They wrote mimes, i.e., simple and usually farcical sketches of familiar incidents, similar to the mimes of Herondas and the fifteenth Idyll of Theocritus, but in prose. There was a tradition that their mimes suggested to Plato the use of dialogue. and to the Socratic dialogues:

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nor again supposing a poet were to make his representation in iambics or elegiacs or any other such metre—except that people attach the word poet(maker)to the name of the metre and speak of elegiac poets and of others as epic poets.

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Thus they do not call them poets in virtue of their representation but apply the name indiscriminately in virtue of the metre.

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For if people publish medical or scientific treatises in metre the custom is to call them poets. But Homer and EmpedoclesEmpedocles (floruit 445 B.C.) expressed his philosophical and religious teaching in hexameter verse, to which Aristotle elsewhere attributes genuine value as poetry, but it is here excluded from the ranks of poetry because the object is definitely. have nothing in common except the metre, so that it would be proper to call the one a poet and the other not a poet but a scientist.

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Similarly if a man makes his representation by combining all the metres, as Chaeremon did when he wrote his rhapsody The Centaur, a medley of all the metres, he too should be given the name of poet.Chaeremon was a tragedian and rhapsodist. The Centaur was apparently an experiment which might be classed as either drama or epic. Cf. Aristot. Poet. 24.11. On this point the distinctions thus made may suffice.

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There are certain arts which employ all the means which I have mentioned, such as rhythm and tune and metre—dithyrambic and nomic poetry,The traditional definition is that the Dithyramb was sung to a flute accompaniment by a chorus in honor of Dionysus; and that the Nome was a solo sung to a harp accompaniment in honor of Apollo, but it is not clear that Aristotle regarded the Dithyramb as restricted to the worship of Dionysus. Timotheus’s dithyramb mentioned in Aristot. Poet. 15.8 cannot have been Dionysiac. But there is good evidence to show that the dithyramb was primarily associated with Dionysus. for example, and tragedy too and comedy. The difference here is that some use all these at once, others use now one now another.

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These differences then in the various arts I call the means of representation.

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Since living personsLiterally men doing or experiencing something. are the objects of representation, these must necessarily be either good men or inferior—thus only are characters normally distinguished, since ethical differences depend upon vice and virtue—that is to say either better than ourselves or worse or much what we are. It is the same with painters.

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Polygnotus depicted men as better than they are and Pauson worse, while Dionysius made likenesses.Polygnotus’s portraits were in the grand style and yet expressive of character(cf. Aristot. Poet. 6.15): Aristophanes aIludes to a Pauson as a perfectly wicked caricaturist: Dionysius of Colophon earned the name of the man-painter because he always painted men and presumably made good likenesses.

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Clearly each of the above mentioned arts will admit of these distinctions, and they will differ in representing objects which differ from each other in the way here described.

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In painting too, and flute-playing and harp-playing, these diversities may certainly be found, and it is the same in prose and in unaccompanied verse.

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For instance Homer’s people are better, Cleophon’s are like, while in Hegemon of Thasos, the first writer of parodies, and in Nicochares, the author of the Poltrooniad, they are worse.Cleophon wrote epics (i.e., hexameter poems), describing scenes of daily life in commonplace diction (cf. Aristot. Poet. 22.2): Hegemon wrote mock epics in the style of the surviving Battle of Frog and Mice: of Nicochares nothing is known, but his forte was evidently satire.

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It is the same in dithyrambic and nomic poetry, for instance . . . a writer might draw characters like the Cyclops as drawn by Timotheus and Philoxenus.Both famous dithyramhic poets. There is evidence that Philoxenus treated Polyphemus in the vein of satire: Timotheus may have drawn a more dignified picture.

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It is just in this respect that tragedy differs from comedy. The latter sets out to represent people as worse than they are to-day, the former as better.

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A third difference in these arts is the manner in which one may represent each of these objects.

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For in representing the same objects by the same means it is possible to proceed either partly by narrative and partly by assuming a character other than your own—this is Homer’s method—or by remaining yourself without any such change, or else to represent the characters as carrying out the whole action themselves.

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These, as we said above, are the three differences which form the several species of the art of representation, the means, the objects, and the manner.

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It follows that in one respect Sophocles would be the same kind of artist as Homer, for both represent good men, and in another respect he would resemble Aristophanes, for they both represent men in action and doing things. And that according to some is the reason why they are called dramas, because they present people as doingDrama being derived from δρᾶν to do. things.

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And for this reason the Dorians claim as their own both tragedy and comedy—comedy is claimed both by the Megarians here in Greece, who say that it originated in the days of their democracy, and by the Megarians in Sicily,The inhabitants of Megara Hyblaea. for it was from there the poet EpicharmusEpicharmus of Cos wrote in Sicily burlesques and mimes depicting scenes of daily life. He and Phormis were originators of comedy in that they sketched types instead of lampooning individuals (cf. Aristot. Poet. 5.5): of Chionides and Magnes we only know that they were early comedians, i.e., in the first half of the fifth century B.C. came, who was much earlier than Chionides and Magnes; and tragedy some of the Peloponnesians claim. Their evidence is the two names.

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Their name, they say, for suburb villages is κῶμαι—the Athenians call them Demes—and comedians are so called not from κωμάζειν, to revel, but because they were turned out of the towns and went strolling round the villages( κῶμαι). Their word for action, they add, is δρᾶν, whereas the Athenian word is πράττειν. So much then for the differences, their number, and their nature.

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Speaking generally, poetry seems to owe its origin to two particular causes, both natural.

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From childhood men have an instinct for representation, and in this respect, differs from the other animals that he is far more imitative and learns his first lessons by representing things. And then there is the enjoyment people always get from representations.

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What happens in actual experience proves this, for we enjoy looking at accurate likenesses of things which are themselves painful to see, obscene beasts, for instance, and corpses.

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The reason is this: Learning things gives great pleasure not only to philosophers but also in the same way to all other men, though they share this pleasure only to a small degree.

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The reason why we enjoy seeing likenesses is that, as we look, we learn and infer what each is, for instance, that is so and so.

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If we have never happened to see the original, our pleasure is not due to the representation as such but to the technique or the color or some other such cause.

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We have, then, a natural instinct for representation and for tune and rhythmIt is not clear wheter the two general causes are (1) the instinct for imitation, (2) the natural enjoyment of mimicry by others; or whether these two are combined into one and the second cause is the instinct for tune and rhythm. Obviously this last is an essential cause of poetry.—for the metres are obviously sections of rhythmse.g., the rhythm of the blacksmith’s hammer or of a trotting horse is dactylic, but the hexameter is a section or slice of that rhythm; it is cut up into sixes.—and starting with these instincts men very gradually developed them until they produced poetry out of their improvisations.

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Poetry then split into two kinds according to the poet’s nature. For the more serious poets represented fine doings and the doings of fine men, while those of a less exalted nature represented the actions of inferior men, at first writing satire just as the others at first wrote hymns and eulogies.

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Before Homer we cannot indeed name any such poem, though there were probably many satirical poets,

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but starting from Homer, there is, for instance, his MargitesA famous burlesque which Aristotle attributes to Homer. Other similar poems must mean other early burlesques not necessarily attributed to Homer. and other similar poems. For these the iambic metre was fittingly introduced and that is why it is still called iambic, because it was the metre in which they lampooned each other.Since the iambic came to be the metre of invective, the verb ἰαμβίζειν acquired the meaning to lampoon. There is probably implied a derivation from ἰάπτειν, to assail.

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Of the ancients some wrote heroic verse and some iambic.

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And just as Homer was a supreme poet in the serious style, since he alone made his representations not only good but also dramatic, so, too, he was the first to mark out the main lines of comedy, since he made his drama not out of personal satire but out of the laughable as such. His Margites indeed provides an analogy: as are the Iliad and Odyssey to our tragedies, so is the Margites to our comedies.

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When tragedy and comedy came to light, poets were drawn by their natural bent towards one or the other. Some became writers of comedies instead of lampoons, the others produced tragedies instead of epics; the reason being that the former is in each case a higher kind of art and has greater value.

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To consider whether tragedy is fully developed by now in all its various species or not, and to criticize it both in itself and in relation to the stage, that is another question.

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At any rate it originated in improvisation—both tragedy itself and comedy. The one came from the preludeBefore the chorus began (or in pauses between their songs) the leader of the performance would improvise some appropriate tale or state the theme which they were to elaborate. Thus he was called ὁ ἐξάρχων or the starter, and became in time the first actor. to the dithyramb and the other from the prelude to the phallic songs which still survive as institutions in many cities.

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Tragedy then gradually evolved as men developed each element that came to light and after going through many changes, it stopped when it had found its own natural form.

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Thus it was Aeschylus who first raised the number of the actors from one to two. He also curtailed the chorus and gave the dialogue the leading part. Three actors and scene-painting Sophocles introduced.

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Then as to magnitude.Being a development of the Satyr play,A Satyr play was an interlude performed by a troupe of actors dressed as the goat-like followers of Dionysus. Hence τραγῳδία, goat-song. Aristotle seems so clear about this that he does not trouble to give a full explanation. But we can see from this passage that the Satyr plays were short, jocose and in the trochaic metre which suited their dances, and that in Aristotle’s view tragedy was evolved from these. No example of a primitive Satyr play survives, but we can make inferences from the later, more sophisticated Cyclops of Euripides and the fragments of Sophocles’ <foreign xml:lang="grc">Ἰχνευταί</foreign>, The Trackers. We cannot be certain that Aristotle’s theory is historically correct; the balance of evidence is against it. it was quite late before tragedy rose from short plots and comic diction to its full dignity, and that the iambic metre was used instead of the trochaic tetrameter.

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At first they used the tetrameter because its poetry suited the Satyrs and was better for dancing, but when dialogue was introduced, Nature herself discovered the proper metre. The iambic is indeed the most conversational of the metres,

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and the proof is that in talking to each other we most often use iambic lines but very rarely hexameters and only when we rise above the ordinary pitch of conversation.

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Then there is the number of acts. The further embellishmentsMasks, costumes, etc. and the story of their introduction one by one we may take as told,

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for it would probably be a long task to go through them in detail.

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Comedy, as we have said, is a representation of inferior people, not indeed in the full sense of the word bad, but the laughable is a species of the base or ugly.Ugly was to a Greek an equivalent of bad. The persons in Comedy are inferior (see chapter 2.), but have only one of the many qualities which make up Ugliness or Badness, viz. the quality of being ludicrous and therefore in some degree contemptible.

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It consists in some blunder or ugliness that does not cause pain or disaster, an obvious example being the comic mask which is ugly and distorted but not painful.

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The various stages of tragedy and the originators of each are well known, but comedy remains obscure because it was not at first treated seriously. Indeed it is only quite late in its historyProbably about 465 B.C. that the archon granted a chorus for a comic poet; before that they were volunteers.In the fifth century dramatists submitted their plays to the archon in charge of the festival at which they wished them to be performed. He selected the number required by the particular festival, and to the poets thus selected granted a chorus, i.e., provided a choregus who paid the expenses of the chorus. The earlier volunteers had themselves paid for and produced their plays.

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Comedy had already taken certain forms before there is any mention of those who are called its poets. Who introduced masks or prologues, the number of actors, and so on, is not known.

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Plot making [Epicharmus and Phormis]Epicharmus and Phormis, being both early Sicilian comedians, are appropriate here. Either part of a sentence is lost or an explanatory note has got into the text. originally came from Sicily,

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and of the Athenian poets CratesFragments of his comedies survive, dating about the middle of the fifth century B.C. was the first to give up the lampooning form and to generalize his dialogue and plots.

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Epic poetry agreed with tragedy only in so far as it was a metrical representation of heroic action, but inasmuch as it has a single metre and is narrative in that respect they are different.

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And then as regards length, tragedy tends to fall within a single revolution of the sun or slightly to exceed that, whereas epic is unlimited in point of time;

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and that is another difference, although originally the practice was the same in tragedy as in epic poetry.

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The constituent parts are some of them the same and some peculiar to tragedy.

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Consequently any one who knows about tragedy, good and bad, knows about epics too, since tragedy has all the elements of epic poetry, though the elements of tragedy are not all present in the epic.

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With the representation of life in hexameter versei.e., epic poetry. and with comedy we will deal later. We must now treat of tragedy after first gathering up the definition of its nature which results from what we have said already.

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Tragedy is, then, a representation of an actionMargoliouth’s phrase a chapter of life, illuminates the meaning, since πρᾶξις includes what the hero does and what happens to him. (Cf. Aristot. Poet. 2.1 and note.) that is heroic and complete and of a certain magnitude—by means of language enriched with all kinds of ornament, each used separately in the different parts of the play: it represents men in action and does not use narrative, and through pity and fear it effects relief to these and similar emotions.The sense of the pity of it and fear lest such disasters might befall ourselves are not the only emotions which tragedy releases, but Aristotle specifies them as the most characteristic. For κάθαρσις, see Introduction.

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By language enriched I mean that which has rhythm and tune, i.e., song,

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and by the kinds separately I mean that some effects are produced by verse alone and some again by song.

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Since the representation is performed by living persons, it follows at once that one essential part of a tragedy is the spectacular effect, and, besides that, song-making and diction. For these are the means of the representation.

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By diction I mean here the metrical arrangement of the words; and song making I use in the full, obvious sense of the word.

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And since tragedy represents action and is acted by living persons, who must of necessity have certain qualities of character and thought—for it is these which determine the quality of an action; indeed thought and character are the natural causes of any action and it is in virtue of these that all men succeed or fail—

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it follows then that it is the plot which represents the action. By plot I mean here the arrangement of the incidents: character is that which determines the quality of the agents, and thought appears wherever in the dialogue they put forward an argument or deliver an opinion.

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Necessarily then every tragedy has six constituent parts, and on these its quality depends. These are plot, character, diction, thought, spectacle, and song.

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Two of these are the means of representation: one is the manner: three are the objects represented.The means are diction and music: the manner is spectacle: the objects represented are actions or experiences and the moral or intellectual qualities of the dramatis personae.

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This list is exhaustive, and practically all the poets employ these elements, for every drama includes alike spectacle and character and plot and diction and song and thought.

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The most important of these is the arrangement of the incidents,i.e., plot, as defined above. for tragedy is not a representation of men but of a piece of action, of life, of happiness and unhappiness, which come under the head of action, and the end aimed at is the representation not of qualities of character but of some action; and while character makes men what they are,it’s their actions and experiences that make them happy or the opposite.

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They do not therefore act to represent character, but character-study is included for the sake of the action. It follows that the incidents and the plot are the end at which tragedy aims, and in everything the end aimed at is of prime importance.

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Moreover, you could not have a tragedy without action, but you can have one with out character-study.

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Indeed the tragedies of most modern poets are without this, and, speaking generally, there are many such writers, whose case is like that of Zeuxis compared with Polygnotus.Zeuxis’s portraits were ideal (cf. Aristot. Poet. 25.28). The latter was good at depicting character, but there is nothing of this in Zeuxis’s painting.

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A further argument is that if a man writes a series of speeches full of character and excellent in point of diction and thought, he will not achieve the proper function of tragedy nearly so well as a tragedy which, while inferior in these qualities, has a plot or arrangement of incidents.

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And furthermore, two of the most important elements in the emotional effect of tragedy, reversals and discoveries,See chapter 11. are parts of the plot.

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And here is further proof: those who try to write tragedy are much sooner successful in language and character-study than in arranging the incidents. It is the same with almost all the earliest poets.

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The plot then is the first principle and as it were the soul of tragedy: character comes second.

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It is much the same also in painting; if a man smeared a canvas with the loveliest colors at random, it would not give as much pleasure as an outline in black and white.Selection and design are necessary for any work of representation.

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And it is mainly because a play is a representation of action that it also for that reason represents people.

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Third comes thought. This means the ability to say what is possible and appropriate. It comes in the dialogue and is the function of the statesman’s or the rhetorician’s art.Cf. chapter 6.

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The old writers made their characters talk like statesmen,Or in the style of ordinary people, without obvious rhetorical artifice. the moderns like rhetoricians.

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Character is that which reveals choiceπροαίρεσις is a technical term in Aristotle’s ethics, corresponding to our use of the term Will, the deliberate adoption of any course of conduct or line of action. It is a man’s will or choice in the sense that determines the goodness or badness of his character. If character is to be revealed in drama, a man must be shown in the exercise of his will, choosing between one line of conduct and another, and he must be placed in circumstances in wbich the choice is not obvious, i.e., circumstances in which everybody’s choice would not be the same. The choice of death rather than disbonourable wealth reveals character; the choice of a nectarine rather than a turnip does not., shows what sort of thing a man chooses or avoids in circumstances where the choice is not obvious, so those speeches convey no character in which there is nothing whatever which the speaker chooses or avoids.

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Thought you find in speeches which contain an argument that something is or is not, or a general expression of opinion.

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The fourth of the literary elements is the language. By this I mean, as we said above, the expression of meaning in words,This seems to be a mistaken reference to 6 above where diction is defined as the metrical arrangement of the words. In poetry they come to the same thing. and this is essentially the same in verse and in prose.

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Of the other elements which enrichSee Aristot. Poet. 6.2. tragedy the most important is song-making.

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Spectacle, while highly effective, is yet quite foreign to the art and has nothing to do with poetry. Indeed the effect of tragedy does not depend on its performance by actors, and, moreover,for achieving the spectacular effects the art of the costumier is more authoritative than that of the poet.

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After these definitions we must next discuss the proper arrangement of the incidents since this is the first and most important thing in tragedy.

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We have laid it down that tragedy is a representation of an action that is whole and complete and of a certain magnitude, since a thing may be a whole and yet have no magnitude.

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A whole is what has a beginning and middle and end.

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A beginning is that which is not a necessary consequent of anything else but after which something else exists or happens as a natural result.

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An end on the contrary is that which is inevitably or, as a rule, the natural result of something else but from which nothing else follows;

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a middle follows something else and something follows from it.

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Well constructed plots must not therefore begin and end at random, but must embody the formulae we have stated.

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Moreover, in everything that is beautiful, whether it be a living creature or any organism composed of parts, these parts must not only be orderly arranged but must also have a certain magnitude of their own;

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for beauty consists in magnitude and ordered arrangement. From which it follows that neither would a very small creature be beautiful—for our view of it is almost instantaneous and therefore confusedWith a very small object the duration of our vision is, as it were, so rapid that the parts are invisible; we, therefore, cannot appreciate their proportion and arrangement, in which beauty consists.—nor a very large one, since being unable to view it all at once, we lose the effect of a single whole; for instance, suppose a creature a thousand miles long.

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As then creatures and other organic structures must have a certain magnitude and yet be easily taken in by the eye, so too with plots: they must have length but must be easily taken in by the memory.

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The limit of length considered in relation to competitions and productionαἴσθησις is the play’s perception by an audience—how much an audience will stand. before an audience does not concern this treatise. Had it been the rule to produce a hundred tragedies, the performance would have been regulated by the water clock, as it is said they did once in other days.

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But as for the natural limit of the action, the longer the better as far as magnitude goes, provided it can all be grasped at once. To give a simple definition: the magnitude which admits of a change from bad fortune to good or from good fortune to bad, in a sequence of events which follow one another either inevitably or according to probability, that is the proper limit.

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A plot does not have unity, as some people think, simply because it deals with a single hero. Many and indeed innumerable things happen to an individual, some of which do not go to make up any unity, and similarly an individual is concerned in many actions which do not combine into a single piece of action.

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It seems therefore that all those poets are wrong who have written a Heracleid or Theseid or other such poems.Aristotle condemns them all, assuming—or perhaps assured by experience—that their sole claim to unity lay in the fact that all the stories in the poem had a common hero. They think that because Heracles was a single individual the plot must for that reason have unity.

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But Homer, supreme also in all other respects, was apparently well aware of this truth either by instinct or from knowledge of his art. For in writing an Odyssey he did not put in all that ever happened to Odysseus, his being wounded on Parnassus, for instance, or his feigned madness when the host was gathered(these being events neither of which necessarily or probably led to the other), but he constructed his Odyssey round a single action in our sense of the phrase. And the Iliad the same.

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As then in the other arts of representation a single representation means a representation of a single object, so too the plot being a representation of a piece of action must represent a single piece of action and the whole of it; and the component incidents must be so arranged that if one of them be transposed or removed, the unity of the whole is dislocated and destroyed. For if the presence or absence of a thing makes no visible difference, then it is not an integral part of the whole.

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What we have said already makes it further clear that a poet’s object is not to tell what actually happened but what could and would happen either probably or inevitably.

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The difference between a historian and a poet is not that one writes in prose and the other in verse— indeed the writings of Herodotus could be put into verse and yet would still be a kind of history, whether written in metre or not. The real difference is this, that one tells what happened and the other what might happen.

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For this reason poetry is something more scientific and serious than history, because poetry tends to give general truths while history gives particular facts.

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By a general truth I mean the sort of thing that a certain type of man will do or say either probably or necessarily. That is what poetry aims at in giving names to the characters.The names indicate types. This is obvious, as he says, in Comedy and is also true of Greek Tragedy, which, although it deals with traditional heroes regarded as real people, yet keeps to a few stories in which each character has become a type. In Chapter 17. the dramatist is recommended to sketch first his outline plot, making it clear and coherent, before he puts in the names. A particular fact is what Alcibiades did or what was done to him.

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In the case of comedy this has now become obvious, for comedians construct their plots out of probable incidents and then put in any names that occur to them. They do not, like the iambic satirists, write about individuals.Aristophanes of course did write about individuals. But Aristotle is thinking of the New Comedy, where the names of the characters were invented by the author and there was no reference to real people.

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In tragedy, on the other hand, they keep to real names. The reason is that what is possible carries conviction. If a thing has not happened, we do not yet believe in its possibility, but what has happened is obviously possible. Had it been impossible, it would not have happened.

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It is true that in some tragedies one or two of the names are familiar and the rest invented; indeed in some they are all invented, as for instance in Agathon’s Antheus,The name, apparently, of an imaginary hero. The word might be Ἄνθος, but The Flower is an unlikely title for a Greek tragedy. where both the incidents and the names are invented and yet it is none the less a favourite.

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One need not therefore endeavor invariably to keep to the traditional stories with which our tragedies deal. Indeed it would be absurd to do that, seeing that the familiar themes are familiar only to a few and yet please all.The reason why Greek tragedy dealt only with a few familiar themes is to be found of course in its religious origin. It was the function of tragedy to interpret and embroider myths. Aristotle never gives this reason, but offers instead the unconvincing explanation that tragedians adhered to certain real stories to gain verisimilitude—and yet he has to admit that, since to many of the auditors these stories were unfamiliar and none the less attractive, dramatists might just as well invent new themes.

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It is clear, then, from what we have said that the poet must be a maker not of verses but of stories, since he is a poet in virtue of his representation, and what he represents is action.

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Even supposing he represents what has actually happened, he is none the less a poet, for there is nothing to prevent some actual occurrences being the sort of thing that would probably or inevitably happen, and it is in virtue of that that he is their maker.

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Of simpleThis term is defined in the next chapter. It seems odd to use it before its meaning is explained. Perhaps we should read ἄλλων(Tyrwhitt) and translate of all plots. plots and actions the worst are those which are episodic. By this I mean a plot in which the episodes do not follow each other probably or inevitably.

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Bad poets write such plays because they cannot help it, and good poets write them to please the actors. Writing as they do for competition, they often strain a plot beyond its capacity and are thus obliged to sacrifice continuity.Or logic. He means the chain of cause and effect, wherein each incident is the result of what has gone before. See the end of the next chapter.

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But this is bad work, since tragedy represents not only a complete action but also incidents that cause fear and pity, and this happens most of all when the incidents are unexpected and yet one is a consequence of the other.The logic suffers from ellipse. Plays which fail to exhibit the sequence of cause and effect are condemned (1) because they lack the unity which befits tragedy, (2) because they miss that supreme effect of fear or pity produced by incidents which, though unexpected, are seen to be no mere accident but the inevitable result of what has gone before.

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For in that way the incidents will cause more amazement than if they happened mechanically and accidentally, since the most amazing accidental occurrences are those which seem to have been providential, for instance when the statue of Mitys at Argos killed the man who caused Mitys’s death by falling on him at a festival. Such events do not seem to be mere accidents.

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So such plots as these must necessarily be the best.

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Some plots are simple and some complex, as indeed the actions represented by the plots are obviously such.

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By a simple action I mean one that is single and continuous in the sense of our definition above,In chapters 7 and 8. wherein the change of fortune occurs without reversal or discovery;

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by a complex action I mean one wherein the change coincides with a discovery or reversal or both.

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These should result from the actual structure of the plot in such a way that what has already happened makes the result inevitable or probable;for there is indeed a vast difference between what happens propter hoc and post hoc.

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A reversal is a change of the situation into the opposite, as described above,At the end of chapter 7. Vahlen and many other exponents of the Politics confine the meaning of “reversal” to the situation in which the hero’s action has consequences directly opposite to his intention and expectation. There is much to be said for this interpretation, which stresses the irony at the heart of all tragedy. But it is too narrow for Aristotle’s theory. All tragedy involves a change of fortune ( μετάβασις). In a “simple” plot this is gradual; in a “complex” plot it is catastrophic, a sudden revolution of fortune’s wheel. In some of the greatest tragedies, but not in all, this is the result of action designed to produce the opposite effect. this change being, moreover, as we are saying, probable or inevitable—

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like the man in the Oedipus who came to cheer Oedipus and rid him of his anxiety about his mother by revealing his parentage and changed the whole situation.The messenger for Corinth announces the death of Polybus and Oedipus’s succession to the throne. Oedipus, feeling now safe from the prophecy that he would murder his father, still fears to return to Corinth, lest he should fulfil the other prophecy and marry his mother. The messenger seeks to reassure him by announcing that Polybus and Merope are not his parents. But the effect of this was to change the whole situation for Oedipus by revealing the truth that he a murdered his father, Laius, and married his mother, Jocasta. This reversal is the more effective because it is immediately coincident with the discovery of the truth. In the Lynceus, too, there is the man led off to execution and

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Danaus following to kill him, and the result of what had already happened was that the latter was killed and the former escaped.Lynceus married Hypermnestra who disobeyed Danaus in not murdering him. Danaus trying by process of law to compass the death of their son Abas was killed himself. The dog it was that died.

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A discovery, as the term itself implies, is a change from ignorance to knowledge, producing either friendship or hatred in those who are destined for good fortune or ill.

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A discovery is most effective when it coincides with reversals, such as that involved by the discovery in the Oedipus.

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There are also other forms of discovery, for what we have described may in a sense occur in relation to inanimate and trivial objects, or one may discover whether some one has done something or not.

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But the discovery which is most essentially part of the plot and part of the action is of the kind described above, for such a discovery and reversal of fortune will involve either pity or fear, and it is actions such as these which, according to our hypothesis, tragedy represents; and, moreover, misfortune and good fortune are likely to turn upon such incidents.

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Now since the discovery is somebody’s discovery, in some scenes one character only is discovered to another, the identity of the other being obvious; but sometimes each must discover the other. Thus Iphigeneia was discovered to Orestes through the sending of the letter, but a separate discovery was needed to make him known to Iphigeneia.Euripides’ Iphigeneia in Tauris—Orestes and Pylades arriving among the Tauri are by the custom of the country to be sacrificed to Artemis by her priestess, Iphigeneia. It is agreed that Pylades shall be spared to carry a letter from Iphigeneia to Orestes, whom she supposes to be in Argos. In order that Pylades may deliver the message, even if he should lose the letter, she reads it aloud. Orestes thus discovers who she is. He then reveals himself to her by declaring who he is and proving his identity by his memories of their home.

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We see then that two elements of the plot, reversal and discovery, turn upon these incidents. A third element is a calamity. Of these three elements we have already described reversal and discovery.

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A calamity is a destructive or painful occurrence, such as a death on the stage, acute suffering and wounding and so on.

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We have alreadyIn chapter 6. spoken of the constituent parts to be used as ingredients of tragedy. The separable members into which it is quantitatively divided are these: Prologue, Episode, Exode, Choral Song,

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the last being divided into Parode and Stasimon.

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These are common to all tragedies; songs sung by actors on the stage and commoi are peculiar to certain plays.

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A prologue is the whole of that part of a tragedy which precedes the entrance of the chorus.

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An episode is the whole of that part of a tragedy which falls between whole choral songs.

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An exode is the whole of that part of a tragedy which is not followed by a song of the chorus.

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A parode is the whole of the first utterance of the chorus.

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A stasimon is a choral song without anapaests or trochaics.This does not apply to surviving Greek tragedies, but may be true of those of Aristotle’s time. The word Stasimon is applied to all choruses in a tragedy other than those sung during entry or exit. It is usually explained as meaning a stationary song, because it was sung after the chorus had taken up its station in the orchestra.

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A commos is a song of lament shared by the chorus and the actors on the stage.

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The constituent parts to be used as ingredients of tragedy have been described above; these are the separable members into which it is quantitatively divided.The whole of chapter 12. bears marks of belonging to the Poetics but seems out of place, since it interrupts the discussion of plot.

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Following upon what has been said above we should next state what ought to be aimed at and what avoided in the construction of a plot, and the means by which the object of tragedy may be achieved.

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Since then the structure of the best tragedy should be not simple but complexSee chapter 10. and one that represents incidents arousing fear and pity—for that is peculiar to this form of art—it is obvious to begin with that one should not show worthy men passing from good fortune to bad. That does not arouse fear or pity but shocks our feelings.

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Nor again wicked people passing from bad fortune to good. That is the most untragic of all, having none of the requisite qualities, since it does not satisfy our feelingsi.e., our preference for poetic justice. or arouse pity or fear.

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Nor again the passing of a thoroughly bad man from good fortune to bad fortune. Such a structure might satisfy our feelings but it arouses neither pity nor fear, the one being for the man who does not deserve his misfortune and the other for the man who is like ourselves—pity for the undeserved misfortune, fear for the man like ourselves—so that the result will arouse neither pity nor fear.

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There remains then the mean between these. This is the sort of man who is not pre-eminently virtous and just, and yet it is through no badness or villainy of his own that he falls into the fortune, but rather through some flaw in him,Whether Aristotle regards the “flaw” as intellectual or moral has been hotly discussed. It may cover both senses. The hero must not deserve his misfortune, but he must cause it by making a fatal mistake, an error of judgement, which may well involve some imperfection of character but not such as to make us regard him as “morally responsible” for the disasters although they are nevertheless the consequences of the flaw in him, and his wrong decision at a crisis is the inevitable outcome of his character(cf. Aristot. Poet. 6.24.). he being one of those who are in high station and good fortune, like Oedipus and Thyestes and the famous men of such families as those.

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The successful plot must then have a singleἁπλοῦς elsewhere in the Poetics means simple as opposed to πεπλεγμένος, complex; here it is opposed to διπλοῦς, which describes a double denouement, involving happiness for some and disaster for others. and not, as some say, a double issue; and the change must be not to good fortune from bad but, on the contrary, from good to bad fortune, and it must not be due to villainy but to some great flaw in such a man as we have described, or of one who is better rather than worse.

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This can be seen also in actual practice. For at first poets accepted any plots, but to-day the best tragedies are written about a few families—Alcmaeon for instance and Oedipus and Orestes and Meleager and Thyestes and Telephus and all the others whom it befell to suffer or inflict terrible disasters.

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Judged then by the theory of the art, the bestThis is modified by 19 in the following chapter, where he finds an even better formula for the tragic effect. tragedy is of this construction.

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Those critics are therefore wrong who charge Euripides with doing this in his tragedies, and say that many of his end in misfortune.

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That is, as we have shown, correct. And there is very good evidence of this, for on the stage and in competitions such plays appear the most tragic of all, if they are successful, and even if Euripides is in other respects a bad manager,Against Euripides Aristotle makes the following criticisms: (1)his choruses are often irrelevant; (2)the character of the heroine in his Iphigeneia in Tauris is inconsistent; (3)in the Medea the deliberate killing of the children is ineffective and the play is inartistically ended by the machina; (4)the character of Menelaus in the Orestes is needlessly depraved; (5)Melanippe is too philosophical for a woman. yet he is certainly the most tragic of the poets.

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Next in order comes the structure which some put first, that which has a double issue, like the Odyssey, and ends in opposite ways for the good characters and the bad.

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It is the sentimentality of the audience which makes this seem the best form; for the poets follow the wish of the spectators.

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But this is not the true tragic pleasure but rather characteristic of comedy, where those who are bitter enemies in the story, Orestes and Aegisthus, for instance, go off at the end, having made friends, and nobody kills anybody.

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Fear and pity sometimes result from the spectacle and are sometimes aroused by the actual arrangement of the incidents, which is preferable and the mark of a better poet.

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The plot should be so constructed that even without seeing the play anyone hearing of the incidents happening thrills with fear and pity as a result of what occurs. So would anyone feel who heard the story of Oedipus.

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To produce this effect by means of an appeal to the eye is inartistic and needs adventitious aid,

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while those who by such means produce an effect which is not fearful but merely monstrous have nothing in common with tragedy.that here were plays which relied for their effect on the scenery and make up is clear from chapter 17:—The Phorcides and Prometheus and Scenes laid in Hades. It was even possible to produce the Eumenides so badly as to bring it into this category. But Aristotle’s criticism here includes the more important point that the poignancy of a Greek tragedy is due to what happens and not to our seeing it happen. That Medea murders her children is tragic: to display the murder coram populo would add either nothing or something merely monstrous. And although Sophocles shows Oedipus with his eyes out, it is the fact and not the sight which is properly tragic. For one should not seek from tragedy all kinds of pleasure but that which is peculiar to tragedy,

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and since the poet must by representation produce the pleasure which comes from feeling pity and fear, obviously this quality must be embodied in the incidents.

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We must now decide what incidents seem dreadful or rather pitiable. Such must necessarily be the actions of friends to each other or of enemies or of people that are neither.

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Now if an enemy does it to an enemy, there is nothing pitiable either in the deed or the intention,

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except so far as the actual calamity goes.

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Nor would there be if they were neither friends nor enemies. But when these calamities happen among friends,when for instance brother kills brother, or son father, or mother son, or son mother—either kills or intends to kill, or does something of the kind, that is what we must look for.

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Now it is not right to break up the traditional stories, I mean, for instance, Clytaemnestra being killed by Orestes and Eriphyle by Alcmaeon,

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but the poet must show invention and make a skilful use of the tradition.

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But we must state more clearly what is meant by skilful.

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The action may happen in the way in which the old dramatists made their characters act—consciously and knowing the facts, as EuripidesThis does not necessarily imply that Aristotle reckons Euripides “a modern,” since the Greek can equally mean “Euripides as well as other old dramatists.” also made his Medea kill her children.

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Or they may do the deed but without realizing the horror of it and then discover the relationship afterwards, like Oedipus in Sophocles. That indeed lies outside the play,i.e., Oedipus kills his father Laius before the play opens. but an example of this in the tragedy itself is the Alcmaeon of AstydamasA prolific tragedian of the fourth century. or Telegonus in the Wounded Odysseus.

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A third alternative is to intend to do some irremediable action in ignorance and to discover the truth before doing it.

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Besides these there is no other way, for they must either do the deed or not, either knowing or unknowing.

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The worst of these is to intend the action with full knowledge and not to perform it. That outrages the feelings and is not tragic, for there is no calamity. So nobody does that, except occasionally, as, for instance, Haemon and CreonHaemon, discovered by his father Creon embracing the dead body of Antigone, drew his sword on him but missed his aim and Creon fled. in the Antigone.

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Next comes the doing of the deed.

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It is better to act in ignorance and discover afterwards. Our feelings are not outraged and the discovery is startling.

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Best of all is the last; in the Cresphontes,By Euripides. Polyphontes killed Cresphontes, king of Messenia, and gained possession of his kingdom and his wife, Merope. She had concealed her son, Aepytus, in Arcadia, and when he returned, seeking vengeance, she nearly killed him in ignorance but discovered who he was. He then killed Polyphontes and reigned in his stead. for instance, Merope intends to kill her son and does not kill him but discovers; and in the IphigeneiaIn Tauris. See Aristot. Poet. 11.8, note. the case of the sister and brother; and in the HelleAuthor and play unknown. the son discovers just as he is on the point of giving up his mother.

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So this is the reason, as was said above,See Aristot. Poet. 13.7. why tragedies are about a few families. For in their experiments it was from no technical knowledge but purely by chance that they found out how to produce such an effect in their stories. So they are obliged to have recourse to those families in which such calamities befell.See Aristot. Poet. 9.8, note.

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Now concerning the structure of the incidents and the proper character of the plots enough has been said.

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Concerning character there are four points to aim at. The first and most important is that the character should be good.

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The play will show character if, as we said above,See Aristot. Poet. 6.24. either the dialogue or the actions reveal some choice; and the character will be good, if the choice is good.

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But this is relative to each class of people. Even a woman is good and so is a slave, although it may be said that a woman is an inferior thing and a slave beneath consideration.

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The second point is that the characters should be appropriate. A character may be manly, but it is not appropriate for a woman to be manly or clever.

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Thirdly, it should be like.The meaning probably is like the traditional person, e.g. Achilles must not be soft nor Odysseus stupid. Cf. Horace Ars Poet. 120 famam sequere. This is different from making the character good and from making it appropriate in the sense of the word as used above.

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Fourthly, it should be consistent. Even if the original be inconsistent and offers such a character to the poet for representation, still he must be consistently inconsistent.

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An example of unnecessary badness of character is Menelaos in the OrestesAristotle has a personal distaste for this character on the ground that Euripides made him a creature meaner than the plot demands.;

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of character that is unfitting and inappropriate the lament of Odysseus in the ScyllaA dithyramb by Timotheus. Cf. Aristot. Poet. 26.3. and Melanippe’s speechA fragment survives (Eur. Fr. 484 (Nauck)). Euripides seems to have given her a knowledge of science and philosophy inappropriate to a woman.;

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of inconsistent character Iphigeneia in Aulis, for the suppliant Iphigeneia is not at all like her later character.

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In character-drawing just as much as in the arrangement of the incidents one should always seek what is inevitable or probable, so as to make it inevitable or probable that such and such a person should say or do such and such; and inevitable or probable that one thing should follow another.

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Clearly therefore the denouementOr unravelling. of each play should also be the result of the plot itself and not produced mechanically as in the Medea and the incident of the embarkation in the Iliad. Hom. Il. 2.155-181, where it is only the arbitrary (i.e., uncaused) intervention of Athene which stays the flight of the Greeks. In the Medea the heroine, having killed her rival and her children, is spirited away in the chariot ot the Sun, a result not caused by what has gone before.

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The god in the carThe μηχανή or car was a sort of crane with a pulley attached, which was fixed at the top of the back-scene in the left corner of the stage. By it a god or hero could be lowered or raised or exhibited motionless in mid-air. Weak dramatists thus introduced a car to cut the knot by declaring the denouement instead of unravelling the plot by the logic of cause and effect. It was presumably on such a car that Medea was borne away. should only be used to explain what lies outside the play, either what happened earlier and is therefore beyond human knowledge, or what happens later and needs to be foretold in a proclamation. For we ascribe to the gods the power of seeing everything.

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There must, however, be nothing inexplicable in the incidents, or, if there is, it must lie outside the tragedy. There is an example in Sophocles’ Oedipus.i.e., Oedipus had killed Laius in a wayside quarrel, not knowing who he was. When his subjects at Thebes crave his help to remove the curse which is blighting their crops, he pledges himself to discover the murderer of Laius. It may seem odd that he should not know enough about the details of the murder to connect it in his mind with his own murderous quarrel. But that was long ago, and neither an audience nor a novel-reader is critical about incidents which occur long before the point at which the story begins. See chapter Aristot. Poet. 24.20.

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Since tragedy is a representation of men better than ourselves we must copy the good portrait-painters who, while rendering the distinctive form and making a likeness, yet paint people better than they are. It is the same with the poet. When representing people who are hot-tempered or lazy, or have other such traits of character, he should make them such, yet men of worth [an example of hardness]Apparently a note on Achilles which has been copied by mistake into the text.; take the way in which Agathon and Homer portray Achilles.

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Keep, then, a careful eye on these rules and also on the appeal to the eyei.e., stage-craft rather than staging. which is necessarily bound up with the poet’s business; for that offers many opportunities of going wrong. But this subject has been adequately discussed in the published treatises.As distinct from the body of esoteric doctrine circulated by oral teaching among Aristotle’s pupils.

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What a Discovery is has been already stated.In chapter 11.As for kinds of Discovery, first comes the least artistic kind, which is largely used owing to incompetence—discovery by tokens.

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These may be congenital, like the spear the Earth-born bear or stars, like those which CarcinusA prolific tragedian of the early fourth century. The family are agreeably ridiculed in Aristophanes’ Wasps. uses in his ThyestesThese were birth-marks. The spear-head distinguished the descendants of the Spartoi at Thebes; the star or bright spot on the descendants of Pelops commemorated his ivory shoulder, and in Carcinus’s play it seems to have survived cooking.;

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or they may be acquired and these may be on the body, for instance, wounds, or external things like necklaces, and in the TyroA play by Sophocles. Tyro’s twins by Poseidon, who appeared to her in the guise of the river Enipeus, were exposed in a little boat or ark, like Moses in the bulrushes, and this led to their identification. the discovery by means of the boat.

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There is a better and a worse way of using these tokens; for instance Odysseus, by means of his wound, was discovered in one way by the nurse and in another way by the swine-herds.Hom. Od. 19.386ff., 205ff. The first came about automatically, the second was a deliberate demonstration to prove the point. Aristotle here distinguishes between a discovery inevitably produced by the logic of events (e.g. it was inevitable or at least probable that Odysseus, arriving as a strange traveller, should be washed by Eurycleia, and that she should thus see the old scar on his thigh and discover his identity) and a discovery produced by a deliberate declaration (e.g. Odysseus’s declaration of his identity to Eumaeus). The latter kind is manufactured by the poet, not logically caused by what has gone before.

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Discovery scenes constructed to prove the point are inartistic and so are all such scenes, but those are better which arise out of a reversal scene, as, for instance, in The Washing.Hom. Od. 19.392. See preceding note.

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In the second place come those which are manufactured by the poet and are therefore inartistic. For instance, in the IphigeneiaEuripides’ Iphigeneia in Tauris. See Aristot. Poet. 11.8, note. Orestes revealed himself. She was revealed to him through the letter,

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but Orestes says himself what the poet wants and not what the plot requires. So this comes near to the fault already mentioned, for he might just as well have actually brought some tokens.To prove his identity Orestes mentions Pelops’ lance and other things from home, which is much the same as producing visible tokens. And there is the voice of the shuttleWhen Philomela’s tongue was cut out, she wove in embroidery the story of her rape by Tereus. Thus the facts were discovered to her sister, Procne, by deliberate demonstration. In Sophocles’ Tereus.

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The third kind is due to memory, to showing distress on seeing something. An example of this is the scene in the Cyprians by Dicaeogenes; on seeing the picture he burst into tearsTeucer, returning to Salamis in disguise and seeing a portrait of his dead father Telamon, burst into tears and was thus discovered. So, too, in The Two Gentlemen of <placeName key="perseus,Verona">Verona</placeName> Julia is discovered because she swoons on hearing Valentine offer Sylvia to his rival.: and again in the Tale of Alcinous, Hom. Od. 8.521ff. hearing the minstrel he remembered and burst into tears; and thus they were recognized.

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The fourth kind results from an inference; for instance, in the Choephoroe Someone like me has come; but nobody is like me except Orestes; therefore he has come. And there is Polyidus’sA Sophist who either wrote an Iphigeneia with this denouement or more probably suggested in a work of criticism (cf. Aristot. Poet. 17.6) that Orestes on being led to his fate should speculate aloud upon the odd coincidence that both he and his sister should be sacrificed, thus revealing his identity to Iphigeneia. Like most critics, Polyidos would have been a poor dramatist. There is an example of this form of discovery in the French opera Coeur de Lion, where the old knight says goddam and is thus discovered to be an Englishman. idea about Iphigeneia, for it is likely enough that Orestes should make an inference that, whereas his sister was sacrificed, here is the same thing happening to him. And in Theodectes’ Tydeus that having come to find a son, he is perishing himself. And the scene in the Phineidae, where on seeing the spot the women inferred their fate, that they were meant to die there for it was there that they had been exposed.In these cases the inference was presumably uttered aloud and hence the identity of the speakers discovered. Nothing else is known of these plays.

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There is also a kind of fictitious discovery which depends on a false inference on the part of the audience, for instance in Odysseus the False Messenger, he said he would recognize the bow, which as a matter of fact he had not seen, but to assume that he really would reveal himself by this means is a false inference.The text is obscure, and our ignorance of the play or rhapsody adds to the darkness, but the reference may be to the ruse, common in detective stories, of misleading the audience by false clues in order to make the final revelation more effective.

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Best of all is the discovery which is brought about directly by the incidents, the surprise being produced by means of what is likely—take the scene in Sophocles’ Oedipus or in the Iphigeneia—for it is likely enough that she should want to send a letter. These are the only discovery scenes which dispense with artificial tokens, like necklaces.The classical example of these tokens in English drama is the strawberry mark on the left arm in Box and Cox. But Aristotle seems here to use tokens in a wider sense than at the beginning of the chapter and to include not only birthmarks, necklaces, etc., but any statement or action which may be used as a sign in the scene of Discovery.

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In the second place come those that are the result of inference.

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In constructing plots and completing the effect by the help of dialogue the poet should, as far as possible, keep the scene before his eyes. Only thus by getting the picture as clear as if he were present at the actual event, will he find what is fitting and detect contradictions.

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The censure upon Carcinos is evidence of this. Amphiaraos was was made to rise from a temple. The poet did not visualize the scene and therefore this escaped his notice, but on the stage it was a failure since the audience objected.The example is obscure. Clearly Carcinus introduced an absurdity which escaped notice until the play was staged. Margoliouth suggests that if Amphiaraus were a god he should come down, and if a mere hero, he sould not have a temple. In The Master of Ballantrae Mrs. Henry cleans a sword by thrusting it up to the hilt in the ground—which is iron-bound by frost. The would be noticed on the stage: a reader may miss the incongruity.

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The poet should also, as far as possible, complete the effect by using the gestures. For, if their natural powers are equal, those who are actually in the emotions are the most convincing; he who is agitated blusters and the angry man rages with the maximum of conviction.Sir Joshua Reynolds used thus to simulate emotion before a mirror. In his Preface to the Lyrical Ballads Wordsworth says that the Poet will wish to bring his feelings near to those of the persons whose feelings he describes . . . and even confound and identify his own feelings with theirs. See also Burke, On the Sublime and Beautiful,4. 4.

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And that is why poetry needs either a sympathetic nature or a madman,Genius to madness near allied is the meaning of μανικός as used here. Plato held that the only excuse for a poet was that he couldn’t help it. the former being impressionable and the latter inspired.

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The stories, whether they are traditional or whether you make them up yourself, should first be sketched in outline and then expanded by putting in episodes.

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I mean that one might look at the general outline, say of the Iphigeneia, like this: A certain maiden has been sacrificed, and has disappeared beyond the ken of those who sacrificed her and has been established in another country, where it is a custom to sacrifice strangers to the goddess; and this priesthood she holds. Some time afterwards it happens that the brother of the priestess arrives there—the fact that the god told him to go there, and why, and the object of his journey, lie outside the outline-plot. He arrives, is seized, and is on the point of being sacrificed, when he reveals his identity either by Euripides’ method or according to Polyidos, by making the very natural remark that after all it is not only his sister who was born to be sacrificed but himself too; and thus he is saved.

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Not until this has been done should you put in names and insert the episodes;

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and you must mind that the episodes are appropriate, as, for instance, in the case of Orestes the madness that led to his capture and his escape by means of the purification.In the Iphigeneia in Tauris Orestes is captured because he is suffering from a fit of mania; and at the end Iphigeneia pretends that the image of Artemis has been infected by the blood-guiltiness of the Greek strangers, and that, before they can be sacrificed, she must cleanse both image and strangers secretly in the sea. Thus they all escape together by boat.

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Now in drama the episodes are short, but it is by them that the epic gains its length.

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The story of the Odyssey is quite short. A man is for many years away from home and his footsteps are dogged by Poseidon and he is all alone. Moreover,affairs at home are in such a state that his estate is being wasted by suitors and a plot laid against his son, but after being storm-tossed he arrives himself, reveals who he is, and attacks them, with the result that he is saved and destroys his enemies.

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That is the essence, the rest is episodes.

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In every tragedy there is a complication and a denouement.The Greek says simply tying and loosing. Complication and denouement seem clumsy equivalents, yet they are the words we use in dramatic criticism. The incidents outside the plot and some of those in it usually form the complication, the rest is the denouement.

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I mean this, that the complication is the part from the beginning up to the point which immediately precedes the occurrence of a change from bad to good fortune or from good fortune to bad; the denouement is from the beginning of the change down to the end.

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For instance, in the Lynceus of Theodectes the complication is the preceding events, and the seizure of the boy, and then their own seizure; and the denouement is from the capital charge to the end.The boy must be Abas, and they are presumably Danaus and perhaps his other daughters. Aristotle seems to regard the arrest of Danaus not as part of the λύσις, but as the end of the δέσις.

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Tragedies should properly be classed as the same or different mainly in virtue of the plot, that is to say those that have the same entanglement and denouement. Many who entangle well are bad at the denouement. Both should always be mastered.

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There are four varieties of tragedy—the same as the number given for the elementsApparently the reference here is to the four elements into which in the course of chapters 10-15. Plot has been analysed, Reversal, Discovery, Calamity, and Character. But the symmetry is spoilt by the fact that his first species, the complex play, corresponds to the first two of these four elements, viz. to Reversal and Discovery. Thus his fourth species is left in the air and he hurriedly introduces Spectacle as the fourth corresponding element. Other explanations seem even sillier than this.—

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first the complex kind, which all turns on reversal and discovery;

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the calamity play like the stories of Ajax and Ixion;

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the character play like the Phthian WomenBy Sophocles. and the PeleusBoth Sophocles and Euripides wrote a Peleus..

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The fourth element is spectacle, like the PhorcidesThe text is obscure, and our ignorance of the play or rhapsody adds to the darkness, but the reference may be to the ruse, common in detective stories, of misleading the audience by false clues in order to make the final revelation more effective. and Prometheus, and all scenes laid in Hades.

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One should ideally try to include all these elements or, failing that, the most important and as many as possible, especially since it is the modern fashion to carp at poets, and, because there have been good poets in each style, to demand that a single author should surpass the peculiar merits of each.

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One must remember, as we have often said, not to make a tragedy an epic structure:

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by epic I mean made up of many stories—suppose, for instance, one were to dramatize the IIiad as a whole.

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The length of the IIiad allows to the parts their proper size, but in plays the result is full of disappointment.

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And the proof is that all who have dramatized the Sack of Troy as a whole, and not, like Euripides, piecemeal, or the Niobe story as a whole and not like Aeschylus, either fail or fare badly in competition. Indeed even Agathon failed in this point alone.

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In reversals, however, and in simple storiesi.e., those that have no Discovery or Reversal. See chapter 10. too,they admirably achieve their end, which is a tragic effect that also satisfies your feelings.

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This is achieved when the wise man, who is, however, unscrupulous, is deceived—like Sisyphus—and the man who is brave but wicked is worsted.

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And this, as Agathon says, is a likely result, since it is likely that many quite unlikely things should happen.

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The chorus too must be regarded as one of the actors. It must be part of the whole and share in the action, not as in Euripides but as in Sophocles.

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In the others the choral odes have no more to do with the plot than with any other tragedy. And so they sing interludes, a practice begun by Agathon. And yet to sing interludes is quite as bad as transferring a whole speech or scene from one play to another.

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The other factors have been already discussed. It remains to speak of Diction and Thought.

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All that concerns Thought may be left to the treatise on Rhetoric, for the subject is more proper to that inquiry.Thought—no English word exactly corresponds with διάνοια—is all that which is expressed or effected by the words (cf. Aristot. Poet. 6.22, 23, and 25). Thus the student is rightly referred to the Art of Rhetoric, where he learns what to say in every case. Aristotle adds that the rules there given for the use of ideas will guide him also in the use of incidents, since the same effect may be produced either by talk or by situation.

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Under the head of Thought come all the effects to be produced by the language.

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Some of these are proof and refutation, the arousing of feelings like pity, fear, anger, and so on, and then again exaggeration and depreciation.It is an important part of the orator’s skill to depreciate what is important and to exaggerate trivial points.

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It is clear that in the case of the incidents, too, one should work on the same principles, when effects of pity or terror or exaggeration or probability have to be produced.

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There is just this difference, that some effects must be clear without explanation,Those produced by situation. whereas others are produced in the speeches by the speaker and are due to the speeches. For what would be the use of a speaker, if the required effect were likely to be felt without the aid of the speeches?

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Under the head of Diction one subject of inquiry is the various modes of speech, the knowledge of which is proper to elocution or to the man who knows the master artRhetoric is a master art in relation to elocution, since it decides the effects to be produced, and elocution decides how to produce them. So the doctor’s art is master to that of the dispenser, and the art of riding to that of the maker of bridles.—I mean for instance, what is a command, a prayer, a statement, a threat, question, answer, and so on.

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The knowledge or ignorance of such matters brings upon the poet no censure worth serious consideration. For who could suppose that there is any fault in the passage which Protagoras censures, because Homer, intending to utter a prayer, gives a command when he says, Sing, goddess, the wrath? To order something to be done or not is, he points out, a command.

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So we may leave this topic as one that belongs not to poetry but to another art.

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Diction as a wholeA translator is bound to render this chapter, since the balance of evidence is in favour of its inclusion. But the readaer is advised to skip it, since it is written from the point of view of grammar and philology, and does not, like the succeeding chapter, deal with the literary use of words. It is also very obscure. Students should refer to Bywater’s edition. is made up of these parts: letter, syllable, conjunction, joint,A joint, as defined below, appears to be a word which indicates the beginning or end of a clause. noun, verb, case, phrase.

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A letter is an indivisible sound, not every such sound but one of which an intelligible sound can be formed. Animals utter indivisible sounds but none that I should call a letter.

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Such sounds may be subdivided into vowel, semi-vowel, and mute. A vowel is that which without any addition has an audible sound; a semivowel needs the addition of another letter to give it audible sound, for instance S and R; a mute is that which with addition has no sound of its own but becomes audible when combined with some of the letters which have a sound. Examples of mutes are G and D.

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Letters differ according to the shape of the mouth and the place at which they are sounded; in being with or without aspiration; in being long and short; and lastly in having an acute, grave, or intermediate accent. But the detailed study of these matters properly concerns students of metre.

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A syllable is a sound without meaning, composed of a mute and a letter that has a sound. GR, for example, without A is a syllable just as much as GRA with an A. But these distinctions also belong to the theory of metre. words. It is also very obscure. Students should refer to Bywater’s edition.

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A conjunction is a sound without meaning, which neither hinders nor causes the formation of a single significant sound or phrase out of several sounds, and which, if the phrase stands by itself, cannot properly stand at the beginning of it, e.g. μέν, δή, τοί, δέ; or else it is a sound without meaning capable of forming one significant sound or phrase out of several sounds having each a meaning of their own, e.g. ἀμφί, περί.

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A joint is a sound without meaning which marks the beginning or end of a phrase or a division in it, and naturally stands at either end or in the middle.This paragraph remains a cause of despair. Bywater’s notes suggest a restoration.

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A noun is a composite sound with a meaning, not indicative of time, no part of which has a meaning by itself; for in compounds we do not use each part as having a meaning of its own, for instance, in Theodorus, there is no meaning of δῶρον (gift).

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A verb is a composite sound with a meaning, indicative of time, no part of which has a meaning by itself—just as in nouns. Man or white does not signify time, but walks and has walked connote present and past time respectively.

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A case(or inflection)of a noun or verb is that which signifies either of or to a thing and the like;or gives the sense of one or many e.g. men and man; or else it may depend on the delivery, for example question and command. Walked? and Walk! are verbal cases of this kind.

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A phraseThere is no exact English equivalent of this meaning of λόγος, which has been used already in 7 above without explanation. Statement and proposition also cover part of its meaning. is a composite sound with a meaning, some parts of which mean something by themselves.

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It is not true to say that every phrase is made up of nouns and verbs, e.g. the definition of manProbably one of the two definitions given in the Topics, a two-footed land animal and an animal amenable to reason.; but although it is possible to have a phrase without verbs, yet some part of it will always have a meaning of its own, for example, Cleon in Cleon walks.

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A phrase may be a unit in two ways; either it signifies one thing or it is a combination of several phrases. The unity of the Iliad, for instance, is due to such combination, but the definition of man is one phrase because it signifies one thing.

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Nouns are of two kinds. There is the simple noun, by which I mean one made up of parts that have no meaning, like γῆ, and there is the compound noun.

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These may be made up either of a part which has no meaning and a part which has a meaning—though it does not have its meaning in the compound—or of two parts both having a meaning.

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A compound noun may be triple and quadruple and multiple, e.g. many of the bombastic names like Hermocaicoxanthus.A compound of the names of three rivers, Hermus, Caicus, and Xanthus. . . .

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Every noun is either ordinaryi.e., one which has dined normal currency as contrasted with the rare word, which is confined to a dialect or borrowed from a foreign language. or rare or metaphorical or ornamental or invented or lengthened or curtailed or altered.

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An ordinary word is one used by everybody, a rare word one used by some;

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so that a word may obviously be both ordinary and rare, but not in relation to the same people. σίγυνον,Meaning, spear. for instance, is to the Cypriots an ordinary word but to us a rare one.

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Metaphor is the application of a strange term either transferred from the genus and applied to the species or from the species and applied to the genus, or from one species to another or else by analogy.

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An example of a term transferred from genus to species is Here stands my ship. Riding at anchor is a species of standing.

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An example of transference from species to genus is Indeed ten thousand noble things Odysseus did, for ten thousand, which is a species of many, is here used instead of the word many.

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An example of transference from one species to another is Drawing off his life with the bronze and Severing with the tireless bronze, where drawing off is used for severing and severing for drawing off, both being species of removing.Probably the bronze is in the first case a knife and in the second a cupping-bowl. This would make the metaphor intelligible.

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Metaphor by analogy means this: when B is to A as D is to C, then instead of B the poet will say D and B instead of D.

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And sometimes they add that to which the term supplanted by the metaphor is relative.This may claim to be one of Aristotle’s least lucid sentences. It means this: If Old Age: Life :: Evening: Day, then we may call old age the Evening of Life. In that case old age is the term supplanted by the metaphor, and it is relative to Life; therefore Life (i.e., that to which the term supplanted by the metaphor is relative) is added to the metaphorical (or transferred) term Evening.For instance, a cup is to Dionysus what a shield is to Ares;

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so he will call the cup Dionysus’s shield and the shield Ares’ cup. Or old age is to life as evening is to day; so he will call the evening day’s old-age or use Empedocles’ phraseUnknown to us.; and old age he will call the evening of life or life’s setting sun.

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Sometimes there is no word for some of the terms of the analogy but the metaphor can be used all the same. For instance, to scatter seed is to sow, but there is no word for the action of the sun in scattering its fire. Yet this has to the sunshine the same relation as sowing has to the seed, and so you have the phrase sowing the god-created fire.

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Besides this another way of employing metaphor is to call a thing by the strange name and then to deny it some attribute of that name. For instance, suppose you call the shield not Ares’ cup but a “wineless cup.” . . .Or you might call Love Venus’s bloodless War. At this point a few lines on Ornament have evidently been lost, since this is its place in the catalogue of nouns above. By ornament he seems to mean an embellishing epithet or synonym. In the Rhetoric he quotes Our lady the fig-tree as a misplaced ornament. One might add the seventeenth-century use of Thames for water. . . .

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An invented word is one not used at all by any people and coined by the poet. There seem to be such words, eg. sprouters for horns and pray-er for priest.

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A word is lengthened or curtailed, the former when use is made of a longer vowel than usual or a syllable inserted, and the latter when part of the word is curtailed.

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An example of a lengthened word is πόληος for πολέως and Πηληιάδεω for Πηλείδου; and of a curtailed word κρῖ and δῶ, and e.g. μία γίνεται ἀμφοτέρων ὄψ.κρῖ for κριθή, barley; δῶ for δῶμα house; ὄψ for ὄψις face, eye, or appearance.

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A word is altered when the poet coins part of the word and leaves the rest unchanged, e.g. δεξιτερὸν κατὰ μαζόν instead of δεξιόν.

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Of the nouns themselves, some are masculine, some feminine, and some neuter.This paragraph the reader should either skip or study with Bywater’s notes. Without them these generalizations on gender seem merely wrong.

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Masculine are all that end in N and P and Σ and in the two compounds of Σ, Ψ and Ξ.

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Feminine are all that end in those of the vowels that are always long, for instance Η and Ω, and in Α among vowels that can be lengthened.

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The result is that the number of masculine and feminine terminations is the same, for Ψ and Ξ are the same as Σ.

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No noun ends in a mute or in a short vowel.

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Only three end in Ι, μέλι, κόμμι, and πέπερι. Five end in Υ. The neuters end in these letters and in Ν and Σ.

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The merit of diction is to be clear and not commonplace. The clearest diction is that made up of ordinary words, but it is commonplace.

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An example is the poetry of Cleophon and of Sthenelus.A tragedian whom Aristophanes ridicules for the insipidity of his diction.

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That which employs unfamiliar words is dignified and outside the common usage. By unfamiliar I mean a rare word, a metaphor, a lengthening,See preceding chapter 19. and anything beyond the ordinary use.

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But if a poet writes entirely in such words, the result will be either a riddle or jargon; if made up of metaphors, a riddle and if of rare words, jargon.

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The essence of a riddle consists in describing a fact by an impossible combination of words. By merely combining the ordinary names of things this cannot be done, but it is made possible by combining metaphors. For instance, I saw a man weld bronze upon a man with fire, and so on.The answer is a cupping-bowl. This was a bronze vessel which was applied to the body at the place at which a small incision had been made. Heated lint was placed in the bowl of it and the reduction of air-pressure thus caused a strong flow of blood. For this form of riddle cf. Out of the strong came forth sweetness.

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A medley of rare words is jargon.

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We need then a sort of mixture of the two. For the one kind will save the diction from being prosaic and commonplace, the rare word, for example, and the metaphor and the ornament, whereas the ordinary words give clarity.

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A considerable aid to clarity and distinction are the lengthening and abbreviation and alteration of words. Being otherwise than in the ordinary form and thus unusual, these will produce the effect of distinction, and clarity will be preserved by retaining part of the usual form.

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Those critics are therefore wrong who censure this manner of idiom and poke fun at the poet, as did the elder EucleidesA critic of this name wrote on the drama, but his date is uncertain. who said it was easy to write poetry, granted the right to lengthen syllables at will. He had made a burlesque in this very style: Ἐπιχάρην εἶδον Μαραθῶνάδε βαδίζοντα and οὐκ ἄν γ’ ἐράμενος τὸν ἐκείνου ἐλλέβορον.In Homer we find short vowels lengthened by position, but, whereas Homer uses the licence sparingly, Eucleides raised a laugh by overdoing it and writing in parody such hexameters as those here quoted. A modern parallel may illustrate this. The poet Stephen Phillips employed to excess the licence whihc allows a clash between the natural accent and the metrical ictus, and Mr. Owen Seaman, for the express purpose of raising a laugh, parodied the trick by carrying it to further excess and wrote in blank verse, She a milliner was and her brothers Dynamiters.

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Now to make an obtrusive use of this licence is ridiculous;

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but moderation is a requisite common to all kinds of writing. The same effect could be got by using metaphors and rare words and the rest unsuitably for the express purpose of raising a laugh.

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What a difference is made by the proper use of such licence may be seen in epic poetry, if you substitute in the verse the ordinary forms.

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Take a rare word or metaphor or any of the others and substitute the ordinary word; the truth of our contention will then be obvious.For instance, Aeschylus and Euripides wrote the same iambic line with the change of one word only, a rare word in place of one made ordinary by custom, yet the one line seems beautiful and the other trivial. Aeschylus in the Philoctetes wrote, The ulcer eats the flesh of this my foot, and Euripides instead of eats put feasts upon. Or take I that am small, of no account nor goodly; suppose one were to read the line substituting the ordinary words, I that am little and weak and ugly. Or compare He set a stool unseemly and a table small. with He set a shabby stool and a little table, or the sea-shore is roaring with the sea-shore is shrieking.Similarly we might use ordinary words instead of those which Keats chose so carefully and speak of wonderful windows abutting on to a dangerous sea-shore in a dreary, mysterious country.

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AriphradesUnknown. again made fun of the tragedians because they employ phrases which no one would use in conversation, like δωμάτων ἄπο instead of ἀπὸ δωμάτων and their σέθεν and ἐγὼ δέ νιν and Ἀχιλλέως πέρι for περὶ Ἀχιλλέως, and so on.

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All that sort of thing, not being in the ordinary form, gives distinction to the diction, which was what he failed to understand.

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It is a great thing to make a proper use of each of the elements mentioned, and of double words and rare words too, but by far the greatest thing is the use of metaphor.

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That alone cannot be learnt; it is the token of genius. For the right use of metaphor means an eye for resemblances.i.e., the power of detecting identity in difference which distinguishes also both the philosopher and the scientist.

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Of the various kinds of words the double forms are most suited for dithyrambs, rare words for heroic verse and metaphors for iambics.

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And indeed in heroic verse they are all useful; but since iambic verse is largely an imitation of speech, only those nouns are suitable which might be used in talking. These are the ordinary word, metaphor, and ornament.

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Now concerning tragedy and the art of representing life in action, what we have said already must suffice.

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We come now to the art of representation which is narrative and in metre.i.e., epic. Clearly the story must be constructed as in tragedy, dramatically, round a single piece of action, whole and complete in itself,with a beginning, middle and end, so that like a single living organism it may produce its own peculiar form of pleasure.

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It must not be such as we normally find in history, where what is required is an exposition not of a single piece of action but of a single period of time, showing all that within the period befell one or more persons, events that have a merely casual relation to each other.

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For just as the battle of Salamis occurred at the same time as the Carthaginian battle in Sicily, but they do not converge to the same resultGelo’s defeat of the Carthaginians in Sicily in 480 B.C. took place, according to Herodotus, on the same day as the battle of Salamis.; so, too, in any sequence of time one event may follow another and yet they may not issue in any one result.

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Yet most of the poets do this.

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So in this respect, too, compared with all other poets Homer may seem, as we have already said, divinely inspired, in that even with the Trojan war, which has a beginning and an end, he did not endeavor to dramatize it as a whole, since it would have been either too long to be taken in all at once or, if he had moderated the length, he would have complicated it by the variety of incident. As it is, he takes one part of the story only and uses many incidents from other parts, such as the Catalogue of Ships and other incidents with which he diversifies his poetry.

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The others, on the contrary, all write about a single hero or about a single period or about a single action with a great many parts, the authors, for example, of the Cypria and the Little Iliad.As we have seen already in chapter 8, a poem or a play must be one story and not several stories about one hero. Thus, since the Iliad and Odyssey have this essential unity (i.e., one thread runs through the narrative of each), few plays can be made out of them but many out of the Cypria or the Little Iliad, which are merely collections of lays on similar themes.

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The result is that out of an Iliad or an Odyssey only one tragedy can be made, or two at most, whereas several have been made out of the Cypria, and out of the Little Iliad more than eight, e.g. The Award of Arms, Philoctetes, Neoptolemus, Eurypylus, The Begging, The Laconian Women, The Sack of <placeName key="perseus,Troy">Troy</placeName>, and Sailing of the Fleet, and Sinon, too, and The Trojan Women.

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The next point is that there must be the same varieties of epic as of tragedySee Aristot. Poet. 18.4.: an epic must be simple or complex,See chapter 10. or else turn on character or on calamity.

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The constituent parts, too, are the same with the exception of song and spectacle. Epic needs reversals and discoveries and calamities, and the thought and diction too must be good.

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All these were used by Homer for the first time, and used well. Of his poems he made the one, the Iliad, a simple story turning on calamity, and the Odyssey a complex story—it is full of discoveries—turning on character. Besides this they surpass all other poems in diction and thought.

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Epic differs from tragedy in the length of the composition and in metre.

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The limit of length already givenSee Aristot. Poet. 7.12. will suffice—it must be possible to embrace the beginning and the end in one view,which would be the case if the compositions were shorter than the ancient epics but reached to the length of the tragedies presented at a single entertainment.“Entertainment” must mean a festival. At the City Dionysia three poets competed, each with three tragedies. By the end of the fifth century only one Satyr play was performed at each festival. But the tragedies were longer than those we possess. It is therefore likely that the nine tragedies together with one Satyr play amounted to about 15,000 lines. The Iliad contains between 16,000 and 17,000 lines.

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Epic has a special advantage which enables the length to be increased, because in tragedy it is not possible to represent several parts of the story as going on simultaneously, but only to show what is on the stage, that part of the story which the actors are performing; whereas, in the epic, because it is narrative, several parts can be portrayed as being enacted at the same time.

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If these incidents are relevant, they increase the bulk of the poem, and this increase gives the epic a great advantage in richness as well as the variety due to the diverse incidents; for it is monotony which, soon satiating the audience, makes tragedies fail.

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Experience has shown that the heroic hexameter is the right metre. Were anyone to write a narrative poem in any other metre or in several metres, the effect would be wrong.

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The hexameter is the most sedate and stately of all metres and therefore admits of rare words and metaphors more than others, and narrative poetry is itself elaborate above all others.

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The iambic and the trochaic tetrameter are lively, the latter suits dancing and the former suits real life.

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Still more unsuitable is it to use several metres as Chaeremon did.

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So no one has composed a long poem in any metre other than the heroic hexameter. As we said above, Nature shows that this is the right metre to choose.

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Homer deserves praise for many things and especially for this, that alone of all poets he does not fail to understand what he ought to do himself. The poet should speak as seldom as possible in his own character, since he is not representing the story in that sense.This takes us back to the beginning of chapter 3, where the various manners of representation are distinguished. Homer represents life partly by narration, partly by assuming a character other than his own. Both these manners come under the head of Imitation. When Aristotle says the poet speaks himself and plays a part himself he refers not to narrative, of which there is a great deal in Homer, but to the preludes (cf. φροιμιασάμενος below) in which the poet, invoking the Muse, speaks in his own person. Ridgeway points out that in the whole of the Iliad and Odyssey Homer thus speaks himself only 24 lines.

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Now the other poets play a part themselves throughout the poem and only occasionally represent a few things dramatically, but Homer after a brief prelude at once brings in a man or a woman or some other character, never without character, but all having character of their own.

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Now the marvellous should certainly be portrayed in tragedy, but epic affords greater scope for the inexplicable(which is the chief element in what is marvellous), because we do not actually see the persons of the story.

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The incident of Hector’s pursuitIliad, xxii. 205. sq. “And to the host divine Achilles nodded with his head a sign and let them not launch their bitter darts at Hector, lest another should win glory by shooting him and Achilles himself come second.” would look ridiculous on the stage, the people standing still and not pursuing and Achilles waving them back, but in epic that is not noticed.

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But that the marvellous causes pleasure is shown by the fact that people always tell a piece of news with additions by way of being agreeable.

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Above all, Homer has taught the others the proper way of telling lies,that is, by using a fallacy. When B is true if A is true, or B happens if A happens, people think that if B is true A must be true or happen. But that is false. Consequently if A be untrue but there be something else, B, which is necessarily true or happens if A is true, the proper thing to do is to posit B, for, knowing B to be true, our mind falsely infers that A is true also. This is an example from the Washing.Odyssey 19. Odysseus tells Penelope that he is a Cretan from Gnossus, who once entertained O. on his voyage to Troy. As evidence, he describes O.’s dress and his companions (Hom. Od. 19.164-260). P. commits the fallacy of inferring the truth of the antecedent from the truth of the consequent: “If his story were true, he would know these details; But he does know them; Therefore his story is true.” The artist in fiction uses the same fallacy, e.g.: “If chessmen could come to life the white knight would be a duffer; But he is a most awful duffer (look at him!); Therefore chessmen can come to life.” He makes his deductions so convincing that we falsely infer the truth of his hypothesis.

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What is convincing though impossible should always be preferred to what is possible and unconvincing.

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Stories should not be made up of inexplicable details; so far as possible there should be nothing inexplicable, or, if there is, it should lie outside the story—as, for instance, Oedipus not knowing how Laius died—and not in the play; for example, in the Electra the news of the Pythian games,In Sophocles’Electrathe plot hinges on a false story of Orestes’ death by an accident at the Pythian games. Presumably the anachronism shocked Aristotle. or in the Mysians the man who came from Tegea to Mysia without speaking.Telephus. To say that the plot would otherwise have been ruined is ridiculous.

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One should not in the first instance construct such a plot, and if a poet does write thus, and there seems to be a more reasonable way of treating the incident, then it is positively absurd.

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Even in the Odyssey the inexplicable elements in the story of his landingHom. Od. 13.116ff. It seemed to the critics inexplicable that Odysseus should not awake when his ship ran aground at the harbour of Phorcys in Ithaca and the Phaeacian sailors carried him ashore. would obviously have been intolerable, had they been written by an inferior poet. As it is, Homer conceals the absurdity by the charm of all his other merits.

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The diction should be elaborated only in the idle parts which do not reveal character or thought.The Messengers’ speeches, a regular feature of Greek tragedy, may serve to illustrate what is here called the idle part of a play, i.e., passages which, but for brilliant writing, might be dull, since no character is there elucidated and no important sentiments expressed. Too brilliant diction frustrates its own object by diverting attention from the portrayal of character and thought.

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With regard to problems,A problem in this sense is a difficult passage or expression which explanation and may easily be censured by an unsympathetic critic. Aristotle here classifies the various grounds of censure and the various lines of defence. Most of his illustrations are drawn from the critical objections lodged against the Iliad by Zoilus and other hammerers of Homer. As the reader will see, many of them are abysmally foolish. and the various solutions of them, how many kinds there are, and the nature of each kind, all will be clear if we look at them like this.

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Since the poet represents life, as a painter does or any other maker of likenesses, he must always represent one of three things—either things as they were or are; or things as they are said and seem to be; or things as they should be.

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These are expressed in diction with or without rare words and metaphors, there being many modifications of diction, all of which we allow the poet to use.

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Moreover, the standard of what is correct is not the same in the art of poetry as it is in the art of social conduct or any other art.

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In the actual art of poetry there are two kinds of errors, essential and accidental.

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If a man meant to represent something and failed through incapacity, that is an essential error. But if his error is due to his original conception being wrong and his portraying, for example, a horse advancing both its right legs, that is then a technical error in some special branch of knowledge,in medicine, say, or whatever it may be; or else some sort of impossibility has been portrayed, but that is not an essential error.

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These considerations must, then, be kept in view in meeting the charges contained in these objections.

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Let us first take the charges against the art of poetry itself. If an impossibility has been portrayed, an error has been made.

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But it is justifiable if the poet thus achieves the object of poetry—what that is has been already stated—and makes that part or some other part of the poem more striking. The pursuit of Hector is an example of this.See Aristot. Poet. 24.16 and note.

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If, however, the object could have been achieved better or just as well without sacrifice of technical accuracy, then it is not justifiable, for, if possible, there should be no error at all in any part of the poem.

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Again one must ask of which kind is the error, is it an error in poetic art or a chance error in some other field? It is less of an error not to know that a female stag has no horns than to make a picture that is unrecognizable.

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Next, supposing the charge is That is not true, one can meet it by saying But perhaps it ought to be, just as Sophocles said that he portrayed people as they ought to be and Euripides portrayed them as they are.

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If neither of these will do, then say, Such is the tale; for instance, tales about gods.

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Very likely there is no advantage in telling them, and they are not true either, but may well be what Xenophanes declaredi.e., immoral and therefore untrue. He opened the assault on Homeric theology at the end of the sixth or the beginning of the fifth century B.C.—all the same such is the tale.

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In another case, perhaps, there is no advantage but such was the fact, e.g. the case of the arms, Their spears erect on butt-spikes stood,Hom. Il. 10.152. Problem: Surely a bad stance: they might so easily fall and cause alarm. Solution: Homer does not defend it. He merely states a fact. It is thus that we excuse unpleasant fiction. for that was then the custom, as it still is in Illyria.

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As to the question whether anything that has been said or done is morally good or bad, this must be answered not merely by seeing whether what has actually been done or said is noble or base, but by taking into consideration also the man who did or said it, and seeing to whom he did or said it, and when and for whom and for what reason; for example, to secure a greater good or to avoid a greater evil.

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Some objections may be met by reference to the diction, for example, by pleading rare word, e.g. οὐρῆας μὲν πρῶτον, for perhaps he means not mules but sentinels.Hom. Il. 1.50: The mules and swift-footed hounds he first beset with his arrows. Apollo is sending plague upon the Greek army. Problem: Why should he first attack the mules? Solution: The word may here mean sentiels. And Dolon, One that was verily evil of form, it may be not his deformed body but his ugly face, for the Cretans use fair-formed for fair-featured.Hom. Il. 10.316: One that was verily evil inform but swift in his running. Problem: If Dolon were deformed, how could he run fast? Solution: Form may here mean feature. And again Livelier mix it may mean not undiluted as for drunkards but quicker.Hom. Il. 9.202: Set me, Menoetius’ son, a larger bowl for the mingling, Livelier mix it withal and make ready for each one a beaker. Problem: Livelier suggests intemperance. Solution: Perhaps the word means quicker. Similar scruples emended the lines in Young Lochinvar to read: And now am I come with this pretty maid To dance but one measure, drink one lemonade.

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Other expressions are metaphorical, for example: Then all the other immortals and men lay all night in slumber, while yet he says: Yea, when indeed he gazed at the Trojan plain Agamemnon Marvelled at voices of flutes . . . All is used instead of many metaphorically, all being a species of many.Hom. Il. 2.2 (quoted by mistake for Hom. Il. 10.1) and Hom. Il. 10.13, 14: Then all the other immortals and all the horse-crested heroes Night-long slumbered, but Zeus the sweet sleep held not. . . (Hom. Il. 2.1, 2) Yea, when indeed he gazed at the Trojan plain, Agamemnon Marvelled at voices of flutes and of pipes and the din of the soldiers. (Hom. Il. 10.13, 14) Problem: If all were asleep, who was playing the flute? Solution: This may be a metaphor; as explained in chapter 21, all is one kind or species of many, and thus by transference all is used for many, the species for the genus. And again, Alone unsharingHom. Il. 18.489: She alone of all others shares not in the baths of the Ocean. The reference is to the Great Bear. Problem: Why does Homer say she alone when the other Northern Constellations also do not set? Solution: As in the last instance, the may be metaphorical, i.e., the genus, sole, may be here used by transference for one of its species, best known. is metaphorical; the best known is called the only one.

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By intonation also; for example, the solutions of Hippias of Thasos, his δίδομεν δέ οἱHom. Il. 2.15. Our text is different. Aristotle, who quotes the line agains elsewhere, read thus: No longer the gods in the halls of Olympus Strive in their plans, for Hera has bent them all to her purpose Thus by her prayers; and we grant him to win the boast of great glory. Zeus is instructing the Dream, whom he is sending to lure Agamemnon to disaster. Problem: The last statement is a lie. Solution: Change the accent and the statement δίδομεν δέ οἱ becomes a command (the infinitive διδόμεναι written in a shortened form and used as an imperative). The lie will then be told by the Dream and not by Zeus, who may thus save his reputation for veracity. and τὸ μὲν οὗ καταπύθεται ὄμβρῳHom. Il. 23.327: A fathom high from the earth there rises a stump all withered, A stump of an oak or a pine, that rots not at all in the rain. Problem: The last statement is incredible. Solution: Alter the breathing and τὸ μὲν οὐ becomes τὸ μὲν οὗ and means part of it rots in the rain.;

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and by punctuation; for example, the lines of Empedocles: Soon mortal grow they that aforetime learnt Immortal ways, and pure erstwhile commingled.The Problem is erstwhile goes with pure or with commingled. The former interpretation seems to give the best solution. Empedocles is speaking of the elements or atoms.

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Or again by ambiguity, e.g. παρῴχηκεν δὲ πλέω νύξ, where πλείω is ambiguous.Hom. Il. 10.252: Come now, the night is far spent and at hand is the dawning, Far across are the stars and more than two parts of the night-time Are gone, but a third is still left us. Problem: If more than two parts are gone, a third cannot be left. Solution: πλέω here means full, i.e., the full night of two-thirds = full two-thirds of the night is gone, and so Homer’s arithmetic is saved.

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Others according to the habitual use of the phrase, e.g. wine and water is called wine so you get the phrase greaves of new-wrought tin;Problem: Greaves are made not of tin but of an alloy of tin and copper. Solution: Compounds are called by the name of the more important partner. Just as a mixture of wine and water is called wine, so here an alloy of tin and copper is called tin. So, too, is whisky and water called whisky. or workers in iron are called braziers, and so Ganymede is said to pour wine for Zeus, though they do not drink wine. This last might however be metaphorical.Nectar:gods :: wine: men. Therefore, according to the rules of metaphor in chapter 21, nectar may be called wine or the wine of the gods.

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Whenever a word seems to involve a contradiction, one should consider how many different meanings it might bear in the passage, e.g. in There the bronzen shaft was stayed,Hom. Il. 20.272: Nay but the weighty shaft of the warlike hero Aeneas Brake not the shield; for the gold, the gift of a god, did withstand it. Through two folds it drave, yet three were beneath, for Hephaestus, Crook-footed god, five folds had hammered; two were of bronze-work, Two underneath were of tin and one was of gold; there the bronzen Shaft of the hero was stayed in the gold. Problem: Since the gold was presumably outside for the sake of ornament, how could the spear he stayed in the gold and yet penetrate two folds? Bywater suggests as a solution that the plate of gold sufficed to stop the course of the spear, though the spear-point actually pierced it and indented the underlying plates of brass. we should ask in how many ways being stayed might be taken,

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interpreting the passage in this sense or in that, and keeping as far as possible from the attitude which GlauconThis may well be the Glaucon mentioned in Plato’s Ion as an authority on Homer. describes

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when he says that people make some unwarrantable presupposition and having themselves given an adverse verdict proceed to argue from it, and if what they think the poet has said does not agree with their own preconceived ideas, they censure him, as if that was what he had said.

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This is what has happened in the case of Icarius.Penelope’s father. They assume that he was a Spartan and therefore find it odd that when Telemachus went to Sparta he did not meet him. But the truth may be, as the Cephallenians say, that Odysseus married a wife from their country and that the name was not Icarius but Icadius. So the objection is probably due to a mistake.

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In general any impossibility may be defended by reference to the poetic effect or to the ideal or to current opinion.

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For poetic effect a convincing impossibility is preferable to that which is unconvincing though possible.

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It may be impossible that there should be such people as ZeuxisSee Aristot. Poet. 6.15. used to paint, but it would be better if there were; for the type should improve on the actual.

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Popular tradition may be used to defend what seems irrational, and you can also say that sometimes it is not irrational, for it is likely that unlikely things should happen.

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Contradictions in terms must be examined in the same way as an opponent’s refutations in argument, to see whether the poet refers to the same thing in the same relation and in the same sense, and has contradicted either what he expressly says himself or what an intelligent person would take to be his meaning.

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It is right, however, to censure both improbability and depravity where there is no necessity and no use is made of the improbability.An example is Euripides’ intro duction of AegeusEur. Medea 663. In Aristotle’s opinion there is no good reason for Aegeus’s appearance and no good use is made of it. or(of depravity)the character of Menelans in the Orestes.

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The censures they bring are of five kinds; that things are either impossible or irrational or harmful or inconsistent or contrary to artistic correctness. The solutions must be studied under the heads specified above, twelve in number.i.e., any expression that is criticized should be considered with reference to (1) things as they were; (2) things as thy are; (3) things as they are said to be; (4) things as they seem to be; (5) things as they ought to be. Further, we should consider whether (6) a rare word or (7) a metaphor is used; what is the right (8) accent and (9) punctuation; also where there may be (10) ambiguity and what is (11) the habitual use of the phrase; also we may refer to (12) the proper standard of correctness in poetry as distinct from other arts.

- - - Poetics -

- LetThe text here printed is based on Vahlen's - third edition(Leipzig, - 1885), and the chief deviations from it are noted at the foot of each - page. The prime source of all existing texts of the Poetics is the eleventh - century Paris manuscript, No. 1741, designated as Ac. To the manuscripts of the - Renaissance few, except Dr. Margoliouth, now assign any independent value, but - they contain useful suggestions for the correction of obvious errors and defects - in Ac. These are here designated “copies.”V. stands for - Vahlen's third edition, and By. for the late Professor Ingram Bywater, who has - earned the gratitude and admiration of all students of the Poetics by his - services both to the text and to its interpretation. Then there is the Arabic - transcript. Translated in the eleventh century from a Syriac translation made in - the eighth century, it appears to make little sense, but sometimes gives dim - visions of the readings of a manuscript three centuries older but not - necessarily better than Ac, readings which confirm some of the improvements - introduced into Renaissance texts. us here deal with Poetry, its essence - and its several species, with the characteristic function of each species and the - way in which plots must be constructed if the poem is to be a success; and also with - the number and character of the constituent parts of a poem, and similarly with all - other matters proper to this same inquiry; and let us, as nature directs, begin - first with first principles. Epic poetry, then, and the poetry of tragic drama, and, - moreover, comedy and dithyrambic poetry, and most flute-playing and harp-playing, - these, speaking generally, may all be said to be "representations of life."The explanation of MI/MHSIS, as Aristotle uses the word, demands a treatise; all - that a footnote can say is this:—Life "presents" to the artist the - phenomena of sense, which the artist "re-presents" in his own medium, giving - coherence, designing a pattern. That this is true not only of drama and fiction - but also of instrumental music ("most flute-playing and harp-playing") was more - obvious to a Greek than to us, since Greek instrumental music was more - definitely imitative. The technical display of the virtuoso Plato describes as - "a beastly noise." Since MI/MHSIS in this sense - and MIMHTH/S and the verb MIMEI=SQAI have a wider scope than any one English word, it is - necessary to use more than one word in translation, e.g. MIMHTH/S is what we call an "artist"; and for MI/MHSIS where "representation" would be clumsy we - may use the word "art"; the adjective must be "imitative," since - "representative" has other meanings. - But they differ one from another in - three ways: either in using means generically differenti.e., means that can be divided into separate categories. or - in representing different objects or in representing objects not in the same way but - in a different manner. For just as by - the use both of color and form people represent many objects, making likenesses of - them—some having a - knowledge of art and some working empirically—and just as others use the - human voice; so is it also in the arts which we have mentioned, they all make their - representations in rhythm and language and tune, using these means either separately - or in combination. For tune and rhythm - alone are employed in flute-playing and harp-playing and in any other arts which - have a similar function, as, for example, pipe-playing. Rhythm alone without tune is employed by dancers in their - representations, for by means of rhythmical gestures they represent both character - and experiences and actions.PA/QH KAI\ PRA/CEIS cover the whole field of life, what men do - (PRA/CEIS) and what men experience (PA/QH). Since PA/QH - means also "emotions" and that sense may be present here, but as a technical - term in this treatise PA/QOS is a calamity or - tragic incident, something that happens to the hero. But the art which - employs words either in bare prose or in metres, either in one kind of metre or - combining several, happens up to the present day to have no name. For we can find no common term to apply to the mimes - of Sophron and XenarchusSophron and Xenarchus, said - to he father and son, lived in Syracuse, the elder a contemporary of Euripides. They wrote - "mimes," i.e., simple and usually farcical sketches of familiar incidents, - similar to the mimes of Herondas and the fifteenth Idyll of Theocritus, but in - prose. There was a tradition that their mimes suggested to Plato the use of - dialogue. and to the Socratic dialogues: nor again supposing a poet were to make his representation in - iambics or elegiacs or any other such metre—except that people attach the - word poet(maker)to the name of the metre and speak of elegiac - poets and of others as epic poets. - Thus they do not call them poets in virtue of their representation but apply the - name indiscriminately in virtue of the metre. For if people publish medical or scientific treatises in - metre the custom is to call them poets. But Homer and EmpedoclesEmpedocles (floruit 445 B.C.) expressed - his philosophical and religious teaching in hexameter verse, to which Aristotle - elsewhere attributes genuine value as poetry, but it is here excluded from the - ranks of poetry because the object is definitely. have nothing in common - except the metre, so that it would be proper to call the one a poet and the other not - a poet but a scientist. Similarly if a man makes his representation - by combining all the metres, as Chaeremon did when he wrote his rhapsody The - Centaur, a medley of all the metres, he too should be given the name of - poet.Chaeremon was a tragedian and rhapsodist. - The Centaur was apparently an experiment which might be classed - as either drama or epic. Cf. Aristot. Poet. - 24.11. On this point the distinctions thus made may - suffice. There are certain arts which employ all the means which I - have mentioned, such as rhythm and tune and metre—dithyrambic and "nomic" - poetry,The traditional definition is that the - Dithyramb was sung to a flute accompaniment by a chorus in honor of Dionysus; - and that the Nome was a solo sung to a harp accompaniment in honor of Apollo, - but it is not clear that Aristotle regarded the Dithyramb as restricted to the - worship of Dionysus. Timotheus's dithyramb mentioned in Aristot. Poet. 15.8 cannot have been - Dionysiac. But there is good evidence to show that the dithyramb was primarily - associated with Dionysus. for example, and tragedy too and comedy. The - difference here is that some use all these at once, others use now one now another. - These differences then in the - various arts I call the means of representation. Since living personsLiterally "men doing or experiencing - something." are the objects of representation, these must necessarily be - either good men or inferior—thus only are characters normally - distinguished, since ethical differences depend upon vice and virtue—that - is to say either better than ourselves or worse or much what we are. It is the same - with painters. Polygnotus depicted men - as better than they are and Pauson worse, while Dionysius made likenesses.Polygnotus's portraits were in the grand style and - yet expressive of character(cf. Aristot. - Poet. 6.15): Aristophanes aIludes to a Pauson as a - "perfectly wicked caricaturist": Dionysius of Colophon earned the name of "the man-painter" because he always - painted men and presumably made "good likenesses." - Clearly each of the above mentioned - arts will admit of these distinctions, and they will differ in representing objects - which differ from each other in the way here described. In painting too, and flute-playing and harp-playing, these - diversities may certainly be found, and it is the same in prose and in unaccompanied - verse. For instance Homer's people are - "better," Cleophon's are "like," while in Hegemon of Thasos, the first writer of parodies, and in Nicochares, the author - of the Poltrooniad, they are "worse."Cleophon wrote "epics" (i.e., hexameter poems), describing scenes of daily life - in commonplace diction (cf. Aristot. Poet. - 22.2): Hegemon wrote mock epics in the style of the surviving - Battle of Frog and Mice: of Nicochares nothing is known, but - his forte was evidently satire. - It is the same in dithyrambic and nomic - poetry, for instance . . . a writer might draw characters like the - Cyclops as drawn by Timotheus and Philoxenus.Both famous dithyramhic poets. There is evidence that - Philoxenus treated Polyphemus in the vein of satire: Timotheus may have drawn a - more dignified picture. - It is just in this respect that tragedy - differs from comedy. The latter sets out to represent people as worse than they are - to-day, the former as better. A third difference in these arts is the manner in - which one may represent each of these objects. For in representing - the same objects by the same means it is possible to proceed either partly by - narrative and partly by assuming a character other than your own—this is - Homer's method—or by remaining yourself without any such change, or else - to represent the characters as carrying out the whole action themselves. These, as we - said above, are the three differences which form the several species of the art of - representation, the means, the objects, and the manner. It follows that in one respect - Sophocles would be the same kind of artist as Homer, for both represent good men, - and in another respect he would resemble Aristophanes, for they both represent men - in action and doing things. And that according to some is the reason why they are - called "dramas," because they present people as doing"Drama" being derived from DRA=N "to - do." things. And for this - reason the Dorians claim as their own both tragedy and comedy—comedy is - claimed both by the Megarians here in Greece, who say that it originated in the days of their democracy, - and by the Megarians in Sicily,The inhabitants of Megara Hyblaea. for it was - from there the poet EpicharmusEpicharmus of Cos - wrote in Sicily burlesques and "mimes" - depicting scenes of daily life. He and Phormis were "originators of comedy" in - that they sketched types instead of lampooning individuals (cf. Aristot. Poet. 5.5): of Chionides and Magnes - we only know that they were "early" comedians, i.e., in the first half of the - fifth century B.C. came, who was much earlier than Chionides and Magnes; - and tragedy some of the Peloponnesians claim. Their evidence is the two names. - Their name, they say, for suburb - villages is KW=MAI—the Athenians call them - "Demes"—and comedians are so called not from KWMA/ZEIN, "to revel," but because they were turned out of the towns - and went strolling round the villages( KW=MAI). Their word for action, they add, is DRA=N, whereas the Athenian word is PRA/TTEIN. So much then for the differences, their number, and their - nature. Speaking generally, poetry seems to owe its origin to two particular causes, both - natural. From childhood men have an - instinct for representation, and in this respect, differs from the other animals - that he is far more imitative and learns his first lessons by representing things. - And then there is the enjoyment people always get from representations. What happens in actual experience proves this, - for we enjoy looking at accurate likenesses of things which are themselves painful - to see, obscene beasts, for instance, and corpses. The reason is this: Learning things gives great pleasure not - only to philosophers but also in the same way to all other men, though they share - this pleasure only to a small degree. - The reason why we enjoy seeing likenesses is that, as we look, we learn and infer - what each is, for instance, "that is so and so." If we have never happened to see the original, our pleasure - is not due to the representation as such but to the technique or the color or some - other such cause. We have, then, a - natural instinct for representation and for tune and rhythmIt is not clear wheter the "two general causes" are (1) the instinct - for imitation, (2) the natural enjoyment of mimicry by others; or whether these - two are combined into one and the second cause is the instinct for tune and - rhythm. Obviously this last is an essential cause of - poetry.—for the metres are obviously sections of rhythmse.g., the rhythm of the blacksmith's hammer or of a - trotting horse is dactylic, but the hexameter is a "section" or slice of that - rhythm; it is cut up into sixes.—and starting with these - instincts men very gradually developed them until they produced poetry out of their - improvisations. Poetry then split into - two kinds according to the poet's nature. For the more serious poets represented - fine doings and the doings of fine men, while those of a less exalted nature - represented the actions of inferior men, at first writing satire just as the others - at first wrote hymns and eulogies. - Before Homer we cannot indeed name any such poem, though there were probably many - satirical poets, but starting from - Homer, there is, for instance, his MargitesA famous burlesque which Aristotle attributes to Homer. "Other - similar poems" must mean other early burlesques not necessarily attributed to - Homer. and other similar poems. For these the iambic metre was fittingly - introduced and that is why it is still called iambic, because it was the metre in - which they lampooned each other.Since the iambic - came to be the metre of invective, the verb I)AMBI/ZEIN acquired the meaning "to lampoon." There is probably - implied a derivation from I)A/PTEIN, " to - assail." - Of the ancients some wrote heroic - verse and some iambic. And just as - Homer was a supreme poet in the serious style, since he alone made his - representations not only good but also dramatic, so, too, he was the first to mark - out the main lines of comedy, since he made his drama not out of personal satire but - out of the laughable as such. His Margites indeed provides an - analogy: as are the Iliad and Odyssey to our - tragedies, so is the Margites to our comedies. When tragedy and - comedy came to light, poets were drawn by their natural bent towards one or the - other. Some became writers of comedies instead of lampoons, the others produced - tragedies instead of epics; the reason being that the former is in each case a - higher kind of art and has greater value.To consider - whether tragedy is fully developed by now in all its various species or not, and to - criticize it both in itself and in relation to the stage, that is another question. - At any rate it originated in - improvisation—both tragedy itself and comedy. The one came from the - preludeBefore the chorus began (or in - pauses between their songs) the leader of the performance would - improvise some appropriate tale or state the theme which they were to elaborate. - Thus he was called O( E)CA/RXWN or "the - starter," and became in time the first "actor." to the dithyramb and the - other from the prelude to the phallic songs which still survive as institutions in - many cities. Tragedy then gradually - evolved as men developed each element that came to light and after going through - many changes, it stopped when it had found its own natural form. Thus it was Aeschylus who first raised the number of - the actors from one to two. He also curtailed the chorus and gave the dialogue the - leading part. Three actors and scene-painting Sophocles introduced. Then as to magnitude.Being a development of the Satyr play,A Satyr play was an interlude performed by a troupe - of actors dressed as the goat-like followers of Dionysus. Hence TRAGW|DI/A, "goat-song." Aristotle seems so clear - about this that he does not trouble to give a full explanation. But we can see - from this passage that the Satyr plays were short, jocose and in the trochaic - metre which suited their dances, and that in Aristotle's view tragedy was - evolved from these. No example of a primitive Satyr play survives, but we can - make inferences from the later, more sophisticated - Cyclops - of Euripides and the fragments of Sophocles' <foreign lang="greek">*)IXNEUTAI/</foreign>, The Trackers. We cannot be - certain that Aristotle's theory is historically correct; the balance of evidence - is against it. it was quite late before tragedy rose from short plots and - comic diction to its full dignity, and that the iambic metre was used instead of the - trochaic tetrameter. At first they - used the tetrameter because its poetry suited the Satyrs and was better for dancing, - but when dialogue was introduced, Nature herself discovered the proper metre. The - iambic is indeed the most conversational of the metres, and the proof is that in talking to each other we most often - use iambic lines but very rarely hexameters and only when we rise above the ordinary - pitch of conversation. Then there is - the number of acts. The further embellishmentsMasks, costumes, etc. and the story of their introduction one by one we - may take as told, for it would - probably be a long task to go through them in detail. Comedy, as we have said, is a - representation of inferior people, not indeed in the full sense of the word bad, but - the laughable is a species of the base or ugly."Ugly" was to a Greek an equivalent of "bad." The persons in Comedy are - "inferior" (see chapter 2.), but have only one of the many - qualities which make up Ugliness or Badness, viz. the quality of being ludicrous - and therefore in some degree contemptible. - It consists in some blunder or ugliness - that does not cause pain or disaster, an obvious example being the comic mask which - is ugly and distorted but not painful. The various stages of tragedy and the - originators of each are well known, but comedy remains obscure because it was not at - first treated seriously. Indeed it is only quite late in its historyProbably about 465 - B.C. that the archon granted a chorus for a comic poet; before that they - were volunteers.In the fifth century dramatists - submitted their plays to the archon in charge of the festival at which they - wished them to be performed. He selected the number required by the particular - festival, and to the poets thus selected "granted a chorus," i.e., provided a - choregus who paid the expenses of the chorus. The earlier "volunteers" had - themselves paid for and produced their plays. - Comedy had already taken certain forms - before there is any mention of those who are called its poets. Who introduced masks - or prologues, the number of actors, and so on, is not known. Plot making [Epicharmus and - Phormis]Epicharmus and Phormis, being - both early Sicilian "comedians", are appropriate here. Either part of a sentence - is lost or an explanatory note has got into the text. originally came - from Sicily, and of the Athenian poets CratesFragments of his comedies survive, dating about the middle of the - fifth century B.C. was the first to give up the lampooning form and to - generalize his dialogue and plots. Epic poetry agreed with tragedy only in so far as it - was a metrical representation of heroic action, but inasmuch as it has a single - metre and is narrative in that respect they are different. And then as regards length, tragedy tends to fall within a - single revolution of the sun or slightly to exceed that, whereas epic is unlimited - in point of time; and that is another - difference, although originally the practice was the same in tragedy as in epic - poetry. The constituent parts are some of them the same and some - peculiar to tragedy. Consequently any - one who knows about tragedy, good and bad, knows about epics too, since tragedy has - all the elements of epic poetry, though the elements of tragedy are not all present - in the epic. With the representation of life - in hexameter versei.e., epic poetry. and - with comedy we will deal later. We must now treat of tragedy after first gathering - up the definition of its nature which results from what we have said already. - Tragedy is, then, a representation - of an actionMargoliouth's phrase "a chapter of - life," illuminates the meaning, since PRA=CIS - includes what the hero does and what happens to him. (Cf. Aristot. Poet. 2.1 and note.) that is - heroic and complete and of a certain magnitude—by means of language - enriched with all kinds of ornament, each used separately in the different parts of - the play: it represents men in action and does not use narrative, and through pity - and fear it effects relief to these and similar emotions.The sense of "the pity of it "and fear lest such disasters might - befall ourselves are not the only emotions which tragedy releases, but Aristotle - specifies them as the most characteristic. For KA/QARSIS, see Introduction. - By "language enriched" I mean that - which has rhythm and tune, i.e., song, - and by "the kinds separately" I mean that some effects are produced by verse alone - and some again by song. Since the representation is performed by living persons, it - follows at once that one essential part of a tragedy is the spectacular effect, and, - besides that, song-making and diction. For these are the means of the - representation. By "diction" I mean - here the metrical arrangement of the words; and "song making" I use in the full, - obvious sense of the word. And since - tragedy represents action and is acted by living persons, who must of necessity have - certain qualities of character and thought—for it is these which determine - the quality of an action; indeed thought and character are the natural causes of - any action and it is in virtue of these that all men succeed or - fail— it follows then that - it is the plot which represents the action. By "plot" I mean here the arrangement of - the incidents: "character" is that which determines the quality of the agents, and - "thought" appears wherever in the dialogue they put forward an argument or deliver - an opinion. Necessarily then every tragedy has six constituent parts, and on these its - quality depends. These are plot, character, diction, thought, spectacle, and song. - Two of these are the means of - representation: one is the manner: three are the objects represented.The "means" are diction and music: the "manner" is - "spectacle": the "objects" represented are actions or experiences and the moral - or intellectual qualities of the dramatis personae. - This list is exhaustive, and - practically all the poets employ these elements, for every drama includes alike - spectacle and character and plot and diction and song and thought. The most important of - these is the arrangement of the incidents,i.e., - "plot," as defined above. for tragedy is not a representation of men but - of a piece of action, of life, of happiness and unhappiness, which come under the - head of action, and the end aimed at is the representation not of qualities of - character but of some action; and while character makes men what they are,it's their actions and experiences that make - them happy or the opposite. They do - not therefore act to represent character, but character-study is included for the - sake of the action. It follows that the incidents and the plot are the end at which - tragedy aims, and in everything the end aimed at is of prime importance. Moreover, you could not have a tragedy - without action, but you can have one with out character-study. Indeed the tragedies of most modern poets are without - this, and, speaking generally, there are many such writers, whose case is like that - of Zeuxis compared with Polygnotus.Zeuxis's - portraits were "ideal" (cf. Aristot. Poet. - 25.28). The latter was good at depicting character, but there - is nothing of this in Zeuxis's painting. A further argument is that if a man writes a series of speeches full of character - and excellent in point of diction and thought, he will not achieve the proper - function of tragedy nearly so well as a tragedy which, while inferior in these - qualities, has a plot or arrangement of incidents. And furthermore, two of the most important elements in the - emotional effect of tragedy, "reversals" and "discoveries,"See chapter 11. are parts of the plot. And here is further proof: those who try to write - tragedy are much sooner successful in language and character-study than in arranging - the incidents. It is the same with almost all the earliest poets. The plot then is the - first principle and as it were the soul of tragedy: character comes second. - It is much the same also in - painting; if a man smeared a canvas with the loveliest colors at random, it - would not give as much pleasure as an outline in black and white.Selection and design are necessary for aay work of - "representation." - And it is mainly because a play is a - representation of action that it also for that reason represents people. Third comes - "thought." This means the ability to say what is possible and appropriate. It comes - in the dialogue and is the function of the statesman's or the rhetorician's - art.Cf. chapter 6. - The old writers made their characters - talk like statesmen,Or "in the style of ordinary - people," without obvious rhetorical artifice. the moderns like - rhetoricians. Character is that which reveals choicePROAI/RESIS is a technical term in - Aristotle's ethics, corresponding to our use of the term "Will," the deliberate - adoption of any course of conduct or line of action. It is a man's will or - choice in the sense that determines the goodness or badness of his character. If - character is to be revealed in drama, a man must be shown in the exercise of his - will, choosing between one line of conduct and another, and he must be placed in - circumstances in wbich the choice is not obvious, i.e., circumstances in which - everybody's choice would not be the same. The choice of death rather than - disbonourable wealth reveals character; the choice of a nectarine rather than a - turnip does not., shows what sort of thing a man chooses or avoids in - circumstances where the choice is not obvious, so those speeches convey no character - in which there is nothing whatever which the speaker chooses or avoids. "Thought" you - find in speeches which contain an argument that something is or is not, or a general - expression of opinion. The fourth of the literary elements is the language. By this - I mean, as we said above, the expression of meaning in words,This seems to be a mistaken reference to 6 above where "diction" is - defined as "the metrical arrangement of the words." In poetry they come to the - same thing. and this is essentially the same in verse and in - prose. Of the other elements which "enrich"See Aristot. Poet. 6.2. tragedy the most - important is song-making. Spectacle, - while highly effective, is yet quite foreign to the art and has nothing to do with - poetry. Indeed the effect of tragedy does not depend on its performance by actors, - and, moreover,for achieving the - spectacular effects the art of the costumier is more authoritative than that of the - poet. - After these definitions we must next discuss the proper arrangement of the incidents - since this is the first and most important thing in tragedy. We have laid it down that tragedy is a representation - of an action that is whole and complete and of a certain magnitude, since a thing - may be a whole and yet have no magnitude. A whole is what has a beginning and middle and end. A beginning is that which is not a necessary consequent of - anything else but after which something else exists or happens as a natural result. - An end on the contrary is that - which is inevitably or, as a rule, the natural result of something else but from - which nothing else follows; a middle - follows something else and something follows from it. Well constructed plots must not therefore begin and end at - random, but must embody the formulae we have stated. Moreover, in everything that is - beautiful, whether it be a living creature or any organism composed of parts, these - parts must not only be orderly arranged but must also have a certain magnitude of - their own; for beauty consists in - magnitude and ordered arrangement. From which it follows that neither would a very - small creature be beautiful—for our view of it is almost instantaneous and - therefore confusedWith a very small object the - duration of our vision is, as it were, so rapid that the parts are invisible; - we, therefore, cannot appreciate their proportion and arrangement, in which - beauty consists.—nor a very large one, since being unable to - view it all at once, we lose the effect of a single whole; for instance, suppose a - creature a thousand miles long. As - then creatures and other organic structures must have a certain magnitude and yet be - easily taken in by the eye, so too with plots: they must have length but must be - easily taken in by the memory. The limit of length considered in relation to - competitions and productionAI)/SQHSIS is the play's "perception" by an - audience—how much an audience will stand. before an audience - does not concern this treatise. Had it been the rule to produce a hundred tragedies, - the performance would have been regulated by the water clock, as it is said they did - once in other days. But as for the - natural limit of the action, the longer the better as far as magnitude goes, - provided it can all be grasped at once. To give a simple definition: the magnitude - which admits of a change from bad fortune to good or from good fortune to bad, in a - sequence of events which follow one another either inevitably or according to - probability, that is the proper limit. A plot does not have unity, as some people - think, simply because it deals with a single hero. Many and indeed innumerable - things happen to an individual, some of which do not go to make up any unity, and - similarly an individual is concerned in many actions which do not combine into a - single piece of action. It seems therefore that all those poets are wrong who - have written a Heracleid or Theseid or other such - poems.Aristotle condemns them all, - assuming—or perhaps assured by experience—that their sole - claim to unity lay in the fact that all the stories in the poem had a common - hero. They think that because Heracles was a single individual the plot - must for that reason have unity. But - Homer, supreme also in all other respects, was apparently well aware of this truth - either by instinct or from knowledge of his art. For in writing an - Odyssey he did not put in all that ever happened to Odysseus, his - being wounded on Parnassus, for instance, - or his feigned madness when the host was gathered(these being events - neither of which necessarily or probably led to the other), but he - constructed his Odyssey round a single action in our sense of the - phrase. And the Iliad the same. As then in the other arts of representation a single - representation means a representation of a single object, so too the plot being a - representation of a piece of action must represent a single piece of action and the - whole of it; and the component incidents must be so arranged that if one of them be - transposed or removed, the unity of the whole is dislocated and destroyed. For if - the presence or absence of a thing makes no visible difference, then it is not an - integral part of the whole. What we have said already makes it further clear that a - poet's object is not to tell what actually happened but what could and would happen - either probably or inevitably. The - difference between a historian and a poet is not that one writes in prose and the - other in verse— indeed the writings of Herodotus could be put into - verse and yet would still be a kind of history, whether written in metre or not. The - real difference is this, that one tells what happened and the other what might - happen. For this reason poetry is - something more scientific and serious than history, because poetry tends to give - general truths while history gives particular facts. By a "general truth" I mean the - sort of thing that a certain type of man will do or say either probably or - necessarily. That is what poetry aims at in giving names to the characters.The names indicate types. This is obvious, as he - says, in Comedy and is also true of Greek Tragedy, which, although it deals with - traditional heroes regarded as "real people," yet keeps to a few stories in - which each character has become a type. In Chapter 17. the dramatist is - recommended to sketch first his outline plot, making it clear and coherent, - before he puts in the names. A "particular fact" is what Alcibiades did - or what was done to him. In the case of - comedy this has now become obvious, for comedians construct their plots out of - probable incidents and then put in any names that occur to them. They do not, like - the iambic satirists, write about individuals.Aristophanes of course did write about individuals. But Aristotle is thinking - of the New Comedy, where the names of the characters were invented by the author - and there was no reference to real people. - In tragedy, on the other hand, they - keep to real names. The reason is that what is possible carries conviction. If a - thing has not happened, we do not yet believe in its possibility, but what has - happened is obviously possible. Had it been impossible, it would not have - happened. It is true that in some tragedies one or two of the names are - familiar and the rest invented; indeed in some they are all invented, as for - instance in Agathon's Antheus,The - name, apparently, of an imaginary hero. The word might be *)/ANQOS, but "The Flower" is an unlikely title for a Greek - tragedy. where both the incidents and the names are invented and yet it - is none the less a favourite. One need - not therefore endeavor invariably to keep to the traditional stories with which our - tragedies deal. Indeed it would be absurd to do that, seeing that the familiar - themes are familiar only to a few and yet please all.The reason why Greek tragedy dealt only with a few familiar themes - is to be found of course in its religious origin. It was the function of tragedy - to interpret and embroider myths. Aristotle never gives this reason, but offers - instead tbe unconvincing explanation that tragedians adhered to certain "real" - stories to gain verisimilitude—and yet he has to admit that, since to - many of the auditors these stories were unfamiliar and none the less attractive, - dramatists might just as well invent new themes. It is clear, then, - from what we have said that the poet must be a "maker" not of verses but of stories, - since he is a poet in virtue of his "representation," and what he represents is - action. Even supposing he represents - what has actually happened, he is none the less a poet, for there is nothing to - prevent some actual occurrences being the sort of thing that would probably or - inevitably happen, and it is in virtue of that that he is their "maker." Of - "simple"This term is defined in the next - chapter. It seems odd to use it before its meaning is explained. Perhaps we - should read A)/LLWN(Tyrwhitt)and translate "of all - plots." plots and actions the worst are those which are "episodic." By - this I mean a plot in which the episodes do not follow each other probably or - inevitably. Bad poets write such - plays because they cannot help it, and good poets write them to please the actors. - Writing as they do for competition, they often strain a plot beyond its capacity and - are thus obliged to sacrifice continuity.Or - "logic." He means the chain of cause and effect, wherein each incident is the - result of what has gone before. See the end of the next chapter. - But this is bad work, since - tragedy represents not only a complete action but also incidents that cause fear and - pity, and this happens most of all when the incidents are unexpected and yet one is - a consequence of the other.The logic suffers from - ellipse. Plays which fail to exhibit the sequence of cause and effect are - condemned (1) because they lack the unity which befits - tragedy, (2) because they miss that supreme effect of fear or - pity produced by incidents which, though unexpected, are seen to be no mere - accident but the inevitable result of what has gone before. - For in that way the incidents will - cause more amazement than if they happened mechanically and accidentally, since the - most amazing accidental occurrences are those which seem to have been providential, - for instance when the statue of Mitys at Argos killed the man who caused Mitys's death by falling on him at - a festival. Such events do not seem to be mere accidents. So such plots as these must necessarily be the - best. Some plots are "simple" and some "complex," as indeed the actions represented by - the plots are obviously such. By a - simple action I mean one that is single and continuous in the sense of our - definition above,In chapters 7 and 8. - wherein the change of fortune occurs without "reversal" or "discovery"; by a complex action I mean one wherein the - change coincides with a "discovery" or "reversal" or both. These should result from the actual structure of the - plot in such a way that what has already happened makes the result inevitable or - probable;for there is indeed a vast - difference between what happens propter hoc and post hoc. A "reversal" is a - change of the situation into the opposite, as described above,At the end of chapter 7. Vahlen and many other exponents of the - Politics confine the meaning of - “reversal” to the situation in which the hero's action has - consequences directly opposite to his intention and expectation. There is much - to be said for this interpretation, which stresses the irony at the heart of all - tragedy. But it is too narrow for Aristotle's theory. All tragedy involves a - change of fortune ( META/BASIS). In a “simple” plot this is - gradual; in a “complex” plot it is catastrophic, a sudden - revolution of fortune's wheel. In some of the greatest tragedies, but not in - all, this is the result of action designed to produce the opposite - effect. this change being, moreover, as we are saying, probable or - inevitable— like the man - in the Oedipus who came to cheer Oedipus and rid him of his anxiety - about his mother by revealing his parentage and changed the whole situation.The messenger for Corinth announces the death of Polybus and Oedipus's succession - to the throne. Oedipus, feeling now safe from the prophecy that he would murder - his father, still fears to return to Corinth, lest he should fulfil the other prophecy and marry his - mother. The messenger seeks to reassure him by announcing that Polybus and - Merope are not his parents. But the effect of this was to "change the whole - situation" for Oedipus by revealing the truth that he a murdered his father, - Laius, and married his mother, Jocasta. This "reversal" is the more effective - because it is immediately coincident with the discovery of the truth. In - the Lynceus, too, there is the man led off to execution and - Danaus following to kill him, and - the result of what had already happened was that the latter was killed and the - former escaped.Lynceus married Hypermnestra who - disobeyed Danaus in not murdering him. Danaus trying by process of law to - compass the death of their son Abas was killed himself. "The dog it was that - died." A "discovery," as the term itself implies, is a change from - ignorance to knowledge, producing either friendship or hatred in those who are - destined for good fortune or ill. A - discovery is most effective when it coincides with reversals, such as that involved - by the discovery in the Oedipus. There are also other forms of discovery, for what we have - described may in a sense occur in relation to inanimate and trivial objects, or one - may discover whether some one has done something or not. But the discovery which is most essentially part of the plot - and part of the action is of the kind described above, for such a discovery and - reversal of fortune will involve either pity or fear, and it is actions such - as these which, according to our hypothesis, tragedy represents; and, moreover, - misfortune and good fortune are likely to turn upon such incidents. Now since the - discovery is somebody's discovery, in some scenes one character only is discovered - to another, the identity of the other being obvious; but sometimes each must - discover the other. Thus Iphigeneia was discovered to Orestes through the sending of - the letter, but a separate discovery was needed to make him known to - Iphigeneia.Euripides' Iphigeneia in - - Tauris—Orestes and Pylades arriving among the - Tauri are by the custom of the country to be sacrificed to Artemis by her - priestess, Iphigeneia. It is agreed that Pylades shall be spared to carry a - letter from Iphigeneia to Orestes, whom she supposes to be in Argos. In order that Pylades may deliver the - message, even if he should lose the letter, she reads it aloud. Orestes thus - discovers who she is. He then reveals himself to her by declaring who he is and - proving his identity by his memories of their home. We see then that two - elements of the plot, reversal and discovery, turn upon these incidents. A third - element is a calamity. Of these three elements we have already described reversal - and discovery. A calamity is a - destructive or painful occurrence, such as a death on the stage, acute suffering and - wounding and so on. We have alreadyIn chapter - 6. spoken of the constituent parts to be used as ingredients of tragedy. - The separable members into which it is quantitatively divided are these: Prologue, - Episode, Exode, Choral Song, the last - being divided into Parode and Stasimon. These are common to all tragedies; songs sung by actors on the stage and "commoi" - are peculiar to certain plays. A prologue is the whole of that part of a tragedy - which precedes the entrance of the chorus. An episode is the whole of that - part of a tragedy which falls between whole choral songs. An exode is the whole of that part of a tragedy which is not - followed by a song of the chorus. A - parode is the whole of the first utterance of the chorus. A stasimon is a choral song without anapaests or - trochaics.This does not apply to surviving - Greek tragedies, but may be true of those of Aristotle's time. The word Stasimon - is applied to all choruses in a tragedy other than those sung during entry or - exit. It is usually explained as meaning a "stationary song," because it was - sung after the chorus had taken up its "station" in the orchestra. - A commos is a song of lament shared by - the chorus and the actors on the stage. The constituent parts to be used as - ingredients of tragedy have been described above; these are the separable members - into which it is quantitatively divided.The whole - of chapter 12. bears marks of belonging to the Poetics but seems out of place, - since it interrupts the discussion of "plot." Following upon what - has been said above we should next state what ought to be aimed at and what avoided - in the construction of a plot, and the means by which the object of tragedy may be - achieved. Since then the structure of - the best tragedy should be not simple but complexSee chapter 10. and one that represents incidents arousing fear and - pity—for that is peculiar to this form of art—it is obvious to - begin with that one should not show worthy men passing from good fortune to bad. - That does not arouse fear or pity but shocks our feelings. Nor again wicked people passing from bad fortune to - good. That is the most untragic of all, having none of the requisite qualities, - since it does not satisfy our feelingsi.e., our - preference for "poetic justice." or arouse pity or fear. Nor again the passing of a thoroughly bad man - from good fortune to bad fortune. Such a structure might satisfy our feelings but it - arouses neither pity nor fear, the one being for the man who does not deserve his - misfortune and the other for the man who is like ourselves—pity for the - undeserved misfortune, fear for the man like ourselves—so that the result - will arouse neither pity nor fear. There remains then the mean between these. This is the - sort of man who is not pre-eminently virtous and just, and yet it is through no - badness or villainy of his own that he falls into the fortune, but rather through - some flaw in him,Whether Aristotle regards the - “flaw” as intellectual or moral has been hotly discussed. It - may cover both senses. The hero must not deserve his misfortune, but he must - cause it by making a fatal mistake, an error of judgement, which may well - involve some imperfection of character but not such as to make us regard him as - “morally responsible” for the disasters although they are - nevertheless the consequences of the flaw in him, and his wrong decision at a - crisis is the inevitable outcome of his character(cf. Aristot. Poet. 6.24.). he - being one of those who are in high station and good fortune, like Oedipus and - Thyestes and the famous men of such families as those. The successful plot must then have a singleA(PLOU=S elsewhere in - the Poetics means "simple" as opposed to PEPLEGME/NOS, "complex"; here it is opposed to DIPLOU=S, which describes a double denouement, - involving happiness for some and disaster for others. and not, as some - say, a double issue; and the change must be not to good fortune from bad but, on the - contrary, from good to bad fortune, and it must not be due to villainy but to some - great flaw in such a man as we have described, or of one who is better rather than - worse. This can be seen also in actual - practice. For at first poets accepted any plots, but to-day the best tragedies are - written about a few families—Alcmaeon for instance and Oedipus and Orestes and Meleager and Thyestes and - Telephus and all the others whom it befell to suffer or inflict terrible - disasters. Judged then by the theory of the art, the bestThis is modified by 19 in the following chapter, - where he finds an even better formula for the tragic effect. tragedy is - of this construction. Those critics - are therefore wrong who charge Euripides with doing this in his tragedies, and say - that many of his end in misfortune. - That is, as we have shown, correct. And there is very good evidence of this, for on - the stage and in competitions such plays appear the most tragic of all, if they are - successful, and even if Euripides is in other respects a bad manager,Against Euripides Aristotle makes the following - criticisms: (1)his choruses are often irrelevant; - (2)the character of the heroine in his Iphigeneia in - Tauris is inconsistent; - (3)in the Medea the deliberate killing of the - children is ineffective and the play is inartistically ended by the machina; - (4)the character of Menelaus in the Orestes is - needlessly depraved; (5)Melanippe is too philosophical for a - woman. yet he is certainly the most tragic of the poets. Next in order comes - the structure which some put first, that which has a double issue, like the - Odyssey, and ends in opposite ways for the good characters and - the bad. It is the sentimentality of - the audience which makes this seem the best form; for the poets follow the wish of - the spectators. But this is not the - true tragic pleasure but rather characteristic of comedy, where those who are bitter - enemies in the story, Orestes and Aegisthus, for instance, go off at the end, having - made friends, and nobody kills anybody. Fear and pity sometimes result - from the spectacle and are sometimes aroused by the actual arrangement of the - incidents, which is preferable and the mark of a better poet. The plot should be so constructed that even without - seeing the play anyone hearing of the incidents happening thrills with fear and pity - as a result of what occurs. So would anyone feel who heard the story of Oedipus. - To produce this effect by means of - an appeal to the eye is inartistic and needs adventitious aid, while those who by such means produce an effect which - is not fearful but merely monstrous have nothing in common with tragedy.that here were plays which relied for their effect on - the scenery and "make up" is clear from chapter 17:—"The Phorcides and - Prometheus and Scenes laid in Hades." It was even possible to produce the - Eumenides so badly as to bring it into this category. But - Aristotle's criticism here includes the more important point that the poignancy - of a Greek tragedy is due to what happens and not to our seeing it happen. That - Medea murders her children is tragic: to display the murder coram populo would - add either nothing or something merely "monstrous." And although Sophocles shows - Oedipus with his eyes out, it is the fact and not the sight which is properly - "tragic." For one should not seek from tragedy all kinds of pleasure but - that which is peculiar to tragedy, and - since the poet must by "representation" produce the pleasure which comes from - feeling pity and fear, obviously this quality must be embodied in the - incidents. We must now decide what incidents seem dreadful or rather - pitiable. Such must necessarily be the actions of friends to each other or of - enemies or of people that are neither. - Now if an enemy does it to an enemy, there is nothing pitiable either in the deed or - the intention, except so far as the - actual calamity goes. Nor would there - be if they were neither friends nor enemies. But when these calamities happen among - friends,when for instance brother - kills brother, or son father, or mother son, or son mother—either kills or - intends to kill, or does something of the kind, that is what we must look - for. Now it is not right to break up the traditional stories, I mean, for instance, - Clytaemnestra being killed by Orestes and Eriphyle by Alcmaeon, but the poet must show invention and make a skilful - use of the tradition.But we must state more clearly - what is meant by "skilful." The - action may happen in the way in which the old dramatists made their characters - act—consciously and knowing the facts, as EuripidesThis does not necessarily imply that Aristotle reckons Euripides - “a modern,” since the Greek can equally mean - “Euripides as well as other old dramatists.” also - made his Medea kill her children. Or - they may do the deed but without realizing the horror of it and then discover the - relationship afterwards, like Oedipus in Sophocles. That indeed lies outside the - play,i.e., Oedipus kills his father Laius - before the play opens. but an example of this in the tragedy itself is - the Alcmaeon of AstydamasA prolific - tragedian of the fourth century. or Telegonus in the Wounded - Odysseus. A third - alternative is to intend to do some irremediable action in ignorance and to discover - the truth before doing it. Besides - these there is no other way, for they must either do the deed or not, either knowing - or unknowing. The worst of these is - to intend the action with full knowledge and not to perform it. That outrages the - feelings and is not tragic, for there is no calamity. So nobody does that, - except occasionally, as, for instance, Haemon and CreonHaemon, discovered by his father Creon embracing the dead body of - Antigone, drew his sword on him but missed his aim and Creon fled. in the - Antigone. Next - comes the doing of the deed. It is - better to act in ignorance and discover afterwards. Our feelings are not outraged - and the discovery is startling. Best - of all is the last; in the Cresphontes,By Euripides. Polyphontes killed Cresphontes, king of Messenia, and gained possession of his kingdom - and his wife, Merope. She had concealed her son, Aepytus, in Arcadia, and when he returned, seeking - vengeance, she nearly killed him in ignorance but discovered who he was. He then - killed Polyphontes and reigned in his stead. for instance, Merope intends - to kill her son and does not kill him but discovers; and in the - IphigeneiaIn - Tauris. See Aristot. Poet. 11.8, note. the case - of the sister and brother; and in the HelleAuthor and play unknown. the son discovers just as he is on - the point of giving up his mother. So this is the reason, as was said - above,See Aristot. Poet. 13.7. why tragedies are about a few families. - For in their experiments it was from no technical knowledge but purely by chance - that they found out how to produce such an effect in their stories. So they are - obliged to have recourse to those families in which such calamities befell.See Aristot. Poet. - 9.8, note. Now concerning the structure of the incidents and the - proper character of the plots enough has been said. Concerning "character" there are - four points to aim at. The first and most important is that the character should be - good. The play will show character if, - as we said above,See Aristot. Poet. 6.24. either the dialogue or the actions - reveal some choice; and the character will be good, if the choice is good. - But this is relative to each class of people. Even a woman is "good" and so is a - slave, although it may be said that a woman is an inferior thing and a slave beneath - consideration. The second point is that the characters should be - appropriate. A character may be manly, but it is not appropriate for a woman to be - manly or clever. Thirdly, it should be "like."The meaning probably is "like the traditional person," e.g. Achilles must not - be soft nor Odysseus stupid. Cf. Horace Ars Poet. - 120 "famam sequere." This is different from making the - character good and from making it appropriate in the sense of the word as used - above. Fourthly, it should be consistent. Even if the original be inconsistent and - offers such a character to the poet for representation, still he must be - consistently inconsistent. An example of unnecessary badness of character is Menelaos in - the OrestesAristotle has a personal - distaste for this character on the ground that Euripides made him a creature - meaner than the plot demands.; of character that is unfitting and inappropriate the lament - of Odysseus in the ScyllaA dithyramb - by Timotheus. Cf. Aristot. Poet. - 26.3. and Melanippe's speechA - fragment survives (Eur. Fr. 484 - (Nauck)). Euripides seems to have given her a knowledge of - science and philosophy inappropriate to a woman.; of inconsistent character Iphigeneia in Aulis, for the suppliant Iphigeneia is not at - all like her later character. In character-drawing just as much as in the - arrangement of the incidents one should always seek what is inevitable or probable, - so as to make it inevitable or probable that such and such a person should say or do - such and such; and inevitable or probable that one thing should follow - another. Clearly therefore the "denouement"Or "unravelling." of each play should also be the result of - the plot itself and not produced mechanically as in the Medea and the - incident of the embarkation in the Iliad. Hom. Il. 2.155-181, where it is only the - arbitrary (i.e., uncaused) intervention of Athene which stays the flight of the - Greeks. In the Medea the heroine, having killed her rival and her - children, is spirited away in the chariot ot the Sun, a result not "caused" by - what has gone before.The - "god in the car"The MHXANH/ or "car" was a sort of crane with a pulley attached, - which was fixed at the top of the back-scene in the left corner of the stage. By - it a god or hero could be lowered or raised or exhibited motionless in mid-air. - Weak dramatists thus introduced a car to "cut the knot" by declaring the - denouement instead of unravelling the plot by the logic of cause and effect. It - was presumably on such a "car" that Medea was borne away. should only be - used to explain what lies outside the play, either what happened earlier and is - therefore beyond human knowledge, or what happens later and needs to be foretold in - a proclamation. For we ascribe to the gods the power of seeing everything. - There must, however, be nothing - inexplicable in the incidents, or, if there is, it must lie outside the tragedy. - There is an example in Sophocles' Oedipus.i.e., Oedipus had killed Laius in a wayside quarrel, not knowing who - he was. When his subjects at Thebes - crave his help to remove the curse which is blighting their crops, he pledges - himself to discover the murderer of Laius. It may seem odd that he should not - know enough about the details of the murder to connect it in his mind with his - own murderous quarrel. But that was long ago, and neither an audience nor a - novel-reader is critical about incidents which occur long before the point at - which the story begins. See chapter Aristot. - Poet. 24.20. Since tragedy is a representation of men - better than ourselves we must copy the good portrait-painters who, while rendering - the distinctive form and making a likeness, yet paint people better than they are. - It is the same with the poet. When representing people who are hot-tempered or lazy, - or have other such traits of character, he should make them such, yet men of worth - [an example of hardness]Apparently a note on Achilles which has been copied by mistake into the - text.; take the way in which Agathon and Homer portray - Achilles. Keep, then, a careful eye on these rules and also on the - appeal to the eyei.e., stage-craft rather than - staging. which is necessarily bound up with the poet's business; for that - offers many opportunities of going wrong. But this subject has been adequately - discussed in the published treatises.As distinct - from the body of "esoteric" doctrine circulated by oral teaching among - Aristotle's pupils. What a "Discovery" is has been already stated.In chapter 11.As for kinds of Discovery, first comes the least artistic kind, - which is largely used owing to incompetence—discovery by tokens. - These may be congenital, like "the - spear the Earth-born bear" or stars, like those which CarcinusA prolific tragedian of the early fourth century. The family are - agreeably ridiculed in Aristophanes' Wasps. uses in his - ThyestesThese were - "birth-marks." The "spear-head" distinguished the descendants of the Spartoi at - Thebes; the star or bright spot - on the descendants of Pelops commemorated his ivory shoulder, and in Carcinus's - play it seems to have survived cooking.; or they may be acquired and these may be on the body, for - instance, wounds, or external things like necklaces, and in the - TyroA play by Sophocles. Tyro's - twins by Poseidon, who appeared to her in the guise of the river Enipeus, were - exposed in a little boat or ark, like Moses in the bulrushes, and this led to - their identification. the discovery by means of the boat. There is a better and a worse way of using - these tokens; for instance Odysseus, by means of his wound, was discovered in one - way by the nurse and in another way by the swine-herds.Hom. Od. 19.386ff., 205ff. The - first came about automatically, the second was a deliberate demonstration "to - prove the point." Aristotle here distinguishes between a discovery inevitably - produced by the logic of events (e.g. it was inevitable or at least probable - that Odysseus, arriving as a strange traveller, should be washed by Eurycleia, - and that she should thus see the old scar on his thigh and discover his - identity) and a discovery produced by a deliberate declaration (e.g. Odysseus's - declaration of his identity to Eumaeus). The latter kind is "manufactured by the - poet," not logically caused by what has gone before. - Discovery scenes constructed to prove - the point are inartistic and so are all such scenes, but those are better which - arise out of a reversal scene, as, for instance, in "The Washing."Hom. Od. 19.392. See - preceding note. - In the second place come those which - are manufactured by the poet and are therefore inartistic. For instance, in the - IphigeneiaEuripides' - Iphigeneia in - Tauris. See Aristot. Poet. - 11.8, note. Orestes revealed himself. She was revealed to him - through the letter, but Orestes says - himself what the poet wants and not what the plot requires. So this comes near to - the fault already mentioned, for he might just as well have actually brought some - tokens.To prove his identity Orestes mentions - Pelops' lance and other "things from home," which is much the same as producing - visible tokens. And there is "the voice of the shuttle"When Philomela's tongue was cut out, she wove in - embroidery the story of her rape by Tereus. Thus the facts were discovered to - her sister, Procne, by deliberate demonstration. In Sophocles' - Tereus. The third kind is due to memory, to showing distress on - seeing something. An example of this is the scene in the Cyprians by - Dicaeogenes; on seeing the picture he burst into tearsTeucer, returning to Salamis in disguise and seeing a portrait of his dead father - Telamon, burst into tears and was thus discovered. So, too, in The Two - Gentlemen of <placeName key="perseus,Verona">Verona</placeName> - Julia is discovered because she swoons on hearing Valentine offer Sylvia to his - rival.: and again in the "Tale of Alcinous," - Hom. Od. 8.521ff. - hearing the minstrel he remembered and burst into tears; and thus they were - recognized. The fourth kind results - from an inference; for instance, in the Choephoroe "Someone like me - has come; but nobody is like me except Orestes; therefore he has come." And there is - Polyidus'sA Sophist who either wrote an - Iphigeneia with this denouement or more probably suggested in - a work of criticism (cf. Aristot. Poet. - 17.6) that Orestes on being led to his fate should speculate aloud - upon the odd coincidence that both he and his sister should be sacrificed, thus - revealing his identity to Iphigeneia. Like most critics, Polyidos would have - been a poor dramatist. There is an example of this form of discovery in the - French opera Coeur de Lion, where the old knight says "goddam" - and is thus discovered to be an Englishman. idea about Iphigeneia, for it - is likely enough that Orestes should make an inference that, whereas his sister was - sacrificed, here is the same thing happening to him. And in Theodectes' - Tydeus that "having come to find a son, he is perishing himself." - And the scene in the Phineidae, where on seeing the spot the women - inferred their fate, that they were meant to die there for it was there that they - had been exposed.In these cases the inference was - presumably uttered aloud and hence the identity of the speakers discovered. - Nothing else is known of these plays. There is also a kind of - fictitious discovery which depends on a false inference on the part of the audience, - for instance in Odysseus the False Messenger, he said he would - recognize the bow, which as a matter of fact he had not seen, but to assume that he - really would reveal himself by this means is a false inference.The text is obscure, and our ignorance of the play or rhapsody adds - to the darkness, but the reference may be to the ruse, common in detective - stories, of misleading the audience by false clues in order to make the final - revelation more effective. Best of all is the discovery which is - brought about directly by the incidents, the surprise being produced by means of - what is likely—take the scene in Sophocles' Oedipus or in - the Iphigeneia—for it is likely enough that she should want - to send a letter. These are the only discovery scenes which dispense with artificial - tokens, like necklaces.The classical example of - these tokens in English drama is "the strawberry mark on the left arm" in - Box and Cox. But Aristotle seems here to use "tokens" in a - wider sense than at the beginning of the chapter and to include not only - birthmarks, necklaces, etc., but any statement or action which may be used as a - sign in the scene of Discovery. In the second place come those - that are the result of inference. In constructing plots and completing the effect by the - help of dialogue the poet should, as far as possible, keep the scene before his - eyes. Only thus by getting the picture as clear as if he were present at the actual - event, will he find what is fitting and detect contradictions. The censure upon Carcinos is evidence of this. - Amphiaraos was was made to rise from a temple. The poet did not visualize the scene - and therefore this escaped his notice, but on the stage it was a failure since the - audience objected.The example is obscure. Clearly - Carcinus introduced an absurdity which escaped notice until the play was staged. - Margoliouth suggests that if Amphiaraus were a god he should come down, and if a - mere hero, he sould not have a temple. In The Master of - Ballantrae Mrs. Henry cleans a - sword by thrusting it up to the hilt in the ground—which is iron-bound - by frost. The would be noticed on the stage: a reader may miss the - incongruity. - The poet should also, as far as - possible, complete the effect by using the gestures. For, if their natural powers - are equal, those who are actually in the emotions are the most convincing; he who is - agitated blusters and the angry man rages with the maximum of conviction.Sir Joshua Reynolds used thus to simulate emotion - before a mirror. In his Preface to the Lyrical Ballads Wordsworth - says that the Poet will wish "to bring his feelings near to those of the persons - whose feelings he describes . . . and even confound and identify his own - feelings with theirs." See also Burke, On the Sublime and - Beautiful,4. 4. - And that is why poetry needs either a - sympathetic nature or a madman,"Genius to madness - near allied" is the meaning of MANIKO/S as used - here. Plato held that the only excuse for a poet was that he couldn't help - it. the former being impressionable and the latter inspired. The stories, - whether they are traditional or whether you make them up yourself, should first - be sketched in outline and then expanded by putting in episodes. I mean that one might look at the general outline, say - of the Iphigeneia, like this: A certain maiden has been sacrificed, - and has disappeared beyond the ken of those who sacrificed her and has been - established in another country, where it is a custom to sacrifice strangers to the - goddess; and this priesthood she holds. Some time afterwards it happens that the - brother of the priestess arrives there—the fact that the god told him to - go there, and why, and the object of his journey, lie outside the outline-plot. He - arrives, is seized, and is on the point of being sacrificed, when he reveals his - identity either by Euripides' method or according to Polyidos, by making the very - natural remark that after all it is not only his sister who was born to be - sacrificed but himself too; and thus he is saved. Not until this has been done should you put in names and - insert the episodes; and you must mind - that the episodes are appropriate, as, for instance, in the case of Orestes the - madness that led to his capture and his escape by means of the purification.In the Iphigeneia in - Tauris Orestes is captured because - he is suffering from a fit of mania; and at the end Iphigeneia pretends that the - image of Artemis has been infected by the blood-guiltiness of the Greek - strangers, and that, before they can be sacrificed, she must cleanse both image - and strangers secretly in the sea. Thus they all escape together by - boat. Now in drama the episodes are short, but it is by them that - the epic gains its length. The story - of the Odyssey is quite short. A man is for many years away from home and his - footsteps are dogged by Poseidon and he is all alone. Moreover,affairs at home are in such a state that his estate is - being wasted by suitors and a plot laid against his son, but after being - storm-tossed he arrives himself, reveals who he is, and attacks them, with the - result that he is saved and destroys his enemies. That is the essence, the rest is episodes. In every tragedy - there is a complication and a denouement.The Greek - says simply "tying" and "loosing." Complication and denouement seem clumsy - equivalents, yet they are the words we use in dramatic criticism. The - incidents outside the plot and some of those in it usually form the complication, - the rest is the denouement. I mean - this, that the complication is the part from the beginning up to the point which - immediately precedes the occurrence of a change from bad to good fortune or from - good fortune to bad; the denouement is from the beginning of the change down to the - end. For instance, in the - Lynceus of Theodectes the complication is the preceding events, - and the seizure of the boy, and then their own seizure; and the denouement is from - the capital charge to the end.The boy must be Abas, - and "they" are presumably Danaus and perhaps his other daughters. Aristotle - seems to regard the arrest of Danaus not as part of the LU/SIS, but as the end of the DE/SIS. Tragedies should properly be classed as the same or - different mainly in virtue of the plot, that is to say those that have the same - entanglement and denouement. Many who entangle well are bad at the denouement. Both - should always be mastered.There are four varieties of - tragedy—the same as the number given for the "elements"Apparently the reference here is to the four elements - into which in the course of chapters 10-15. Plot has been analysed, "Reversal," - "Discovery," "Calamity," and "Character." But the symmetry is spoilt by the fact - that his first species, "the complex play," corresponds to the first two of - these four elements, viz. to "Reversal" and "Discovery." Thus his fourth species - is left in the air and he hurriedly introduces "Spectacle" as the fourth - corresponding element. Other explanations seem even sillier than - this.— first the - complex kind, which all turns on reversal and discovery; the "calamity play" like the stories of Ajax and Ixion; - the "character play" like the - Phthian WomenBy - Sophocles. and the PeleusBoth Sophocles and Euripides wrote a Peleus.. The fourth element is spectacle, like the - PhorcidesThe text is obscure, - and our ignorance of the play or rhapsody adds to the darkness, but the - reference may be to the ruse, common in detective stories, of misleading the - audience by false clues in order to make the final revelation more - effective. and Prometheus, and all scenes laid in Hades. - One should ideally try to include - all these elements or, failing that, the most important and as many as possible, - especially since it is the modern fashion to carp at poets, and, because there have - been good poets in each style, to demand that a single author should surpass the - peculiar merits of each. One must remember, as we have often said, not to make a - tragedy an epic structure: by epic I - mean made up of many stories—suppose, for instance, one were to dramatize - the IIiad as a whole. - The length of the IIiad allows to the parts their proper size, but in - plays the result is full of disappointment. And the proof is that all who have dramatized the Sack of - Troy as a whole, and not, like - Euripides, piecemeal, or the Niobe story as a whole and not like Aeschylus, either - fail or fare badly in competition. Indeed even Agathon failed in this point alone. - In "reversals," however, and in - "simple" storiesi.e., those that have no - "Discovery" or "Reversal." See chapter 10. too,they admirably achieve their end, which is a tragic - effect that also satisfies your feelings. This is achieved when the wise man, who is, however, - unscrupulous, is deceived—like Sisyphus—and the man who is brave - but wicked is worsted. And this, as - Agathon says, is a likely result, since it is likely that many quite unlikely things - should happen. The chorus too must be regarded as one of the actors. It must - be part of the whole and share in the action, not as in Euripides but as in - Sophocles. In the others the choral - odes have no more to do with the plot than with any other tragedy. And so they sing - interludes, a practice begun by Agathon. And yet to sing interludes is quite as bad - as transferring a whole speech or scene from one play to another. The other factors - have been already discussed. It remains to speak of "Diction" and "Thought." - All that concerns Thought may be - left to the treatise on Rhetoric, for the subject is more proper to that - inquiry."Thought"—no English word - exactly corresponds with DIA/NOIA—is - all that which is expressed or effected by the words (cf. Aristot. Poet. 6.22, 23, and 25). Thus the - student is rightly referred to the Art of Rhetoric, where he - learns "what to say in every case." Aristotle adds that the rules there given - for the use of ideas will guide him also in the use of incidents, since the same - effect may be produced either by talk or by "situation." - Under the head of Thought come all the - effects to be produced by the language. Some of these are proof and refutation, the arousing of feelings like pity, - fear, anger, and so on, and then again exaggeration and depreciation.It is an important part of the orator's skill to - depreciate what is important and to exaggerate trivial points. - It is clear that in the case of the - incidents, too, one should work on the same principles, when effects of pity or - terror or exaggeration or probability have to be produced. There is just this difference, that some effects must - be clear without explanation,Those produced by - "situation." whereas others are produced in the speeches by the speaker - and are due to the speeches. For what would be the use of a speaker, if the required - effect were likely to be felt without the aid of the speeches? Under the head of - Diction one subject of inquiry is the various modes of speech, the knowledge of - which is proper to elocution or to the man who knows the master artRhetoric is a "master art" in relation to elocution, - since it decides the effects to be produced, and elocution decides how to - produce them. So the doctor's art is "master" to that of the dispenser, and the - art of riding to that of the maker of bridles.—I mean for - instance, what is a command, a prayer, a statement, a threat, question, answer, and - so on. The knowledge or ignorance of - such matters brings upon the poet no censure worth serious consideration. For who - could suppose that there is any fault in the passage which Protagoras censures, - because Homer, intending to utter a prayer, gives a command when he says, "Sing, - goddess, the wrath"? To order something to be done or not is, he points out, a - command. So we may leave this topic as one that belongs not to poetry - but to another art. Diction as a - wholeA translator is bound to render this - chapter, since the balance of evidence is in favour of its inclusion. But the - readaer is advised to skip it, since it is written from the point of view of - grammar and philology, and does not, like the succeeding chapter, deal with the - literary use of words. It is also very obscure. Students should refer to - Bywater's edition. is made up of these parts: letter, syllable, - conjunction, joint,A "joint," as defined below, - appears to be a word which indicates the beginning or end of a clause. - noun, verb, case, phrase. A letter is - an indivisible sound, not every such sound but one of which an intelligible sound - can be formed. Animals utter indivisible sounds but none that I should call a - letter. Such sounds may be subdivided - into vowel, semi-vowel, and mute. A vowel is that which without any addition has an - audible sound; a semivowel needs the addition of another letter to give it audible - sound, for instance S and R; a mute is that which with addition has no sound of its - own but becomes audible when combined with some of the letters which have a sound. - Examples of mutes are G and D. Letters - differ according to the shape of the mouth and the place at which they are sounded; - in being with or without aspiration; in being long and short; and lastly in having - an acute, grave, or intermediate accent. But the detailed study of these matters - properly concerns students of metre. A syllable is a sound without meaning, - composed of a mute and a letter that has a sound. GR, for example, without A is a - syllable just as much as GRA with an A. But these distinctions also belong to the - theory of metre. words. It is also very obscure. Students should refer to Bywater's - edition. A conjunction is a sound without meaning, which - neither hinders nor causes the formation of a single significant sound or phrase out - of several sounds, and which, if the phrase stands by itself, cannot properly stand - at the beginning of it, e.g. ME/N, DH/, TOI/, DE/; - or else it is a sound without meaning capable of forming one significant sound or - phrase out of several sounds having each a meaning of their own, e.g. A)MFI/, PERI/. A joint is a sound without meaning which - marks the beginning or end of a phrase or a division in it, and naturally stands at - either end or in the middle.This paragraph remains - a cause of despair. Bywater's notes suggest a restoration. A noun is a - composite sound with a meaning, not indicative of time, no part of which has a - meaning by itself; for in compounds we do not use each part as having a meaning of - its own, for instance, in "Theodorus," there is no meaning of DW=RON (gift). A verb is a composite sound with - a meaning, indicative of time, no part of which has a meaning by - itself—just as in nouns. "Man" or "white" does not signify time, but - "walks" and "has walked" connote present and past time respectively. A - case(or inflection)of a noun or verb is that which signifies - either "of" or "to" a thing and the like;or gives the sense of "one or many" e.g. men and man; or else it may depend on the - delivery, for example question and command. "Walked?" and "Walk!" are verbal "cases" - of this kind. A phraseThere is no exact - English equivalent of this meaning of LO/GOS, - which has been used already in 7 above without explanation. "Statement" and - "proposition" also cover part of its meaning. is a composite sound with a - meaning, some parts of which mean something by themselves. It is not true to say that every "phrase" is made up - of nouns and verbs, e.g. the definition of manProbably one of the two definitions given in the Topics, "a - two-footed land animal" and "an animal amenable to reason."; but although - it is possible to have a "phrase" without verbs, yet some part of it will always - have a meaning of its own, for example, Cleon in "Cleon walks." A "phrase" may be a unit in two ways; either it - signifies one thing or it is a combination of several "phrases." The unity of the - Iliad, for instance, is due to such combination, but the - definition of man is "one phrase" because it signifies one thing. Nouns are of two - kinds. There is the simple noun, by which I mean one made up of parts that have no - meaning, like GH=, and there is the compound noun. - These may be made up either of a - part which has no meaning and a part which has a meaning—though it does - not have its meaning in the compound—or of two parts both having a - meaning. A compound noun may be triple - and quadruple and multiple, e.g. many of the bombastic names like - Hermocaicoxanthus.A compound of the names of - three rivers, Hermus, Caicus, and - Xanthus. - . . - . Every noun is either "ordinary"i.e., one which has dined normal currency as - contrasted with the "rare word," which is confined to a dialect or borrowed from - a foreign language. or "rare" or "metaphorical" or "ornamental" or - "invented" or "lengthened" or "curtailed" or "altered." An "ordinary" word is one used by everybody, a "rare" word - one used by some; so that a word may - obviously be both "ordinary" and "rare," but not in relation to the same people. - SI/GUNON,Meaning, "spear." for instance, is to the Cypriots an "ordinary" word - but to us a "rare" one. Metaphor is the application of a strange term either - transferred from the genus and applied to the species or from the species and - applied to the genus, or from one species to another or else by analogy. An example of a term transferred from genus - to species is "Here stands my ship." Riding at anchor is a species of standing. - An example of transference from - species to genus is "Indeed ten thousand noble things Odysseus did," for ten - thousand, which is a species of many, is here used instead of the word "many." - An example of transference from - one species to another is "Drawing off his life with the bronze" and "Severing with - the tireless bronze," where "drawing off" is used for "severing" and "severing" for - "drawing off," both being species of "removing."Probably "the bronze" is in the first case a knife and in the second a - cupping-bowl. This would make the metaphor intelligible. Metaphor by analogy - means this: when B is to A as D is to C, then instead of B the poet will say D and B - instead of D. And sometimes they add - that to which the term supplanted by the metaphor is relative.This may claim to be one of Aristotle's least lucid sentences. It - means this: If Old Age: Life:: Evening: Day, then we may call old age " the - Evening of Life." In that case "old age" is the "term supplanted by the - metaphor," and it is relative to " Life"; therefore "Life" (i.e., "that - to which the term supplanted by the metaphor is relative")is added to - the metaphorical (or "transferred") term - "Evening."For instance, a cup - is to Dionysus what a shield is to Ares; so he will call the cup "Dionysus's shield" and the shield - "Ares' cup." Or old age is to life as evening is to day; so he will call the evening - "day's old-age" or use Empedocles' phraseUnknown to - us.; and old age he will call "the evening of life" or "life's setting - sun." Sometimes there is no word for - some of the terms of the analogy but the metaphor can be used all the same. For - instance, to scatter seed is to sow, but there is no word for the action of the sun - in scattering its fire. Yet this has to the sunshine the same relation as sowing has - to the seed, and so you have the phrase "sowing the god-created fire." Besides this - another way of employing metaphor is to call a thing by the strange name and then to - deny it some attribute of that name. For instance, suppose you call the shield not - "Ares' cup" but a “wineless cup.” . . .Or you might call Love "Venus's bloodless War." At this point a few - lines on "Ornament" have evidently been lost, since this is its place in the - catalogue of nouns above. By "ornament" he seems to mean an embellishing epithet - or synonym. In the Rhetoric he quotes "Our lady the fig-tree" as - a misplaced "ornament." One might add the seventeenth-century use of "Thames" for "water." . . . An invented - word is one not used at all by any people and coined by the poet. There seem to be - such words, eg. "sprouters" for horns and "pray-er" for priest. A word is - "lengthened" or "curtailed," the former when use is made of a longer vowel than - usual or a syllable inserted, and the latter when part of the word is curtailed. - An example of a lengthened word - is PO/LHOS for POLE/WS and *PHLHIA/DEW for *PHLEI/DOU; and of a curtailed word KRI= and DW=, and e.g. MI/A GI/NETAI A)MFOTE/RWN O)/Y.KRI= for KRIQH/, "barley"; DW= for - DW=MA "house"; O)/Y for O)/YIS "face, eye, or - appearance." A word is "altered" when the poet coins part of the word and - leaves the rest unchanged, e.g. DECITERO\N KATA\ - MAZO/N instead of DECIO/N. Of the nouns - themselves, some are masculine, some feminine, and some neuter.This paragraph the reader should either skip or study with Bywater's - notes. Without them these generalizations on gender seem merely wrong. - Masculine are all that end in N and P - and *S and in the two compounds of *S, *Y and *C. Feminine are all that end in those of the - vowels that are always long, for instance *H and - *W, and in *A - among vowels that can be lengthened. - The result is that the number of masculine and feminine terminations is the same, - for *Y and *C are - the same as *S. No noun ends in a mute or in a short vowel. Only three end in *I, - ME/LI, KO/MMI, and PE/PERI. Five end - in *U. The neuters end in these letters and in - *N and *S. The merit of diction is to be clear and not commonplace. The - clearest diction is that made up of ordinary words, but it is commonplace. An - example is the poetry of Cleophon and of Sthenelus.A tragedian whom Aristophanes ridicules for the insipidity of his - diction. - That which employs unfamiliar words is - dignified and outside the common usage. By "unfamiliar" I mean a rare word, a - metaphor, a lengthening,See preceding chapter - 19. and anything beyond the ordinary use. But if a poet writes entirely in such words, the result will - be either a riddle or jargon; if made up of metaphors, a riddle and if of rare - words, jargon. The essence of a riddle - consists in describing a fact by an impossible combination of words. By merely - combining the ordinary names of things this cannot be done, but it is made possible - by combining metaphors. For instance, "I saw a man weld bronze upon a man with - fire," and so on.The answer is a cupping-bowl. This - was a bronze vessel which was applied to the body at the place at which a small - incision had been made. Heated lint was placed in the bowl of it and the - reduction of air-pressure thus caused a strong flow of blood. For this form of - riddle cf. "Out of the strong came forth sweetness." - A medley of rare words is jargon. - We need then a sort of mixture of - the two. For the one kind will save the diction from being prosaic and commonplace, - the rare word, for example, and the metaphor and the "ornament," whereas the - ordinary words give clarity. A considerable aid to clarity and distinction are the - lengthening and abbreviation and alteration of words. Being otherwise than in the - ordinary form and thus unusual, these will produce the effect of distinction, and - clarity will be preserved by retaining part of the usual form. Those critics are therefore wrong who censure this - manner of idiom and poke fun at the poet, as did the elder EucleidesA critic of this name wrote on the drama, but his - date is uncertain. who said it was easy to write poetry, granted the - right to lengthen syllables at will. He had made a burlesque in this very style: - *)EPIXA/RHN EI)=DON *MARAQW=NA/DE BADI/ZONTA and - OU)K A)/N G' E)RA/MENOS TO\N E)KEI/NOU - E)LLE/BORON.In Homer we find short - vowels lengthened "by position," but, whereas Homer uses the licence sparingly, - Eucleides raised a laugh by overdoing it and writing in parody such hexameters - as those here quoted. A modern parallel may illustrate this. The poet Stephen - Phillips employed to excess the licence whihc allows a clash between the natural - accent and the metrical ictus, and Mr. Owen Seaman, "for the express purpose of - raising a laugh," parodied the trick by carrying it to further excess and wrote - in blank verse, "She a milliner was and her brothers - Dynamiters." Now to make an obtrusive use of this licence is ridiculous; - but moderation is a requisite - common to all kinds of writing. The same effect could be got by using metaphors and - rare words and the rest unsuitably for the express purpose of raising a - laugh. What a difference is made by the proper use of such licence - may be seen in epic poetry, if you substitute in the verse the ordinary forms. - Take a rare word or metaphor or - any of the others and substitute the ordinary word; the truth of our contention will - then be obvious.For instance, Aeschylus - and Euripides wrote the same iambic line with the change of one word only, a rare - word in place of one made ordinary by custom, yet the one line seems beautiful and - the other trivial. Aeschylus in the Philoctetes wrote, "The ulcer - eats the flesh of this my foot," and Euripides instead of "eats" put "feasts upon." - Or take "I that am small, of no account nor goodly;" suppose one were to read the - line substituting the ordinary words, "I that am little and weak and ugly." Or - compare "He set a stool unseemly and a table small." with "He set a shabby stool and - a little table," or "the sea-shore is roaring" with "the sea-shore is - shrieking."Similarly we might use "ordinary" - words instead of those which Keats chose so carefully and speak of "wonderful - windows abutting on to a dangerous sea-shore in a dreary, mysterious - country." AriphradesUnknown. - again made fun of the tragedians because they employ phrases which no one would use - in conversation, like " DWMA/TWN A)/PO" instead of - A)PO\ DWMA/TWN and their " SE/QEN"and " E)GW\ DE/ NIN"and " - *)AXILLE/WS PE/RI" for PERI\ *)AXILLE/WS, and so on. All that sort of thing, not being in the ordinary form, gives - distinction to the diction, which was what he failed to understand. It is a great thing - to make a proper use of each of the elements mentioned, and of double words and rare - words too, but by far the greatest thing is the use of metaphor. That alone cannot be learnt; it is the token - of genius. For the right use of metaphor means an eye for resemblances.i.e., the power of detecting "identity in difference" - which distinguishes also both the philosopher and the - scientist. Of the various kinds of words the double forms are most - suited for dithyrambs, rare words for heroic verse and metaphors for iambics. - And indeed in heroic verse they - are all useful; but since iambic verse is largely an imitation of speech, only those - nouns are suitable which might be used in talking. These are the ordinary word, - metaphor, and "ornament." Now concerning tragedy and the art of representing life in - action, what we have said already must suffice. We come now to the art of - representation which is narrative and in metre.i.e., epic. Clearly the story must be constructed as in tragedy, - dramatically, round a single piece of action, whole and complete in - itself,with a beginning, middle and - end, so that like a single living organism it may produce its own peculiar form of - pleasure. It must not be such as we - normally find in history, where what is required is an exposition not of a single - piece of action but of a single period of time, showing all that within the period - befell one or more persons, events that have a merely casual relation to each other. - For just as the battle of - Salamis occurred at the same time as - the Carthaginian battle in Sicily, but they - do not converge to the same resultGelo's defeat of - the Carthaginians in Sicily in 480 B.C. took place, according to Herodotus, on the same - day as the battle of Salamis.; - so, too, in any sequence of time one event may follow another and yet they may not - issue in any one result. Yet most of - the poets do this. So in this respect, - too, compared with all other poets Homer may seem, as we have already said, divinely - inspired, in that even with the Trojan war, which has a beginning and an end, he did - not endeavor to dramatize it as a whole, since it would have been either too long to - be taken in all at once or, if he had moderated the length, he would have - complicated it by the variety of incident. As it is, he takes one part of the story - only and uses many incidents from other parts, such as the Catalogue of Ships and - other incidents with which he diversifies his poetry. The others, on the contrary, all write about a single hero or - about a single period or about a single action with a great many parts, the authors, - for example, of the Cypria and the Little - Iliad.As we have seen already in chapter 8, a poem or a play must be one story and - not several stories about one hero. Thus, since the Iliad and - Odyssey have this essential unity (i.e., one thread runs - through the narrative of each), few plays can be made out of them but many out - of the Cypria or the Little Iliad, which are - merely collections of lays on similar themes. - The result is that out of an - Iliad or an Odyssey only one tragedy can be made, - or two at most, whereas several have been made out of the Cypria, and - out of the Little Iliad more than eight, e.g. The Award of - Arms, Philoctetes, Neoptolemus, - Eurypylus, The Begging, The Laconian - Women, The Sack of <placeName key="perseus,Troy">Troy</placeName>, and Sailing of the Fleet, and - Sinon, too, and The Trojan Women. The next point is - that there must be the same varieties of epic as of tragedySee Aristot. Poet. - 18.4.: an epic must be "simple or complex,"See chapter 10. or else turn on "character" or on "calamity." - The constituent parts, too, are - the same with the exception of song and spectacle. Epic needs reversals and - discoveries and calamities, and the thought and diction too must be good. All these were used by Homer for the first - time, and used well. Of his poems he made the one, the - Iliad - , a "simple" story turning on "calamity," and the Odyssey a - "complex" story—it is full of "discoveries"—turning on - character. Besides this they surpass all other poems in diction and - thought. Epic differs from tragedy in the length of the composition - and in metre. The limit of length - already givenSee Aristot. Poet. 7.12. will suffice—it must be - possible to embrace the beginning and the end in one view,which would be the case if the compositions were - shorter than the ancient epics but reached to the length of the tragedies presented - at a single entertainment.“Entertainment” must mean a festival. At the City Dionysia - three poets competed, each with three tragedies. By the end of the fifth century - only one Satyr play was performed at each festival. But the tragedies were - longer than those we possess. It is therefore likely that the nine tragedies - together with one Satyr play amounted to about 15,000 lines. The - Iliad - contains between 16,000 and 17,000 lines. - Epic has a special advantage which - enables the length to be increased, because in tragedy it is not possible to - represent several parts of the story as going on simultaneously, but only to show - what is on the stage, that part of the story which the actors are performing; - whereas, in the epic, because it is narrative, several parts can be portrayed as - being enacted at the same time. If - these incidents are relevant, they increase the bulk of the poem, and this increase - gives the epic a great advantage in richness as well as the variety due to the - diverse incidents; for it is monotony which, soon satiating the audience, makes - tragedies fail. Experience has shown that the heroic hexameter is the right - metre. Were anyone to write a narrative poem in any other metre or in several - metres, the effect would be wrong. The - hexameter is the most sedate and stately of all metres and therefore admits of rare - words and metaphors more than others, and narrative poetry is itself elaborate above - all others. The iambic and the - trochaic tetrameter are lively, the latter suits dancing and the former suits real - life. Still more unsuitable is it to - use several metres as Chaeremon did. - So no one has composed a long poem in any metre other than the heroic hexameter. As - we said above, Nature shows that this is the right metre to choose. Homer deserves - praise for many things and especially for this, that alone of all poets he does not - fail to understand what he ought to do himself. The poet should speak as seldom as - possible in his own character, since he is not "representing" the story in that - sense.This takes us back to the beginning of - chapter 3, where the various "manners" of representation are distinguished. - Homer represents life partly by narration, partly by assuming a character other - than his own. Both these "manners" come under the head of "Imitation." When - Aristotle says "the poet speaks himself" and "plays a part himself" he refers - not to narrative, of which there is a great deal in Homer, but to the "preludes" - (cf. FROIMIASA/MENOS below) in - which the poet, invoking the Muse, speaks in his own person. - Ridgeway points out that in the whole of the - Iliad - and Odyssey Homer thus "speaks himself" only 24 - lines. - Now the other poets play a part - themselves throughout the poem and only occasionally "represent" a few things - dramatically, but Homer after a brief prelude at once brings in a man or a woman or - some other character, never without character, but all having character of their - own. Now the marvellous should certainly be portrayed in tragedy, but epic affords - greater scope for the inexplicable(which is the chief element in what is - marvellous), because we do not actually see the persons of the story. - The incident of - Hector's pursuitIliad, xxii. 205. sq. “And to the host divine Achilles nodded with his head a sign and let them not launch their bitter darts at Hector, lest another should win glory by shooting him and Achilles himself come second.” would look ridiculous - on the stage, the people standing still and not pursuing and Achilles waving them - back, but in epic that is not noticed. But that the marvellous causes pleasure is shown by the fact that people always - tell a piece of news with additions by way of being agreeable. Above all, Homer has - taught the others the proper way of telling lies,that is, by using a fallacy. When B is true if A is true, or B - happens if A happens, people think that if B is true A must be true or happen. But - that is false. Consequently if A be untrue but there be something else, B, which is - necessarily true or happens if A is true, the proper thing to do is to posit B, for, - knowing B to be true, our mind falsely infers that A is true also. This is an - example from the Washing.Odyssey 19. - Odysseus tells Penelope that he is a Cretan from Gnossus, who once entertained - O. on his voyage to Troy. As evidence, - he describes O.'s dress and his companions (Hom. Od. - 19.164-260). P. commits the fallacy of inferring the truth of the - antecedent from the truth of the consequent: “If his story were true, - he would know these details; But he does know them; Therefore his story is - true.” The artist in fiction uses the same fallacy, e.g.: - “If chessmen could come to life the white knight would be a duffer; - But he is a most awful duffer (look at him!); Therefore - chessmen can come to life.” He makes his deductions so convincing that - we falsely infer the truth of his hypothesis. What is convincing - though impossible should always be preferred to what is possible and unconvincing. - Stories should not be made up of - inexplicable details; so far as possible there should be nothing inexplicable, or, - if there is, it should lie outside the story—as, for instance, Oedipus not - knowing how Laius died—and not in the play; for example, in the - Electra the news of the Pythian games,In Sophocles'Electrathe plot hinges on a false story - of Orestes' death by an accident at the Pythian games. Presumably the - anachronism shocked Aristotle. or in the Mysians the man who came from - Tegea to Mysia without speaking.Telephus. To say that the plot would otherwise have been ruined is - ridiculous. One should not in the - first instance construct such a plot, and if a poet does write thus, and there seems - to be a more reasonable way of treating the incident, then it is positively absurd. - Even in the - Odyssey the inexplicable elements in the story of his - landingHom. Od. - 13.116ff. It seemed to the critics inexplicable that Odysseus should - not awake when his ship ran aground at the harbour of Phorcys in Ithaca and the Phaeacian sailors carried him - ashore. would obviously have been intolerable, had they been written by - an inferior poet. As it is, Homer conceals the absurdity by the charm of all his - other merits. The diction should be elaborated only in the "idle" parts - which do not reveal character or thought.The - Messengers' speeches, a regular feature o Greek tragedy, may serve to illustrate - what is here called the "idle part" of a play, i.e., passages which, but for - brilliant writing, might be dull, since no character is there elucidated and no - important "sentiments" expressed. Too brilliant diction frustrates its - own object by diverting attention from the portrayal of character and - thought. With regard to problems,A - "problem" in this sense is a difficult passage or expression which explanation - and may easily be censured by an unsympathetic critic. Aristotle here classifies - the various grounds of censure and the various lines of defence. Most of his - illustrations are drawn from the critical objections lodged against the - Iliad by Zoilus and other "hammerers of Homer." As the reader - will see, many of them are abysmally foolish. and the various solutions - of them, how many kinds there are, and the nature of each kind, all will be clear if - we look at them like this. Since the - poet represents life, as a painter does or any other maker of likenesses, he must - always represent one of three things—either things as they were or are; or - things as they are said and seem to be; or things as they should be. These are expressed in diction with or - without rare words and metaphors, there being many modifications of diction, all of - which we allow the poet to use. - Moreover, the standard of what is correct is not the same in the art of poetry as it - is in the art of social conduct or any other art. In the actual art of poetry there are two kinds of errors, - essential and accidental. If a man - meant to represent something and failed through incapacity, that is an essential - error. But if his error is due to his original conception being wrong and his - portraying, for example, a horse advancing both its right legs, that is then a - technical error in some special branch of knowledge,in medicine, say, or whatever it may be; or else some sort of - impossibility has been portrayed, but that is not an essential error. These considerations must, then, be kept in - view in meeting the charges contained in these objections.Let us first take the charges against the art of poetry itself. If - an impossibility has been portrayed, an error has been made. But it is justifiable if the poet thus achieves the - object of poetry—what that is has been already stated—and makes - that part or some other part of the poem more striking. The pursuit of - Hector is an example of this.See Aristot. Poet. 24.16 and - note. - If, however, the object could have - been achieved better or just as well without sacrifice of technical accuracy, then - it is not justifiable, for, if possible, there should be no error at all in any part - of the poem. Again one must ask of - which kind is the error, is it an error in poetic art or a chance error in some - other field? It is less of an error not to know that a female stag has no horns than - to make a picture that is unrecognizable. Next, supposing the charge is "That is not - true," one can meet it by saying "But perhaps it ought to be," just as Sophocles - said that he portrayed people as they ought to be and Euripides portrayed them as - they are. If neither of these will - do, then say, "Such is the tale"; for instance, tales about gods. Very likely there is no advantage in telling - them, and they are not true either, but may well be what Xenophanes declaredi.e., immoral and therefore untrue. He opened the - assault on Homeric theology at the end of the sixth or the beginning of the - fifth century B.C.—all the same such is the tale. In another case, perhaps, there is no - advantage but "such was the fact," e.g. the case of the arms, "Their spears erect on - butt-spikes stood,"Hom. - Il. 10.152. Problem: "Surely a bad stance: they might so easily fall - and cause alarm." Solution: "Homer does not defend it. He merely states a fact." - It is thus that we excuse "unpleasant" fiction. for that was then the - custom, as it still is in Illyria. As to the question whether anything that has been said or - done is morally good or bad, this must be answered not merely by seeing whether what - has actually been done or said is noble or base, but by taking into consideration - also the man who did or said it, and seeing to whom he did or said it, and when and - for whom and for what reason; for example, to secure a greater good or to avoid a - greater evil. Some objections may be met by reference to the diction, for - example, by pleading "rare word," e.g. OU)RH=AS ME\N - PRW=TON, for perhaps he means not mules but sentinels.Hom. Il. 1.50: "The - mules and swift-footed hounds he first beset with his arrows." Apollo is sending - plague upon the Greek army. Problem: "Why should he first attack the mules?" - Solution: "The word may here mean 'sentiels.'" And Dolon, "One that was - verily evil of form," it may be not his deformed body but his ugly face, for the - Cretans use "fair-formed" for "fair-featured."Hom. Il. 10.316: "One that was verily evil inform - but swift in his running." Problem: "If Dolon were deformed, how could he run - fast?" Solution: "'Form' may here mean 'feature.'" And again "Livelier - mix it" may mean not undiluted as for drunkards but quicker.Hom. Il. 9.202: "Set me, Menoetius' - son, a larger bowl for the mingling, Livelier mix it withal and make ready for - each one a beaker." Problem: "'Livelier' suggests intemperance." Solution: - "Perhaps the word means 'quicker.'" Similar scruples emended the lines in "Young - Lochinvar" to read: "And now am I come with this pretty maid To dance but one - measure, drink one lemonade." - Other expressions are metaphorical, - for example: Then all the other immortals and men lay all night in slumber," while - yet he says: "Yea, when indeed he gazed at the Trojan plain Agamemnon Marvelled at - voices of flutes . . ." "All" is used - instead of "many" metaphorically, "all" being a species of "many."Hom. Il. 2.2 (quoted by - mistake for Hom. Il. 10.1) and Hom. Il. 10.13, 14: "Then all the other immortals - and all the horse-crested heroes Night-long slumbered, but Zeus the sweet sleep - held not. . . (Hom. Il. 2.1, 2) Yea, when indeed - he gazed at the Trojan plain, Agamemnon Marvelled at voices of flutes and of - pipes and the din of the soldiers." (Hom. Il. 10.13, - 14) Problem: "If all were asleep, who was playing the flute?" - Solution: "This may be a metaphor; as explained in chapter 21, 'all' is one kind - or species of 'many,' and thus by transference 'all' is used for 'many,' the - species for the genus." And again, "Alone unsharing "Hom. Il. 18.489: "She alone of all - others shares not in the baths of the Ocean." The reference is to the Great - Bear. Problem: "Why does Homer say 'she alone' when the other Northern - Constellations also do not set?" Solution: "As in the last instance, the may be - 'metaphorical,' i.e., the genus, 'sole,' may be here used by transference for - one of its species, 'best known.'" is metaphorical; the best known is - called the only one. By intonation also; for example, the solutions of Hippias of - Thasos, his " DI/DOMEN DE/ OI("Hom. Il. 2.15. Our text is different. Aristotle, - who quotes the line agains elsewhere, read thus: "No longer the gods in the - halls of Olympus Strive in their plans, for Hera has bent them all to her - purpose Thus by her prayers; and we grant him to win the boast of great glory." - Zeus is instructing the Dream, whom he is sending to lure Agamemnon to disaster. - Problem: "The last statement is a lie." Solution: "Change the accent and the - statement DI/DOMEN DE/ OI( becomes a command - (the infinitive DIDO/MENAI written in a - shortened form and used as an imperative). The lie will then be told by - the Dream and not by Zeus, who may thus save his reputation for - veracity." and TO\ ME\N OU(= KATAPU/QETAI - O)/MBRW|Hom. Il. 23.327: "A fathom high from the earth there rises a stump - all withered, A stump of an oak or a pine, that rots not at all in the rain." - Problem: "The last statement is incredible." Solution: "Alter the breathing and - TO\ ME\N OU) becomes TO\ ME\N OU(= and means part of it rots in the rain.'"; - and by punctuation; for example, - the lines of Empedocles: Soon mortal grow they that aforetime learnt Immortal ways, - and pure erstwhile commingled.The Problem is - "erstwhile" goes with "pure" or with "commingled." The former interpretation - seems to give the best solution. Empedocles is speaking of the elements or - atoms. - Or again by ambiguity, e.g. PARW/|XHKEN DE\ PLE/W NU/C, where PLEI/W is ambiguous.Hom. Il. 10.252: "Come now, the night is far - spent and at hand is the dawning, Far across are the stars and more than two - parts of the night-time Are gone, but a third is still left us." Problem: If - "more than two parts" are gone, a third cannot be left. Solution: PLE/W here means "full," i.e., " the full night of - two-thirds"="full two-thirds of the night is gone," and so Homer's - arithmetic is saved. Others - according to the habitual use of the phrase, e.g. wine and water is called "wine" so - you get the phrase "greaves of new-wrought tin";Problem: "Greaves are made not of tin but of an alloy of tin and copper." - Solution: "Compounds are called by the name of the more important partner. Just - as a mixture of wine and water is called 'wine,' so here an alloy of tin and - copper is called 'tin.'" So, too, is whisky and water called "whisky." or - workers in iron are called "braziers," and so Ganymede is said to pour wine for - Zeus, though they do not drink wine. This last might however be metaphorical.Nectar:gods::wine: men. Therefore, according to the - rules of metaphor in chapter 21, nectar may be called "wine" or "the wine of the - gods." Whenever a word seems to involve a contradiction, one should - consider how many different meanings it might bear in the passage, e.g. in "There - the bronzen shaft was stayed,"Hom. Il. 20.272: "Nay but the weighty shaft of - the warlike hero Aeneas Brake not the shield; for the gold, the gift of a god, - did withstand it. Through two folds it drave, yet three were beneath, for - Hephaestus, Crook-footed god, five folds had hammered; two were of bronze-work, - Two underneath were of tin and one was of gold; there the bronzen Shaft of the - hero was stayed in the gold." Problem: "Since the gold was presumably outside - for the sake of ornament, how could the spear he stayed in the gold and yet - penetrate two folds?" Bywater suggests as a solution that "the plate of gold - sufficed to stop the course of the spear, though the spear-point actually - pierced it and indented the underlying plates of brass." we should ask in - how many ways "being stayed" might be taken, interpreting the passage in this sense or in that, and - keeping as far as possible from the attitude which GlauconThis may well be the Glaucon mentioned in - Plato's Ion as an authority on - Homer. describes when he - says that people make some unwarrantable presupposition and having themselves given - an adverse verdict proceed to argue from it, and if what they think the poet has - said does not agree with their own preconceived ideas, they censure him, as if that - was what he had said. This is what - has happened in the case of Icarius.Penelope's - father. They assume that he was a Spartan and therefore find it odd that - when Telemachus went to Sparta he did not - meet him. But the truth may be, as the Cephallenians say, that Odysseus married a - wife from their country and that the name was not Icarius but Icadius. So the - objection is probably due to a mistake. In general any "impossibility" may be - defended by reference to the poetic effect or to the ideal or to current opinion. - For poetic effect a convincing - impossibility is preferable to that which is unconvincing though possible. - It may be impossible that there - should be such people as ZeuxisSee Aristot. Poet. 6.15. used to paint, - but it would be better if there were; for the type should improve on the - actual. Popular tradition may be used to defend what seems - irrational, and you can also say that sometimes it is not irrational, for it is - likely that unlikely things should happen. Contradictions in terms must be examined in the same way as - an opponent's refutations in argument, to see whether the poet refers to the same - thing in the same relation and in the same sense, and has contradicted either what - he expressly says himself or what an intelligent person would take to be his - meaning. It is right, however, to - censure both improbability and depravity where there is no necessity and no use is - made of the improbability.An example is - Euripides' intro duction of AegeusEur. Medea 663. In Aristotle's opinion there is no - good reason for Aegeus's appearance and no good use is made of it. - or(of depravity)the character of Menelans in the - Orestes. The censures they bring are of five kinds; that things - are either impossible or irrational or harmful or inconsistent or contrary to - artistic correctness. The solutions must be studied under the heads specified above, - twelve in number.i.e., any expression that is - criticized should be considered with reference to (1) things as they were; (2) - things as thy are; (3) things as they are said to be; (4) things as they seem to - be; (5) things as they ought to be. Further, we should consider whether (6) a - rare word or (7) a metaphor is used; what is the right (8) accent and (9) - punctuation; also where there may be (10) ambiguity and what is (11) the - habitual use of the phrase; also we may refer to (12) the proper standard of - correctness in poetry as distinct from other arts. The question may be - raised whether the epic or the tragic form of representation is the better. - If the better is the less vulgar - and the less vulgar is always that which appeals to the better audience, then - obviously the art which makes its appeal to everybody is eminently vulgar.Aristotle first states the popular condemnation of - tragedy on the ground that it can be and often is spoilt by the stupid vulgarity - of actors. So might spectators of certain productions of - Shakespeare in their haste condemn the poet. - The refutation of this view begins at 6. And indeed actors think the audience do not understand unless - they put in something of their own, and so they strike all sorts of attitudes, as - you see bad flute-players whirling about if they have to do "the - Discus," or mauling the leader of the chorus when - they are playing the "Scylla."Cf. Aristot. Poet. 15.8 So tragedy is something like what the older - school of actors thought of their successors, for Mynniscus used to call Callippides - "the monkey," because he overacted, and the same was said of Pindarus.Mynniscus acted for Aeschylus: Callippides belonged - to the next generation, end of fifth century. Pindarus is unknown. - The whole tragic art, then, is - to epic poetry what these later actors were compared to their predecessors, since - according to this view epic appeals to a cultivated audience which has no need of - actor's poses, while tragedy appeals to a lower class. If then it is vulgar, it must - obviously be inferior. First of all, this is not a criticism of poetry but of - acting: even in reciting a minstrel can overdo his gestures, as Sosistratus did, or - in a singing competition, like Mnasitheus of Opus.Both unknown. Besides it is - not all attitudinizing that ought to be barred any more than all dancing, but only - the attitudes of inferior people. That was the objection to Callippides; and modern - actors are similarly criticized for representing women who are not ladies. - Moreover, tragedy fulfils its - function even without acting, just as much as epic, and its quality can be gauged by - reading aloud. So, if it is in other respects superior, this disadvantage is not - necessarily inherent. Secondly, tragedy has all the elements of the - epic—it can even use the hexameter— and in addition a considerable element of its own in the - spectacle and the music, which make the pleasure all the more vivid; and this vividness can be felt whether it is - read or acted. Another point is - that it attains its end with greater economy of length. What is concentrated is - always more effective than what is spread over a long period; suppose, for example, - Sophocles'Oedipuswere to be turned into as many lines as there - are in the - Iliad - . Again, the art of the epic - has less unity, as is shown by the fact that any one epic makes several tragedies. - The result is that, if the epic poet takes a single plot, either it is set forth so - briefly as to seem curtailed, or if it conforms to the limit of lengthLiterally "the length of the (proper) limit." - it seems thin and diluted.In saying that epic has - less unity I mean an epic made up of several separate actions. The Iliad has many such parts and so - has the Odyssey, and each by itself has a certain magnitude. And yet - the composition of these poems is as perfect as can be and each of them - is—as far as an epic may be—a representation of a single action. - If then tragedy is superior in - these respects and also in fulfilling its artistic function—for tragedies - and epics should produce not any form of pleasure but the pleasure we have - describedi.e., the pleasure felt when by the - representation of life in art “relief is given” to pity, - fear, and other such emotions, or, to use a term now prevalent, when such - emotions are “released.”Cf. Aristot. Poet. 14.3.—then obviously, since it - attains its object better than the epic, the better of the two is tragedy. This must - suffice for our treatment of tragedy and epic, their characteristics, their species, - their constituent parts, and their number and attributes; for the causes of success - and failure; and for critical problems and their solutions. . . .

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The question may be raised whether the epic or the tragic form of representation is the better.

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If the better is the less vulgar and the less vulgar is always that which appeals to the better audience, then obviously the art which makes its appeal to everybody is eminently vulgar.Aristotle first states the popular condemnation of tragedy on the ground that it can be and often is spoilt by the stupid vulgarity of actors. So might spectators of certain productions of Shakespeare in their haste condemn the poet. The refutation of this view begins at 6.

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And indeed actors think the audience do not understand unless they put in something of their own, and so they strike all sorts of attitudes, as you see bad flute-players whirling about if they have to do the Discus, or mauling the leader of the chorus when they are playing the Scylla.Cf. Aristot. Poet. 15.8

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So tragedy is something like what the older school of actors thought of their successors, for Mynniscus used to call Callippides the monkey, because he overacted, and the same was said of Pindarus.Mynniscus acted for Aeschylus: Callippides belonged to the next generation, end of fifth century. Pindarus is unknown.

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The whole tragic art, then, is to epic poetry what these later actors were compared to their predecessors, since according to this view epic appeals to a cultivated audience which has no need of actor’s poses, while tragedy appeals to a lower class. If then it is vulgar, it must obviously be inferior.

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First of all, this is not a criticism of poetry but of acting: even in reciting a minstrel can overdo his gestures, as Sosistratus did, or in a singing competition, like Mnasitheus of Opus.Both unknown.

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Besides it is not all attitudinizing that ought to be barred any more than all dancing, but only the attitudes of inferior people. That was the objection to Callippides; and modern actors are similarly criticized for representing women who are not ladies.

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Moreover, tragedy fulfils its function even without acting, just as much as epic, and its quality can be gauged by reading aloud. So, if it is in other respects superior, this disadvantage is not necessarily inherent.

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Secondly, tragedy has all the elements of the epic—it can even use the hexameter—

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and in addition a considerable element of its own in the spectacle and the music, which make the pleasure all the more vivid;

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and this vividness can be felt whether it is read or acted.

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Another point is that it attains its end with greater economy of length. What is concentrated is always more effective than what is spread over a long period; suppose, for example, Sophocles’Oedipuswere to be turned into as many lines as there are in the Iliad .

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Again, the art of the epic has less unity, as is shown by the fact that any one epic makes several tragedies. The result is that, if the epic poet takes a single plot, either it is set forth so briefly as to seem curtailed, or if it conforms to the limit of lengthLiterally the length of the (proper) limit. it seems thin and diluted.

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In saying that epic has less unity I mean an epic made up of several separate actions.

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The Iliad has many such parts and so has the Odyssey, and each by itself has a certain magnitude. And yet the composition of these poems is as perfect as can be and each of them is—as far as an epic may be—a representation of a single action.

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If then tragedy is superior in these respects and also in fulfilling its artistic function—for tragedies and epics should produce not any form of pleasure but the pleasure we have describedi.e., the pleasure felt when by the representation of life in art “relief is given” to pity, fear, and other such emotions, or, to use a term now prevalent, when such emotions are “released.”Cf. Aristot. Poet. 14.3.—then obviously, since it attains its object better than the epic, the better of the two is tragedy.

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This must suffice for our treatment of tragedy and epic, their characteristics, their species, their constituent parts, and their number and attributes; for the causes of success and failure; and for critical problems and their solutions. . . .

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This pointer pattern extracts chapter and subchapter.

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+ + + + + + + English + Greek + + + + + EpiDoc and CTS conversion and general header review. + fixed three typos based on user report + cleaned up bad place tags in a few texts and cleaned up the document format + more reorganizing of texts module by collection + began reorganizing texts module by collection. created separate work directory in texts module to keep hopper files separate from in progress files + fixed typo + fixed cvs log keyword + edited entity tags CEH + fixed bibl errors - zr + added cvs log keyword + Corrected two typos in 1449a. + Put Bekker line 1 milestone tags at the beginning of each section so that the incoming list creator would work. Changed RREFDECL. + Tagged in conformance with Prose.e dtd. + Text was scanned at St. Olaf Spring, 1992. + + + + + +
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+LetThe text here printed is based on Vahlen’s third edition(Leipzig, 1885), and the chief deviations from it are noted at the foot of each page. The prime source of all existing texts of the Poetics is the eleventh century Paris manuscript, No. 1741, designated as Ac. To the manuscripts of the Renaissance few, except Dr. Margoliouth, now assign any independent value, but they contain useful suggestions for the correction of obvious errors and defects in Ac. These are here designated “copies.”V. stands for Vahlen’s third edition, and By. for the late Professor Ingram Bywater, who has earned the gratitude and admiration of all students of the Poetics by his services both to the text and to its interpretation. Then there is the Arabic transcript. Translated in the eleventh century from a Syriac translation made in the eighth century, it appears to make little sense, but sometimes gives dim visions of the readings of a manuscript three centuries older but not necessarily better than Ac, readings which confirm some of the improvements introduced into Renaissance texts. us here deal with Poetry, its essence and its several species, with the characteristic function of each species and the way in which plots must be constructed if the poem is to be a success; and also with the number and character of the constituent parts of a poem, and similarly with all other matters proper to this same inquiry; and let us, as nature directs, begin first with first principles.

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Epic poetry, then, and the poetry of tragic drama, and, moreover, comedy and dithyrambic poetry, and most flute-playing and harp-playing, these, speaking generally, may all be said to be representations of life.The explanation of μίμησις, as Aristotle uses the word, demands a treatise; all that a footnote can say is this:—Life presents to the artist the phenomena of sense, which the artist re-presents in his own medium, giving coherence, designing a pattern. That this is true not only of drama and fiction but also of instrumental music (most flute-playing and harp-playing) was more obvious to a Greek than to us, since Greek instrumental music was more definitely imitative. The technical display of the virtuoso Plato describes as a beastly noise. Since μίμησις in this sense and μιμητής and the verb μιμεῖσθαι have a wider scope than any one English word, it is necessary to use more than one word in translation, e.g. μιμητής is what we call an artist; and for μίμησις where representation would be clumsy we may use the word art; the adjective must be imitative, since representative has other meanings.

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But they differ one from another in three ways: either in using means generically differenti.e., means that can be divided into separate categories. or in representing different objects or in representing objects not in the same way but in a different manner.

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For just as by the use both of color and form people represent many objects, making likenesses of them—some having a knowledge of art and some working empirically—and just as others use the human voice; so is it also in the arts which we have mentioned, they all make their representations in rhythm and language and tune, using these means either separately or in combination.

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For tune and rhythm alone are employed in flute-playing and harp-playing and in any other arts which have a similar function, as, for example, pipe-playing.

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Rhythm alone without tune is employed by dancers in their representations, for by means of rhythmical gestures they represent both character and experiences and actions.πάθη καὶ πράξεις cover the whole field of life, what men do (πράξεις) and what men experience (πάθη). Since πάθη means also emotions and that sense may be present here, but as a technical term in this treatise πάθος is a calamity or tragic incident, something that happens to the hero.

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But the art which employs words either in bare prose or in metres, either in one kind of metre or combining several, happens up to the present day to have no name.

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For we can find no common term to apply to the mimes of Sophron and XenarchusSophron and Xenarchus, said to he father and son, lived in Syracuse, the elder a contemporary of Euripides. They wrote mimes, i.e., simple and usually farcical sketches of familiar incidents, similar to the mimes of Herondas and the fifteenth Idyll of Theocritus, but in prose. There was a tradition that their mimes suggested to Plato the use of dialogue. and to the Socratic dialogues:

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nor again supposing a poet were to make his representation in iambics or elegiacs or any other such metre—except that people attach the word poet(maker)to the name of the metre and speak of elegiac poets and of others as epic poets.

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Thus they do not call them poets in virtue of their representation but apply the name indiscriminately in virtue of the metre.

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For if people publish medical or scientific treatises in metre the custom is to call them poets. But Homer and EmpedoclesEmpedocles (floruit 445 B.C.) expressed his philosophical and religious teaching in hexameter verse, to which Aristotle elsewhere attributes genuine value as poetry, but it is here excluded from the ranks of poetry because the object is definitely. have nothing in common except the metre, so that it would be proper to call the one a poet and the other not a poet but a scientist.

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Similarly if a man makes his representation by combining all the metres, as Chaeremon did when he wrote his rhapsody The Centaur, a medley of all the metres, he too should be given the name of poet.Chaeremon was a tragedian and rhapsodist. The Centaur was apparently an experiment which might be classed as either drama or epic. Cf. Aristot. Poet. 24.11. On this point the distinctions thus made may suffice.

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There are certain arts which employ all the means which I have mentioned, such as rhythm and tune and metre—dithyrambic and nomic poetry,The traditional definition is that the Dithyramb was sung to a flute accompaniment by a chorus in honor of Dionysus; and that the Nome was a solo sung to a harp accompaniment in honor of Apollo, but it is not clear that Aristotle regarded the Dithyramb as restricted to the worship of Dionysus. Timotheus’s dithyramb mentioned in Aristot. Poet. 15.8 cannot have been Dionysiac. But there is good evidence to show that the dithyramb was primarily associated with Dionysus. for example, and tragedy too and comedy. The difference here is that some use all these at once, others use now one now another.

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These differences then in the various arts I call the means of representation.

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Since living personsLiterally men doing or experiencing something. are the objects of representation, these must necessarily be either good men or inferior—thus only are characters normally distinguished, since ethical differences depend upon vice and virtue—that is to say either better than ourselves or worse or much what we are. It is the same with painters.

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Polygnotus depicted men as better than they are and Pauson worse, while Dionysius made likenesses.Polygnotus’s portraits were in the grand style and yet expressive of character(cf. Aristot. Poet. 6.15): Aristophanes aIludes to a Pauson as a perfectly wicked caricaturist: Dionysius of Colophon earned the name of the man-painter because he always painted men and presumably made good likenesses.

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Clearly each of the above mentioned arts will admit of these distinctions, and they will differ in representing objects which differ from each other in the way here described.

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In painting too, and flute-playing and harp-playing, these diversities may certainly be found, and it is the same in prose and in unaccompanied verse.

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For instance Homer’s people are better, Cleophon’s are like, while in Hegemon of Thasos, the first writer of parodies, and in Nicochares, the author of the Poltrooniad, they are worse.Cleophon wrote epics (i.e., hexameter poems), describing scenes of daily life in commonplace diction (cf. Aristot. Poet. 22.2): Hegemon wrote mock epics in the style of the surviving Battle of Frog and Mice: of Nicochares nothing is known, but his forte was evidently satire.

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It is the same in dithyrambic and nomic poetry, for instance . . . a writer might draw characters like the Cyclops as drawn by Timotheus and Philoxenus.Both famous dithyramhic poets. There is evidence that Philoxenus treated Polyphemus in the vein of satire: Timotheus may have drawn a more dignified picture.

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It is just in this respect that tragedy differs from comedy. The latter sets out to represent people as worse than they are to-day, the former as better.

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A third difference in these arts is the manner in which one may represent each of these objects.

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For in representing the same objects by the same means it is possible to proceed either partly by narrative and partly by assuming a character other than your own—this is Homer’s method—or by remaining yourself without any such change, or else to represent the characters as carrying out the whole action themselves.

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These, as we said above, are the three differences which form the several species of the art of representation, the means, the objects, and the manner.

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It follows that in one respect Sophocles would be the same kind of artist as Homer, for both represent good men, and in another respect he would resemble Aristophanes, for they both represent men in action and doing things. And that according to some is the reason why they are called dramas, because they present people as doingDrama being derived from δρᾶν to do. things.

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And for this reason the Dorians claim as their own both tragedy and comedy—comedy is claimed both by the Megarians here in Greece, who say that it originated in the days of their democracy, and by the Megarians in Sicily,The inhabitants of Megara Hyblaea. for it was from there the poet EpicharmusEpicharmus of Cos wrote in Sicily burlesques and mimes depicting scenes of daily life. He and Phormis were originators of comedy in that they sketched types instead of lampooning individuals (cf. Aristot. Poet. 5.5): of Chionides and Magnes we only know that they were early comedians, i.e., in the first half of the fifth century B.C. came, who was much earlier than Chionides and Magnes; and tragedy some of the Peloponnesians claim. Their evidence is the two names.

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Their name, they say, for suburb villages is κῶμαι—the Athenians call them Demes—and comedians are so called not from κωμάζειν, to revel, but because they were turned out of the towns and went strolling round the villages( κῶμαι). Their word for action, they add, is δρᾶν, whereas the Athenian word is πράττειν. So much then for the differences, their number, and their nature.

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Speaking generally, poetry seems to owe its origin to two particular causes, both natural.

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From childhood men have an instinct for representation, and in this respect, differs from the other animals that he is far more imitative and learns his first lessons by representing things. And then there is the enjoyment people always get from representations.

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What happens in actual experience proves this, for we enjoy looking at accurate likenesses of things which are themselves painful to see, obscene beasts, for instance, and corpses.

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The reason is this: Learning things gives great pleasure not only to philosophers but also in the same way to all other men, though they share this pleasure only to a small degree.

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The reason why we enjoy seeing likenesses is that, as we look, we learn and infer what each is, for instance, that is so and so.

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If we have never happened to see the original, our pleasure is not due to the representation as such but to the technique or the color or some other such cause.

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We have, then, a natural instinct for representation and for tune and rhythmIt is not clear wheter the two general causes are (1) the instinct for imitation, (2) the natural enjoyment of mimicry by others; or whether these two are combined into one and the second cause is the instinct for tune and rhythm. Obviously this last is an essential cause of poetry.—for the metres are obviously sections of rhythmse.g., the rhythm of the blacksmith’s hammer or of a trotting horse is dactylic, but the hexameter is a section or slice of that rhythm; it is cut up into sixes.—and starting with these instincts men very gradually developed them until they produced poetry out of their improvisations.

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Poetry then split into two kinds according to the poet’s nature. For the more serious poets represented fine doings and the doings of fine men, while those of a less exalted nature represented the actions of inferior men, at first writing satire just as the others at first wrote hymns and eulogies.

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Before Homer we cannot indeed name any such poem, though there were probably many satirical poets,

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but starting from Homer, there is, for instance, his MargitesA famous burlesque which Aristotle attributes to Homer. Other similar poems must mean other early burlesques not necessarily attributed to Homer. and other similar poems. For these the iambic metre was fittingly introduced and that is why it is still called iambic, because it was the metre in which they lampooned each other.Since the iambic came to be the metre of invective, the verb ἰαμβίζειν acquired the meaning to lampoon. There is probably implied a derivation from ἰάπτειν, to assail.

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Of the ancients some wrote heroic verse and some iambic.

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And just as Homer was a supreme poet in the serious style, since he alone made his representations not only good but also dramatic, so, too, he was the first to mark out the main lines of comedy, since he made his drama not out of personal satire but out of the laughable as such. His Margites indeed provides an analogy: as are the Iliad and Odyssey to our tragedies, so is the Margites to our comedies.

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When tragedy and comedy came to light, poets were drawn by their natural bent towards one or the other. Some became writers of comedies instead of lampoons, the others produced tragedies instead of epics; the reason being that the former is in each case a higher kind of art and has greater value.

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To consider whether tragedy is fully developed by now in all its various species or not, and to criticize it both in itself and in relation to the stage, that is another question.

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At any rate it originated in improvisation—both tragedy itself and comedy. The one came from the preludeBefore the chorus began (or in pauses between their songs) the leader of the performance would improvise some appropriate tale or state the theme which they were to elaborate. Thus he was called ὁ ἐξάρχων or the starter, and became in time the first actor. to the dithyramb and the other from the prelude to the phallic songs which still survive as institutions in many cities.

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Tragedy then gradually evolved as men developed each element that came to light and after going through many changes, it stopped when it had found its own natural form.

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Thus it was Aeschylus who first raised the number of the actors from one to two. He also curtailed the chorus and gave the dialogue the leading part. Three actors and scene-painting Sophocles introduced.

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Then as to magnitude.Being a development of the Satyr play,A Satyr play was an interlude performed by a troupe of actors dressed as the goat-like followers of Dionysus. Hence τραγῳδία, goat-song. Aristotle seems so clear about this that he does not trouble to give a full explanation. But we can see from this passage that the Satyr plays were short, jocose and in the trochaic metre which suited their dances, and that in Aristotle’s view tragedy was evolved from these. No example of a primitive Satyr play survives, but we can make inferences from the later, more sophisticated Cyclops of Euripides and the fragments of Sophocles’ <foreign xml:lang="grc">Ἰχνευταί</foreign>, The Trackers. We cannot be certain that Aristotle’s theory is historically correct; the balance of evidence is against it. it was quite late before tragedy rose from short plots and comic diction to its full dignity, and that the iambic metre was used instead of the trochaic tetrameter.

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At first they used the tetrameter because its poetry suited the Satyrs and was better for dancing, but when dialogue was introduced, Nature herself discovered the proper metre. The iambic is indeed the most conversational of the metres,

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and the proof is that in talking to each other we most often use iambic lines but very rarely hexameters and only when we rise above the ordinary pitch of conversation.

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Then there is the number of acts. The further embellishmentsMasks, costumes, etc. and the story of their introduction one by one we may take as told,

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for it would probably be a long task to go through them in detail.

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Comedy, as we have said, is a representation of inferior people, not indeed in the full sense of the word bad, but the laughable is a species of the base or ugly.Ugly was to a Greek an equivalent of bad. The persons in Comedy are inferior (see chapter 2.), but have only one of the many qualities which make up Ugliness or Badness, viz. the quality of being ludicrous and therefore in some degree contemptible.

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It consists in some blunder or ugliness that does not cause pain or disaster, an obvious example being the comic mask which is ugly and distorted but not painful.

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The various stages of tragedy and the originators of each are well known, but comedy remains obscure because it was not at first treated seriously. Indeed it is only quite late in its historyProbably about 465 B.C. that the archon granted a chorus for a comic poet; before that they were volunteers.In the fifth century dramatists submitted their plays to the archon in charge of the festival at which they wished them to be performed. He selected the number required by the particular festival, and to the poets thus selected granted a chorus, i.e., provided a choregus who paid the expenses of the chorus. The earlier volunteers had themselves paid for and produced their plays.

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Comedy had already taken certain forms before there is any mention of those who are called its poets. Who introduced masks or prologues, the number of actors, and so on, is not known.

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Plot making [Epicharmus and Phormis]Epicharmus and Phormis, being both early Sicilian comedians, are appropriate here. Either part of a sentence is lost or an explanatory note has got into the text. originally came from Sicily,

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and of the Athenian poets CratesFragments of his comedies survive, dating about the middle of the fifth century B.C. was the first to give up the lampooning form and to generalize his dialogue and plots.

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Epic poetry agreed with tragedy only in so far as it was a metrical representation of heroic action, but inasmuch as it has a single metre and is narrative in that respect they are different.

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And then as regards length, tragedy tends to fall within a single revolution of the sun or slightly to exceed that, whereas epic is unlimited in point of time;

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and that is another difference, although originally the practice was the same in tragedy as in epic poetry.

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The constituent parts are some of them the same and some peculiar to tragedy.

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Consequently any one who knows about tragedy, good and bad, knows about epics too, since tragedy has all the elements of epic poetry, though the elements of tragedy are not all present in the epic.

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With the representation of life in hexameter versei.e., epic poetry. and with comedy we will deal later. We must now treat of tragedy after first gathering up the definition of its nature which results from what we have said already.

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Tragedy is, then, a representation of an actionMargoliouth’s phrase a chapter of life, illuminates the meaning, since πρᾶξις includes what the hero does and what happens to him. (Cf. Aristot. Poet. 2.1 and note.) that is heroic and complete and of a certain magnitude—by means of language enriched with all kinds of ornament, each used separately in the different parts of the play: it represents men in action and does not use narrative, and through pity and fear it effects relief to these and similar emotions.The sense of the pity of it and fear lest such disasters might befall ourselves are not the only emotions which tragedy releases, but Aristotle specifies them as the most characteristic. For κάθαρσις, see Introduction.

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By language enriched I mean that which has rhythm and tune, i.e., song,

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and by the kinds separately I mean that some effects are produced by verse alone and some again by song.

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Since the representation is performed by living persons, it follows at once that one essential part of a tragedy is the spectacular effect, and, besides that, song-making and diction. For these are the means of the representation.

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By diction I mean here the metrical arrangement of the words; and song making I use in the full, obvious sense of the word.

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And since tragedy represents action and is acted by living persons, who must of necessity have certain qualities of character and thought—for it is these which determine the quality of an action; indeed thought and character are the natural causes of any action and it is in virtue of these that all men succeed or fail—

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it follows then that it is the plot which represents the action. By plot I mean here the arrangement of the incidents: character is that which determines the quality of the agents, and thought appears wherever in the dialogue they put forward an argument or deliver an opinion.

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Necessarily then every tragedy has six constituent parts, and on these its quality depends. These are plot, character, diction, thought, spectacle, and song.

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Two of these are the means of representation: one is the manner: three are the objects represented.The means are diction and music: the manner is spectacle: the objects represented are actions or experiences and the moral or intellectual qualities of the dramatis personae.

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This list is exhaustive, and practically all the poets employ these elements, for every drama includes alike spectacle and character and plot and diction and song and thought.

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The most important of these is the arrangement of the incidents,i.e., plot, as defined above. for tragedy is not a representation of men but of a piece of action, of life, of happiness and unhappiness, which come under the head of action, and the end aimed at is the representation not of qualities of character but of some action; and while character makes men what they are,it’s their actions and experiences that make them happy or the opposite.

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They do not therefore act to represent character, but character-study is included for the sake of the action. It follows that the incidents and the plot are the end at which tragedy aims, and in everything the end aimed at is of prime importance.

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Moreover, you could not have a tragedy without action, but you can have one with out character-study.

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Indeed the tragedies of most modern poets are without this, and, speaking generally, there are many such writers, whose case is like that of Zeuxis compared with Polygnotus.Zeuxis’s portraits were ideal (cf. Aristot. Poet. 25.28). The latter was good at depicting character, but there is nothing of this in Zeuxis’s painting.

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A further argument is that if a man writes a series of speeches full of character and excellent in point of diction and thought, he will not achieve the proper function of tragedy nearly so well as a tragedy which, while inferior in these qualities, has a plot or arrangement of incidents.

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And furthermore, two of the most important elements in the emotional effect of tragedy, reversals and discoveries,See chapter 11. are parts of the plot.

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And here is further proof: those who try to write tragedy are much sooner successful in language and character-study than in arranging the incidents. It is the same with almost all the earliest poets.

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The plot then is the first principle and as it were the soul of tragedy: character comes second.

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It is much the same also in painting; if a man smeared a canvas with the loveliest colors at random, it would not give as much pleasure as an outline in black and white.Selection and design are necessary for any work of representation.

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And it is mainly because a play is a representation of action that it also for that reason represents people.

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Third comes thought. This means the ability to say what is possible and appropriate. It comes in the dialogue and is the function of the statesman’s or the rhetorician’s art.Cf. chapter 6.

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The old writers made their characters talk like statesmen,Or in the style of ordinary people, without obvious rhetorical artifice. the moderns like rhetoricians.

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Character is that which reveals choiceπροαίρεσις is a technical term in Aristotle’s ethics, corresponding to our use of the term Will, the deliberate adoption of any course of conduct or line of action. It is a man’s will or choice in the sense that determines the goodness or badness of his character. If character is to be revealed in drama, a man must be shown in the exercise of his will, choosing between one line of conduct and another, and he must be placed in circumstances in wbich the choice is not obvious, i.e., circumstances in which everybody’s choice would not be the same. The choice of death rather than disbonourable wealth reveals character; the choice of a nectarine rather than a turnip does not., shows what sort of thing a man chooses or avoids in circumstances where the choice is not obvious, so those speeches convey no character in which there is nothing whatever which the speaker chooses or avoids.

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Thought you find in speeches which contain an argument that something is or is not, or a general expression of opinion.

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The fourth of the literary elements is the language. By this I mean, as we said above, the expression of meaning in words,This seems to be a mistaken reference to 6 above where diction is defined as the metrical arrangement of the words. In poetry they come to the same thing. and this is essentially the same in verse and in prose.

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Of the other elements which enrichSee Aristot. Poet. 6.2. tragedy the most important is song-making.

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Spectacle, while highly effective, is yet quite foreign to the art and has nothing to do with poetry. Indeed the effect of tragedy does not depend on its performance by actors, and, moreover,for achieving the spectacular effects the art of the costumier is more authoritative than that of the poet.

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After these definitions we must next discuss the proper arrangement of the incidents since this is the first and most important thing in tragedy.

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We have laid it down that tragedy is a representation of an action that is whole and complete and of a certain magnitude, since a thing may be a whole and yet have no magnitude.

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A whole is what has a beginning and middle and end.

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A beginning is that which is not a necessary consequent of anything else but after which something else exists or happens as a natural result.

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An end on the contrary is that which is inevitably or, as a rule, the natural result of something else but from which nothing else follows;

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a middle follows something else and something follows from it.

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Well constructed plots must not therefore begin and end at random, but must embody the formulae we have stated.

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Moreover, in everything that is beautiful, whether it be a living creature or any organism composed of parts, these parts must not only be orderly arranged but must also have a certain magnitude of their own;

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for beauty consists in magnitude and ordered arrangement. From which it follows that neither would a very small creature be beautiful—for our view of it is almost instantaneous and therefore confusedWith a very small object the duration of our vision is, as it were, so rapid that the parts are invisible; we, therefore, cannot appreciate their proportion and arrangement, in which beauty consists.—nor a very large one, since being unable to view it all at once, we lose the effect of a single whole; for instance, suppose a creature a thousand miles long.

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As then creatures and other organic structures must have a certain magnitude and yet be easily taken in by the eye, so too with plots: they must have length but must be easily taken in by the memory.

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The limit of length considered in relation to competitions and productionαἴσθησις is the play’s perception by an audience—how much an audience will stand. before an audience does not concern this treatise. Had it been the rule to produce a hundred tragedies, the performance would have been regulated by the water clock, as it is said they did once in other days.

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But as for the natural limit of the action, the longer the better as far as magnitude goes, provided it can all be grasped at once. To give a simple definition: the magnitude which admits of a change from bad fortune to good or from good fortune to bad, in a sequence of events which follow one another either inevitably or according to probability, that is the proper limit.

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A plot does not have unity, as some people think, simply because it deals with a single hero. Many and indeed innumerable things happen to an individual, some of which do not go to make up any unity, and similarly an individual is concerned in many actions which do not combine into a single piece of action.

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It seems therefore that all those poets are wrong who have written a Heracleid or Theseid or other such poems.Aristotle condemns them all, assuming—or perhaps assured by experience—that their sole claim to unity lay in the fact that all the stories in the poem had a common hero. They think that because Heracles was a single individual the plot must for that reason have unity.

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But Homer, supreme also in all other respects, was apparently well aware of this truth either by instinct or from knowledge of his art. For in writing an Odyssey he did not put in all that ever happened to Odysseus, his being wounded on Parnassus, for instance, or his feigned madness when the host was gathered(these being events neither of which necessarily or probably led to the other), but he constructed his Odyssey round a single action in our sense of the phrase. And the Iliad the same.

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As then in the other arts of representation a single representation means a representation of a single object, so too the plot being a representation of a piece of action must represent a single piece of action and the whole of it; and the component incidents must be so arranged that if one of them be transposed or removed, the unity of the whole is dislocated and destroyed. For if the presence or absence of a thing makes no visible difference, then it is not an integral part of the whole.

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What we have said already makes it further clear that a poet’s object is not to tell what actually happened but what could and would happen either probably or inevitably.

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The difference between a historian and a poet is not that one writes in prose and the other in verse— indeed the writings of Herodotus could be put into verse and yet would still be a kind of history, whether written in metre or not. The real difference is this, that one tells what happened and the other what might happen.

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For this reason poetry is something more scientific and serious than history, because poetry tends to give general truths while history gives particular facts.

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By a general truth I mean the sort of thing that a certain type of man will do or say either probably or necessarily. That is what poetry aims at in giving names to the characters.The names indicate types. This is obvious, as he says, in Comedy and is also true of Greek Tragedy, which, although it deals with traditional heroes regarded as real people, yet keeps to a few stories in which each character has become a type. In Chapter 17. the dramatist is recommended to sketch first his outline plot, making it clear and coherent, before he puts in the names. A particular fact is what Alcibiades did or what was done to him.

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In the case of comedy this has now become obvious, for comedians construct their plots out of probable incidents and then put in any names that occur to them. They do not, like the iambic satirists, write about individuals.Aristophanes of course did write about individuals. But Aristotle is thinking of the New Comedy, where the names of the characters were invented by the author and there was no reference to real people.

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In tragedy, on the other hand, they keep to real names. The reason is that what is possible carries conviction. If a thing has not happened, we do not yet believe in its possibility, but what has happened is obviously possible. Had it been impossible, it would not have happened.

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It is true that in some tragedies one or two of the names are familiar and the rest invented; indeed in some they are all invented, as for instance in Agathon’s Antheus,The name, apparently, of an imaginary hero. The word might be Ἄνθος, but The Flower is an unlikely title for a Greek tragedy. where both the incidents and the names are invented and yet it is none the less a favourite.

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One need not therefore endeavor invariably to keep to the traditional stories with which our tragedies deal. Indeed it would be absurd to do that, seeing that the familiar themes are familiar only to a few and yet please all.The reason why Greek tragedy dealt only with a few familiar themes is to be found of course in its religious origin. It was the function of tragedy to interpret and embroider myths. Aristotle never gives this reason, but offers instead the unconvincing explanation that tragedians adhered to certain real stories to gain verisimilitude—and yet he has to admit that, since to many of the auditors these stories were unfamiliar and none the less attractive, dramatists might just as well invent new themes.

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It is clear, then, from what we have said that the poet must be a maker not of verses but of stories, since he is a poet in virtue of his representation, and what he represents is action.

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Even supposing he represents what has actually happened, he is none the less a poet, for there is nothing to prevent some actual occurrences being the sort of thing that would probably or inevitably happen, and it is in virtue of that that he is their maker.

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Of simpleThis term is defined in the next chapter. It seems odd to use it before its meaning is explained. Perhaps we should read ἄλλων(Tyrwhitt) and translate of all plots. plots and actions the worst are those which are episodic. By this I mean a plot in which the episodes do not follow each other probably or inevitably.

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Bad poets write such plays because they cannot help it, and good poets write them to please the actors. Writing as they do for competition, they often strain a plot beyond its capacity and are thus obliged to sacrifice continuity.Or logic. He means the chain of cause and effect, wherein each incident is the result of what has gone before. See the end of the next chapter.

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But this is bad work, since tragedy represents not only a complete action but also incidents that cause fear and pity, and this happens most of all when the incidents are unexpected and yet one is a consequence of the other.The logic suffers from ellipse. Plays which fail to exhibit the sequence of cause and effect are condemned (1) because they lack the unity which befits tragedy, (2) because they miss that supreme effect of fear or pity produced by incidents which, though unexpected, are seen to be no mere accident but the inevitable result of what has gone before.

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For in that way the incidents will cause more amazement than if they happened mechanically and accidentally, since the most amazing accidental occurrences are those which seem to have been providential, for instance when the statue of Mitys at Argos killed the man who caused Mitys’s death by falling on him at a festival. Such events do not seem to be mere accidents.

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So such plots as these must necessarily be the best.

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Some plots are simple and some complex, as indeed the actions represented by the plots are obviously such.

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By a simple action I mean one that is single and continuous in the sense of our definition above,In chapters 7 and 8. wherein the change of fortune occurs without reversal or discovery;

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by a complex action I mean one wherein the change coincides with a discovery or reversal or both.

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These should result from the actual structure of the plot in such a way that what has already happened makes the result inevitable or probable;for there is indeed a vast difference between what happens propter hoc and post hoc.

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A reversal is a change of the situation into the opposite, as described above,At the end of chapter 7. Vahlen and many other exponents of the Politics confine the meaning of “reversal” to the situation in which the hero’s action has consequences directly opposite to his intention and expectation. There is much to be said for this interpretation, which stresses the irony at the heart of all tragedy. But it is too narrow for Aristotle’s theory. All tragedy involves a change of fortune ( μετάβασις). In a “simple” plot this is gradual; in a “complex” plot it is catastrophic, a sudden revolution of fortune’s wheel. In some of the greatest tragedies, but not in all, this is the result of action designed to produce the opposite effect. this change being, moreover, as we are saying, probable or inevitable—

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like the man in the Oedipus who came to cheer Oedipus and rid him of his anxiety about his mother by revealing his parentage and changed the whole situation.The messenger for Corinth announces the death of Polybus and Oedipus’s succession to the throne. Oedipus, feeling now safe from the prophecy that he would murder his father, still fears to return to Corinth, lest he should fulfil the other prophecy and marry his mother. The messenger seeks to reassure him by announcing that Polybus and Merope are not his parents. But the effect of this was to change the whole situation for Oedipus by revealing the truth that he a murdered his father, Laius, and married his mother, Jocasta. This reversal is the more effective because it is immediately coincident with the discovery of the truth. In the Lynceus, too, there is the man led off to execution and

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Danaus following to kill him, and the result of what had already happened was that the latter was killed and the former escaped.Lynceus married Hypermnestra who disobeyed Danaus in not murdering him. Danaus trying by process of law to compass the death of their son Abas was killed himself. The dog it was that died.

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A discovery, as the term itself implies, is a change from ignorance to knowledge, producing either friendship or hatred in those who are destined for good fortune or ill.

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A discovery is most effective when it coincides with reversals, such as that involved by the discovery in the Oedipus.

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There are also other forms of discovery, for what we have described may in a sense occur in relation to inanimate and trivial objects, or one may discover whether some one has done something or not.

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But the discovery which is most essentially part of the plot and part of the action is of the kind described above, for such a discovery and reversal of fortune will involve either pity or fear, and it is actions such as these which, according to our hypothesis, tragedy represents; and, moreover, misfortune and good fortune are likely to turn upon such incidents.

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Now since the discovery is somebody’s discovery, in some scenes one character only is discovered to another, the identity of the other being obvious; but sometimes each must discover the other. Thus Iphigeneia was discovered to Orestes through the sending of the letter, but a separate discovery was needed to make him known to Iphigeneia.Euripides’ Iphigeneia in Tauris—Orestes and Pylades arriving among the Tauri are by the custom of the country to be sacrificed to Artemis by her priestess, Iphigeneia. It is agreed that Pylades shall be spared to carry a letter from Iphigeneia to Orestes, whom she supposes to be in Argos. In order that Pylades may deliver the message, even if he should lose the letter, she reads it aloud. Orestes thus discovers who she is. He then reveals himself to her by declaring who he is and proving his identity by his memories of their home.

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We see then that two elements of the plot, reversal and discovery, turn upon these incidents. A third element is a calamity. Of these three elements we have already described reversal and discovery.

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A calamity is a destructive or painful occurrence, such as a death on the stage, acute suffering and wounding and so on.

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We have alreadyIn chapter 6. spoken of the constituent parts to be used as ingredients of tragedy. The separable members into which it is quantitatively divided are these: Prologue, Episode, Exode, Choral Song,

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the last being divided into Parode and Stasimon.

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These are common to all tragedies; songs sung by actors on the stage and commoi are peculiar to certain plays.

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A prologue is the whole of that part of a tragedy which precedes the entrance of the chorus.

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An episode is the whole of that part of a tragedy which falls between whole choral songs.

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An exode is the whole of that part of a tragedy which is not followed by a song of the chorus.

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A parode is the whole of the first utterance of the chorus.

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A stasimon is a choral song without anapaests or trochaics.This does not apply to surviving Greek tragedies, but may be true of those of Aristotle’s time. The word Stasimon is applied to all choruses in a tragedy other than those sung during entry or exit. It is usually explained as meaning a stationary song, because it was sung after the chorus had taken up its station in the orchestra.

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A commos is a song of lament shared by the chorus and the actors on the stage.

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The constituent parts to be used as ingredients of tragedy have been described above; these are the separable members into which it is quantitatively divided.The whole of chapter 12. bears marks of belonging to the Poetics but seems out of place, since it interrupts the discussion of plot.

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Following upon what has been said above we should next state what ought to be aimed at and what avoided in the construction of a plot, and the means by which the object of tragedy may be achieved.

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Since then the structure of the best tragedy should be not simple but complexSee chapter 10. and one that represents incidents arousing fear and pity—for that is peculiar to this form of art—it is obvious to begin with that one should not show worthy men passing from good fortune to bad. That does not arouse fear or pity but shocks our feelings.

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Nor again wicked people passing from bad fortune to good. That is the most untragic of all, having none of the requisite qualities, since it does not satisfy our feelingsi.e., our preference for poetic justice. or arouse pity or fear.

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Nor again the passing of a thoroughly bad man from good fortune to bad fortune. Such a structure might satisfy our feelings but it arouses neither pity nor fear, the one being for the man who does not deserve his misfortune and the other for the man who is like ourselves—pity for the undeserved misfortune, fear for the man like ourselves—so that the result will arouse neither pity nor fear.

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There remains then the mean between these. This is the sort of man who is not pre-eminently virtous and just, and yet it is through no badness or villainy of his own that he falls into the fortune, but rather through some flaw in him,Whether Aristotle regards the “flaw” as intellectual or moral has been hotly discussed. It may cover both senses. The hero must not deserve his misfortune, but he must cause it by making a fatal mistake, an error of judgement, which may well involve some imperfection of character but not such as to make us regard him as “morally responsible” for the disasters although they are nevertheless the consequences of the flaw in him, and his wrong decision at a crisis is the inevitable outcome of his character(cf. Aristot. Poet. 6.24.). he being one of those who are in high station and good fortune, like Oedipus and Thyestes and the famous men of such families as those.

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The successful plot must then have a singleἁπλοῦς elsewhere in the Poetics means simple as opposed to πεπλεγμένος, complex; here it is opposed to διπλοῦς, which describes a double denouement, involving happiness for some and disaster for others. and not, as some say, a double issue; and the change must be not to good fortune from bad but, on the contrary, from good to bad fortune, and it must not be due to villainy but to some great flaw in such a man as we have described, or of one who is better rather than worse.

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This can be seen also in actual practice. For at first poets accepted any plots, but to-day the best tragedies are written about a few families—Alcmaeon for instance and Oedipus and Orestes and Meleager and Thyestes and Telephus and all the others whom it befell to suffer or inflict terrible disasters.

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Judged then by the theory of the art, the bestThis is modified by 19 in the following chapter, where he finds an even better formula for the tragic effect. tragedy is of this construction.

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Those critics are therefore wrong who charge Euripides with doing this in his tragedies, and say that many of his end in misfortune.

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That is, as we have shown, correct. And there is very good evidence of this, for on the stage and in competitions such plays appear the most tragic of all, if they are successful, and even if Euripides is in other respects a bad manager,Against Euripides Aristotle makes the following criticisms: (1)his choruses are often irrelevant; (2)the character of the heroine in his Iphigeneia in Tauris is inconsistent; (3)in the Medea the deliberate killing of the children is ineffective and the play is inartistically ended by the machina; (4)the character of Menelaus in the Orestes is needlessly depraved; (5)Melanippe is too philosophical for a woman. yet he is certainly the most tragic of the poets.

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Next in order comes the structure which some put first, that which has a double issue, like the Odyssey, and ends in opposite ways for the good characters and the bad.

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It is the sentimentality of the audience which makes this seem the best form; for the poets follow the wish of the spectators.

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But this is not the true tragic pleasure but rather characteristic of comedy, where those who are bitter enemies in the story, Orestes and Aegisthus, for instance, go off at the end, having made friends, and nobody kills anybody.

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Fear and pity sometimes result from the spectacle and are sometimes aroused by the actual arrangement of the incidents, which is preferable and the mark of a better poet.

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The plot should be so constructed that even without seeing the play anyone hearing of the incidents happening thrills with fear and pity as a result of what occurs. So would anyone feel who heard the story of Oedipus.

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To produce this effect by means of an appeal to the eye is inartistic and needs adventitious aid,

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while those who by such means produce an effect which is not fearful but merely monstrous have nothing in common with tragedy.that here were plays which relied for their effect on the scenery and make up is clear from chapter 17:—The Phorcides and Prometheus and Scenes laid in Hades. It was even possible to produce the Eumenides so badly as to bring it into this category. But Aristotle’s criticism here includes the more important point that the poignancy of a Greek tragedy is due to what happens and not to our seeing it happen. That Medea murders her children is tragic: to display the murder coram populo would add either nothing or something merely monstrous. And although Sophocles shows Oedipus with his eyes out, it is the fact and not the sight which is properly tragic. For one should not seek from tragedy all kinds of pleasure but that which is peculiar to tragedy,

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and since the poet must by representation produce the pleasure which comes from feeling pity and fear, obviously this quality must be embodied in the incidents.

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We must now decide what incidents seem dreadful or rather pitiable. Such must necessarily be the actions of friends to each other or of enemies or of people that are neither.

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Now if an enemy does it to an enemy, there is nothing pitiable either in the deed or the intention,

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except so far as the actual calamity goes.

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Nor would there be if they were neither friends nor enemies. But when these calamities happen among friends,when for instance brother kills brother, or son father, or mother son, or son mother—either kills or intends to kill, or does something of the kind, that is what we must look for.

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Now it is not right to break up the traditional stories, I mean, for instance, Clytaemnestra being killed by Orestes and Eriphyle by Alcmaeon,

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but the poet must show invention and make a skilful use of the tradition.

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But we must state more clearly what is meant by skilful.

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The action may happen in the way in which the old dramatists made their characters act—consciously and knowing the facts, as EuripidesThis does not necessarily imply that Aristotle reckons Euripides “a modern,” since the Greek can equally mean “Euripides as well as other old dramatists.” also made his Medea kill her children.

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Or they may do the deed but without realizing the horror of it and then discover the relationship afterwards, like Oedipus in Sophocles. That indeed lies outside the play,i.e., Oedipus kills his father Laius before the play opens. but an example of this in the tragedy itself is the Alcmaeon of AstydamasA prolific tragedian of the fourth century. or Telegonus in the Wounded Odysseus.

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A third alternative is to intend to do some irremediable action in ignorance and to discover the truth before doing it.

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Besides these there is no other way, for they must either do the deed or not, either knowing or unknowing.

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The worst of these is to intend the action with full knowledge and not to perform it. That outrages the feelings and is not tragic, for there is no calamity. So nobody does that, except occasionally, as, for instance, Haemon and CreonHaemon, discovered by his father Creon embracing the dead body of Antigone, drew his sword on him but missed his aim and Creon fled. in the Antigone.

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Next comes the doing of the deed.

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It is better to act in ignorance and discover afterwards. Our feelings are not outraged and the discovery is startling.

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Best of all is the last; in the Cresphontes,By Euripides. Polyphontes killed Cresphontes, king of Messenia, and gained possession of his kingdom and his wife, Merope. She had concealed her son, Aepytus, in Arcadia, and when he returned, seeking vengeance, she nearly killed him in ignorance but discovered who he was. He then killed Polyphontes and reigned in his stead. for instance, Merope intends to kill her son and does not kill him but discovers; and in the IphigeneiaIn Tauris. See Aristot. Poet. 11.8, note. the case of the sister and brother; and in the HelleAuthor and play unknown. the son discovers just as he is on the point of giving up his mother.

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So this is the reason, as was said above,See Aristot. Poet. 13.7. why tragedies are about a few families. For in their experiments it was from no technical knowledge but purely by chance that they found out how to produce such an effect in their stories. So they are obliged to have recourse to those families in which such calamities befell.See Aristot. Poet. 9.8, note.

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Now concerning the structure of the incidents and the proper character of the plots enough has been said.

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Concerning character there are four points to aim at. The first and most important is that the character should be good.

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The play will show character if, as we said above,See Aristot. Poet. 6.24. either the dialogue or the actions reveal some choice; and the character will be good, if the choice is good.

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But this is relative to each class of people. Even a woman is good and so is a slave, although it may be said that a woman is an inferior thing and a slave beneath consideration.

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The second point is that the characters should be appropriate. A character may be manly, but it is not appropriate for a woman to be manly or clever.

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Thirdly, it should be like.The meaning probably is like the traditional person, e.g. Achilles must not be soft nor Odysseus stupid. Cf. Horace Ars Poet. 120 famam sequere. This is different from making the character good and from making it appropriate in the sense of the word as used above.

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Fourthly, it should be consistent. Even if the original be inconsistent and offers such a character to the poet for representation, still he must be consistently inconsistent.

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An example of unnecessary badness of character is Menelaos in the OrestesAristotle has a personal distaste for this character on the ground that Euripides made him a creature meaner than the plot demands.;

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of character that is unfitting and inappropriate the lament of Odysseus in the ScyllaA dithyramb by Timotheus. Cf. Aristot. Poet. 26.3. and Melanippe’s speechA fragment survives (Eur. Fr. 484 (Nauck)). Euripides seems to have given her a knowledge of science and philosophy inappropriate to a woman.;

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of inconsistent character Iphigeneia in Aulis, for the suppliant Iphigeneia is not at all like her later character.

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In character-drawing just as much as in the arrangement of the incidents one should always seek what is inevitable or probable, so as to make it inevitable or probable that such and such a person should say or do such and such; and inevitable or probable that one thing should follow another.

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Clearly therefore the denouementOr unravelling. of each play should also be the result of the plot itself and not produced mechanically as in the Medea and the incident of the embarkation in the Iliad. Hom. Il. 2.155-181, where it is only the arbitrary (i.e., uncaused) intervention of Athene which stays the flight of the Greeks. In the Medea the heroine, having killed her rival and her children, is spirited away in the chariot ot the Sun, a result not caused by what has gone before.

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The god in the carThe μηχανή or car was a sort of crane with a pulley attached, which was fixed at the top of the back-scene in the left corner of the stage. By it a god or hero could be lowered or raised or exhibited motionless in mid-air. Weak dramatists thus introduced a car to cut the knot by declaring the denouement instead of unravelling the plot by the logic of cause and effect. It was presumably on such a car that Medea was borne away. should only be used to explain what lies outside the play, either what happened earlier and is therefore beyond human knowledge, or what happens later and needs to be foretold in a proclamation. For we ascribe to the gods the power of seeing everything.

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There must, however, be nothing inexplicable in the incidents, or, if there is, it must lie outside the tragedy. There is an example in Sophocles’ Oedipus.i.e., Oedipus had killed Laius in a wayside quarrel, not knowing who he was. When his subjects at Thebes crave his help to remove the curse which is blighting their crops, he pledges himself to discover the murderer of Laius. It may seem odd that he should not know enough about the details of the murder to connect it in his mind with his own murderous quarrel. But that was long ago, and neither an audience nor a novel-reader is critical about incidents which occur long before the point at which the story begins. See chapter Aristot. Poet. 24.20.

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Since tragedy is a representation of men better than ourselves we must copy the good portrait-painters who, while rendering the distinctive form and making a likeness, yet paint people better than they are. It is the same with the poet. When representing people who are hot-tempered or lazy, or have other such traits of character, he should make them such, yet men of worth [an example of hardness]Apparently a note on Achilles which has been copied by mistake into the text.; take the way in which Agathon and Homer portray Achilles.

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Keep, then, a careful eye on these rules and also on the appeal to the eyei.e., stage-craft rather than staging. which is necessarily bound up with the poet’s business; for that offers many opportunities of going wrong. But this subject has been adequately discussed in the published treatises.As distinct from the body of esoteric doctrine circulated by oral teaching among Aristotle’s pupils.

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What a Discovery is has been already stated.In chapter 11.As for kinds of Discovery, first comes the least artistic kind, which is largely used owing to incompetence—discovery by tokens.

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These may be congenital, like the spear the Earth-born bear or stars, like those which CarcinusA prolific tragedian of the early fourth century. The family are agreeably ridiculed in Aristophanes’ Wasps. uses in his ThyestesThese were birth-marks. The spear-head distinguished the descendants of the Spartoi at Thebes; the star or bright spot on the descendants of Pelops commemorated his ivory shoulder, and in Carcinus’s play it seems to have survived cooking.;

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or they may be acquired and these may be on the body, for instance, wounds, or external things like necklaces, and in the TyroA play by Sophocles. Tyro’s twins by Poseidon, who appeared to her in the guise of the river Enipeus, were exposed in a little boat or ark, like Moses in the bulrushes, and this led to their identification. the discovery by means of the boat.

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There is a better and a worse way of using these tokens; for instance Odysseus, by means of his wound, was discovered in one way by the nurse and in another way by the swine-herds.Hom. Od. 19.386ff., 205ff. The first came about automatically, the second was a deliberate demonstration to prove the point. Aristotle here distinguishes between a discovery inevitably produced by the logic of events (e.g. it was inevitable or at least probable that Odysseus, arriving as a strange traveller, should be washed by Eurycleia, and that she should thus see the old scar on his thigh and discover his identity) and a discovery produced by a deliberate declaration (e.g. Odysseus’s declaration of his identity to Eumaeus). The latter kind is manufactured by the poet, not logically caused by what has gone before.

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Discovery scenes constructed to prove the point are inartistic and so are all such scenes, but those are better which arise out of a reversal scene, as, for instance, in The Washing.Hom. Od. 19.392. See preceding note.

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In the second place come those which are manufactured by the poet and are therefore inartistic. For instance, in the IphigeneiaEuripides’ Iphigeneia in Tauris. See Aristot. Poet. 11.8, note. Orestes revealed himself. She was revealed to him through the letter,

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but Orestes says himself what the poet wants and not what the plot requires. So this comes near to the fault already mentioned, for he might just as well have actually brought some tokens.To prove his identity Orestes mentions Pelops’ lance and other things from home, which is much the same as producing visible tokens. And there is the voice of the shuttleWhen Philomela’s tongue was cut out, she wove in embroidery the story of her rape by Tereus. Thus the facts were discovered to her sister, Procne, by deliberate demonstration. In Sophocles’ Tereus.

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The third kind is due to memory, to showing distress on seeing something. An example of this is the scene in the Cyprians by Dicaeogenes; on seeing the picture he burst into tearsTeucer, returning to Salamis in disguise and seeing a portrait of his dead father Telamon, burst into tears and was thus discovered. So, too, in The Two Gentlemen of <placeName key="perseus,Verona">Verona</placeName> Julia is discovered because she swoons on hearing Valentine offer Sylvia to his rival.: and again in the Tale of Alcinous, Hom. Od. 8.521ff. hearing the minstrel he remembered and burst into tears; and thus they were recognized.

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The fourth kind results from an inference; for instance, in the Choephoroe Someone like me has come; but nobody is like me except Orestes; therefore he has come. And there is Polyidus’sA Sophist who either wrote an Iphigeneia with this denouement or more probably suggested in a work of criticism (cf. Aristot. Poet. 17.6) that Orestes on being led to his fate should speculate aloud upon the odd coincidence that both he and his sister should be sacrificed, thus revealing his identity to Iphigeneia. Like most critics, Polyidos would have been a poor dramatist. There is an example of this form of discovery in the French opera Coeur de Lion, where the old knight says goddam and is thus discovered to be an Englishman. idea about Iphigeneia, for it is likely enough that Orestes should make an inference that, whereas his sister was sacrificed, here is the same thing happening to him. And in Theodectes’ Tydeus that having come to find a son, he is perishing himself. And the scene in the Phineidae, where on seeing the spot the women inferred their fate, that they were meant to die there for it was there that they had been exposed.In these cases the inference was presumably uttered aloud and hence the identity of the speakers discovered. Nothing else is known of these plays.

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There is also a kind of fictitious discovery which depends on a false inference on the part of the audience, for instance in Odysseus the False Messenger, he said he would recognize the bow, which as a matter of fact he had not seen, but to assume that he really would reveal himself by this means is a false inference.The text is obscure, and our ignorance of the play or rhapsody adds to the darkness, but the reference may be to the ruse, common in detective stories, of misleading the audience by false clues in order to make the final revelation more effective.

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Best of all is the discovery which is brought about directly by the incidents, the surprise being produced by means of what is likely—take the scene in Sophocles’ Oedipus or in the Iphigeneia—for it is likely enough that she should want to send a letter. These are the only discovery scenes which dispense with artificial tokens, like necklaces.The classical example of these tokens in English drama is the strawberry mark on the left arm in Box and Cox. But Aristotle seems here to use tokens in a wider sense than at the beginning of the chapter and to include not only birthmarks, necklaces, etc., but any statement or action which may be used as a sign in the scene of Discovery.

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In the second place come those that are the result of inference.

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In constructing plots and completing the effect by the help of dialogue the poet should, as far as possible, keep the scene before his eyes. Only thus by getting the picture as clear as if he were present at the actual event, will he find what is fitting and detect contradictions.

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The censure upon Carcinos is evidence of this. Amphiaraos was was made to rise from a temple. The poet did not visualize the scene and therefore this escaped his notice, but on the stage it was a failure since the audience objected.The example is obscure. Clearly Carcinus introduced an absurdity which escaped notice until the play was staged. Margoliouth suggests that if Amphiaraus were a god he should come down, and if a mere hero, he sould not have a temple. In The Master of Ballantrae Mrs. Henry cleans a sword by thrusting it up to the hilt in the ground—which is iron-bound by frost. The would be noticed on the stage: a reader may miss the incongruity.

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The poet should also, as far as possible, complete the effect by using the gestures. For, if their natural powers are equal, those who are actually in the emotions are the most convincing; he who is agitated blusters and the angry man rages with the maximum of conviction.Sir Joshua Reynolds used thus to simulate emotion before a mirror. In his Preface to the Lyrical Ballads Wordsworth says that the Poet will wish to bring his feelings near to those of the persons whose feelings he describes . . . and even confound and identify his own feelings with theirs. See also Burke, On the Sublime and Beautiful,4. 4.

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And that is why poetry needs either a sympathetic nature or a madman,Genius to madness near allied is the meaning of μανικός as used here. Plato held that the only excuse for a poet was that he couldn’t help it. the former being impressionable and the latter inspired.

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The stories, whether they are traditional or whether you make them up yourself, should first be sketched in outline and then expanded by putting in episodes.

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I mean that one might look at the general outline, say of the Iphigeneia, like this: A certain maiden has been sacrificed, and has disappeared beyond the ken of those who sacrificed her and has been established in another country, where it is a custom to sacrifice strangers to the goddess; and this priesthood she holds. Some time afterwards it happens that the brother of the priestess arrives there—the fact that the god told him to go there, and why, and the object of his journey, lie outside the outline-plot. He arrives, is seized, and is on the point of being sacrificed, when he reveals his identity either by Euripides’ method or according to Polyidos, by making the very natural remark that after all it is not only his sister who was born to be sacrificed but himself too; and thus he is saved.

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Not until this has been done should you put in names and insert the episodes;

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and you must mind that the episodes are appropriate, as, for instance, in the case of Orestes the madness that led to his capture and his escape by means of the purification.In the Iphigeneia in Tauris Orestes is captured because he is suffering from a fit of mania; and at the end Iphigeneia pretends that the image of Artemis has been infected by the blood-guiltiness of the Greek strangers, and that, before they can be sacrificed, she must cleanse both image and strangers secretly in the sea. Thus they all escape together by boat.

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Now in drama the episodes are short, but it is by them that the epic gains its length.

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The story of the Odyssey is quite short. A man is for many years away from home and his footsteps are dogged by Poseidon and he is all alone. Moreover,affairs at home are in such a state that his estate is being wasted by suitors and a plot laid against his son, but after being storm-tossed he arrives himself, reveals who he is, and attacks them, with the result that he is saved and destroys his enemies.

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That is the essence, the rest is episodes.

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In every tragedy there is a complication and a denouement.The Greek says simply tying and loosing. Complication and denouement seem clumsy equivalents, yet they are the words we use in dramatic criticism. The incidents outside the plot and some of those in it usually form the complication, the rest is the denouement.

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I mean this, that the complication is the part from the beginning up to the point which immediately precedes the occurrence of a change from bad to good fortune or from good fortune to bad; the denouement is from the beginning of the change down to the end.

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For instance, in the Lynceus of Theodectes the complication is the preceding events, and the seizure of the boy, and then their own seizure; and the denouement is from the capital charge to the end.The boy must be Abas, and they are presumably Danaus and perhaps his other daughters. Aristotle seems to regard the arrest of Danaus not as part of the λύσις, but as the end of the δέσις.

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Tragedies should properly be classed as the same or different mainly in virtue of the plot, that is to say those that have the same entanglement and denouement. Many who entangle well are bad at the denouement. Both should always be mastered.

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There are four varieties of tragedy—the same as the number given for the elementsApparently the reference here is to the four elements into which in the course of chapters 10-15. Plot has been analysed, Reversal, Discovery, Calamity, and Character. But the symmetry is spoilt by the fact that his first species, the complex play, corresponds to the first two of these four elements, viz. to Reversal and Discovery. Thus his fourth species is left in the air and he hurriedly introduces Spectacle as the fourth corresponding element. Other explanations seem even sillier than this.—

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first the complex kind, which all turns on reversal and discovery;

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the calamity play like the stories of Ajax and Ixion;

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the character play like the Phthian WomenBy Sophocles. and the PeleusBoth Sophocles and Euripides wrote a Peleus..

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The fourth element is spectacle, like the PhorcidesThe text is obscure, and our ignorance of the play or rhapsody adds to the darkness, but the reference may be to the ruse, common in detective stories, of misleading the audience by false clues in order to make the final revelation more effective. and Prometheus, and all scenes laid in Hades.

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One should ideally try to include all these elements or, failing that, the most important and as many as possible, especially since it is the modern fashion to carp at poets, and, because there have been good poets in each style, to demand that a single author should surpass the peculiar merits of each.

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One must remember, as we have often said, not to make a tragedy an epic structure:

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by epic I mean made up of many stories—suppose, for instance, one were to dramatize the IIiad as a whole.

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The length of the IIiad allows to the parts their proper size, but in plays the result is full of disappointment.

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And the proof is that all who have dramatized the Sack of Troy as a whole, and not, like Euripides, piecemeal, or the Niobe story as a whole and not like Aeschylus, either fail or fare badly in competition. Indeed even Agathon failed in this point alone.

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In reversals, however, and in simple storiesi.e., those that have no Discovery or Reversal. See chapter 10. too,they admirably achieve their end, which is a tragic effect that also satisfies your feelings.

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This is achieved when the wise man, who is, however, unscrupulous, is deceived—like Sisyphus—and the man who is brave but wicked is worsted.

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And this, as Agathon says, is a likely result, since it is likely that many quite unlikely things should happen.

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The chorus too must be regarded as one of the actors. It must be part of the whole and share in the action, not as in Euripides but as in Sophocles.

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In the others the choral odes have no more to do with the plot than with any other tragedy. And so they sing interludes, a practice begun by Agathon. And yet to sing interludes is quite as bad as transferring a whole speech or scene from one play to another.

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The other factors have been already discussed. It remains to speak of Diction and Thought.

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All that concerns Thought may be left to the treatise on Rhetoric, for the subject is more proper to that inquiry.Thought—no English word exactly corresponds with διάνοια—is all that which is expressed or effected by the words (cf. Aristot. Poet. 6.22, 23, and 25). Thus the student is rightly referred to the Art of Rhetoric, where he learns what to say in every case. Aristotle adds that the rules there given for the use of ideas will guide him also in the use of incidents, since the same effect may be produced either by talk or by situation.

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Under the head of Thought come all the effects to be produced by the language.

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Some of these are proof and refutation, the arousing of feelings like pity, fear, anger, and so on, and then again exaggeration and depreciation.It is an important part of the orator’s skill to depreciate what is important and to exaggerate trivial points.

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It is clear that in the case of the incidents, too, one should work on the same principles, when effects of pity or terror or exaggeration or probability have to be produced.

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There is just this difference, that some effects must be clear without explanation,Those produced by situation. whereas others are produced in the speeches by the speaker and are due to the speeches. For what would be the use of a speaker, if the required effect were likely to be felt without the aid of the speeches?

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Under the head of Diction one subject of inquiry is the various modes of speech, the knowledge of which is proper to elocution or to the man who knows the master artRhetoric is a master art in relation to elocution, since it decides the effects to be produced, and elocution decides how to produce them. So the doctor’s art is master to that of the dispenser, and the art of riding to that of the maker of bridles.—I mean for instance, what is a command, a prayer, a statement, a threat, question, answer, and so on.

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The knowledge or ignorance of such matters brings upon the poet no censure worth serious consideration. For who could suppose that there is any fault in the passage which Protagoras censures, because Homer, intending to utter a prayer, gives a command when he says, Sing, goddess, the wrath? To order something to be done or not is, he points out, a command.

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So we may leave this topic as one that belongs not to poetry but to another art.

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Diction as a wholeA translator is bound to render this chapter, since the balance of evidence is in favour of its inclusion. But the readaer is advised to skip it, since it is written from the point of view of grammar and philology, and does not, like the succeeding chapter, deal with the literary use of words. It is also very obscure. Students should refer to Bywater’s edition. is made up of these parts: letter, syllable, conjunction, joint,A joint, as defined below, appears to be a word which indicates the beginning or end of a clause. noun, verb, case, phrase.

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A letter is an indivisible sound, not every such sound but one of which an intelligible sound can be formed. Animals utter indivisible sounds but none that I should call a letter.

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Such sounds may be subdivided into vowel, semi-vowel, and mute. A vowel is that which without any addition has an audible sound; a semivowel needs the addition of another letter to give it audible sound, for instance S and R; a mute is that which with addition has no sound of its own but becomes audible when combined with some of the letters which have a sound. Examples of mutes are G and D.

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Letters differ according to the shape of the mouth and the place at which they are sounded; in being with or without aspiration; in being long and short; and lastly in having an acute, grave, or intermediate accent. But the detailed study of these matters properly concerns students of metre.

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A syllable is a sound without meaning, composed of a mute and a letter that has a sound. GR, for example, without A is a syllable just as much as GRA with an A. But these distinctions also belong to the theory of metre. words. It is also very obscure. Students should refer to Bywater’s edition.

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A conjunction is a sound without meaning, which neither hinders nor causes the formation of a single significant sound or phrase out of several sounds, and which, if the phrase stands by itself, cannot properly stand at the beginning of it, e.g. μέν, δή, τοί, δέ; or else it is a sound without meaning capable of forming one significant sound or phrase out of several sounds having each a meaning of their own, e.g. ἀμφί, περί.

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A joint is a sound without meaning which marks the beginning or end of a phrase or a division in it, and naturally stands at either end or in the middle.This paragraph remains a cause of despair. Bywater’s notes suggest a restoration.

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A noun is a composite sound with a meaning, not indicative of time, no part of which has a meaning by itself; for in compounds we do not use each part as having a meaning of its own, for instance, in Theodorus, there is no meaning of δῶρον (gift).

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A verb is a composite sound with a meaning, indicative of time, no part of which has a meaning by itself—just as in nouns. Man or white does not signify time, but walks and has walked connote present and past time respectively.

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A case(or inflection)of a noun or verb is that which signifies either of or to a thing and the like;or gives the sense of one or many e.g. men and man; or else it may depend on the delivery, for example question and command. Walked? and Walk! are verbal cases of this kind.

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A phraseThere is no exact English equivalent of this meaning of λόγος, which has been used already in 7 above without explanation. Statement and proposition also cover part of its meaning. is a composite sound with a meaning, some parts of which mean something by themselves.

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It is not true to say that every phrase is made up of nouns and verbs, e.g. the definition of manProbably one of the two definitions given in the Topics, a two-footed land animal and an animal amenable to reason.; but although it is possible to have a phrase without verbs, yet some part of it will always have a meaning of its own, for example, Cleon in Cleon walks.

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A phrase may be a unit in two ways; either it signifies one thing or it is a combination of several phrases. The unity of the Iliad, for instance, is due to such combination, but the definition of man is one phrase because it signifies one thing.

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Nouns are of two kinds. There is the simple noun, by which I mean one made up of parts that have no meaning, like γῆ, and there is the compound noun.

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These may be made up either of a part which has no meaning and a part which has a meaning—though it does not have its meaning in the compound—or of two parts both having a meaning.

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A compound noun may be triple and quadruple and multiple, e.g. many of the bombastic names like Hermocaicoxanthus.A compound of the names of three rivers, Hermus, Caicus, and Xanthus. . . .

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Every noun is either ordinaryi.e., one which has dined normal currency as contrasted with the rare word, which is confined to a dialect or borrowed from a foreign language. or rare or metaphorical or ornamental or invented or lengthened or curtailed or altered.

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An ordinary word is one used by everybody, a rare word one used by some;

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so that a word may obviously be both ordinary and rare, but not in relation to the same people. σίγυνον,Meaning, spear. for instance, is to the Cypriots an ordinary word but to us a rare one.

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Metaphor is the application of a strange term either transferred from the genus and applied to the species or from the species and applied to the genus, or from one species to another or else by analogy.

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An example of a term transferred from genus to species is Here stands my ship. Riding at anchor is a species of standing.

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An example of transference from species to genus is Indeed ten thousand noble things Odysseus did, for ten thousand, which is a species of many, is here used instead of the word many.

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An example of transference from one species to another is Drawing off his life with the bronze and Severing with the tireless bronze, where drawing off is used for severing and severing for drawing off, both being species of removing.Probably the bronze is in the first case a knife and in the second a cupping-bowl. This would make the metaphor intelligible.

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Metaphor by analogy means this: when B is to A as D is to C, then instead of B the poet will say D and B instead of D.

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And sometimes they add that to which the term supplanted by the metaphor is relative.This may claim to be one of Aristotle’s least lucid sentences. It means this: If Old Age: Life :: Evening: Day, then we may call old age the Evening of Life. In that case old age is the term supplanted by the metaphor, and it is relative to Life; therefore Life (i.e., that to which the term supplanted by the metaphor is relative) is added to the metaphorical (or transferred) term Evening.For instance, a cup is to Dionysus what a shield is to Ares;

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so he will call the cup Dionysus’s shield and the shield Ares’ cup. Or old age is to life as evening is to day; so he will call the evening day’s old-age or use Empedocles’ phraseUnknown to us.; and old age he will call the evening of life or life’s setting sun.

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Sometimes there is no word for some of the terms of the analogy but the metaphor can be used all the same. For instance, to scatter seed is to sow, but there is no word for the action of the sun in scattering its fire. Yet this has to the sunshine the same relation as sowing has to the seed, and so you have the phrase sowing the god-created fire.

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Besides this another way of employing metaphor is to call a thing by the strange name and then to deny it some attribute of that name. For instance, suppose you call the shield not Ares’ cup but a “wineless cup.” . . .Or you might call Love Venus’s bloodless War. At this point a few lines on Ornament have evidently been lost, since this is its place in the catalogue of nouns above. By ornament he seems to mean an embellishing epithet or synonym. In the Rhetoric he quotes Our lady the fig-tree as a misplaced ornament. One might add the seventeenth-century use of Thames for water. . . .

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An invented word is one not used at all by any people and coined by the poet. There seem to be such words, eg. sprouters for horns and pray-er for priest.

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A word is lengthened or curtailed, the former when use is made of a longer vowel than usual or a syllable inserted, and the latter when part of the word is curtailed.

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An example of a lengthened word is πόληος for πολέως and Πηληιάδεω for Πηλείδου; and of a curtailed word κρῖ and δῶ, and e.g. μία γίνεται ἀμφοτέρων ὄψ.κρῖ for κριθή, barley; δῶ for δῶμα house; ὄψ for ὄψις face, eye, or appearance.

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A word is altered when the poet coins part of the word and leaves the rest unchanged, e.g. δεξιτερὸν κατὰ μαζόν instead of δεξιόν.

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Of the nouns themselves, some are masculine, some feminine, and some neuter.This paragraph the reader should either skip or study with Bywater’s notes. Without them these generalizations on gender seem merely wrong.

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Masculine are all that end in N and P and Σ and in the two compounds of Σ, Ψ and Ξ.

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Feminine are all that end in those of the vowels that are always long, for instance Η and Ω, and in Α among vowels that can be lengthened.

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The result is that the number of masculine and feminine terminations is the same, for Ψ and Ξ are the same as Σ.

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No noun ends in a mute or in a short vowel.

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Only three end in Ι, μέλι, κόμμι, and πέπερι. Five end in Υ. The neuters end in these letters and in Ν and Σ.

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The merit of diction is to be clear and not commonplace. The clearest diction is that made up of ordinary words, but it is commonplace.

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An example is the poetry of Cleophon and of Sthenelus.A tragedian whom Aristophanes ridicules for the insipidity of his diction.

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That which employs unfamiliar words is dignified and outside the common usage. By unfamiliar I mean a rare word, a metaphor, a lengthening,See preceding chapter 19. and anything beyond the ordinary use.

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But if a poet writes entirely in such words, the result will be either a riddle or jargon; if made up of metaphors, a riddle and if of rare words, jargon.

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The essence of a riddle consists in describing a fact by an impossible combination of words. By merely combining the ordinary names of things this cannot be done, but it is made possible by combining metaphors. For instance, I saw a man weld bronze upon a man with fire, and so on.The answer is a cupping-bowl. This was a bronze vessel which was applied to the body at the place at which a small incision had been made. Heated lint was placed in the bowl of it and the reduction of air-pressure thus caused a strong flow of blood. For this form of riddle cf. Out of the strong came forth sweetness.

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A medley of rare words is jargon.

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We need then a sort of mixture of the two. For the one kind will save the diction from being prosaic and commonplace, the rare word, for example, and the metaphor and the ornament, whereas the ordinary words give clarity.

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A considerable aid to clarity and distinction are the lengthening and abbreviation and alteration of words. Being otherwise than in the ordinary form and thus unusual, these will produce the effect of distinction, and clarity will be preserved by retaining part of the usual form.

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Those critics are therefore wrong who censure this manner of idiom and poke fun at the poet, as did the elder EucleidesA critic of this name wrote on the drama, but his date is uncertain. who said it was easy to write poetry, granted the right to lengthen syllables at will. He had made a burlesque in this very style: Ἐπιχάρην εἶδον Μαραθῶνάδε βαδίζοντα and οὐκ ἄν γ’ ἐράμενος τὸν ἐκείνου ἐλλέβορον.In Homer we find short vowels lengthened by position, but, whereas Homer uses the licence sparingly, Eucleides raised a laugh by overdoing it and writing in parody such hexameters as those here quoted. A modern parallel may illustrate this. The poet Stephen Phillips employed to excess the licence whihc allows a clash between the natural accent and the metrical ictus, and Mr. Owen Seaman, for the express purpose of raising a laugh, parodied the trick by carrying it to further excess and wrote in blank verse, She a milliner was and her brothers Dynamiters.

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Now to make an obtrusive use of this licence is ridiculous;

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but moderation is a requisite common to all kinds of writing. The same effect could be got by using metaphors and rare words and the rest unsuitably for the express purpose of raising a laugh.

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What a difference is made by the proper use of such licence may be seen in epic poetry, if you substitute in the verse the ordinary forms.

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Take a rare word or metaphor or any of the others and substitute the ordinary word; the truth of our contention will then be obvious.For instance, Aeschylus and Euripides wrote the same iambic line with the change of one word only, a rare word in place of one made ordinary by custom, yet the one line seems beautiful and the other trivial. Aeschylus in the Philoctetes wrote, The ulcer eats the flesh of this my foot, and Euripides instead of eats put feasts upon. Or take I that am small, of no account nor goodly; suppose one were to read the line substituting the ordinary words, I that am little and weak and ugly. Or compare He set a stool unseemly and a table small. with He set a shabby stool and a little table, or the sea-shore is roaring with the sea-shore is shrieking.Similarly we might use ordinary words instead of those which Keats chose so carefully and speak of wonderful windows abutting on to a dangerous sea-shore in a dreary, mysterious country.

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AriphradesUnknown. again made fun of the tragedians because they employ phrases which no one would use in conversation, like δωμάτων ἄπο instead of ἀπὸ δωμάτων and their σέθεν and ἐγὼ δέ νιν and Ἀχιλλέως πέρι for περὶ Ἀχιλλέως, and so on.

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All that sort of thing, not being in the ordinary form, gives distinction to the diction, which was what he failed to understand.

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It is a great thing to make a proper use of each of the elements mentioned, and of double words and rare words too, but by far the greatest thing is the use of metaphor.

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That alone cannot be learnt; it is the token of genius. For the right use of metaphor means an eye for resemblances.i.e., the power of detecting identity in difference which distinguishes also both the philosopher and the scientist.

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Of the various kinds of words the double forms are most suited for dithyrambs, rare words for heroic verse and metaphors for iambics.

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And indeed in heroic verse they are all useful; but since iambic verse is largely an imitation of speech, only those nouns are suitable which might be used in talking. These are the ordinary word, metaphor, and ornament.

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Now concerning tragedy and the art of representing life in action, what we have said already must suffice.

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We come now to the art of representation which is narrative and in metre.i.e., epic. Clearly the story must be constructed as in tragedy, dramatically, round a single piece of action, whole and complete in itself,with a beginning, middle and end, so that like a single living organism it may produce its own peculiar form of pleasure.

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It must not be such as we normally find in history, where what is required is an exposition not of a single piece of action but of a single period of time, showing all that within the period befell one or more persons, events that have a merely casual relation to each other.

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For just as the battle of Salamis occurred at the same time as the Carthaginian battle in Sicily, but they do not converge to the same resultGelo’s defeat of the Carthaginians in Sicily in 480 B.C. took place, according to Herodotus, on the same day as the battle of Salamis.; so, too, in any sequence of time one event may follow another and yet they may not issue in any one result.

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Yet most of the poets do this.

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So in this respect, too, compared with all other poets Homer may seem, as we have already said, divinely inspired, in that even with the Trojan war, which has a beginning and an end, he did not endeavor to dramatize it as a whole, since it would have been either too long to be taken in all at once or, if he had moderated the length, he would have complicated it by the variety of incident. As it is, he takes one part of the story only and uses many incidents from other parts, such as the Catalogue of Ships and other incidents with which he diversifies his poetry.

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The others, on the contrary, all write about a single hero or about a single period or about a single action with a great many parts, the authors, for example, of the Cypria and the Little Iliad.As we have seen already in chapter 8, a poem or a play must be one story and not several stories about one hero. Thus, since the Iliad and Odyssey have this essential unity (i.e., one thread runs through the narrative of each), few plays can be made out of them but many out of the Cypria or the Little Iliad, which are merely collections of lays on similar themes.

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The result is that out of an Iliad or an Odyssey only one tragedy can be made, or two at most, whereas several have been made out of the Cypria, and out of the Little Iliad more than eight, e.g. The Award of Arms, Philoctetes, Neoptolemus, Eurypylus, The Begging, The Laconian Women, The Sack of <placeName key="perseus,Troy">Troy</placeName>, and Sailing of the Fleet, and Sinon, too, and The Trojan Women.

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The next point is that there must be the same varieties of epic as of tragedySee Aristot. Poet. 18.4.: an epic must be simple or complex,See chapter 10. or else turn on character or on calamity.

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The constituent parts, too, are the same with the exception of song and spectacle. Epic needs reversals and discoveries and calamities, and the thought and diction too must be good.

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All these were used by Homer for the first time, and used well. Of his poems he made the one, the Iliad, a simple story turning on calamity, and the Odyssey a complex story—it is full of discoveries—turning on character. Besides this they surpass all other poems in diction and thought.

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Epic differs from tragedy in the length of the composition and in metre.

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The limit of length already givenSee Aristot. Poet. 7.12. will suffice—it must be possible to embrace the beginning and the end in one view,which would be the case if the compositions were shorter than the ancient epics but reached to the length of the tragedies presented at a single entertainment.“Entertainment” must mean a festival. At the City Dionysia three poets competed, each with three tragedies. By the end of the fifth century only one Satyr play was performed at each festival. But the tragedies were longer than those we possess. It is therefore likely that the nine tragedies together with one Satyr play amounted to about 15,000 lines. The Iliad contains between 16,000 and 17,000 lines.

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Epic has a special advantage which enables the length to be increased, because in tragedy it is not possible to represent several parts of the story as going on simultaneously, but only to show what is on the stage, that part of the story which the actors are performing; whereas, in the epic, because it is narrative, several parts can be portrayed as being enacted at the same time.

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If these incidents are relevant, they increase the bulk of the poem, and this increase gives the epic a great advantage in richness as well as the variety due to the diverse incidents; for it is monotony which, soon satiating the audience, makes tragedies fail.

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Experience has shown that the heroic hexameter is the right metre. Were anyone to write a narrative poem in any other metre or in several metres, the effect would be wrong.

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The hexameter is the most sedate and stately of all metres and therefore admits of rare words and metaphors more than others, and narrative poetry is itself elaborate above all others.

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The iambic and the trochaic tetrameter are lively, the latter suits dancing and the former suits real life.

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Still more unsuitable is it to use several metres as Chaeremon did.

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So no one has composed a long poem in any metre other than the heroic hexameter. As we said above, Nature shows that this is the right metre to choose.

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Homer deserves praise for many things and especially for this, that alone of all poets he does not fail to understand what he ought to do himself. The poet should speak as seldom as possible in his own character, since he is not representing the story in that sense.This takes us back to the beginning of chapter 3, where the various manners of representation are distinguished. Homer represents life partly by narration, partly by assuming a character other than his own. Both these manners come under the head of Imitation. When Aristotle says the poet speaks himself and plays a part himself he refers not to narrative, of which there is a great deal in Homer, but to the preludes (cf. φροιμιασάμενος below) in which the poet, invoking the Muse, speaks in his own person. Ridgeway points out that in the whole of the Iliad and Odyssey Homer thus speaks himself only 24 lines.

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Now the other poets play a part themselves throughout the poem and only occasionally represent a few things dramatically, but Homer after a brief prelude at once brings in a man or a woman or some other character, never without character, but all having character of their own.

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Now the marvellous should certainly be portrayed in tragedy, but epic affords greater scope for the inexplicable(which is the chief element in what is marvellous), because we do not actually see the persons of the story.

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The incident of Hector’s pursuitIliad, xxii. 205. sq. “And to the host divine Achilles nodded with his head a sign and let them not launch their bitter darts at Hector, lest another should win glory by shooting him and Achilles himself come second.” would look ridiculous on the stage, the people standing still and not pursuing and Achilles waving them back, but in epic that is not noticed.

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But that the marvellous causes pleasure is shown by the fact that people always tell a piece of news with additions by way of being agreeable.

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Above all, Homer has taught the others the proper way of telling lies,that is, by using a fallacy. When B is true if A is true, or B happens if A happens, people think that if B is true A must be true or happen. But that is false. Consequently if A be untrue but there be something else, B, which is necessarily true or happens if A is true, the proper thing to do is to posit B, for, knowing B to be true, our mind falsely infers that A is true also. This is an example from the Washing.Odyssey 19. Odysseus tells Penelope that he is a Cretan from Gnossus, who once entertained O. on his voyage to Troy. As evidence, he describes O.’s dress and his companions (Hom. Od. 19.164-260). P. commits the fallacy of inferring the truth of the antecedent from the truth of the consequent: “If his story were true, he would know these details; But he does know them; Therefore his story is true.” The artist in fiction uses the same fallacy, e.g.: “If chessmen could come to life the white knight would be a duffer; But he is a most awful duffer (look at him!); Therefore chessmen can come to life.” He makes his deductions so convincing that we falsely infer the truth of his hypothesis.

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What is convincing though impossible should always be preferred to what is possible and unconvincing.

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Stories should not be made up of inexplicable details; so far as possible there should be nothing inexplicable, or, if there is, it should lie outside the story—as, for instance, Oedipus not knowing how Laius died—and not in the play; for example, in the Electra the news of the Pythian games,In Sophocles’Electrathe plot hinges on a false story of Orestes’ death by an accident at the Pythian games. Presumably the anachronism shocked Aristotle. or in the Mysians the man who came from Tegea to Mysia without speaking.Telephus. To say that the plot would otherwise have been ruined is ridiculous.

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One should not in the first instance construct such a plot, and if a poet does write thus, and there seems to be a more reasonable way of treating the incident, then it is positively absurd.

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Even in the Odyssey the inexplicable elements in the story of his landingHom. Od. 13.116ff. It seemed to the critics inexplicable that Odysseus should not awake when his ship ran aground at the harbour of Phorcys in Ithaca and the Phaeacian sailors carried him ashore. would obviously have been intolerable, had they been written by an inferior poet. As it is, Homer conceals the absurdity by the charm of all his other merits.

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The diction should be elaborated only in the idle parts which do not reveal character or thought.The Messengers’ speeches, a regular feature of Greek tragedy, may serve to illustrate what is here called the idle part of a play, i.e., passages which, but for brilliant writing, might be dull, since no character is there elucidated and no important sentiments expressed. Too brilliant diction frustrates its own object by diverting attention from the portrayal of character and thought.

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With regard to problems,A problem in this sense is a difficult passage or expression which explanation and may easily be censured by an unsympathetic critic. Aristotle here classifies the various grounds of censure and the various lines of defence. Most of his illustrations are drawn from the critical objections lodged against the Iliad by Zoilus and other hammerers of Homer. As the reader will see, many of them are abysmally foolish. and the various solutions of them, how many kinds there are, and the nature of each kind, all will be clear if we look at them like this.

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Since the poet represents life, as a painter does or any other maker of likenesses, he must always represent one of three things—either things as they were or are; or things as they are said and seem to be; or things as they should be.

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These are expressed in diction with or without rare words and metaphors, there being many modifications of diction, all of which we allow the poet to use.

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Moreover, the standard of what is correct is not the same in the art of poetry as it is in the art of social conduct or any other art.

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In the actual art of poetry there are two kinds of errors, essential and accidental.

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If a man meant to represent something and failed through incapacity, that is an essential error. But if his error is due to his original conception being wrong and his portraying, for example, a horse advancing both its right legs, that is then a technical error in some special branch of knowledge,in medicine, say, or whatever it may be; or else some sort of impossibility has been portrayed, but that is not an essential error.

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These considerations must, then, be kept in view in meeting the charges contained in these objections.

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Let us first take the charges against the art of poetry itself. If an impossibility has been portrayed, an error has been made.

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But it is justifiable if the poet thus achieves the object of poetry—what that is has been already stated—and makes that part or some other part of the poem more striking. The pursuit of Hector is an example of this.See Aristot. Poet. 24.16 and note.

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If, however, the object could have been achieved better or just as well without sacrifice of technical accuracy, then it is not justifiable, for, if possible, there should be no error at all in any part of the poem.

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Again one must ask of which kind is the error, is it an error in poetic art or a chance error in some other field? It is less of an error not to know that a female stag has no horns than to make a picture that is unrecognizable.

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Next, supposing the charge is That is not true, one can meet it by saying But perhaps it ought to be, just as Sophocles said that he portrayed people as they ought to be and Euripides portrayed them as they are.

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If neither of these will do, then say, Such is the tale; for instance, tales about gods.

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Very likely there is no advantage in telling them, and they are not true either, but may well be what Xenophanes declaredi.e., immoral and therefore untrue. He opened the assault on Homeric theology at the end of the sixth or the beginning of the fifth century B.C.—all the same such is the tale.

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In another case, perhaps, there is no advantage but such was the fact, e.g. the case of the arms, Their spears erect on butt-spikes stood,Hom. Il. 10.152. Problem: Surely a bad stance: they might so easily fall and cause alarm. Solution: Homer does not defend it. He merely states a fact. It is thus that we excuse unpleasant fiction. for that was then the custom, as it still is in Illyria.

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As to the question whether anything that has been said or done is morally good or bad, this must be answered not merely by seeing whether what has actually been done or said is noble or base, but by taking into consideration also the man who did or said it, and seeing to whom he did or said it, and when and for whom and for what reason; for example, to secure a greater good or to avoid a greater evil.

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Some objections may be met by reference to the diction, for example, by pleading rare word, e.g. οὐρῆας μὲν πρῶτον, for perhaps he means not mules but sentinels.Hom. Il. 1.50: The mules and swift-footed hounds he first beset with his arrows. Apollo is sending plague upon the Greek army. Problem: Why should he first attack the mules? Solution: The word may here mean sentiels. And Dolon, One that was verily evil of form, it may be not his deformed body but his ugly face, for the Cretans use fair-formed for fair-featured.Hom. Il. 10.316: One that was verily evil inform but swift in his running. Problem: If Dolon were deformed, how could he run fast? Solution: Form may here mean feature. And again Livelier mix it may mean not undiluted as for drunkards but quicker.Hom. Il. 9.202: Set me, Menoetius’ son, a larger bowl for the mingling, Livelier mix it withal and make ready for each one a beaker. Problem: Livelier suggests intemperance. Solution: Perhaps the word means quicker. Similar scruples emended the lines in Young Lochinvar to read: And now am I come with this pretty maid To dance but one measure, drink one lemonade.

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Other expressions are metaphorical, for example: Then all the other immortals and men lay all night in slumber, while yet he says: Yea, when indeed he gazed at the Trojan plain Agamemnon Marvelled at voices of flutes . . . All is used instead of many metaphorically, all being a species of many.Hom. Il. 2.2 (quoted by mistake for Hom. Il. 10.1) and Hom. Il. 10.13, 14: Then all the other immortals and all the horse-crested heroes Night-long slumbered, but Zeus the sweet sleep held not. . . (Hom. Il. 2.1, 2) Yea, when indeed he gazed at the Trojan plain, Agamemnon Marvelled at voices of flutes and of pipes and the din of the soldiers. (Hom. Il. 10.13, 14) Problem: If all were asleep, who was playing the flute? Solution: This may be a metaphor; as explained in chapter 21, all is one kind or species of many, and thus by transference all is used for many, the species for the genus. And again, Alone unsharingHom. Il. 18.489: She alone of all others shares not in the baths of the Ocean. The reference is to the Great Bear. Problem: Why does Homer say she alone when the other Northern Constellations also do not set? Solution: As in the last instance, the may be metaphorical, i.e., the genus, sole, may be here used by transference for one of its species, best known. is metaphorical; the best known is called the only one.

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By intonation also; for example, the solutions of Hippias of Thasos, his δίδομεν δέ οἱHom. Il. 2.15. Our text is different. Aristotle, who quotes the line agains elsewhere, read thus: No longer the gods in the halls of Olympus Strive in their plans, for Hera has bent them all to her purpose Thus by her prayers; and we grant him to win the boast of great glory. Zeus is instructing the Dream, whom he is sending to lure Agamemnon to disaster. Problem: The last statement is a lie. Solution: Change the accent and the statement δίδομεν δέ οἱ becomes a command (the infinitive διδόμεναι written in a shortened form and used as an imperative). The lie will then be told by the Dream and not by Zeus, who may thus save his reputation for veracity. and τὸ μὲν οὗ καταπύθεται ὄμβρῳHom. Il. 23.327: A fathom high from the earth there rises a stump all withered, A stump of an oak or a pine, that rots not at all in the rain. Problem: The last statement is incredible. Solution: Alter the breathing and τὸ μὲν οὐ becomes τὸ μὲν οὗ and means part of it rots in the rain.;

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and by punctuation; for example, the lines of Empedocles: Soon mortal grow they that aforetime learnt Immortal ways, and pure erstwhile commingled.The Problem is erstwhile goes with pure or with commingled. The former interpretation seems to give the best solution. Empedocles is speaking of the elements or atoms.

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Or again by ambiguity, e.g. παρῴχηκεν δὲ πλέω νύξ, where πλείω is ambiguous.Hom. Il. 10.252: Come now, the night is far spent and at hand is the dawning, Far across are the stars and more than two parts of the night-time Are gone, but a third is still left us. Problem: If more than two parts are gone, a third cannot be left. Solution: πλέω here means full, i.e., the full night of two-thirds = full two-thirds of the night is gone, and so Homer’s arithmetic is saved.

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Others according to the habitual use of the phrase, e.g. wine and water is called wine so you get the phrase greaves of new-wrought tin;Problem: Greaves are made not of tin but of an alloy of tin and copper. Solution: Compounds are called by the name of the more important partner. Just as a mixture of wine and water is called wine, so here an alloy of tin and copper is called tin. So, too, is whisky and water called whisky. or workers in iron are called braziers, and so Ganymede is said to pour wine for Zeus, though they do not drink wine. This last might however be metaphorical.Nectar:gods :: wine: men. Therefore, according to the rules of metaphor in chapter 21, nectar may be called wine or the wine of the gods.

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Whenever a word seems to involve a contradiction, one should consider how many different meanings it might bear in the passage, e.g. in There the bronzen shaft was stayed,Hom. Il. 20.272: Nay but the weighty shaft of the warlike hero Aeneas Brake not the shield; for the gold, the gift of a god, did withstand it. Through two folds it drave, yet three were beneath, for Hephaestus, Crook-footed god, five folds had hammered; two were of bronze-work, Two underneath were of tin and one was of gold; there the bronzen Shaft of the hero was stayed in the gold. Problem: Since the gold was presumably outside for the sake of ornament, how could the spear he stayed in the gold and yet penetrate two folds? Bywater suggests as a solution that the plate of gold sufficed to stop the course of the spear, though the spear-point actually pierced it and indented the underlying plates of brass. we should ask in how many ways being stayed might be taken,

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interpreting the passage in this sense or in that, and keeping as far as possible from the attitude which GlauconThis may well be the Glaucon mentioned in Plato’s Ion as an authority on Homer. describes

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when he says that people make some unwarrantable presupposition and having themselves given an adverse verdict proceed to argue from it, and if what they think the poet has said does not agree with their own preconceived ideas, they censure him, as if that was what he had said.

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This is what has happened in the case of Icarius.Penelope’s father. They assume that he was a Spartan and therefore find it odd that when Telemachus went to Sparta he did not meet him. But the truth may be, as the Cephallenians say, that Odysseus married a wife from their country and that the name was not Icarius but Icadius. So the objection is probably due to a mistake.

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In general any impossibility may be defended by reference to the poetic effect or to the ideal or to current opinion.

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For poetic effect a convincing impossibility is preferable to that which is unconvincing though possible.

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It may be impossible that there should be such people as ZeuxisSee Aristot. Poet. 6.15. used to paint, but it would be better if there were; for the type should improve on the actual.

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Popular tradition may be used to defend what seems irrational, and you can also say that sometimes it is not irrational, for it is likely that unlikely things should happen.

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Contradictions in terms must be examined in the same way as an opponent’s refutations in argument, to see whether the poet refers to the same thing in the same relation and in the same sense, and has contradicted either what he expressly says himself or what an intelligent person would take to be his meaning.

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It is right, however, to censure both improbability and depravity where there is no necessity and no use is made of the improbability.An example is Euripides’ intro duction of AegeusEur. Medea 663. In Aristotle’s opinion there is no good reason for Aegeus’s appearance and no good use is made of it. or(of depravity)the character of Menelans in the Orestes.

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The censures they bring are of five kinds; that things are either impossible or irrational or harmful or inconsistent or contrary to artistic correctness. The solutions must be studied under the heads specified above, twelve in number.i.e., any expression that is criticized should be considered with reference to (1) things as they were; (2) things as thy are; (3) things as they are said to be; (4) things as they seem to be; (5) things as they ought to be. Further, we should consider whether (6) a rare word or (7) a metaphor is used; what is the right (8) accent and (9) punctuation; also where there may be (10) ambiguity and what is (11) the habitual use of the phrase; also we may refer to (12) the proper standard of correctness in poetry as distinct from other arts.

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The question may be raised whether the epic or the tragic form of representation is the better.

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If the better is the less vulgar and the less vulgar is always that which appeals to the better audience, then obviously the art which makes its appeal to everybody is eminently vulgar.Aristotle first states the popular condemnation of tragedy on the ground that it can be and often is spoilt by the stupid vulgarity of actors. So might spectators of certain productions of Shakespeare in their haste condemn the poet. The refutation of this view begins at 6.

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And indeed actors think the audience do not understand unless they put in something of their own, and so they strike all sorts of attitudes, as you see bad flute-players whirling about if they have to do the Discus, or mauling the leader of the chorus when they are playing the Scylla.Cf. Aristot. Poet. 15.8

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So tragedy is something like what the older school of actors thought of their successors, for Mynniscus used to call Callippides the monkey, because he overacted, and the same was said of Pindarus.Mynniscus acted for Aeschylus: Callippides belonged to the next generation, end of fifth century. Pindarus is unknown.

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The whole tragic art, then, is to epic poetry what these later actors were compared to their predecessors, since according to this view epic appeals to a cultivated audience which has no need of actor’s poses, while tragedy appeals to a lower class. If then it is vulgar, it must obviously be inferior.

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First of all, this is not a criticism of poetry but of acting: even in reciting a minstrel can overdo his gestures, as Sosistratus did, or in a singing competition, like Mnasitheus of Opus.Both unknown.

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Besides it is not all attitudinizing that ought to be barred any more than all dancing, but only the attitudes of inferior people. That was the objection to Callippides; and modern actors are similarly criticized for representing women who are not ladies.

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Moreover, tragedy fulfils its function even without acting, just as much as epic, and its quality can be gauged by reading aloud. So, if it is in other respects superior, this disadvantage is not necessarily inherent.

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Secondly, tragedy has all the elements of the epic—it can even use the hexameter—

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and in addition a considerable element of its own in the spectacle and the music, which make the pleasure all the more vivid;

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and this vividness can be felt whether it is read or acted.

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Another point is that it attains its end with greater economy of length. What is concentrated is always more effective than what is spread over a long period; suppose, for example, Sophocles’Oedipuswere to be turned into as many lines as there are in the Iliad .

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Again, the art of the epic has less unity, as is shown by the fact that any one epic makes several tragedies. The result is that, if the epic poet takes a single plot, either it is set forth so briefly as to seem curtailed, or if it conforms to the limit of lengthLiterally the length of the (proper) limit. it seems thin and diluted.

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In saying that epic has less unity I mean an epic made up of several separate actions.

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The Iliad has many such parts and so has the Odyssey, and each by itself has a certain magnitude. And yet the composition of these poems is as perfect as can be and each of them is—as far as an epic may be—a representation of a single action.

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If then tragedy is superior in these respects and also in fulfilling its artistic function—for tragedies and epics should produce not any form of pleasure but the pleasure we have describedi.e., the pleasure felt when by the representation of life in art “relief is given” to pity, fear, and other such emotions, or, to use a term now prevalent, when such emotions are “released.”Cf. Aristot. Poet. 14.3.—then obviously, since it attains its object better than the epic, the better of the two is tragedy.

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This must suffice for our treatment of tragedy and epic, their characteristics, their species, their constituent parts, and their number and attributes; for the causes of success and failure; and for critical problems and their solutions. . . .

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This pointer pattern extracts chapter and subchapter.

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This pointer pattern extracts chapter.

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-LetThe text here printed is based on Vahlen’s third edition(Leipzig, 1885), and the chief deviations from it are noted at the foot of each page. The prime source of all existing texts of the Poetics is the eleventh century Paris manuscript, No. 1741, designated as Ac. To the manuscripts of the Renaissance few, except Dr. Margoliouth, now assign any independent value, but they contain useful suggestions for the correction of obvious errors and defects in Ac. These are here designated “copies.”V. stands for Vahlen’s third edition, and By. for the late Professor Ingram Bywater, who has earned the gratitude and admiration of all students of the Poetics by his services both to the text and to its interpretation. Then there is the Arabic transcript. Translated in the eleventh century from a Syriac translation made in the eighth century, it appears to make little sense, but sometimes gives dim visions of the readings of a manuscript three centuries older but not necessarily better than Ac, readings which confirm some of the improvements introduced into Renaissance texts. us here deal with Poetry, its essence and its several species, with the characteristic function of each species and the way in which plots must be constructed if the poem is to be a success; and also with the number and character of the constituent parts of a poem, and similarly with all other matters proper to this same inquiry; and let us, as nature directs, begin first with first principles.

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Epic poetry, then, and the poetry of tragic drama, and, moreover, comedy and dithyrambic poetry, and most flute-playing and harp-playing, these, speaking generally, may all be said to be representations of life.The explanation of μίμησις, as Aristotle uses the word, demands a treatise; all that a footnote can say is this:—Life presents to the artist the phenomena of sense, which the artist re-presents in his own medium, giving coherence, designing a pattern. That this is true not only of drama and fiction but also of instrumental music (most flute-playing and harp-playing) was more obvious to a Greek than to us, since Greek instrumental music was more definitely imitative. The technical display of the virtuoso Plato describes as a beastly noise. Since μίμησις in this sense and μιμητής and the verb μιμεῖσθαι have a wider scope than any one English word, it is necessary to use more than one word in translation, e.g. μιμητής is what we call an artist; and for μίμησις where representation would be clumsy we may use the word art; the adjective must be imitative, since representative has other meanings.

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But they differ one from another in three ways: either in using means generically differenti.e., means that can be divided into separate categories. or in representing different objects or in representing objects not in the same way but in a different manner.

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For just as by the use both of color and form people represent many objects, making likenesses of them—some having a knowledge of art and some working empirically—and just as others use the human voice; so is it also in the arts which we have mentioned, they all make their representations in rhythm and language and tune, using these means either separately or in combination.

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For tune and rhythm alone are employed in flute-playing and harp-playing and in any other arts which have a similar function, as, for example, pipe-playing.

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Rhythm alone without tune is employed by dancers in their representations, for by means of rhythmical gestures they represent both character and experiences and actions.πάθη καὶ πράξεις cover the whole field of life, what men do (πράξεις) and what men experience (πάθη). Since πάθη means also emotions and that sense may be present here, but as a technical term in this treatise πάθος is a calamity or tragic incident, something that happens to the hero.

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But the art which employs words either in bare prose or in metres, either in one kind of metre or combining several, happens up to the present day to have no name.

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For we can find no common term to apply to the mimes of Sophron and XenarchusSophron and Xenarchus, said to he father and son, lived in Syracuse, the elder a contemporary of Euripides. They wrote mimes, i.e., simple and usually farcical sketches of familiar incidents, similar to the mimes of Herondas and the fifteenth Idyll of Theocritus, but in prose. There was a tradition that their mimes suggested to Plato the use of dialogue. and to the Socratic dialogues:

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nor again supposing a poet were to make his representation in iambics or elegiacs or any other such metre—except that people attach the word poet(maker)to the name of the metre and speak of elegiac poets and of others as epic poets.

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Thus they do not call them poets in virtue of their representation but apply the name indiscriminately in virtue of the metre.

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For if people publish medical or scientific treatises in metre the custom is to call them poets. But Homer and EmpedoclesEmpedocles (floruit 445 B.C.) expressed his philosophical and religious teaching in hexameter verse, to which Aristotle elsewhere attributes genuine value as poetry, but it is here excluded from the ranks of poetry because the object is definitely. have nothing in common except the metre, so that it would be proper to call the one a poet and the other not a poet but a scientist.

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Similarly if a man makes his representation by combining all the metres, as Chaeremon did when he wrote his rhapsody The Centaur, a medley of all the metres, he too should be given the name of poet.Chaeremon was a tragedian and rhapsodist. The Centaur was apparently an experiment which might be classed as either drama or epic. Cf. Aristot. Poet. 24.11. On this point the distinctions thus made may suffice.

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There are certain arts which employ all the means which I have mentioned, such as rhythm and tune and metre—dithyrambic and nomic poetry,The traditional definition is that the Dithyramb was sung to a flute accompaniment by a chorus in honor of Dionysus; and that the Nome was a solo sung to a harp accompaniment in honor of Apollo, but it is not clear that Aristotle regarded the Dithyramb as restricted to the worship of Dionysus. Timotheus’s dithyramb mentioned in Aristot. Poet. 15.8 cannot have been Dionysiac. But there is good evidence to show that the dithyramb was primarily associated with Dionysus. for example, and tragedy too and comedy. The difference here is that some use all these at once, others use now one now another.

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These differences then in the various arts I call the means of representation.

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Since living personsLiterally men doing or experiencing something. are the objects of representation, these must necessarily be either good men or inferior—thus only are characters normally distinguished, since ethical differences depend upon vice and virtue—that is to say either better than ourselves or worse or much what we are. It is the same with painters.

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Polygnotus depicted men as better than they are and Pauson worse, while Dionysius made likenesses.Polygnotus’s portraits were in the grand style and yet expressive of character(cf. Aristot. Poet. 6.15): Aristophanes aIludes to a Pauson as a perfectly wicked caricaturist: Dionysius of Colophon earned the name of the man-painter because he always painted men and presumably made good likenesses.

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Clearly each of the above mentioned arts will admit of these distinctions, and they will differ in representing objects which differ from each other in the way here described.

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In painting too, and flute-playing and harp-playing, these diversities may certainly be found, and it is the same in prose and in unaccompanied verse.

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For instance Homer’s people are better, Cleophon’s are like, while in Hegemon of Thasos, the first writer of parodies, and in Nicochares, the author of the Poltrooniad, they are worse.Cleophon wrote epics (i.e., hexameter poems), describing scenes of daily life in commonplace diction (cf. Aristot. Poet. 22.2): Hegemon wrote mock epics in the style of the surviving Battle of Frog and Mice: of Nicochares nothing is known, but his forte was evidently satire.

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It is the same in dithyrambic and nomic poetry, for instance . . . a writer might draw characters like the Cyclops as drawn by Timotheus and Philoxenus.Both famous dithyramhic poets. There is evidence that Philoxenus treated Polyphemus in the vein of satire: Timotheus may have drawn a more dignified picture.

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It is just in this respect that tragedy differs from comedy. The latter sets out to represent people as worse than they are to-day, the former as better.

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A third difference in these arts is the manner in which one may represent each of these objects.

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For in representing the same objects by the same means it is possible to proceed either partly by narrative and partly by assuming a character other than your own—this is Homer’s method—or by remaining yourself without any such change, or else to represent the characters as carrying out the whole action themselves.

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These, as we said above, are the three differences which form the several species of the art of representation, the means, the objects, and the manner.

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It follows that in one respect Sophocles would be the same kind of artist as Homer, for both represent good men, and in another respect he would resemble Aristophanes, for they both represent men in action and doing things. And that according to some is the reason why they are called dramas, because they present people as doingDrama being derived from δρᾶν to do. things.

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And for this reason the Dorians claim as their own both tragedy and comedy—comedy is claimed both by the Megarians here in Greece, who say that it originated in the days of their democracy, and by the Megarians in Sicily,The inhabitants of Megara Hyblaea. for it was from there the poet EpicharmusEpicharmus of Cos wrote in Sicily burlesques and mimes depicting scenes of daily life. He and Phormis were originators of comedy in that they sketched types instead of lampooning individuals (cf. Aristot. Poet. 5.5): of Chionides and Magnes we only know that they were early comedians, i.e., in the first half of the fifth century B.C. came, who was much earlier than Chionides and Magnes; and tragedy some of the Peloponnesians claim. Their evidence is the two names.

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Their name, they say, for suburb villages is κῶμαι—the Athenians call them Demes—and comedians are so called not from κωμάζειν, to revel, but because they were turned out of the towns and went strolling round the villages( κῶμαι). Their word for action, they add, is δρᾶν, whereas the Athenian word is πράττειν. So much then for the differences, their number, and their nature.

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Speaking generally, poetry seems to owe its origin to two particular causes, both natural.

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From childhood men have an instinct for representation, and in this respect, differs from the other animals that he is far more imitative and learns his first lessons by representing things. And then there is the enjoyment people always get from representations.

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What happens in actual experience proves this, for we enjoy looking at accurate likenesses of things which are themselves painful to see, obscene beasts, for instance, and corpses.

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The reason is this: Learning things gives great pleasure not only to philosophers but also in the same way to all other men, though they share this pleasure only to a small degree.

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The reason why we enjoy seeing likenesses is that, as we look, we learn and infer what each is, for instance, that is so and so.

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If we have never happened to see the original, our pleasure is not due to the representation as such but to the technique or the color or some other such cause.

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We have, then, a natural instinct for representation and for tune and rhythmIt is not clear wheter the two general causes are (1) the instinct for imitation, (2) the natural enjoyment of mimicry by others; or whether these two are combined into one and the second cause is the instinct for tune and rhythm. Obviously this last is an essential cause of poetry.—for the metres are obviously sections of rhythmse.g., the rhythm of the blacksmith’s hammer or of a trotting horse is dactylic, but the hexameter is a section or slice of that rhythm; it is cut up into sixes.—and starting with these instincts men very gradually developed them until they produced poetry out of their improvisations.

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Poetry then split into two kinds according to the poet’s nature. For the more serious poets represented fine doings and the doings of fine men, while those of a less exalted nature represented the actions of inferior men, at first writing satire just as the others at first wrote hymns and eulogies.

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Before Homer we cannot indeed name any such poem, though there were probably many satirical poets,

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but starting from Homer, there is, for instance, his MargitesA famous burlesque which Aristotle attributes to Homer. Other similar poems must mean other early burlesques not necessarily attributed to Homer. and other similar poems. For these the iambic metre was fittingly introduced and that is why it is still called iambic, because it was the metre in which they lampooned each other.Since the iambic came to be the metre of invective, the verb ἰαμβίζειν acquired the meaning to lampoon. There is probably implied a derivation from ἰάπτειν, to assail.

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Of the ancients some wrote heroic verse and some iambic.

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And just as Homer was a supreme poet in the serious style, since he alone made his representations not only good but also dramatic, so, too, he was the first to mark out the main lines of comedy, since he made his drama not out of personal satire but out of the laughable as such. His Margites indeed provides an analogy: as are the Iliad and Odyssey to our tragedies, so is the Margites to our comedies.

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When tragedy and comedy came to light, poets were drawn by their natural bent towards one or the other. Some became writers of comedies instead of lampoons, the others produced tragedies instead of epics; the reason being that the former is in each case a higher kind of art and has greater value.

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To consider whether tragedy is fully developed by now in all its various species or not, and to criticize it both in itself and in relation to the stage, that is another question.

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At any rate it originated in improvisation—both tragedy itself and comedy. The one came from the preludeBefore the chorus began (or in pauses between their songs) the leader of the performance would improvise some appropriate tale or state the theme which they were to elaborate. Thus he was called ὁ ἐξάρχων or the starter, and became in time the first actor. to the dithyramb and the other from the prelude to the phallic songs which still survive as institutions in many cities.

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Tragedy then gradually evolved as men developed each element that came to light and after going through many changes, it stopped when it had found its own natural form.

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Thus it was Aeschylus who first raised the number of the actors from one to two. He also curtailed the chorus and gave the dialogue the leading part. Three actors and scene-painting Sophocles introduced.

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Then as to magnitude.Being a development of the Satyr play,A Satyr play was an interlude performed by a troupe of actors dressed as the goat-like followers of Dionysus. Hence τραγῳδία, goat-song. Aristotle seems so clear about this that he does not trouble to give a full explanation. But we can see from this passage that the Satyr plays were short, jocose and in the trochaic metre which suited their dances, and that in Aristotle’s view tragedy was evolved from these. No example of a primitive Satyr play survives, but we can make inferences from the later, more sophisticated Cyclops of Euripides and the fragments of Sophocles’ <foreign xml:lang="grc">Ἰχνευταί</foreign>, The Trackers. We cannot be certain that Aristotle’s theory is historically correct; the balance of evidence is against it. it was quite late before tragedy rose from short plots and comic diction to its full dignity, and that the iambic metre was used instead of the trochaic tetrameter.

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At first they used the tetrameter because its poetry suited the Satyrs and was better for dancing, but when dialogue was introduced, Nature herself discovered the proper metre. The iambic is indeed the most conversational of the metres,

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and the proof is that in talking to each other we most often use iambic lines but very rarely hexameters and only when we rise above the ordinary pitch of conversation.

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Then there is the number of acts. The further embellishmentsMasks, costumes, etc. and the story of their introduction one by one we may take as told,

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for it would probably be a long task to go through them in detail.

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Comedy, as we have said, is a representation of inferior people, not indeed in the full sense of the word bad, but the laughable is a species of the base or ugly.Ugly was to a Greek an equivalent of bad. The persons in Comedy are inferior (see chapter 2.), but have only one of the many qualities which make up Ugliness or Badness, viz. the quality of being ludicrous and therefore in some degree contemptible.

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It consists in some blunder or ugliness that does not cause pain or disaster, an obvious example being the comic mask which is ugly and distorted but not painful.

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The various stages of tragedy and the originators of each are well known, but comedy remains obscure because it was not at first treated seriously. Indeed it is only quite late in its historyProbably about 465 B.C. that the archon granted a chorus for a comic poet; before that they were volunteers.In the fifth century dramatists submitted their plays to the archon in charge of the festival at which they wished them to be performed. He selected the number required by the particular festival, and to the poets thus selected granted a chorus, i.e., provided a choregus who paid the expenses of the chorus. The earlier volunteers had themselves paid for and produced their plays.

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Comedy had already taken certain forms before there is any mention of those who are called its poets. Who introduced masks or prologues, the number of actors, and so on, is not known.

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Plot making [Epicharmus and Phormis]Epicharmus and Phormis, being both early Sicilian comedians, are appropriate here. Either part of a sentence is lost or an explanatory note has got into the text. originally came from Sicily,

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and of the Athenian poets CratesFragments of his comedies survive, dating about the middle of the fifth century B.C. was the first to give up the lampooning form and to generalize his dialogue and plots.

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Epic poetry agreed with tragedy only in so far as it was a metrical representation of heroic action, but inasmuch as it has a single metre and is narrative in that respect they are different.

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And then as regards length, tragedy tends to fall within a single revolution of the sun or slightly to exceed that, whereas epic is unlimited in point of time;

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and that is another difference, although originally the practice was the same in tragedy as in epic poetry.

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The constituent parts are some of them the same and some peculiar to tragedy.

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Consequently any one who knows about tragedy, good and bad, knows about epics too, since tragedy has all the elements of epic poetry, though the elements of tragedy are not all present in the epic.

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With the representation of life in hexameter versei.e., epic poetry. and with comedy we will deal later. We must now treat of tragedy after first gathering up the definition of its nature which results from what we have said already.

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Tragedy is, then, a representation of an actionMargoliouth’s phrase a chapter of life, illuminates the meaning, since πρᾶξις includes what the hero does and what happens to him. (Cf. Aristot. Poet. 2.1 and note.) that is heroic and complete and of a certain magnitude—by means of language enriched with all kinds of ornament, each used separately in the different parts of the play: it represents men in action and does not use narrative, and through pity and fear it effects relief to these and similar emotions.The sense of the pity of it and fear lest such disasters might befall ourselves are not the only emotions which tragedy releases, but Aristotle specifies them as the most characteristic. For κάθαρσις, see Introduction.

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By language enriched I mean that which has rhythm and tune, i.e., song,

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and by the kinds separately I mean that some effects are produced by verse alone and some again by song.

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Since the representation is performed by living persons, it follows at once that one essential part of a tragedy is the spectacular effect, and, besides that, song-making and diction. For these are the means of the representation.

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By diction I mean here the metrical arrangement of the words; and song making I use in the full, obvious sense of the word.

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And since tragedy represents action and is acted by living persons, who must of necessity have certain qualities of character and thought—for it is these which determine the quality of an action; indeed thought and character are the natural causes of any action and it is in virtue of these that all men succeed or fail—

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it follows then that it is the plot which represents the action. By plot I mean here the arrangement of the incidents: character is that which determines the quality of the agents, and thought appears wherever in the dialogue they put forward an argument or deliver an opinion.

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Necessarily then every tragedy has six constituent parts, and on these its quality depends. These are plot, character, diction, thought, spectacle, and song.

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Two of these are the means of representation: one is the manner: three are the objects represented.The means are diction and music: the manner is spectacle: the objects represented are actions or experiences and the moral or intellectual qualities of the dramatis personae.

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This list is exhaustive, and practically all the poets employ these elements, for every drama includes alike spectacle and character and plot and diction and song and thought.

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The most important of these is the arrangement of the incidents,i.e., plot, as defined above. for tragedy is not a representation of men but of a piece of action, of life, of happiness and unhappiness, which come under the head of action, and the end aimed at is the representation not of qualities of character but of some action; and while character makes men what they are,it’s their actions and experiences that make them happy or the opposite.

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They do not therefore act to represent character, but character-study is included for the sake of the action. It follows that the incidents and the plot are the end at which tragedy aims, and in everything the end aimed at is of prime importance.

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Moreover, you could not have a tragedy without action, but you can have one with out character-study.

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Indeed the tragedies of most modern poets are without this, and, speaking generally, there are many such writers, whose case is like that of Zeuxis compared with Polygnotus.Zeuxis’s portraits were ideal (cf. Aristot. Poet. 25.28). The latter was good at depicting character, but there is nothing of this in Zeuxis’s painting.

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A further argument is that if a man writes a series of speeches full of character and excellent in point of diction and thought, he will not achieve the proper function of tragedy nearly so well as a tragedy which, while inferior in these qualities, has a plot or arrangement of incidents.

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And furthermore, two of the most important elements in the emotional effect of tragedy, reversals and discoveries,See chapter 11. are parts of the plot.

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And here is further proof: those who try to write tragedy are much sooner successful in language and character-study than in arranging the incidents. It is the same with almost all the earliest poets.

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The plot then is the first principle and as it were the soul of tragedy: character comes second.

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It is much the same also in painting; if a man smeared a canvas with the loveliest colors at random, it would not give as much pleasure as an outline in black and white.Selection and design are necessary for any work of representation.

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And it is mainly because a play is a representation of action that it also for that reason represents people.

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Third comes thought. This means the ability to say what is possible and appropriate. It comes in the dialogue and is the function of the statesman’s or the rhetorician’s art.Cf. chapter 6.

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The old writers made their characters talk like statesmen,Or in the style of ordinary people, without obvious rhetorical artifice. the moderns like rhetoricians.

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Character is that which reveals choiceπροαίρεσις is a technical term in Aristotle’s ethics, corresponding to our use of the term Will, the deliberate adoption of any course of conduct or line of action. It is a man’s will or choice in the sense that determines the goodness or badness of his character. If character is to be revealed in drama, a man must be shown in the exercise of his will, choosing between one line of conduct and another, and he must be placed in circumstances in wbich the choice is not obvious, i.e., circumstances in which everybody’s choice would not be the same. The choice of death rather than disbonourable wealth reveals character; the choice of a nectarine rather than a turnip does not., shows what sort of thing a man chooses or avoids in circumstances where the choice is not obvious, so those speeches convey no character in which there is nothing whatever which the speaker chooses or avoids.

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Thought you find in speeches which contain an argument that something is or is not, or a general expression of opinion.

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The fourth of the literary elements is the language. By this I mean, as we said above, the expression of meaning in words,This seems to be a mistaken reference to 6 above where diction is defined as the metrical arrangement of the words. In poetry they come to the same thing. and this is essentially the same in verse and in prose.

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Of the other elements which enrichSee Aristot. Poet. 6.2. tragedy the most important is song-making.

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Spectacle, while highly effective, is yet quite foreign to the art and has nothing to do with poetry. Indeed the effect of tragedy does not depend on its performance by actors, and, moreover,for achieving the spectacular effects the art of the costumier is more authoritative than that of the poet.

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After these definitions we must next discuss the proper arrangement of the incidents since this is the first and most important thing in tragedy.

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We have laid it down that tragedy is a representation of an action that is whole and complete and of a certain magnitude, since a thing may be a whole and yet have no magnitude.

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A whole is what has a beginning and middle and end.

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A beginning is that which is not a necessary consequent of anything else but after which something else exists or happens as a natural result.

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An end on the contrary is that which is inevitably or, as a rule, the natural result of something else but from which nothing else follows;

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a middle follows something else and something follows from it.

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Well constructed plots must not therefore begin and end at random, but must embody the formulae we have stated.

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Moreover, in everything that is beautiful, whether it be a living creature or any organism composed of parts, these parts must not only be orderly arranged but must also have a certain magnitude of their own;

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for beauty consists in magnitude and ordered arrangement. From which it follows that neither would a very small creature be beautiful—for our view of it is almost instantaneous and therefore confusedWith a very small object the duration of our vision is, as it were, so rapid that the parts are invisible; we, therefore, cannot appreciate their proportion and arrangement, in which beauty consists.—nor a very large one, since being unable to view it all at once, we lose the effect of a single whole; for instance, suppose a creature a thousand miles long.

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As then creatures and other organic structures must have a certain magnitude and yet be easily taken in by the eye, so too with plots: they must have length but must be easily taken in by the memory.

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The limit of length considered in relation to competitions and productionαἴσθησις is the play’s perception by an audience—how much an audience will stand. before an audience does not concern this treatise. Had it been the rule to produce a hundred tragedies, the performance would have been regulated by the water clock, as it is said they did once in other days.

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But as for the natural limit of the action, the longer the better as far as magnitude goes, provided it can all be grasped at once. To give a simple definition: the magnitude which admits of a change from bad fortune to good or from good fortune to bad, in a sequence of events which follow one another either inevitably or according to probability, that is the proper limit.

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A plot does not have unity, as some people think, simply because it deals with a single hero. Many and indeed innumerable things happen to an individual, some of which do not go to make up any unity, and similarly an individual is concerned in many actions which do not combine into a single piece of action.

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It seems therefore that all those poets are wrong who have written a Heracleid or Theseid or other such poems.Aristotle condemns them all, assuming—or perhaps assured by experience—that their sole claim to unity lay in the fact that all the stories in the poem had a common hero. They think that because Heracles was a single individual the plot must for that reason have unity.

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But Homer, supreme also in all other respects, was apparently well aware of this truth either by instinct or from knowledge of his art. For in writing an Odyssey he did not put in all that ever happened to Odysseus, his being wounded on Parnassus, for instance, or his feigned madness when the host was gathered(these being events neither of which necessarily or probably led to the other), but he constructed his Odyssey round a single action in our sense of the phrase. And the Iliad the same.

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As then in the other arts of representation a single representation means a representation of a single object, so too the plot being a representation of a piece of action must represent a single piece of action and the whole of it; and the component incidents must be so arranged that if one of them be transposed or removed, the unity of the whole is dislocated and destroyed. For if the presence or absence of a thing makes no visible difference, then it is not an integral part of the whole.

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What we have said already makes it further clear that a poet’s object is not to tell what actually happened but what could and would happen either probably or inevitably.

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The difference between a historian and a poet is not that one writes in prose and the other in verse— indeed the writings of Herodotus could be put into verse and yet would still be a kind of history, whether written in metre or not. The real difference is this, that one tells what happened and the other what might happen.

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For this reason poetry is something more scientific and serious than history, because poetry tends to give general truths while history gives particular facts.

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By a general truth I mean the sort of thing that a certain type of man will do or say either probably or necessarily. That is what poetry aims at in giving names to the characters.The names indicate types. This is obvious, as he says, in Comedy and is also true of Greek Tragedy, which, although it deals with traditional heroes regarded as real people, yet keeps to a few stories in which each character has become a type. In Chapter 17. the dramatist is recommended to sketch first his outline plot, making it clear and coherent, before he puts in the names. A particular fact is what Alcibiades did or what was done to him.

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In the case of comedy this has now become obvious, for comedians construct their plots out of probable incidents and then put in any names that occur to them. They do not, like the iambic satirists, write about individuals.Aristophanes of course did write about individuals. But Aristotle is thinking of the New Comedy, where the names of the characters were invented by the author and there was no reference to real people.

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In tragedy, on the other hand, they keep to real names. The reason is that what is possible carries conviction. If a thing has not happened, we do not yet believe in its possibility, but what has happened is obviously possible. Had it been impossible, it would not have happened.

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It is true that in some tragedies one or two of the names are familiar and the rest invented; indeed in some they are all invented, as for instance in Agathon’s Antheus,The name, apparently, of an imaginary hero. The word might be Ἄνθος, but The Flower is an unlikely title for a Greek tragedy. where both the incidents and the names are invented and yet it is none the less a favourite.

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One need not therefore endeavor invariably to keep to the traditional stories with which our tragedies deal. Indeed it would be absurd to do that, seeing that the familiar themes are familiar only to a few and yet please all.The reason why Greek tragedy dealt only with a few familiar themes is to be found of course in its religious origin. It was the function of tragedy to interpret and embroider myths. Aristotle never gives this reason, but offers instead the unconvincing explanation that tragedians adhered to certain real stories to gain verisimilitude—and yet he has to admit that, since to many of the auditors these stories were unfamiliar and none the less attractive, dramatists might just as well invent new themes.

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It is clear, then, from what we have said that the poet must be a maker not of verses but of stories, since he is a poet in virtue of his representation, and what he represents is action.

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Even supposing he represents what has actually happened, he is none the less a poet, for there is nothing to prevent some actual occurrences being the sort of thing that would probably or inevitably happen, and it is in virtue of that that he is their maker.

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Of simpleThis term is defined in the next chapter. It seems odd to use it before its meaning is explained. Perhaps we should read ἄλλων(Tyrwhitt) and translate of all plots. plots and actions the worst are those which are episodic. By this I mean a plot in which the episodes do not follow each other probably or inevitably.

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Bad poets write such plays because they cannot help it, and good poets write them to please the actors. Writing as they do for competition, they often strain a plot beyond its capacity and are thus obliged to sacrifice continuity.Or logic. He means the chain of cause and effect, wherein each incident is the result of what has gone before. See the end of the next chapter.

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But this is bad work, since tragedy represents not only a complete action but also incidents that cause fear and pity, and this happens most of all when the incidents are unexpected and yet one is a consequence of the other.The logic suffers from ellipse. Plays which fail to exhibit the sequence of cause and effect are condemned (1) because they lack the unity which befits tragedy, (2) because they miss that supreme effect of fear or pity produced by incidents which, though unexpected, are seen to be no mere accident but the inevitable result of what has gone before.

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For in that way the incidents will cause more amazement than if they happened mechanically and accidentally, since the most amazing accidental occurrences are those which seem to have been providential, for instance when the statue of Mitys at Argos killed the man who caused Mitys’s death by falling on him at a festival. Such events do not seem to be mere accidents.

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So such plots as these must necessarily be the best.

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Some plots are simple and some complex, as indeed the actions represented by the plots are obviously such.

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By a simple action I mean one that is single and continuous in the sense of our definition above,In chapters 7 and 8. wherein the change of fortune occurs without reversal or discovery;

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by a complex action I mean one wherein the change coincides with a discovery or reversal or both.

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These should result from the actual structure of the plot in such a way that what has already happened makes the result inevitable or probable;for there is indeed a vast difference between what happens propter hoc and post hoc.

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A reversal is a change of the situation into the opposite, as described above,At the end of chapter 7. Vahlen and many other exponents of the Politics confine the meaning of “reversal” to the situation in which the hero’s action has consequences directly opposite to his intention and expectation. There is much to be said for this interpretation, which stresses the irony at the heart of all tragedy. But it is too narrow for Aristotle’s theory. All tragedy involves a change of fortune ( μετάβασις). In a “simple” plot this is gradual; in a “complex” plot it is catastrophic, a sudden revolution of fortune’s wheel. In some of the greatest tragedies, but not in all, this is the result of action designed to produce the opposite effect. this change being, moreover, as we are saying, probable or inevitable—

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like the man in the Oedipus who came to cheer Oedipus and rid him of his anxiety about his mother by revealing his parentage and changed the whole situation.The messenger for Corinth announces the death of Polybus and Oedipus’s succession to the throne. Oedipus, feeling now safe from the prophecy that he would murder his father, still fears to return to Corinth, lest he should fulfil the other prophecy and marry his mother. The messenger seeks to reassure him by announcing that Polybus and Merope are not his parents. But the effect of this was to change the whole situation for Oedipus by revealing the truth that he a murdered his father, Laius, and married his mother, Jocasta. This reversal is the more effective because it is immediately coincident with the discovery of the truth. In the Lynceus, too, there is the man led off to execution and

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Danaus following to kill him, and the result of what had already happened was that the latter was killed and the former escaped.Lynceus married Hypermnestra who disobeyed Danaus in not murdering him. Danaus trying by process of law to compass the death of their son Abas was killed himself. The dog it was that died.

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A discovery, as the term itself implies, is a change from ignorance to knowledge, producing either friendship or hatred in those who are destined for good fortune or ill.

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A discovery is most effective when it coincides with reversals, such as that involved by the discovery in the Oedipus.

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There are also other forms of discovery, for what we have described may in a sense occur in relation to inanimate and trivial objects, or one may discover whether some one has done something or not.

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But the discovery which is most essentially part of the plot and part of the action is of the kind described above, for such a discovery and reversal of fortune will involve either pity or fear, and it is actions such as these which, according to our hypothesis, tragedy represents; and, moreover, misfortune and good fortune are likely to turn upon such incidents.

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Now since the discovery is somebody’s discovery, in some scenes one character only is discovered to another, the identity of the other being obvious; but sometimes each must discover the other. Thus Iphigeneia was discovered to Orestes through the sending of the letter, but a separate discovery was needed to make him known to Iphigeneia.Euripides’ Iphigeneia in Tauris—Orestes and Pylades arriving among the Tauri are by the custom of the country to be sacrificed to Artemis by her priestess, Iphigeneia. It is agreed that Pylades shall be spared to carry a letter from Iphigeneia to Orestes, whom she supposes to be in Argos. In order that Pylades may deliver the message, even if he should lose the letter, she reads it aloud. Orestes thus discovers who she is. He then reveals himself to her by declaring who he is and proving his identity by his memories of their home.

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We see then that two elements of the plot, reversal and discovery, turn upon these incidents. A third element is a calamity. Of these three elements we have already described reversal and discovery.

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A calamity is a destructive or painful occurrence, such as a death on the stage, acute suffering and wounding and so on.

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We have alreadyIn chapter 6. spoken of the constituent parts to be used as ingredients of tragedy. The separable members into which it is quantitatively divided are these: Prologue, Episode, Exode, Choral Song,

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the last being divided into Parode and Stasimon.

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These are common to all tragedies; songs sung by actors on the stage and commoi are peculiar to certain plays.

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A prologue is the whole of that part of a tragedy which precedes the entrance of the chorus.

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An episode is the whole of that part of a tragedy which falls between whole choral songs.

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An exode is the whole of that part of a tragedy which is not followed by a song of the chorus.

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A parode is the whole of the first utterance of the chorus.

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A stasimon is a choral song without anapaests or trochaics.This does not apply to surviving Greek tragedies, but may be true of those of Aristotle’s time. The word Stasimon is applied to all choruses in a tragedy other than those sung during entry or exit. It is usually explained as meaning a stationary song, because it was sung after the chorus had taken up its station in the orchestra.

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A commos is a song of lament shared by the chorus and the actors on the stage.

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The constituent parts to be used as ingredients of tragedy have been described above; these are the separable members into which it is quantitatively divided.The whole of chapter 12. bears marks of belonging to the Poetics but seems out of place, since it interrupts the discussion of plot.

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Following upon what has been said above we should next state what ought to be aimed at and what avoided in the construction of a plot, and the means by which the object of tragedy may be achieved.

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Since then the structure of the best tragedy should be not simple but complexSee chapter 10. and one that represents incidents arousing fear and pity—for that is peculiar to this form of art—it is obvious to begin with that one should not show worthy men passing from good fortune to bad. That does not arouse fear or pity but shocks our feelings.

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Nor again wicked people passing from bad fortune to good. That is the most untragic of all, having none of the requisite qualities, since it does not satisfy our feelingsi.e., our preference for poetic justice. or arouse pity or fear.

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Nor again the passing of a thoroughly bad man from good fortune to bad fortune. Such a structure might satisfy our feelings but it arouses neither pity nor fear, the one being for the man who does not deserve his misfortune and the other for the man who is like ourselves—pity for the undeserved misfortune, fear for the man like ourselves—so that the result will arouse neither pity nor fear.

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There remains then the mean between these. This is the sort of man who is not pre-eminently virtous and just, and yet it is through no badness or villainy of his own that he falls into the fortune, but rather through some flaw in him,Whether Aristotle regards the “flaw” as intellectual or moral has been hotly discussed. It may cover both senses. The hero must not deserve his misfortune, but he must cause it by making a fatal mistake, an error of judgement, which may well involve some imperfection of character but not such as to make us regard him as “morally responsible” for the disasters although they are nevertheless the consequences of the flaw in him, and his wrong decision at a crisis is the inevitable outcome of his character(cf. Aristot. Poet. 6.24.). he being one of those who are in high station and good fortune, like Oedipus and Thyestes and the famous men of such families as those.

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The successful plot must then have a singleἁπλοῦς elsewhere in the Poetics means simple as opposed to πεπλεγμένος, complex; here it is opposed to διπλοῦς, which describes a double denouement, involving happiness for some and disaster for others. and not, as some say, a double issue; and the change must be not to good fortune from bad but, on the contrary, from good to bad fortune, and it must not be due to villainy but to some great flaw in such a man as we have described, or of one who is better rather than worse.

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This can be seen also in actual practice. For at first poets accepted any plots, but to-day the best tragedies are written about a few families—Alcmaeon for instance and Oedipus and Orestes and Meleager and Thyestes and Telephus and all the others whom it befell to suffer or inflict terrible disasters.

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Judged then by the theory of the art, the bestThis is modified by 19 in the following chapter, where he finds an even better formula for the tragic effect. tragedy is of this construction.

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Those critics are therefore wrong who charge Euripides with doing this in his tragedies, and say that many of his end in misfortune.

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That is, as we have shown, correct. And there is very good evidence of this, for on the stage and in competitions such plays appear the most tragic of all, if they are successful, and even if Euripides is in other respects a bad manager,Against Euripides Aristotle makes the following criticisms: (1)his choruses are often irrelevant; (2)the character of the heroine in his Iphigeneia in Tauris is inconsistent; (3)in the Medea the deliberate killing of the children is ineffective and the play is inartistically ended by the machina; (4)the character of Menelaus in the Orestes is needlessly depraved; (5)Melanippe is too philosophical for a woman. yet he is certainly the most tragic of the poets.

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Next in order comes the structure which some put first, that which has a double issue, like the Odyssey, and ends in opposite ways for the good characters and the bad.

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It is the sentimentality of the audience which makes this seem the best form; for the poets follow the wish of the spectators.

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But this is not the true tragic pleasure but rather characteristic of comedy, where those who are bitter enemies in the story, Orestes and Aegisthus, for instance, go off at the end, having made friends, and nobody kills anybody.

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Fear and pity sometimes result from the spectacle and are sometimes aroused by the actual arrangement of the incidents, which is preferable and the mark of a better poet.

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The plot should be so constructed that even without seeing the play anyone hearing of the incidents happening thrills with fear and pity as a result of what occurs. So would anyone feel who heard the story of Oedipus.

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To produce this effect by means of an appeal to the eye is inartistic and needs adventitious aid,

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while those who by such means produce an effect which is not fearful but merely monstrous have nothing in common with tragedy.that here were plays which relied for their effect on the scenery and make up is clear from chapter 17:—The Phorcides and Prometheus and Scenes laid in Hades. It was even possible to produce the Eumenides so badly as to bring it into this category. But Aristotle’s criticism here includes the more important point that the poignancy of a Greek tragedy is due to what happens and not to our seeing it happen. That Medea murders her children is tragic: to display the murder coram populo would add either nothing or something merely monstrous. And although Sophocles shows Oedipus with his eyes out, it is the fact and not the sight which is properly tragic. For one should not seek from tragedy all kinds of pleasure but that which is peculiar to tragedy,

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and since the poet must by representation produce the pleasure which comes from feeling pity and fear, obviously this quality must be embodied in the incidents.

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We must now decide what incidents seem dreadful or rather pitiable. Such must necessarily be the actions of friends to each other or of enemies or of people that are neither.

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Now if an enemy does it to an enemy, there is nothing pitiable either in the deed or the intention,

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except so far as the actual calamity goes.

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Nor would there be if they were neither friends nor enemies. But when these calamities happen among friends,when for instance brother kills brother, or son father, or mother son, or son mother—either kills or intends to kill, or does something of the kind, that is what we must look for.

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Now it is not right to break up the traditional stories, I mean, for instance, Clytaemnestra being killed by Orestes and Eriphyle by Alcmaeon,

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but the poet must show invention and make a skilful use of the tradition.

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But we must state more clearly what is meant by skilful.

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The action may happen in the way in which the old dramatists made their characters act—consciously and knowing the facts, as EuripidesThis does not necessarily imply that Aristotle reckons Euripides “a modern,” since the Greek can equally mean “Euripides as well as other old dramatists.” also made his Medea kill her children.

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Or they may do the deed but without realizing the horror of it and then discover the relationship afterwards, like Oedipus in Sophocles. That indeed lies outside the play,i.e., Oedipus kills his father Laius before the play opens. but an example of this in the tragedy itself is the Alcmaeon of AstydamasA prolific tragedian of the fourth century. or Telegonus in the Wounded Odysseus.

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A third alternative is to intend to do some irremediable action in ignorance and to discover the truth before doing it.

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Besides these there is no other way, for they must either do the deed or not, either knowing or unknowing.

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The worst of these is to intend the action with full knowledge and not to perform it. That outrages the feelings and is not tragic, for there is no calamity. So nobody does that, except occasionally, as, for instance, Haemon and CreonHaemon, discovered by his father Creon embracing the dead body of Antigone, drew his sword on him but missed his aim and Creon fled. in the Antigone.

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Next comes the doing of the deed.

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It is better to act in ignorance and discover afterwards. Our feelings are not outraged and the discovery is startling.

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Best of all is the last; in the Cresphontes,By Euripides. Polyphontes killed Cresphontes, king of Messenia, and gained possession of his kingdom and his wife, Merope. She had concealed her son, Aepytus, in Arcadia, and when he returned, seeking vengeance, she nearly killed him in ignorance but discovered who he was. He then killed Polyphontes and reigned in his stead. for instance, Merope intends to kill her son and does not kill him but discovers; and in the IphigeneiaIn Tauris. See Aristot. Poet. 11.8, note. the case of the sister and brother; and in the HelleAuthor and play unknown. the son discovers just as he is on the point of giving up his mother.

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So this is the reason, as was said above,See Aristot. Poet. 13.7. why tragedies are about a few families. For in their experiments it was from no technical knowledge but purely by chance that they found out how to produce such an effect in their stories. So they are obliged to have recourse to those families in which such calamities befell.See Aristot. Poet. 9.8, note.

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Now concerning the structure of the incidents and the proper character of the plots enough has been said.

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Concerning character there are four points to aim at. The first and most important is that the character should be good.

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The play will show character if, as we said above,See Aristot. Poet. 6.24. either the dialogue or the actions reveal some choice; and the character will be good, if the choice is good.

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But this is relative to each class of people. Even a woman is good and so is a slave, although it may be said that a woman is an inferior thing and a slave beneath consideration.

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The second point is that the characters should be appropriate. A character may be manly, but it is not appropriate for a woman to be manly or clever.

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Thirdly, it should be like.The meaning probably is like the traditional person, e.g. Achilles must not be soft nor Odysseus stupid. Cf. Horace Ars Poet. 120 famam sequere. This is different from making the character good and from making it appropriate in the sense of the word as used above.

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Fourthly, it should be consistent. Even if the original be inconsistent and offers such a character to the poet for representation, still he must be consistently inconsistent.

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An example of unnecessary badness of character is Menelaos in the OrestesAristotle has a personal distaste for this character on the ground that Euripides made him a creature meaner than the plot demands.;

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of character that is unfitting and inappropriate the lament of Odysseus in the ScyllaA dithyramb by Timotheus. Cf. Aristot. Poet. 26.3. and Melanippe’s speechA fragment survives (Eur. Fr. 484 (Nauck)). Euripides seems to have given her a knowledge of science and philosophy inappropriate to a woman.;

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of inconsistent character Iphigeneia in Aulis, for the suppliant Iphigeneia is not at all like her later character.

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In character-drawing just as much as in the arrangement of the incidents one should always seek what is inevitable or probable, so as to make it inevitable or probable that such and such a person should say or do such and such; and inevitable or probable that one thing should follow another.

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Clearly therefore the denouementOr unravelling. of each play should also be the result of the plot itself and not produced mechanically as in the Medea and the incident of the embarkation in the Iliad. Hom. Il. 2.155-181, where it is only the arbitrary (i.e., uncaused) intervention of Athene which stays the flight of the Greeks. In the Medea the heroine, having killed her rival and her children, is spirited away in the chariot ot the Sun, a result not caused by what has gone before.

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The god in the carThe μηχανή or car was a sort of crane with a pulley attached, which was fixed at the top of the back-scene in the left corner of the stage. By it a god or hero could be lowered or raised or exhibited motionless in mid-air. Weak dramatists thus introduced a car to cut the knot by declaring the denouement instead of unravelling the plot by the logic of cause and effect. It was presumably on such a car that Medea was borne away. should only be used to explain what lies outside the play, either what happened earlier and is therefore beyond human knowledge, or what happens later and needs to be foretold in a proclamation. For we ascribe to the gods the power of seeing everything.

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There must, however, be nothing inexplicable in the incidents, or, if there is, it must lie outside the tragedy. There is an example in Sophocles’ Oedipus.i.e., Oedipus had killed Laius in a wayside quarrel, not knowing who he was. When his subjects at Thebes crave his help to remove the curse which is blighting their crops, he pledges himself to discover the murderer of Laius. It may seem odd that he should not know enough about the details of the murder to connect it in his mind with his own murderous quarrel. But that was long ago, and neither an audience nor a novel-reader is critical about incidents which occur long before the point at which the story begins. See chapter Aristot. Poet. 24.20.

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Since tragedy is a representation of men better than ourselves we must copy the good portrait-painters who, while rendering the distinctive form and making a likeness, yet paint people better than they are. It is the same with the poet. When representing people who are hot-tempered or lazy, or have other such traits of character, he should make them such, yet men of worth [an example of hardness]Apparently a note on Achilles which has been copied by mistake into the text.; take the way in which Agathon and Homer portray Achilles.

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Keep, then, a careful eye on these rules and also on the appeal to the eyei.e., stage-craft rather than staging. which is necessarily bound up with the poet’s business; for that offers many opportunities of going wrong. But this subject has been adequately discussed in the published treatises.As distinct from the body of esoteric doctrine circulated by oral teaching among Aristotle’s pupils.

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What a Discovery is has been already stated.In chapter 11.As for kinds of Discovery, first comes the least artistic kind, which is largely used owing to incompetence—discovery by tokens.

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These may be congenital, like the spear the Earth-born bear or stars, like those which CarcinusA prolific tragedian of the early fourth century. The family are agreeably ridiculed in Aristophanes’ Wasps. uses in his ThyestesThese were birth-marks. The spear-head distinguished the descendants of the Spartoi at Thebes; the star or bright spot on the descendants of Pelops commemorated his ivory shoulder, and in Carcinus’s play it seems to have survived cooking.;

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or they may be acquired and these may be on the body, for instance, wounds, or external things like necklaces, and in the TyroA play by Sophocles. Tyro’s twins by Poseidon, who appeared to her in the guise of the river Enipeus, were exposed in a little boat or ark, like Moses in the bulrushes, and this led to their identification. the discovery by means of the boat.

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There is a better and a worse way of using these tokens; for instance Odysseus, by means of his wound, was discovered in one way by the nurse and in another way by the swine-herds.Hom. Od. 19.386ff., 205ff. The first came about automatically, the second was a deliberate demonstration to prove the point. Aristotle here distinguishes between a discovery inevitably produced by the logic of events (e.g. it was inevitable or at least probable that Odysseus, arriving as a strange traveller, should be washed by Eurycleia, and that she should thus see the old scar on his thigh and discover his identity) and a discovery produced by a deliberate declaration (e.g. Odysseus’s declaration of his identity to Eumaeus). The latter kind is manufactured by the poet, not logically caused by what has gone before.

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Discovery scenes constructed to prove the point are inartistic and so are all such scenes, but those are better which arise out of a reversal scene, as, for instance, in The Washing.Hom. Od. 19.392. See preceding note.

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In the second place come those which are manufactured by the poet and are therefore inartistic. For instance, in the IphigeneiaEuripides’ Iphigeneia in Tauris. See Aristot. Poet. 11.8, note. Orestes revealed himself. She was revealed to him through the letter,

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but Orestes says himself what the poet wants and not what the plot requires. So this comes near to the fault already mentioned, for he might just as well have actually brought some tokens.To prove his identity Orestes mentions Pelops’ lance and other things from home, which is much the same as producing visible tokens. And there is the voice of the shuttleWhen Philomela’s tongue was cut out, she wove in embroidery the story of her rape by Tereus. Thus the facts were discovered to her sister, Procne, by deliberate demonstration. In Sophocles’ Tereus.

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The third kind is due to memory, to showing distress on seeing something. An example of this is the scene in the Cyprians by Dicaeogenes; on seeing the picture he burst into tearsTeucer, returning to Salamis in disguise and seeing a portrait of his dead father Telamon, burst into tears and was thus discovered. So, too, in The Two Gentlemen of <placeName key="perseus,Verona">Verona</placeName> Julia is discovered because she swoons on hearing Valentine offer Sylvia to his rival.: and again in the Tale of Alcinous, Hom. Od. 8.521ff. hearing the minstrel he remembered and burst into tears; and thus they were recognized.

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The fourth kind results from an inference; for instance, in the Choephoroe Someone like me has come; but nobody is like me except Orestes; therefore he has come. And there is Polyidus’sA Sophist who either wrote an Iphigeneia with this denouement or more probably suggested in a work of criticism (cf. Aristot. Poet. 17.6) that Orestes on being led to his fate should speculate aloud upon the odd coincidence that both he and his sister should be sacrificed, thus revealing his identity to Iphigeneia. Like most critics, Polyidos would have been a poor dramatist. There is an example of this form of discovery in the French opera Coeur de Lion, where the old knight says goddam and is thus discovered to be an Englishman. idea about Iphigeneia, for it is likely enough that Orestes should make an inference that, whereas his sister was sacrificed, here is the same thing happening to him. And in Theodectes’ Tydeus that having come to find a son, he is perishing himself. And the scene in the Phineidae, where on seeing the spot the women inferred their fate, that they were meant to die there for it was there that they had been exposed.In these cases the inference was presumably uttered aloud and hence the identity of the speakers discovered. Nothing else is known of these plays.

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There is also a kind of fictitious discovery which depends on a false inference on the part of the audience, for instance in Odysseus the False Messenger, he said he would recognize the bow, which as a matter of fact he had not seen, but to assume that he really would reveal himself by this means is a false inference.The text is obscure, and our ignorance of the play or rhapsody adds to the darkness, but the reference may be to the ruse, common in detective stories, of misleading the audience by false clues in order to make the final revelation more effective.

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Best of all is the discovery which is brought about directly by the incidents, the surprise being produced by means of what is likely—take the scene in Sophocles’ Oedipus or in the Iphigeneia—for it is likely enough that she should want to send a letter. These are the only discovery scenes which dispense with artificial tokens, like necklaces.The classical example of these tokens in English drama is the strawberry mark on the left arm in Box and Cox. But Aristotle seems here to use tokens in a wider sense than at the beginning of the chapter and to include not only birthmarks, necklaces, etc., but any statement or action which may be used as a sign in the scene of Discovery.

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In the second place come those that are the result of inference.

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In constructing plots and completing the effect by the help of dialogue the poet should, as far as possible, keep the scene before his eyes. Only thus by getting the picture as clear as if he were present at the actual event, will he find what is fitting and detect contradictions.

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The censure upon Carcinos is evidence of this. Amphiaraos was was made to rise from a temple. The poet did not visualize the scene and therefore this escaped his notice, but on the stage it was a failure since the audience objected.The example is obscure. Clearly Carcinus introduced an absurdity which escaped notice until the play was staged. Margoliouth suggests that if Amphiaraus were a god he should come down, and if a mere hero, he sould not have a temple. In The Master of Ballantrae Mrs. Henry cleans a sword by thrusting it up to the hilt in the ground—which is iron-bound by frost. The would be noticed on the stage: a reader may miss the incongruity.

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The poet should also, as far as possible, complete the effect by using the gestures. For, if their natural powers are equal, those who are actually in the emotions are the most convincing; he who is agitated blusters and the angry man rages with the maximum of conviction.Sir Joshua Reynolds used thus to simulate emotion before a mirror. In his Preface to the Lyrical Ballads Wordsworth says that the Poet will wish to bring his feelings near to those of the persons whose feelings he describes . . . and even confound and identify his own feelings with theirs. See also Burke, On the Sublime and Beautiful,4. 4.

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And that is why poetry needs either a sympathetic nature or a madman,Genius to madness near allied is the meaning of μανικός as used here. Plato held that the only excuse for a poet was that he couldn’t help it. the former being impressionable and the latter inspired.

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The stories, whether they are traditional or whether you make them up yourself, should first be sketched in outline and then expanded by putting in episodes.

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I mean that one might look at the general outline, say of the Iphigeneia, like this: A certain maiden has been sacrificed, and has disappeared beyond the ken of those who sacrificed her and has been established in another country, where it is a custom to sacrifice strangers to the goddess; and this priesthood she holds. Some time afterwards it happens that the brother of the priestess arrives there—the fact that the god told him to go there, and why, and the object of his journey, lie outside the outline-plot. He arrives, is seized, and is on the point of being sacrificed, when he reveals his identity either by Euripides’ method or according to Polyidos, by making the very natural remark that after all it is not only his sister who was born to be sacrificed but himself too; and thus he is saved.

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Not until this has been done should you put in names and insert the episodes;

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and you must mind that the episodes are appropriate, as, for instance, in the case of Orestes the madness that led to his capture and his escape by means of the purification.In the Iphigeneia in Tauris Orestes is captured because he is suffering from a fit of mania; and at the end Iphigeneia pretends that the image of Artemis has been infected by the blood-guiltiness of the Greek strangers, and that, before they can be sacrificed, she must cleanse both image and strangers secretly in the sea. Thus they all escape together by boat.

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Now in drama the episodes are short, but it is by them that the epic gains its length.

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The story of the Odyssey is quite short. A man is for many years away from home and his footsteps are dogged by Poseidon and he is all alone. Moreover,affairs at home are in such a state that his estate is being wasted by suitors and a plot laid against his son, but after being storm-tossed he arrives himself, reveals who he is, and attacks them, with the result that he is saved and destroys his enemies.

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That is the essence, the rest is episodes.

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In every tragedy there is a complication and a denouement.The Greek says simply tying and loosing. Complication and denouement seem clumsy equivalents, yet they are the words we use in dramatic criticism. The incidents outside the plot and some of those in it usually form the complication, the rest is the denouement.

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I mean this, that the complication is the part from the beginning up to the point which immediately precedes the occurrence of a change from bad to good fortune or from good fortune to bad; the denouement is from the beginning of the change down to the end.

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For instance, in the Lynceus of Theodectes the complication is the preceding events, and the seizure of the boy, and then their own seizure; and the denouement is from the capital charge to the end.The boy must be Abas, and they are presumably Danaus and perhaps his other daughters. Aristotle seems to regard the arrest of Danaus not as part of the λύσις, but as the end of the δέσις.

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Tragedies should properly be classed as the same or different mainly in virtue of the plot, that is to say those that have the same entanglement and denouement. Many who entangle well are bad at the denouement. Both should always be mastered.

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There are four varieties of tragedy—the same as the number given for the elementsApparently the reference here is to the four elements into which in the course of chapters 10-15. Plot has been analysed, Reversal, Discovery, Calamity, and Character. But the symmetry is spoilt by the fact that his first species, the complex play, corresponds to the first two of these four elements, viz. to Reversal and Discovery. Thus his fourth species is left in the air and he hurriedly introduces Spectacle as the fourth corresponding element. Other explanations seem even sillier than this.—

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first the complex kind, which all turns on reversal and discovery;

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the calamity play like the stories of Ajax and Ixion;

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the character play like the Phthian WomenBy Sophocles. and the PeleusBoth Sophocles and Euripides wrote a Peleus..

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The fourth element is spectacle, like the PhorcidesThe text is obscure, and our ignorance of the play or rhapsody adds to the darkness, but the reference may be to the ruse, common in detective stories, of misleading the audience by false clues in order to make the final revelation more effective. and Prometheus, and all scenes laid in Hades.

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One should ideally try to include all these elements or, failing that, the most important and as many as possible, especially since it is the modern fashion to carp at poets, and, because there have been good poets in each style, to demand that a single author should surpass the peculiar merits of each.

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One must remember, as we have often said, not to make a tragedy an epic structure:

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by epic I mean made up of many stories—suppose, for instance, one were to dramatize the IIiad as a whole.

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The length of the IIiad allows to the parts their proper size, but in plays the result is full of disappointment.

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And the proof is that all who have dramatized the Sack of Troy as a whole, and not, like Euripides, piecemeal, or the Niobe story as a whole and not like Aeschylus, either fail or fare badly in competition. Indeed even Agathon failed in this point alone.

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In reversals, however, and in simple storiesi.e., those that have no Discovery or Reversal. See chapter 10. too,they admirably achieve their end, which is a tragic effect that also satisfies your feelings.

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This is achieved when the wise man, who is, however, unscrupulous, is deceived—like Sisyphus—and the man who is brave but wicked is worsted.

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And this, as Agathon says, is a likely result, since it is likely that many quite unlikely things should happen.

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The chorus too must be regarded as one of the actors. It must be part of the whole and share in the action, not as in Euripides but as in Sophocles.

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In the others the choral odes have no more to do with the plot than with any other tragedy. And so they sing interludes, a practice begun by Agathon. And yet to sing interludes is quite as bad as transferring a whole speech or scene from one play to another.

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The other factors have been already discussed. It remains to speak of Diction and Thought.

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All that concerns Thought may be left to the treatise on Rhetoric, for the subject is more proper to that inquiry.Thought—no English word exactly corresponds with διάνοια—is all that which is expressed or effected by the words (cf. Aristot. Poet. 6.22, 23, and 25). Thus the student is rightly referred to the Art of Rhetoric, where he learns what to say in every case. Aristotle adds that the rules there given for the use of ideas will guide him also in the use of incidents, since the same effect may be produced either by talk or by situation.

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Under the head of Thought come all the effects to be produced by the language.

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Some of these are proof and refutation, the arousing of feelings like pity, fear, anger, and so on, and then again exaggeration and depreciation.It is an important part of the orator’s skill to depreciate what is important and to exaggerate trivial points.

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It is clear that in the case of the incidents, too, one should work on the same principles, when effects of pity or terror or exaggeration or probability have to be produced.

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There is just this difference, that some effects must be clear without explanation,Those produced by situation. whereas others are produced in the speeches by the speaker and are due to the speeches. For what would be the use of a speaker, if the required effect were likely to be felt without the aid of the speeches?

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Under the head of Diction one subject of inquiry is the various modes of speech, the knowledge of which is proper to elocution or to the man who knows the master artRhetoric is a master art in relation to elocution, since it decides the effects to be produced, and elocution decides how to produce them. So the doctor’s art is master to that of the dispenser, and the art of riding to that of the maker of bridles.—I mean for instance, what is a command, a prayer, a statement, a threat, question, answer, and so on.

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The knowledge or ignorance of such matters brings upon the poet no censure worth serious consideration. For who could suppose that there is any fault in the passage which Protagoras censures, because Homer, intending to utter a prayer, gives a command when he says, Sing, goddess, the wrath? To order something to be done or not is, he points out, a command.

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So we may leave this topic as one that belongs not to poetry but to another art.

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Diction as a wholeA translator is bound to render this chapter, since the balance of evidence is in favour of its inclusion. But the readaer is advised to skip it, since it is written from the point of view of grammar and philology, and does not, like the succeeding chapter, deal with the literary use of words. It is also very obscure. Students should refer to Bywater’s edition. is made up of these parts: letter, syllable, conjunction, joint,A joint, as defined below, appears to be a word which indicates the beginning or end of a clause. noun, verb, case, phrase.

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A letter is an indivisible sound, not every such sound but one of which an intelligible sound can be formed. Animals utter indivisible sounds but none that I should call a letter.

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Such sounds may be subdivided into vowel, semi-vowel, and mute. A vowel is that which without any addition has an audible sound; a semivowel needs the addition of another letter to give it audible sound, for instance S and R; a mute is that which with addition has no sound of its own but becomes audible when combined with some of the letters which have a sound. Examples of mutes are G and D.

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Letters differ according to the shape of the mouth and the place at which they are sounded; in being with or without aspiration; in being long and short; and lastly in having an acute, grave, or intermediate accent. But the detailed study of these matters properly concerns students of metre.

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A syllable is a sound without meaning, composed of a mute and a letter that has a sound. GR, for example, without A is a syllable just as much as GRA with an A. But these distinctions also belong to the theory of metre. words. It is also very obscure. Students should refer to Bywater’s edition.

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A conjunction is a sound without meaning, which neither hinders nor causes the formation of a single significant sound or phrase out of several sounds, and which, if the phrase stands by itself, cannot properly stand at the beginning of it, e.g. μέν, δή, τοί, δέ; or else it is a sound without meaning capable of forming one significant sound or phrase out of several sounds having each a meaning of their own, e.g. ἀμφί, περί.

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A joint is a sound without meaning which marks the beginning or end of a phrase or a division in it, and naturally stands at either end or in the middle.This paragraph remains a cause of despair. Bywater’s notes suggest a restoration.

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A noun is a composite sound with a meaning, not indicative of time, no part of which has a meaning by itself; for in compounds we do not use each part as having a meaning of its own, for instance, in Theodorus, there is no meaning of δῶρον (gift).

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A verb is a composite sound with a meaning, indicative of time, no part of which has a meaning by itself—just as in nouns. Man or white does not signify time, but walks and has walked connote present and past time respectively.

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A case(or inflection)of a noun or verb is that which signifies either of or to a thing and the like;or gives the sense of one or many e.g. men and man; or else it may depend on the delivery, for example question and command. Walked? and Walk! are verbal cases of this kind.

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A phraseThere is no exact English equivalent of this meaning of λόγος, which has been used already in 7 above without explanation. Statement and proposition also cover part of its meaning. is a composite sound with a meaning, some parts of which mean something by themselves.

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It is not true to say that every phrase is made up of nouns and verbs, e.g. the definition of manProbably one of the two definitions given in the Topics, a two-footed land animal and an animal amenable to reason.; but although it is possible to have a phrase without verbs, yet some part of it will always have a meaning of its own, for example, Cleon in Cleon walks.

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A phrase may be a unit in two ways; either it signifies one thing or it is a combination of several phrases. The unity of the Iliad, for instance, is due to such combination, but the definition of man is one phrase because it signifies one thing.

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Nouns are of two kinds. There is the simple noun, by which I mean one made up of parts that have no meaning, like γῆ, and there is the compound noun.

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These may be made up either of a part which has no meaning and a part which has a meaning—though it does not have its meaning in the compound—or of two parts both having a meaning.

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A compound noun may be triple and quadruple and multiple, e.g. many of the bombastic names like Hermocaicoxanthus.A compound of the names of three rivers, Hermus, Caicus, and Xanthus. . . .

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Every noun is either ordinaryi.e., one which has dined normal currency as contrasted with the rare word, which is confined to a dialect or borrowed from a foreign language. or rare or metaphorical or ornamental or invented or lengthened or curtailed or altered.

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An ordinary word is one used by everybody, a rare word one used by some;

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so that a word may obviously be both ordinary and rare, but not in relation to the same people. σίγυνον,Meaning, spear. for instance, is to the Cypriots an ordinary word but to us a rare one.

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Metaphor is the application of a strange term either transferred from the genus and applied to the species or from the species and applied to the genus, or from one species to another or else by analogy.

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An example of a term transferred from genus to species is Here stands my ship. Riding at anchor is a species of standing.

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An example of transference from species to genus is Indeed ten thousand noble things Odysseus did, for ten thousand, which is a species of many, is here used instead of the word many.

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An example of transference from one species to another is Drawing off his life with the bronze and Severing with the tireless bronze, where drawing off is used for severing and severing for drawing off, both being species of removing.Probably the bronze is in the first case a knife and in the second a cupping-bowl. This would make the metaphor intelligible.

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Metaphor by analogy means this: when B is to A as D is to C, then instead of B the poet will say D and B instead of D.

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And sometimes they add that to which the term supplanted by the metaphor is relative.This may claim to be one of Aristotle’s least lucid sentences. It means this: If Old Age: Life :: Evening: Day, then we may call old age the Evening of Life. In that case old age is the term supplanted by the metaphor, and it is relative to Life; therefore Life (i.e., that to which the term supplanted by the metaphor is relative) is added to the metaphorical (or transferred) term Evening.For instance, a cup is to Dionysus what a shield is to Ares;

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so he will call the cup Dionysus’s shield and the shield Ares’ cup. Or old age is to life as evening is to day; so he will call the evening day’s old-age or use Empedocles’ phraseUnknown to us.; and old age he will call the evening of life or life’s setting sun.

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Sometimes there is no word for some of the terms of the analogy but the metaphor can be used all the same. For instance, to scatter seed is to sow, but there is no word for the action of the sun in scattering its fire. Yet this has to the sunshine the same relation as sowing has to the seed, and so you have the phrase sowing the god-created fire.

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Besides this another way of employing metaphor is to call a thing by the strange name and then to deny it some attribute of that name. For instance, suppose you call the shield not Ares’ cup but a “wineless cup.” . . .Or you might call Love Venus’s bloodless War. At this point a few lines on Ornament have evidently been lost, since this is its place in the catalogue of nouns above. By ornament he seems to mean an embellishing epithet or synonym. In the Rhetoric he quotes Our lady the fig-tree as a misplaced ornament. One might add the seventeenth-century use of Thames for water. . . .

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An invented word is one not used at all by any people and coined by the poet. There seem to be such words, eg. sprouters for horns and pray-er for priest.

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A word is lengthened or curtailed, the former when use is made of a longer vowel than usual or a syllable inserted, and the latter when part of the word is curtailed.

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An example of a lengthened word is πόληος for πολέως and Πηληιάδεω for Πηλείδου; and of a curtailed word κρῖ and δῶ, and e.g. μία γίνεται ἀμφοτέρων ὄψ.κρῖ for κριθή, barley; δῶ for δῶμα house; ὄψ for ὄψις face, eye, or appearance.

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A word is altered when the poet coins part of the word and leaves the rest unchanged, e.g. δεξιτερὸν κατὰ μαζόν instead of δεξιόν.

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Of the nouns themselves, some are masculine, some feminine, and some neuter.This paragraph the reader should either skip or study with Bywater’s notes. Without them these generalizations on gender seem merely wrong.

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Masculine are all that end in N and P and Σ and in the two compounds of Σ, Ψ and Ξ.

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Feminine are all that end in those of the vowels that are always long, for instance Η and Ω, and in Α among vowels that can be lengthened.

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The result is that the number of masculine and feminine terminations is the same, for Ψ and Ξ are the same as Σ.

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No noun ends in a mute or in a short vowel.

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Only three end in Ι, μέλι, κόμμι, and πέπερι. Five end in Υ. The neuters end in these letters and in Ν and Σ.

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The merit of diction is to be clear and not commonplace. The clearest diction is that made up of ordinary words, but it is commonplace.

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An example is the poetry of Cleophon and of Sthenelus.A tragedian whom Aristophanes ridicules for the insipidity of his diction.

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That which employs unfamiliar words is dignified and outside the common usage. By unfamiliar I mean a rare word, a metaphor, a lengthening,See preceding chapter 19. and anything beyond the ordinary use.

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But if a poet writes entirely in such words, the result will be either a riddle or jargon; if made up of metaphors, a riddle and if of rare words, jargon.

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The essence of a riddle consists in describing a fact by an impossible combination of words. By merely combining the ordinary names of things this cannot be done, but it is made possible by combining metaphors. For instance, I saw a man weld bronze upon a man with fire, and so on.The answer is a cupping-bowl. This was a bronze vessel which was applied to the body at the place at which a small incision had been made. Heated lint was placed in the bowl of it and the reduction of air-pressure thus caused a strong flow of blood. For this form of riddle cf. Out of the strong came forth sweetness.

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A medley of rare words is jargon.

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We need then a sort of mixture of the two. For the one kind will save the diction from being prosaic and commonplace, the rare word, for example, and the metaphor and the ornament, whereas the ordinary words give clarity.

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A considerable aid to clarity and distinction are the lengthening and abbreviation and alteration of words. Being otherwise than in the ordinary form and thus unusual, these will produce the effect of distinction, and clarity will be preserved by retaining part of the usual form.

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Those critics are therefore wrong who censure this manner of idiom and poke fun at the poet, as did the elder EucleidesA critic of this name wrote on the drama, but his date is uncertain. who said it was easy to write poetry, granted the right to lengthen syllables at will. He had made a burlesque in this very style: Ἐπιχάρην εἶδον Μαραθῶνάδε βαδίζοντα and οὐκ ἄν γ’ ἐράμενος τὸν ἐκείνου ἐλλέβορον.In Homer we find short vowels lengthened by position, but, whereas Homer uses the licence sparingly, Eucleides raised a laugh by overdoing it and writing in parody such hexameters as those here quoted. A modern parallel may illustrate this. The poet Stephen Phillips employed to excess the licence whihc allows a clash between the natural accent and the metrical ictus, and Mr. Owen Seaman, for the express purpose of raising a laugh, parodied the trick by carrying it to further excess and wrote in blank verse, She a milliner was and her brothers Dynamiters.

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Now to make an obtrusive use of this licence is ridiculous;

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but moderation is a requisite common to all kinds of writing. The same effect could be got by using metaphors and rare words and the rest unsuitably for the express purpose of raising a laugh.

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What a difference is made by the proper use of such licence may be seen in epic poetry, if you substitute in the verse the ordinary forms.

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Take a rare word or metaphor or any of the others and substitute the ordinary word; the truth of our contention will then be obvious.For instance, Aeschylus and Euripides wrote the same iambic line with the change of one word only, a rare word in place of one made ordinary by custom, yet the one line seems beautiful and the other trivial. Aeschylus in the Philoctetes wrote, The ulcer eats the flesh of this my foot, and Euripides instead of eats put feasts upon. Or take I that am small, of no account nor goodly; suppose one were to read the line substituting the ordinary words, I that am little and weak and ugly. Or compare He set a stool unseemly and a table small. with He set a shabby stool and a little table, or the sea-shore is roaring with the sea-shore is shrieking.Similarly we might use ordinary words instead of those which Keats chose so carefully and speak of wonderful windows abutting on to a dangerous sea-shore in a dreary, mysterious country.

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AriphradesUnknown. again made fun of the tragedians because they employ phrases which no one would use in conversation, like δωμάτων ἄπο instead of ἀπὸ δωμάτων and their σέθεν and ἐγὼ δέ νιν and Ἀχιλλέως πέρι for περὶ Ἀχιλλέως, and so on.

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All that sort of thing, not being in the ordinary form, gives distinction to the diction, which was what he failed to understand.

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It is a great thing to make a proper use of each of the elements mentioned, and of double words and rare words too, but by far the greatest thing is the use of metaphor.

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That alone cannot be learnt; it is the token of genius. For the right use of metaphor means an eye for resemblances.i.e., the power of detecting identity in difference which distinguishes also both the philosopher and the scientist.

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Of the various kinds of words the double forms are most suited for dithyrambs, rare words for heroic verse and metaphors for iambics.

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And indeed in heroic verse they are all useful; but since iambic verse is largely an imitation of speech, only those nouns are suitable which might be used in talking. These are the ordinary word, metaphor, and ornament.

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Now concerning tragedy and the art of representing life in action, what we have said already must suffice.

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We come now to the art of representation which is narrative and in metre.i.e., epic. Clearly the story must be constructed as in tragedy, dramatically, round a single piece of action, whole and complete in itself,with a beginning, middle and end, so that like a single living organism it may produce its own peculiar form of pleasure.

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It must not be such as we normally find in history, where what is required is an exposition not of a single piece of action but of a single period of time, showing all that within the period befell one or more persons, events that have a merely casual relation to each other.

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For just as the battle of Salamis occurred at the same time as the Carthaginian battle in Sicily, but they do not converge to the same resultGelo’s defeat of the Carthaginians in Sicily in 480 B.C. took place, according to Herodotus, on the same day as the battle of Salamis.; so, too, in any sequence of time one event may follow another and yet they may not issue in any one result.

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Yet most of the poets do this.

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So in this respect, too, compared with all other poets Homer may seem, as we have already said, divinely inspired, in that even with the Trojan war, which has a beginning and an end, he did not endeavor to dramatize it as a whole, since it would have been either too long to be taken in all at once or, if he had moderated the length, he would have complicated it by the variety of incident. As it is, he takes one part of the story only and uses many incidents from other parts, such as the Catalogue of Ships and other incidents with which he diversifies his poetry.

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The others, on the contrary, all write about a single hero or about a single period or about a single action with a great many parts, the authors, for example, of the Cypria and the Little Iliad.As we have seen already in chapter 8, a poem or a play must be one story and not several stories about one hero. Thus, since the Iliad and Odyssey have this essential unity (i.e., one thread runs through the narrative of each), few plays can be made out of them but many out of the Cypria or the Little Iliad, which are merely collections of lays on similar themes.

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The result is that out of an Iliad or an Odyssey only one tragedy can be made, or two at most, whereas several have been made out of the Cypria, and out of the Little Iliad more than eight, e.g. The Award of Arms, Philoctetes, Neoptolemus, Eurypylus, The Begging, The Laconian Women, The Sack of <placeName key="perseus,Troy">Troy</placeName>, and Sailing of the Fleet, and Sinon, too, and The Trojan Women.

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The next point is that there must be the same varieties of epic as of tragedySee Aristot. Poet. 18.4.: an epic must be simple or complex,See chapter 10. or else turn on character or on calamity.

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The constituent parts, too, are the same with the exception of song and spectacle. Epic needs reversals and discoveries and calamities, and the thought and diction too must be good.

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All these were used by Homer for the first time, and used well. Of his poems he made the one, the Iliad, a simple story turning on calamity, and the Odyssey a complex story—it is full of discoveries—turning on character. Besides this they surpass all other poems in diction and thought.

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Epic differs from tragedy in the length of the composition and in metre.

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The limit of length already givenSee Aristot. Poet. 7.12. will suffice—it must be possible to embrace the beginning and the end in one view,which would be the case if the compositions were shorter than the ancient epics but reached to the length of the tragedies presented at a single entertainment.“Entertainment” must mean a festival. At the City Dionysia three poets competed, each with three tragedies. By the end of the fifth century only one Satyr play was performed at each festival. But the tragedies were longer than those we possess. It is therefore likely that the nine tragedies together with one Satyr play amounted to about 15,000 lines. The Iliad contains between 16,000 and 17,000 lines.

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Epic has a special advantage which enables the length to be increased, because in tragedy it is not possible to represent several parts of the story as going on simultaneously, but only to show what is on the stage, that part of the story which the actors are performing; whereas, in the epic, because it is narrative, several parts can be portrayed as being enacted at the same time.

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If these incidents are relevant, they increase the bulk of the poem, and this increase gives the epic a great advantage in richness as well as the variety due to the diverse incidents; for it is monotony which, soon satiating the audience, makes tragedies fail.

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Experience has shown that the heroic hexameter is the right metre. Were anyone to write a narrative poem in any other metre or in several metres, the effect would be wrong.

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The hexameter is the most sedate and stately of all metres and therefore admits of rare words and metaphors more than others, and narrative poetry is itself elaborate above all others.

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The iambic and the trochaic tetrameter are lively, the latter suits dancing and the former suits real life.

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Still more unsuitable is it to use several metres as Chaeremon did.

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So no one has composed a long poem in any metre other than the heroic hexameter. As we said above, Nature shows that this is the right metre to choose.

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Homer deserves praise for many things and especially for this, that alone of all poets he does not fail to understand what he ought to do himself. The poet should speak as seldom as possible in his own character, since he is not representing the story in that sense.This takes us back to the beginning of chapter 3, where the various manners of representation are distinguished. Homer represents life partly by narration, partly by assuming a character other than his own. Both these manners come under the head of Imitation. When Aristotle says the poet speaks himself and plays a part himself he refers not to narrative, of which there is a great deal in Homer, but to the preludes (cf. φροιμιασάμενος below) in which the poet, invoking the Muse, speaks in his own person. Ridgeway points out that in the whole of the Iliad and Odyssey Homer thus speaks himself only 24 lines.

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Now the other poets play a part themselves throughout the poem and only occasionally represent a few things dramatically, but Homer after a brief prelude at once brings in a man or a woman or some other character, never without character, but all having character of their own.

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Now the marvellous should certainly be portrayed in tragedy, but epic affords greater scope for the inexplicable(which is the chief element in what is marvellous), because we do not actually see the persons of the story.

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The incident of Hector’s pursuitIliad, xxii. 205. sq. “And to the host divine Achilles nodded with his head a sign and let them not launch their bitter darts at Hector, lest another should win glory by shooting him and Achilles himself come second.” would look ridiculous on the stage, the people standing still and not pursuing and Achilles waving them back, but in epic that is not noticed.

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But that the marvellous causes pleasure is shown by the fact that people always tell a piece of news with additions by way of being agreeable.

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Above all, Homer has taught the others the proper way of telling lies,that is, by using a fallacy. When B is true if A is true, or B happens if A happens, people think that if B is true A must be true or happen. But that is false. Consequently if A be untrue but there be something else, B, which is necessarily true or happens if A is true, the proper thing to do is to posit B, for, knowing B to be true, our mind falsely infers that A is true also. This is an example from the Washing.Odyssey 19. Odysseus tells Penelope that he is a Cretan from Gnossus, who once entertained O. on his voyage to Troy. As evidence, he describes O.’s dress and his companions (Hom. Od. 19.164-260). P. commits the fallacy of inferring the truth of the antecedent from the truth of the consequent: “If his story were true, he would know these details; But he does know them; Therefore his story is true.” The artist in fiction uses the same fallacy, e.g.: “If chessmen could come to life the white knight would be a duffer; But he is a most awful duffer (look at him!); Therefore chessmen can come to life.” He makes his deductions so convincing that we falsely infer the truth of his hypothesis.

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What is convincing though impossible should always be preferred to what is possible and unconvincing.

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Stories should not be made up of inexplicable details; so far as possible there should be nothing inexplicable, or, if there is, it should lie outside the story—as, for instance, Oedipus not knowing how Laius died—and not in the play; for example, in the Electra the news of the Pythian games,In Sophocles’Electrathe plot hinges on a false story of Orestes’ death by an accident at the Pythian games. Presumably the anachronism shocked Aristotle. or in the Mysians the man who came from Tegea to Mysia without speaking.Telephus. To say that the plot would otherwise have been ruined is ridiculous.

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One should not in the first instance construct such a plot, and if a poet does write thus, and there seems to be a more reasonable way of treating the incident, then it is positively absurd.

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Even in the Odyssey the inexplicable elements in the story of his landingHom. Od. 13.116ff. It seemed to the critics inexplicable that Odysseus should not awake when his ship ran aground at the harbour of Phorcys in Ithaca and the Phaeacian sailors carried him ashore. would obviously have been intolerable, had they been written by an inferior poet. As it is, Homer conceals the absurdity by the charm of all his other merits.

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The diction should be elaborated only in the idle parts which do not reveal character or thought.The Messengers’ speeches, a regular feature of Greek tragedy, may serve to illustrate what is here called the idle part of a play, i.e., passages which, but for brilliant writing, might be dull, since no character is there elucidated and no important sentiments expressed. Too brilliant diction frustrates its own object by diverting attention from the portrayal of character and thought.

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With regard to problems,A problem in this sense is a difficult passage or expression which explanation and may easily be censured by an unsympathetic critic. Aristotle here classifies the various grounds of censure and the various lines of defence. Most of his illustrations are drawn from the critical objections lodged against the Iliad by Zoilus and other hammerers of Homer. As the reader will see, many of them are abysmally foolish. and the various solutions of them, how many kinds there are, and the nature of each kind, all will be clear if we look at them like this.

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Since the poet represents life, as a painter does or any other maker of likenesses, he must always represent one of three things—either things as they were or are; or things as they are said and seem to be; or things as they should be.

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These are expressed in diction with or without rare words and metaphors, there being many modifications of diction, all of which we allow the poet to use.

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Moreover, the standard of what is correct is not the same in the art of poetry as it is in the art of social conduct or any other art.

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In the actual art of poetry there are two kinds of errors, essential and accidental.

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If a man meant to represent something and failed through incapacity, that is an essential error. But if his error is due to his original conception being wrong and his portraying, for example, a horse advancing both its right legs, that is then a technical error in some special branch of knowledge,in medicine, say, or whatever it may be; or else some sort of impossibility has been portrayed, but that is not an essential error.

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These considerations must, then, be kept in view in meeting the charges contained in these objections.

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Let us first take the charges against the art of poetry itself. If an impossibility has been portrayed, an error has been made.

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But it is justifiable if the poet thus achieves the object of poetry—what that is has been already stated—and makes that part or some other part of the poem more striking. The pursuit of Hector is an example of this.See Aristot. Poet. 24.16 and note.

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If, however, the object could have been achieved better or just as well without sacrifice of technical accuracy, then it is not justifiable, for, if possible, there should be no error at all in any part of the poem.

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Again one must ask of which kind is the error, is it an error in poetic art or a chance error in some other field? It is less of an error not to know that a female stag has no horns than to make a picture that is unrecognizable.

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Next, supposing the charge is That is not true, one can meet it by saying But perhaps it ought to be, just as Sophocles said that he portrayed people as they ought to be and Euripides portrayed them as they are.

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If neither of these will do, then say, Such is the tale; for instance, tales about gods.

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Very likely there is no advantage in telling them, and they are not true either, but may well be what Xenophanes declaredi.e., immoral and therefore untrue. He opened the assault on Homeric theology at the end of the sixth or the beginning of the fifth century B.C.—all the same such is the tale.

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In another case, perhaps, there is no advantage but such was the fact, e.g. the case of the arms, Their spears erect on butt-spikes stood,Hom. Il. 10.152. Problem: Surely a bad stance: they might so easily fall and cause alarm. Solution: Homer does not defend it. He merely states a fact. It is thus that we excuse unpleasant fiction. for that was then the custom, as it still is in Illyria.

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As to the question whether anything that has been said or done is morally good or bad, this must be answered not merely by seeing whether what has actually been done or said is noble or base, but by taking into consideration also the man who did or said it, and seeing to whom he did or said it, and when and for whom and for what reason; for example, to secure a greater good or to avoid a greater evil.

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Some objections may be met by reference to the diction, for example, by pleading rare word, e.g. οὐρῆας μὲν πρῶτον, for perhaps he means not mules but sentinels.Hom. Il. 1.50: The mules and swift-footed hounds he first beset with his arrows. Apollo is sending plague upon the Greek army. Problem: Why should he first attack the mules? Solution: The word may here mean sentiels. And Dolon, One that was verily evil of form, it may be not his deformed body but his ugly face, for the Cretans use fair-formed for fair-featured.Hom. Il. 10.316: One that was verily evil inform but swift in his running. Problem: If Dolon were deformed, how could he run fast? Solution: Form may here mean feature. And again Livelier mix it may mean not undiluted as for drunkards but quicker.Hom. Il. 9.202: Set me, Menoetius’ son, a larger bowl for the mingling, Livelier mix it withal and make ready for each one a beaker. Problem: Livelier suggests intemperance. Solution: Perhaps the word means quicker. Similar scruples emended the lines in Young Lochinvar to read: And now am I come with this pretty maid To dance but one measure, drink one lemonade.

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Other expressions are metaphorical, for example: Then all the other immortals and men lay all night in slumber, while yet he says: Yea, when indeed he gazed at the Trojan plain Agamemnon Marvelled at voices of flutes . . . All is used instead of many metaphorically, all being a species of many.Hom. Il. 2.2 (quoted by mistake for Hom. Il. 10.1) and Hom. Il. 10.13, 14: Then all the other immortals and all the horse-crested heroes Night-long slumbered, but Zeus the sweet sleep held not. . . (Hom. Il. 2.1, 2) Yea, when indeed he gazed at the Trojan plain, Agamemnon Marvelled at voices of flutes and of pipes and the din of the soldiers. (Hom. Il. 10.13, 14) Problem: If all were asleep, who was playing the flute? Solution: This may be a metaphor; as explained in chapter 21, all is one kind or species of many, and thus by transference all is used for many, the species for the genus. And again, Alone unsharingHom. Il. 18.489: She alone of all others shares not in the baths of the Ocean. The reference is to the Great Bear. Problem: Why does Homer say she alone when the other Northern Constellations also do not set? Solution: As in the last instance, the may be metaphorical, i.e., the genus, sole, may be here used by transference for one of its species, best known. is metaphorical; the best known is called the only one.

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By intonation also; for example, the solutions of Hippias of Thasos, his δίδομεν δέ οἱHom. Il. 2.15. Our text is different. Aristotle, who quotes the line agains elsewhere, read thus: No longer the gods in the halls of Olympus Strive in their plans, for Hera has bent them all to her purpose Thus by her prayers; and we grant him to win the boast of great glory. Zeus is instructing the Dream, whom he is sending to lure Agamemnon to disaster. Problem: The last statement is a lie. Solution: Change the accent and the statement δίδομεν δέ οἱ becomes a command (the infinitive διδόμεναι written in a shortened form and used as an imperative). The lie will then be told by the Dream and not by Zeus, who may thus save his reputation for veracity. and τὸ μὲν οὗ καταπύθεται ὄμβρῳHom. Il. 23.327: A fathom high from the earth there rises a stump all withered, A stump of an oak or a pine, that rots not at all in the rain. Problem: The last statement is incredible. Solution: Alter the breathing and τὸ μὲν οὐ becomes τὸ μὲν οὗ and means part of it rots in the rain.;

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and by punctuation; for example, the lines of Empedocles: Soon mortal grow they that aforetime learnt Immortal ways, and pure erstwhile commingled.The Problem is erstwhile goes with pure or with commingled. The former interpretation seems to give the best solution. Empedocles is speaking of the elements or atoms.

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Or again by ambiguity, e.g. παρῴχηκεν δὲ πλέω νύξ, where πλείω is ambiguous.Hom. Il. 10.252: Come now, the night is far spent and at hand is the dawning, Far across are the stars and more than two parts of the night-time Are gone, but a third is still left us. Problem: If more than two parts are gone, a third cannot be left. Solution: πλέω here means full, i.e., the full night of two-thirds = full two-thirds of the night is gone, and so Homer’s arithmetic is saved.

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Others according to the habitual use of the phrase, e.g. wine and water is called wine so you get the phrase greaves of new-wrought tin;Problem: Greaves are made not of tin but of an alloy of tin and copper. Solution: Compounds are called by the name of the more important partner. Just as a mixture of wine and water is called wine, so here an alloy of tin and copper is called tin. So, too, is whisky and water called whisky. or workers in iron are called braziers, and so Ganymede is said to pour wine for Zeus, though they do not drink wine. This last might however be metaphorical.Nectar:gods :: wine: men. Therefore, according to the rules of metaphor in chapter 21, nectar may be called wine or the wine of the gods.

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Whenever a word seems to involve a contradiction, one should consider how many different meanings it might bear in the passage, e.g. in There the bronzen shaft was stayed,Hom. Il. 20.272: Nay but the weighty shaft of the warlike hero Aeneas Brake not the shield; for the gold, the gift of a god, did withstand it. Through two folds it drave, yet three were beneath, for Hephaestus, Crook-footed god, five folds had hammered; two were of bronze-work, Two underneath were of tin and one was of gold; there the bronzen Shaft of the hero was stayed in the gold. Problem: Since the gold was presumably outside for the sake of ornament, how could the spear he stayed in the gold and yet penetrate two folds? Bywater suggests as a solution that the plate of gold sufficed to stop the course of the spear, though the spear-point actually pierced it and indented the underlying plates of brass. we should ask in how many ways being stayed might be taken,

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interpreting the passage in this sense or in that, and keeping as far as possible from the attitude which GlauconThis may well be the Glaucon mentioned in Plato’s Ion as an authority on Homer. describes

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when he says that people make some unwarrantable presupposition and having themselves given an adverse verdict proceed to argue from it, and if what they think the poet has said does not agree with their own preconceived ideas, they censure him, as if that was what he had said.

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This is what has happened in the case of Icarius.Penelope’s father. They assume that he was a Spartan and therefore find it odd that when Telemachus went to Sparta he did not meet him. But the truth may be, as the Cephallenians say, that Odysseus married a wife from their country and that the name was not Icarius but Icadius. So the objection is probably due to a mistake.

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In general any impossibility may be defended by reference to the poetic effect or to the ideal or to current opinion.

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For poetic effect a convincing impossibility is preferable to that which is unconvincing though possible.

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It may be impossible that there should be such people as ZeuxisSee Aristot. Poet. 6.15. used to paint, but it would be better if there were; for the type should improve on the actual.

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Popular tradition may be used to defend what seems irrational, and you can also say that sometimes it is not irrational, for it is likely that unlikely things should happen.

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Contradictions in terms must be examined in the same way as an opponent’s refutations in argument, to see whether the poet refers to the same thing in the same relation and in the same sense, and has contradicted either what he expressly says himself or what an intelligent person would take to be his meaning.

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It is right, however, to censure both improbability and depravity where there is no necessity and no use is made of the improbability.An example is Euripides’ intro duction of AegeusEur. Medea 663. In Aristotle’s opinion there is no good reason for Aegeus’s appearance and no good use is made of it. or(of depravity)the character of Menelans in the Orestes.

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The censures they bring are of five kinds; that things are either impossible or irrational or harmful or inconsistent or contrary to artistic correctness. The solutions must be studied under the heads specified above, twelve in number.i.e., any expression that is criticized should be considered with reference to (1) things as they were; (2) things as thy are; (3) things as they are said to be; (4) things as they seem to be; (5) things as they ought to be. Further, we should consider whether (6) a rare word or (7) a metaphor is used; what is the right (8) accent and (9) punctuation; also where there may be (10) ambiguity and what is (11) the habitual use of the phrase; also we may refer to (12) the proper standard of correctness in poetry as distinct from other arts.

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The question may be raised whether the epic or the tragic form of representation is the better.

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If the better is the less vulgar and the less vulgar is always that which appeals to the better audience, then obviously the art which makes its appeal to everybody is eminently vulgar.Aristotle first states the popular condemnation of tragedy on the ground that it can be and often is spoilt by the stupid vulgarity of actors. So might spectators of certain productions of Shakespeare in their haste condemn the poet. The refutation of this view begins at 6.

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And indeed actors think the audience do not understand unless they put in something of their own, and so they strike all sorts of attitudes, as you see bad flute-players whirling about if they have to do the Discus, or mauling the leader of the chorus when they are playing the Scylla.Cf. Aristot. Poet. 15.8

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So tragedy is something like what the older school of actors thought of their successors, for Mynniscus used to call Callippides the monkey, because he overacted, and the same was said of Pindarus.Mynniscus acted for Aeschylus: Callippides belonged to the next generation, end of fifth century. Pindarus is unknown.

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The whole tragic art, then, is to epic poetry what these later actors were compared to their predecessors, since according to this view epic appeals to a cultivated audience which has no need of actor’s poses, while tragedy appeals to a lower class. If then it is vulgar, it must obviously be inferior.

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First of all, this is not a criticism of poetry but of acting: even in reciting a minstrel can overdo his gestures, as Sosistratus did, or in a singing competition, like Mnasitheus of Opus.Both unknown.

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Besides it is not all attitudinizing that ought to be barred any more than all dancing, but only the attitudes of inferior people. That was the objection to Callippides; and modern actors are similarly criticized for representing women who are not ladies.

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Moreover, tragedy fulfils its function even without acting, just as much as epic, and its quality can be gauged by reading aloud. So, if it is in other respects superior, this disadvantage is not necessarily inherent.

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Secondly, tragedy has all the elements of the epic—it can even use the hexameter—

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and in addition a considerable element of its own in the spectacle and the music, which make the pleasure all the more vivid;

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and this vividness can be felt whether it is read or acted.

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Another point is that it attains its end with greater economy of length. What is concentrated is always more effective than what is spread over a long period; suppose, for example, Sophocles’Oedipuswere to be turned into as many lines as there are in the Iliad .

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Again, the art of the epic has less unity, as is shown by the fact that any one epic makes several tragedies. The result is that, if the epic poet takes a single plot, either it is set forth so briefly as to seem curtailed, or if it conforms to the limit of lengthLiterally the length of the (proper) limit. it seems thin and diluted.

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In saying that epic has less unity I mean an epic made up of several separate actions.

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The Iliad has many such parts and so has the Odyssey, and each by itself has a certain magnitude. And yet the composition of these poems is as perfect as can be and each of them is—as far as an epic may be—a representation of a single action.

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If then tragedy is superior in these respects and also in fulfilling its artistic function—for tragedies and epics should produce not any form of pleasure but the pleasure we have describedi.e., the pleasure felt when by the representation of life in art “relief is given” to pity, fear, and other such emotions, or, to use a term now prevalent, when such emotions are “released.”Cf. Aristot. Poet. 14.3.—then obviously, since it attains its object better than the epic, the better of the two is tragedy.

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This must suffice for our treatment of tragedy and epic, their characteristics, their species, their constituent parts, and their number and attributes; for the causes of success and failure; and for critical problems and their solutions. . . .

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And sometimes they add that to which the term supplanted by the metaphor is relative.This may claim to be one of Aristotle’s least lucid sentences. It means this: If Old Age: Life :: Evening: Day, then we may call old age the Evening of Life. In that case old age is the term supplanted by the metaphor, and it is relative to Life; therefore Life (i.e., that to which the term supplanted by the metaphor is relative) is added to the metaphorical (or transferred) term Evening.For instance, a cup is to Dionysus what a shield is to Ares;

so he will call the cup Dionysus’s shield and the shield Ares’ cup. Or old age is to life as evening is to day; so he will call the evening day’s old-age or use Empedocles’ phraseUnknown to us.; and old age he will call the evening of life or life’s setting sun.

Sometimes there is no word for some of the terms of the analogy but the metaphor can be used all the same. For instance, to scatter seed is to sow, but there is no word for the action of the sun in scattering its fire. Yet this has to the sunshine the same relation as sowing has to the seed, and so you have the phrase sowing the god-created fire.

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Besides this another way of employing metaphor is to call a thing by the strange name and then to deny it some attribute of that name. For instance, suppose you call the shield not Ares’ cup but a “wineless cup.” . . .Or you might call Love Venus’s bloodless War. At this point a few lines on Ornament have evidently been lost, since this is its place in the catalogue of nouns above. By ornament he seems to mean an embellishing epithet or synonym. In the Rhetoric he quotes Our lady the fig-tree as a misplaced ornament. One might add the seventeenth-century use of Thames for water. . . .

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Besides this another way of employing metaphor is to call a thing by the strange name and then to deny it some attribute of that name. For instance, suppose you call the shield not Ares’ cup but a “wineless cup.” . . .Or you might call Love Venus’s bloodless War. At this point a few lines on Ornament have evidently been lost, since this is its place in the catalogue of nouns above. By ornament he seems to mean an embellishing epithet or synonym. In the Rhetoric he quotes Our lady the fig-tree as a misplaced ornament. One might add the seventeenth-century use of Thames for water.

An invented word is one not used at all by any people and coined by the poet. There seem to be such words, eg. sprouters for horns and pray-er for priest.

A word is lengthened or curtailed, the former when use is made of a longer vowel than usual or a syllable inserted, and the latter when part of the word is curtailed.

An example of a lengthened word is πόληος for πολέως and Πηληιάδεω for Πηλείδου; and of a curtailed word κρῖ and δῶ, and e.g. μία γίνεται ἀμφοτέρων ὄψ.κρῖ for κριθή, barley; δῶ for δῶμα house; ὄψ for ὄψις face, eye, or appearance.

From 58510d3efee07fa2b2bfab933eddf840d0f98c4f Mon Sep 17 00:00:00 2001 From: lcerrato Date: Mon, 13 May 2024 16:24:20 -0400 Subject: [PATCH 6/6] (grc_conversation) tlg0086 translation work #1399 --- data/tlg0086/tlg034/tlg0086.tlg034.perseus-eng2.xml | 6 ++++-- 1 file changed, 4 insertions(+), 2 deletions(-) diff --git a/data/tlg0086/tlg034/tlg0086.tlg034.perseus-eng2.xml b/data/tlg0086/tlg034/tlg0086.tlg034.perseus-eng2.xml index 2af1b7162..5fd970665 100644 --- a/data/tlg0086/tlg034/tlg0086.tlg034.perseus-eng2.xml +++ b/data/tlg0086/tlg034/tlg0086.tlg034.perseus-eng2.xml @@ -70,8 +70,10 @@ - English - Greek + English + French + Latin + Greek