Metaphysics

^[1]: Plat. Gorgias 448c, Plat. Gorg. 462b-c.

^[2]: Cf. Plat. Phaedrus 274, Hdt. 2.109.

^[3]: Aristot. Nic. Eth. 6.1139b 14-1141b 8.

^[4]: i.e. Metaphysics.

^[5]: Simon. Fr. 3 (Hiller).

^[6]: Cf. Solon, Fr. 26 (Hiller); Leutsch and Schneidwin, Paroemiographi, 1.371.

^[7]: i.e. the fact that the diagonal of a square cannot be rationally expressed in terms of the side.

^[8]: i.e. δευτέρον ἀμεινόνων(second thoughts are better). Leutsch and Schneidwin 1.62.

^[9]: Phys. 2.3, Phys. 2.7

^[10]: Thales of Miletus, fl. 585 B.C.

^[11]: That of the Ionian monists, who sought a single material principle of everything.

^[12]: Cf. Plat. Crat. 402b, Plat. Theaet. 152e, Plat. Theaet. 180c,d.

^[13]: cf. Hom. Il. 14. 201, Hom. Il. 14.246.

^[14]: Cf. Hom. Il. 2.755, Hom. Il. 14.271, Hom. Il.15.37.

^[15]: 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.

^[16]: The third Milesian monist; fl. circa 545 B.C.

^[17]: Diogenes of Apollonia, an eclectic philosopher roughly contemporary with Hippo.

^[18]: A Pythagorean, probably slightly junior to Heraclitus.

^[19]: Fl. about 500 B.C.

^[20]: Of Acragas; fl. 450 B.C.

^[21]: Cf. Empedocles, Fr. 17 (Diels), R.P. 166; Burnet, E.G.P. 108-109.

^[22]: 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.

^[23]: Cf. Anaxagoras Fr. 4 (Diels); and see Burnet, E.G.P. 130.

^[24]: i.e. the Eleatic school.

^[25]: Founder of the above; fl. about 475.

^[26]: i.e. in the Δόξα. Parmenides Fr. 8 (Diels); R.P. 121.

^[27]: Aristotle is probably thinking of Empedocles. Cf. Aristot. Met. 4.8.

^[28]: Anaxagoras.

^[29]: Cf. Plat. Phaedo 97b-98b.

^[30]: A semi-mythical person supposed to have been a preincarnation of Pythagoras.

^[31]: Probably Aphrodite (so Simplicius, Plutarch).

^[32]: Parmenides Fr. 13 (Diels)

^[33]: Hes. Th. 116-20. The quotation is slightly inaccurate.

^[34]: Empedocles Fr. 17, 26 (Diels); R.P. 166. Cf. Burnet, E.G.P. 108 ff.

^[35]: Aristot. Phys. 2.3, 7.

^[36]: Cf. Plat. Phaedo 98b, Plat. Laws 967b; also Aristot. Met. 7.5.

^[37]: Cf. 3.14.

^[38]: e.g. Empedocles, Fr. 62 (Diels).

^[39]: Of Miletus; fl. circa 440 (?) B.C. See Burnet, E.G.P. 171 ff.

^[40]: Of Abdera; fl. circa 420 B.C. E.G.P loc. cit.

^[41]: 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.

^[42]: i.e., of the atoms.

^[43]: Cf. R.P. 194.

^[44]: These letters will convey Aristotle’s point better to the English reader, but see critical note.

^[45]: Aristotle seems to have regarded Pythagoras as a legendary person.

^[46]: Pythagoras 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.

^[47]: Cf. Aristot. Met. 14.6ff..

^[48]: 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).

^[49]: 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.

^[50]: Or harmony. Cf. Aristot. De Caelo 2.9, and E.G.P. 152.

^[51]: Earth, sun, moon, five planets, and the sphere of the fixed stars.

^[52]: i.e. counter-earth; a planet revolving round the central fire in such a way as to be always in opposition to the earth.

^[53]: In the lost work On the Pythagoreans; but cf. Aristot. De Caelo 2.13.

^[54]: See Burnet, E.G.P 143-146.

^[55]: i.e., as a formal principle. Cf. Ross ad loc.

^[56]: 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).

^[57]: Zeller attributes the authorship of this theory to Philolaus.

^[58]: This statement is probably true, but a later addition.

^[59]: He was generally regarded as a Pythagorean.

^[60]: The section of Pythagoreans mentioned in 6, and Alcmaeon.

^[61]: 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.

^[62]: Of Samos; defeated the Athenian fleet in 441 B.C.

^[63]: Melissus Fr. 8, ll. 32-3, 42-3.

^[64]: Melissus Fr. 3.

^[65]: 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).

^[66]: Aristot. Phys. 1.3

^[67]: Cf. note on Aristot. Met. 3.13.

^[68]: The Pythagoreans; so called because Pythagoras founded his society at Croton.

^[69]: 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.

^[70]: Compare Aristot. Met. 12.4.2-5.

^[71]: Cf. Aristot. Met. 4.5.18.

^[72]: Plat. Crat. 402a (fr. 41 Bywater).

^[73]: 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.

^[74]: For this interpretation of παρὰ ταῦτα see Ross’s note ad loc.

^[75]: i.e. arithmetical numbers and geometrical figures.

^[76]: See Aristot. Met. 4.2.19-20, and cf. Aristot. Met. 8.4.4.

^[77]: ἔξω 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.

^[78]: For a similar use of the word ἐκμαγεῖον cf. Plat. Tim. 50c.

^[79]: 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.

^[80]: Plato 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.

^[81]: Cf. Plat. Phil. 25e-26b.

^[82]: Aristot. Met. 3.17; 4.3.

^[83]: Aristot. Phys. 2.3

^[84]: See note on Aristot. Met. 5.15.

^[85]: The 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.

^[86]: Cf. Aristot. Met. 3.17.

^[87]: Cf. Aristot. Met. 3.5, 8.

^[88]: Cf. Aristot. Met. 4.1.

^[89]: Cf. Aristot. Met. 7.3 n.

^[90]: Aristot. De Caelo, 3.7; Aristot. De Gen. et Corr. 2.6.

^[91]: Cf. Aristot. Met. 4.6.

^[92]: Mind, and the mixture of homoeomerous particles.

^[93]: Anaxagoras. Fr. 12 (Diels).

^[94]: Aristot. Met. 1.8.17.

^[95]: Aristotle 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.

^[96]: i.e., how can number be both reality and the cause of reality?

^[97]: 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.

^[98]: 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.

^[99]: An Idea which represents their common denominator.

^[100]: The heavenly bodies.

^[101]: Aristotle is here speaking as a Platonist. Contrast the language of Aristot. Met. 13.4.7ff., and see Introduction.

^[102]: Scientific knowledge must have a permanent object (cf. Aristot. Met. 1.4.2.

^[103]: Including artificial products; cf. Aristot. Met. 1.15.

^[104]: The fact that several particulars can have a common quality or nature implies a single Idea of which they all partake (Plat. Rep. 596a).

^[105]: 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.

^[106]: Plat. Phaedo 74a-77a, Plat. Rep. 479a-480a.

^[107]: 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.

^[108]: The Indeterminate Dyad, being to Aristotle a glorified 2, falls under the Idea of Number, which is therefore prior to it.

^[109]: This seems to be a development of the same objection. Number, which is relative, becomes prior to the supposedly self-subsistent Dyad.

^[110]: 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.

^[111]: i.e. pairs of sensible objects.

^[112]: i.e. mathematical 2s.

^[113]: 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.

^[114]: This objection, like the next, is chiefly directed against the transcendence of the Ideas. It is anticipated by Plato in Plat. Parm. 134d.

^[115]: Anaxagoras Fr. 12ad fin.

^[116]: See note on Aristot. Met. 12.8.9. Apparently he was a Platonist who regarded the Ideas as immanent in particulars.

^[117]: Plato says the Demiurgus?Plat. Tim. 28c, Plat. Tim. 29a.

^[118]: 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.

^[119]: The species will be the pattern of individuals, and the genus of the species.

^[120]: Cf. Aristot. Met. 1.10.

^[121]: Plat. Phaedo 100d.

^[122]: 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.

^[123]: 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.

^[124]: Cf. vi. 4.

^[125]: 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.

^[126]: In the Aristot. De Gen. et Corr. 320b 23Aristotle says that there is not.

^[127]: 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.

^[128]: The 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.

^[129]: 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?

^[130]: 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.

^[131]: Sc. if the point is the limit of the line.

^[132]: Cf. Aristot. Met. 7.5 and Aristot. Met. 1.9.

^[133]: Aristot. Met. 1.12.

^[134]: The final cause. Cf. Aristot. Met. 1.6.9-10.

^[135]: e.g. Speusippus, for whom see Aristot. Met. 7.2.4.

^[136]: Cf. Plat. Rep.531c-d

^[137]: Cf. iv. 10.

^[138]: The 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).

^[139]: Probably those of relative or negative terms. Cf. Aristot. Met. 1.3.

^[140]: See note on Aristot. Met. 1.23.

^[141]: e.g. Plato’s Dialectic.

^[142]: Cf. the doctrine of ἀνάμνησις (recollection), Plat. Meno 81c, Plat. Phaedo 72e.

^[143]: 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.

^[144]: 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.

^[145]: Aristot. Phys. 2.3, 7.

^[146]: 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.

^[147]: The reference is to Book 3. See Introduction.

^[148]: Leutsch and Schneidewin, Paroemiographi, 2.678.

^[149]: Of Miletus, 446 (?)—357 B.C.

^[150]: 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.

^[151]: Aristotle is evidently thinking of Empedocles’ system.

^[152]: ἐκ 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.

^[153]: 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.

^[154]: i.e. infinitely divisible.

^[155]: 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.

^[156]: 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.

^[157]: i.e. not actually, but only potentially.

^[158]: Cf. the third note above.

^[159]: 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.

^[160]: The principles and causes referred to in Book I.

^[161]: The problem is discussed Aristot. Met. 3.2.1-10, and answered Aristot. Met. 4.1.

^[162]: Discussed Aristot. Met. 3.2.10-15; answered Aristot. Met. 4.2.

^[163]: Discussed Aristot. Met. 3.2.15-17; answered Aristot. Met. 4.2.9-10, Aristot. Met. 6.1.

^[164]: 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.

^[165]: Discussed Aristot. Met. 3.2.18-19; answered Aristot. Met. 4.2.8-25.

^[166]: DiscussedAristot. Met. 3.3; answered Aristot. Met. 7.10, 12-13

^[167]: 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.

^[168]: Discussed Aristot. Met. 3.4.8-10; answered Aristot. Met. 12.4-5, Aristot. Met. 13.10.

^[169]: 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.

^[170]: Discussed Aristot. Met. 3.4.24-34; answered Aristot. Met. 7.16.3-4, Aristot. Met. 10.2.

^[171]: 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.

^[172]: Heraclitus.

^[173]: Thales.

^[174]: Anaximenes.

^[175]: Discussed Aristot. Met. 3.6.7-9; for the answer see Aristot. Met. 7.13-15, Aristot. Met. 13.10.

^[176]: Discussed 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.

^[177]: Discussed Aristot. Met. 3.5; answered Aristot. Met. 13.1-3, 6-9; Aristot. Met. 14.1-3, 5, 6.

^[178]: For another statement of the problems sketched in this chapter see Aristot. Met. 9.1, 2.

^[179]: Founder of the Cyrenaic school in the early fourth century.

^[180]: For a defense of mathematics see Aristot. Met. 13.3.10-12.

^[181]: Cf. Aristot. Met. 1.2.5-6.

^[182]: See Aristot. Met. 4.1

^[183]: sc. the science which studies the four causes.

^[184]: Cf. Aristot. Met. 3.1.5.

^[185]: sc. and so there can be no science which defines them.

^[186]: For the answer see Aristot. Met. 4.3.

^[187]: Cf. Aristot. Met. 3.1.6.

^[188]: For the answer see Aristot. Met. 4.2.9-10, Aristot. Met. 6.1.

^[189]: Cf. Aristot. Met. 3.1.8-10.

^[190]: 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.

^[191]: Aristot. Met. 1.6.

^[192]: 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.

^[193]: sc. of objects of mathematical sciences.

^[194]: 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.

^[195]: 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.

^[196]: i.e., the visible circle which we draw. Like the ruler, it is geometrically imperfect; thus they touch at more than one point.

^[197]: 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.

^[198]: Cf. Aristot. Met. 5.3.3.

^[199]: The Pythagoreans and Plato.

^[200]: i.e., each differentia must have Being and Unity predicated of it.

^[201]: The reasons are given in Aristot. Topica, 144a 36-b11.

^[202]: sc. but the species.

^[203]: For partial solutions to the problem see Aristot. Met. 7.10, 12-13.

^[204]: In Aristot. Met. 3.3.

^[205]: For answers to these questions see Aristot. Met. 7.8, 13-14; Aristot. Met. 12.6-10; Aristot. Met. 13.10.

^[206]: 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.

^[207]: Or letters of the alphabet. Cf. Aristot. Met. 1.9.36n.

^[208]: For the answer to the problem see Aristot. Met. 12.4-5, Aristot. Met. 13.10.

^[209]: The expressions the One and God refer to Empedocles’ Sphere: the universe as ordered and united by Love. Cf. Empedocles, Fr. 26-29 (Diels).

^[210]: Empedocles, Fr. 21. 9-12.

^[211]: Empedocles, Fr. 36. 7.

^[212]: Empedocles, Fr. 109.

^[213]: Cf. Aristot. Met. 1.4.6.

^[214]: i.e., of the Sphere.

^[215]: Empedocles, Fr. 30.

^[216]: i.e., whether all things have the same principles.

^[217]: For Aristotle’s views about the principles of perishable and imperishable things see Aristot. Met. 7.7-10, Aristot. Met. 12.1-7.

^[218]: By 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.

^[219]: Cf. Zeno, Fr. 2, and see Burnet, E.G.P. sects. 157 ff.

^[220]: e.g., a point is indivisible and has no magnitude, yet added to other points it increases their number.

^[221]: The reference is to the Platonists. Cf. Aristot. Met. 14.1.5, 6; Aristot. Met. 14.2.13, 14.

^[222]: For the answer to this problem see Aristot. Met. 7.16.3, 4; Aristot. Met. 10.2; and cf. Aristot. Met. 13.8.

^[223]: Apparently a proverbial expression.

^[224]: 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.

^[225]: Cf. Aristot. Met. 3.2.20ff..

^[226]: Aristot. Met. 3.4.9, 10.

^[227]: This problem is not stated in ch. 1., but is akin to problems 5. and 8., which see.

^[228]: 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.

^[229]: For the answer to this problem see Aristot. Met. 7.13-15, Aristot. Met. 13.10.

^[230]: It is uncertain to what treatise Aristotle refers; in any case it is not extant.

^[231]: See Aristot. Met. 3.1.8-10, Aristot. Met. 3.2.18, 19.

^[232]: Cf. Aristot. Met. 10.4.

^[233]: i.e., Philosophy or Metaphysics.

^[234]: The Pythagoreans.

^[235]: Perhaps Parmenides.

^[236]: The Platonists.

^[237]: Empedocles.

^[238]: For examples of Heraclitus’s paradoxes cf. Heraclitus Fr. 36, 57, 59 (Bywater); and for their meaning see Burnet, E.G.P. 80.

^[239]: sc., in logic.

^[240]: Every proof is based upon some hypothesis, to prove which another hypothesis must be assumed, and so on ad infinitum.

^[241]: i.e. the same as man.

^[242]: Aristot. Met. 4.4.12.

^[243]: i.e., that all appearances and opinions are true.

^[244]: Fr. 1 (Diels).

^[245]: i.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.

^[246]: 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?

^[247]: Aristot. Met. 4.4.27.

^[248]: If everything is both so and not so, nothing has any definite nature.

^[249]: Cf. Aristot. Met. 4.4.28.

^[250]: Cf. Aristot. Met. 1.4.9.

^[251]: Cf. Ritter and Preller, 204.

^[252]: Empedocles Fr. 106.

^[253]: Empedocles Fr. 108.

^[254]: Empedocles Fr. 16; quoted also (in a slightly different form; see critical notes) by Theophrastus, De Sensu 3.

^[255]: 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.

^[256]: Cf. Leutsch and Schneidewin, Paroemiographi Graeci, 2.677.

^[257]: Aristot. Met. 4.4.28.

^[258]: Fl. early 5th century; held views partly Pythagorean, partly Heraclitean.

^[259]: Heraclitus Fr. 41 (Bywater).

^[260]: Aristot. Met. 4.5.7.

^[261]: A concert-hall (used also for other purposes) built by Pericles. It lay to the south-east of the Acropolis.

^[262]: Plat. Theaet. 171e, 178cff..

^[263]: An 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.

^[264]: Cf. Aristot. De Anima 425b 25-426b 8.

^[265]: Aristot. Met. 4.4.2.

^[266]: Aristot. Met. 4.5.7-17.

^[267]: Cf. Aristot. Problemata 958b 14, 959a 5, 965a 36.

^[268]: 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).

^[269]: Aristot. Met. 4.7.1.

^[270]: What definition Aristotle had in mind we cannot tell; but it must have stated that every number is either even or odd.

^[271]: If 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.

^[272]: Cf. Aristot. Met. 4.4.5, 6.

^[273]: Cf. Aristot. Met. 4.3.10.

^[274]: Cf. Aristot. Met. 4.4.28.

^[275]: A stock example of impossibility and falsity; see Index.

^[276]: Aristot. Met. 4.4.5.

^[277]: The sphere of the fixed stars; cf. Aristot. Met. 12.6, 12.7.1, 12.8.18.

^[278]: Cf. Aristot. Met. 12.7.

^[279]: ἀρχή means starting-point, principle, rule or ruler.

^[280]: This was Aristotle’s own view,Aristot. De Gen. An. 738b 16.

^[281]: So Plato held,Plat. Tim. 44 d.

^[282]: As directing principles.

^[283]: sc. of material—metal, wood, etc.

^[284]: 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.

^[285]: The 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)).

^[286]: Cf. Aristot. Met. 3.3.1.

^[287]: This must refer to the highest genera, which have no definition because they cannot be analyzed into genus and differentia ( Ross).

^[288]: On the meaning of φύσις cf. Burnet, E.G.P. pp. 10-12, 363-364.

^[289]: Probably the seed (Bonitz).

^[290]: Empedocles Fr. 8 (Diels).

^[291]: Of Poros; sophist and poet, contemporary with Socrates.

^[292]: Evenus Fr. 8 (Hiller).

^[293]: Soph. El. 256 (the quotation is slightly inaccurate).

^[294]: Coriscus of Scepsis was a Platonist with whom Aristotle was probably acquainted; but the name is of course chosen quite arbitrarily.

^[295]: The categories. For the full list of these see Aristot. Categories 1b 25-27.

^[296]: Cf. Aristot. Met. 1.2.15.

^[297]: Cf. Aristot. Met. 3.5.6.

^[298]: Aristot. Met. 9.9.

^[299]: The Pythagoreans and Platonists.

^[300]: The Pythagoreans and Platonists.

^[301]: The 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).

^[302]: Strictly 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.

^[303]: Not, apparently, in his writings.

^[304]: Or capacity or potentiality.

^[305]: A square was called a δύναμις. Plat. Rep 587d; Plat. Tim. 31c.

^[306]: sc. in a passive sense, which the English word potent cannot bear.

^[307]: i.e., if there are only two.

^[308]: 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.

^[309]: 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.

^[310]: ἕξις means not only having but habit or state. Cf. Latin, habitus.

^[311]: The English equivalent for πάθος in this sense would be calamity or disaster.

^[312]: This is not a proper sense of privation, as Aristotle implies by choosing an example from everyday speech.

^[313]: 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.

^[314]: The qualification refers, I suppose, to the fact that an embryo does not naturally possess sight.

^[315]: The 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).

^[316]: Cf. Hes. Th. 517.

^[317]: e.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).

^[318]: In the sense that στοιχεῖον(letter) forms part of the definition of syllable.

^[319]: The (city) Dionysia were celebrated in March; the Thargelia (a festival in honor of Apollo and Artemis) at the end of May.

^[320]: 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.

^[321]: Wife of Deucalion, the Greek Noah.

^[322]: Here Aristotle is using the word λόγος not in the strict sense of definition but in the looser sense of a statement about something.

^[323]: The 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.

^[324]: Cf. Plat. Euthyd. 283e-284c, 286c, d.

^[325]: Plat. Hipp. Min 365-375.

^[326]: i.e. property.

^[327]: The reference is probably to the Aristot. Analytica Posteriora 75a 18, 39-41.

^[328]: Cf. Plat. Soph. 254a.

^[329]: 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.

^[330]: If Coriscus is the same as cultured Coriscus, he is the same as cultured cultured Coriscus, and soad infinitum. Cf. Soph. Elench. 173a 34.

^[331]: If 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).

^[332]: 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.

^[333]: Cf. Aristot. Met. 5.5.2.

^[334]: Aristot. Met. 5.5.3

^[335]: The period from July 3 to August 11, during which the dog-star Sirius rises and sets with the sun.

^[336]: Cf. Aristot. Met. 12.6-8.

^[337]: On the analogy of accidental events; see 2. 5.

^[338]: sc., or not as a unity but as a succession (this is separating in thought).

^[339]: i.e., the senses in which the verb to be is used to express an accidental or a true relation.

^[340]: This sentence is almost certainly a later and clumsy addition to show the connection with the following book.

^[341]: Aristot. Met. 5.7.

^[342]: The Milesians and Eleatics.

^[343]: The Pythagoreans and Empedocles.

^[344]: Anaxagoras and the Atomists.

^[345]: The Pythagoreans.

^[346]: The pre-Socratics.

^[347]: Plato’s nephew and successor as the head of the Academy.

^[348]: The followers of Xenocrates, successor to Speusippus.

^[349]: sc. 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).

^[350]: Cf. Aristot. Ethics 1129b 5.

^[351]: Aristot. Met. 7.3.1.

^[352]: Cf. Aristot. Met. 5.18.3, 4.

^[353]: 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.

^[354]: Literally cloak, but the word is chosen quite arbitrarily. Cf. Aristot. Met. 8.6.4.

^[355]: sc. to be unknowable.

^[356]: Cf. Aristot. Met. 4.2.2.

^[357]: 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.

^[358]: 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.

^[359]: 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.

^[360]: 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.

^[361]: 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).

^[362]: i.e. to avoid the infinite series implied in the last sentence.

^[363]: 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.

^[364]: e.g. fish (Aristot. Hist. An. 569a 11) and insects (Aristot. Hist. An. 539a 24).

^[365]: In Aristot. Met. 7.9.

^[366]: 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.

^[367]: 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.

^[368]: 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.

^[369]: 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.

^[370]: Stones can fall by themselves, but cannot by themselves build a house; fire can rise by itself, but cannot boil a kettle.

^[371]: e.g., health can be produced as the result of the activity set up by heat in the body.

^[372]: The questions discussed in chs. 10-12 arise out of the consideration of essence as definition.

^[373]: i.e. written on a waxed tablet.

^[374]: Which implies soul.

^[375]: Cf. Aristot. Met. 5.1.1.

^[376]: i.e., something very similar to the Platonic intermediates. Cf. Introduction.

^[377]: See Aristot. Met. 13.2, 3.

^[378]: The Pythagoreans.

^[379]: The 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.

^[380]: Cf. Aristot. Met. 1.5.17.

^[381]: A disciple of the great Socrates; one of the speakers in the PoliticusPlat. Stat. and referred to in Plat. Theaet. 147c, Plat. Soph. 218b.

^[382]: Aristot. Met. 7.10.17.

^[383]: In Books 13 and 14.

^[384]: Aristot. Met. 8.6.

^[385]: Chapters. 10-11; and cf. Aristot. Met. 7.4.

^[386]: Aristot. An. Post. 92a 29.

^[387]: The other type of definition, that which states the constituent parts of a thing, is not discussed here.

^[388]: Chs. 4-5.,10-12.

^[389]: Ch. 3.

^[390]: The Platonists.

^[391]: i.e., the argument in ch. 3 will apply to this case also.

^[392]: See note on Aristot. Met. 1.9.3.

^[393]: Cf. Aristot. De Caelo 303a 6, Aristot. De Gen. et Corr. 325a 35.

^[394]: Aristot. Met. 7.5.5-7.

^[395]: Aristot. Met. 7.15, Aristot. Met. 8.6.

^[396]: Cf. Aristot. Met. 7.8.3.

^[397]: The statement has only been implied in the preceding arguments.

^[398]: sc. in the night.

^[399]: e.g. wasps, bees, tortoises (P. Nat. 467a 18, 468a 25).

^[400]: i.e., it is only when they do not properly constitute a unity that parts can be said to exist actually.

^[401]: 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.

^[402]: i.e. universal; cf. Aristot. Met. 1.9.1.

^[403]: 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.

^[404]: Pure 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.).

^[405]: This sentence is not finished; the parenthesis which follows lasts until the end of the chapter.

^[406]: i.e. the formal cause. Cf. Aristot. Met. 5.4.4-6.

^[407]: Cf. Aristot. Met. 7.1.

^[408]: Cf. Aristot. Met. 7.2.

^[409]: Cf. Aristot. Met. 7.3-4.

^[410]: Cf. Aristot. Met. 7.13.

^[411]: Cf. Aristot. Met. 7.14.

^[412]: Cf. Aristot. Met. 7.4-6, 12, 15.

^[413]: Cf. Aristot. Met. 7.10, 11.

^[414]: Cf. Aristot. Met. 7.13, 16.

^[415]: Books 13 and 14.

^[416]: Cf. Aristot. Met. 7.8.

^[417]: In point of fact the only form which is absolutely separable is Mind or Reason. Cf. Aristot. Met. 12.7, 9.

^[418]: i.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.

^[419]: e.g., the heavenly bodies, though imperishable, can move in space (Aristot. Met. 8.4.7, Aristot. Met. 12.2.4).

^[420]: Aristot. Phys. 225a 12-20; cf. Aristot. De Gen. et Corr. 317a 17-31.

^[421]: Cf. Aristot. Met. 1.4.11.

^[422]: A celebrated Pythagorean, contemporary with Plato.

^[423]: Cf. Aristot. Met. 7.11.6.

^[424]: Cf. Plat. Theaet. 204aff.

^[425]: Cf. Aristot. Met. 7.8.

^[426]: Cf. Aristot. Met. 8.1.6. n..

^[427]: Cf. Aristot. Met. 7.8.6.

^[428]: Cf. Aristot. Met. 5.29.4.

^[429]: Aristotle 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.

^[430]: In Aristot. Categories 3b 33-4a 9 Aristotle does not allow this exception.

^[431]: i.e. from prime matter or the four elements.

^[432]: Cf. Aristot. Met. 8.1.8 n.

^[433]: Cf. Aristot. Met. 6.3.1, Aristot. Met. 7.8.3.

^[434]: Cf. Aristot. Met. 3.5.8, 9.

^[435]: i.e., we must distinguish contraries in the sense of contrary qualities from contraries in the sense of things characterized by contrary qualities.

^[436]: Aristot. Met. 7.12, Aristot. Met. 8.3.10, 11.

^[437]: Literally cloak; cf. Aristot. Met. 7.4.7 n.

^[438]: 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.

^[439]: 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.

^[440]: The highest genera, or categories.

^[441]: The Platonists.

^[442]: A sophist, disciple of Gorgias.

^[443]: Cf. sects. 4, 5.

^[444]: Aristot. Met. 7.1.

^[445]: Cf. Aristot. Met. 6.2.1.

^[446]: Chs. 6-10.

^[447]: Aristot. Met. 5.12.

^[448]: Cf. Aristot. Met. 5.12.11.

^[449]: Cf. Aristot. Met. 5.22.

^[450]: Cf. Aristot. Met. 10.4.7.

^[451]: Literally of the other, i.e. the positive term.

^[452]: The meaning of this awkward sentence is clearly shown in the latter part of 4.

^[453]: Founded by Euclides of Megara, an enthusiastic admirer of Socrates. The Megarics adopted the Eleatic system and developed it along dialectical lines.

^[454]: i.e. the form of house.

^[455]: Cf. IV. v., vi.

^[456]: i.e., we have just said that that which is incapable is deprived of its potency—in this case, of its potency for happening.

^[457]: If it is true to say that a thing which is possible will not be, anything may be possible, and nothing impossible.

^[458]: Cf. Aristot. Met. 9.8.6, 7.

^[459]: Cf. Aristot. Met. 9.2.4, 5.

^[460]: sc., if every potency must act automatically whenever agent and patient meet.

^[461]: For Aristotle’s views about infinity and void see Aristot. Physics 3.4-8, 4.6-9 respectively.

^[462]: 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.

^[463]: 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.

^[464]: Cf. Aristot. Met. 7.7.10-12.

^[465]: Aristot. Met. 5.11.

^[466]: Cf. Aristot. Met. 5.4.1.

^[467]: Aristot. Met. 7.7, 8.

^[468]: Aristot. Physics, 6.6.

^[469]: 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.

^[470]: Cf. 19.

^[471]: e.g. Empedocles; cf. Aristot. Met. 5.23.3 n.

^[472]: Cf. Aristot. De Gen. et Corr. 337a 1-7.

^[473]: Aristot. Met. 9.5.2.

^[474]: For this description of the Platonists cf. Aristot. Met. 1.6.7.

^[475]: 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.

^[476]: 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).

^[477]: The figure, construction and proof are as follows: ***

^[478]: 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.***

^[479]: This whole passage (sects. 4, 5) should be compared with Aristot. Met. 9.8.3-7, where it logically belongs.

^[480]: This appears to contradict Aristot. Met. 6.4.3. But it is just possible to interpret κυριώτατα(with Jaeger) as in the commonest sense.

^[481]: i.e. direct and accurate apprehension.

^[482]: i.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.

^[483]: Aristot. Met. 5.6.

^[484]: This description applies to the celestial spheres.

^[485]: The reference is undoubtedly to Anaximander.

^[486]: i.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.

^[487]: 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.

^[488]: 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.

^[489]: Aristot. Met. 3.4.24-27.

^[490]: Empedocles.

^[491]: Anaximenes.

^[492]: Anaximander.

^[493]: Aristot. Met. 7.13.

^[494]: Cf. Aristot. Met. 3.3.7.

^[495]: Cf. Aristot. Met. 4.2.6-8.

^[496]: Cf. Aristot. Met. 4.2.9.

^[497]: Or the same. Cf. Aristot. Met. 5.9.

^[498]: Or like. Cf. Aristot. Met. 5.9.5.

^[499]: Cf. Aristot. Met. 5.9.4.

^[500]: sc. as opposed to same in sense (a); 3 above.

^[501]: Cf. Aristot. Met. 5.9.4.

^[502]: Cf. Aristot. Met. 5.10.

^[503]: Aristot. Met. 5.28.4.

^[504]: This is not a proper example of privation. Cf. Aristot. Met. 5.22.

^[505]: Held by the Platonists. Cf. Aristot. Met. 14.1.4, 5.

^[506]: Cf. Aristot. Met. 10.3.8

^[507]: i.e., a fluid, which cannot be described as many.

^[508]: Cf. Aristot. Met. 1.3.9.

^[509]: 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.

^[510]: Aristot. Met. 5.15.8, 9.

^[511]: Cf. Aristot. Met. 10.1.19.

^[512]: This is Plato’s definition. Cf. Plat. Tim. 67d, e.

^[513]: Aristotle does not use induction to prove his point; indeed he does not prove it at all.

^[514]: In ch. 4.

^[515]: Or category.

^[516]: i.e., indivisible species and individuals.

^[517]: Cf. Aristot. Met. 5.28.1.

^[518]: 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.

^[519]: 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).

^[520]: Aristot. Met. 1.3-10.

^[521]: Cf. Aristot. Met. 3.1.5, Aristot. Met. 3.2.1-10.

^[522]: Cf. Aristot. Met. 3.1.5,, Aristot. Met. 3.2.10-15, where the problem takes a slightly different form.

^[523]: Cf. Aristot. Met. 3.1.6, Aristot. Met. 3.2.15-17.

^[524]: Cf. Aristot. Met. 3.1.8-10, Aristot. Met. 3.2.18-19.

^[525]: Aristot. Physics 2.3.

^[526]: Cf. Aristot. Met. 3.1.7, Aristot. Met.3.2.20-30.

^[527]: This phrase has no technical sense here; cf. Aristot. Met. 1.9.4.

^[528]: i.e., intelligible matter (cf. Aristot. Met. 7.10.18). This problem is not raised in Book 3.

^[529]: Cf. Aristot. Met. 3.1.10, Aristot. Met. 3.3.

^[530]: Cf. Aristot. Met. 3.1.11, Aristot. Met. 3.4.1-8.

^[531]: Aristot. Met. 11.1.11-13

^[532]: Forms 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).

^[533]: Cf. Aristot. Met. 3.1.12, Aristot. Met. 3.4.11-23.

^[534]: Cf. Aristot. Met. 3.1.13, Aristot. Met. 3.4.24-34.

^[535]: i.e., intelligible surfaces, etc.

^[536]: Cf. Aristot. Met. 3.1.15, Aristot. Met. 3.5.

^[537]: sc. which is liable to generation or destruction.

^[538]: Cf. Aristot. Met. 3.1.14, Aristot. Met. 3.6.7-9.

^[539]: This section belongs to the problem discussed in 1-5 above.

^[540]: Cf. Aristot. Met. 3.1.12, Aristot. Met. 3.4.8-10.

^[541]: This chapter corresponds to Aristot. Met. 4.1, 2, with which it should be compared.

^[542]: Cf. Aristot. Met. 4.2.9 n.

^[543]: i.e., identity, otherness, etc.

^[544]: Aristot. Met. 11.1.1.

^[545]: Also the problem stated in ch. i. 3.

^[546]: This chapter corresponds to Aristot. Met. 4.3.1-6, and answers the problem stated in Aristot. Met. 11.1.2.

^[547]: This chapter corresponds to Aristot. Met. 4.3.7-4.31.

^[548]: sect. 6=Aristot. Met. 4.4.14-16.

^[549]: With this section cf. Aristot. Met. 4.4.26-30.

^[550]: sect. 8=Aristot. Met. 4.3.10.

^[551]: sect. 9-11=Aristot. Met. 4.4.31.

^[552]: Cf. Aristot. Met. 4.8.4, 5.

^[553]: This chapter forms a summary of Aristot. Met. 4.5-8. sect. 1-3=Aristot. Met. 4.5.1-5.

^[554]: With sect. 4, 5 cf. Aristot. Met. 4.5.6.

^[555]: Aristot. Physics 1.7-9.

^[556]: sect. 5-7=Aristot. Met. 4.5.23-27.

^[557]: i.e., that the same thing has contrary qualities.

^[558]: sect. 8, 9 (first half)=Aristot. Met. 4.5.21, 22.

^[559]: Cf. Aristot. Met. 4.5.20, 21.

^[560]: Cf. Aristot. Met. 4.4.39-42.

^[561]: With this section cf. Aristot. Met. 4.5.7-14.

^[562]: With this section cf. Aristot. Met. 4.5.3, 4, Aristot. Met. 4.6.1-3.

^[563]: Cf. Aristot. Met. 4.6.10, 11.

^[564]: Cf. Aristot. Met. 4.7 where, however, the point which is proved is that there can be no intermediate between contradictories.

^[565]: Cf. Aristot. Met. 11.5.8

^[566]: Cf. Aristot. Met. 4.7.8-8.5

^[567]: Anaxagoras. What he really meant was that even the sweetest things contain some bitter particles. Cf. Anaxagoras Fr. 11 (Diels); Burnet, E.G.P. 129.

^[568]: This 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.

^[569]: Aristot. Met. 12.6, 7.

^[570]: Sections 1-9 of this chapter correspond to Aristot. Met. 6.2-4.

^[571]: This 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).

^[572]: Plat. Sop. 254a.

^[573]: Cf. Aristot. Met. 6.2.6.

^[574]: This section is taken from Aristot. Physics 2.5, 6.

^[575]: 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).

^[576]: The discussion of motion in this chapter consists of extracts from Aristot. Physics 3.1-3.

^[577]: i.e., change is substantial (generation and destruction); quantitative (increase and decrease); qualitative (alteration); spatial (locomotion). Cf. Aristot. Met. 11.12.1, 2.

^[578]: This is inaccurate; see previous note.

^[579]: 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.

^[580]: Pythagoreans and Platonists. Cf. Aristot. Met. 1.5.6, Plat. Soph. 256d.

^[581]: 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.

^[582]: Cf. note on sect. 2 (end) above, and Aristot. Met. 9.6.7-10.

^[583]: This chapter consists of extracts from Aristot. Physics 3.4, 5, 7.

^[584]: The Pythagorean and Platonic view.

^[585]: Aristotle has argued that they do not in Aristot. Met. 1.9.16-25.

^[586]: According to Anaximenes; cf. Theophrastus, Phys. Opin. Fr. 2 (Ritter and Preller 26).

^[587]: According to the Pythagoreans. Cf. Aristot. Met. 1.5.5. n

^[588]: This is proved in Aristot. Physics 1.6.

^[589]: sc. and so no other body can exist beside it.

^[590]: Anaximander. 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.

^[591]: Cf. Hereclitus Fr. 20-22 (Bywater).

^[592]: 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.

^[593]: 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.

^[594]: Ross 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.

^[595]: 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.

^[596]: sc. 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

^[597]: sc. in kind or number.

^[598]: Cf. sect. 6 n.

^[599]: Cf. sect. 14 n.

^[600]: i.e., above and below, before and behind, right and left (Aristot. Phys. 205b 31).

^[601]: Cf. Aristot. Met. 5.13.5.

^[602]: 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.

^[603]: i.e., falsity. Cf. Aristot. Met. 9.10.1.

^[604]: sect. 3.

^[605]: 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.

^[606]: There 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.

^[607]: sc. contradictories.

^[608]: sc. contraries.

^[609]: sc. which is absurd.

^[610]: 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.

^[611]: Cf. Aristot. Met. 5.14.

^[612]: i.e., when they occupy one place to the exclusion of anything else. Cf. Aristot. Phys. 209a 33-b 1.

^[613]: 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.

^[614]: I have followed Prantl’s suggestion in transferring this sentence from the end of sect. 13.

^[615]: i.e., the first day of the month.

^[616]: Cf. Aristot. Met. 12.10.14, Aristot. Met. 14.3.9.

^[617]: Platonists.

^[618]: i.e., the celestial bodies.

^[619]: 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.

^[620]: Cf. Aristot. Met. 10.7.

^[621]: i.e., contrary qualities. Cf. Aristot. Met. 8.5.1.

^[622]: Anaxagoras Fr. 1 (Diels).

^[623]: 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.

^[624]: Cf. Aristot. Met. 12.1.3, Aristot. Met. 8.1.7, 8.

^[625]: (1) the negation of a category, (2) falsity, (3) unrealized potentiality. Cf. Aristot. Met. 14.2.10.

^[626]: This classification is found in Aristot. Physics 1.6, 7, but is foreign to the main treatise of the Metaphysics. See Introduction.

^[627]: See Introduction.

^[628]: In 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.

^[629]: Cf. Aristot. Met. 11.8.12 n.

^[630]: Aristotle 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.

^[631]: i.e., form.

^[632]: i.e., in the mind of the architect or doctor.

^[633]: See Introduction.

^[634]: Unity and Being are called intelligibles as being the most universal predicates and as contrasted with particulars, which are sensible.

^[635]: This apparently refers to the elements; fire and air are hot matter, water and earth cold matter.

^[636]: 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.

^[637]: See Introduction.

^[638]: Aristotle is thinking of animals and human beings, which are substances in the truest sense.

^[639]: i.e., of acquiring either of the contrary qualities distinguished by the form and the privation

^[640]: 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.

^[641]: i.e., the proximate efficient cause and proximate matter.

^[642]: Aristot. Met. 12.4.6.

^[643]: i.e., the prime mover.

^[644]: i.e., individual forms and privations of individual things.

^[645]: Aristot. Met. 12.1.3, 4.

^[646]: Cf. Aristot. Physics 8.1-3

^[647]: 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.

^[648]: Cf. Aristot. Met. 11.12.1 n.

^[649]: These statements are proved inAristot. Physics 8.8, 9.

^[650]: As there is not, according to Aristotle; cf. Aristot. Met. 1.7.4.

^[651]: Aristotle 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.

^[652]: Cf. Hes. WD 17, Hes. Th. 116ff.

^[653]: Cf. Aristot. Met. 12.2.3.

^[654]: Cf. Aristot. Met. 1.4.12, Aristot. De Caelo 300b 8, and see Burnet, E.G.P. 178.

^[655]: Cf. Plat. Tim. 30a, and sect. 8 below.

^[656]: Aristotle refers to Plato’s rather inconsistent account in Plat. Tim. 30-34.

^[657]: The reference is probably to 5 above, but cf. Aristot. Met. 9.8.

^[658]: The sphere of the fixed stars, Aristot. Met. 12.8.9; cf. Aristot. De Gen. et Corr. 336a 23ff.

^[659]: The 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.

^[660]: Aristot. Met. 12.6.6

^[661]: Aristot. Met. 12.2.2, 3.

^[662]: This shows that desire in general (of which appetite and will are the irrational and rational aspects) has as its object the good.

^[663]: Aristotle 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.

^[664]: Cf Aristot. Met. 5.6.17.

^[665]: Proved in Aristot. Physics 8.7.

^[666]: Aristot. Physics 8.9

^[667]: 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.

^[668]: Cf. Aristot. Met. 5.5

^[669]: For the relation of pleasure to actuality or activity see Aristot. Nic. Eth. 10.4.

^[670]: 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.

^[671]: In actualization the subject and object of thought (like those of perception, Aristot. De Anima 3.2.) are identical.

^[672]: The view is referred to again in Aristot. Met. 12.10.6, Aristot. Met. 14.4.2, 3, Aristot. Met. 14.5.1.

^[673]: Cf. Aristot. Met. 9.8.4, 5.

^[674]: Cf.Aristot. Physics 266a24-b6.

^[675]: Cf. Aristot. Met. 13.8.17, 20. This was a Pythagorean survival, cf. Vol. I. Introduction. xvi.

^[676]: i.e., the (apparent) diurnal revolution of the heavens.

^[677]: Aristot. Physics 8.8, 9, Aristot. De Caelo 1.2, 2.3-8.

^[678]: Aristot. Met. 12.7.12, 13.

^[679]: Of Cnidus (circa 408 -355 B.C.). He was a pupil of Plato, and a distinguished mathematician.

^[680]: For a full discussion of the theories of Eudoxus and Callipus see Dreyer, Planetary Systems 87-114; Heath,Aristarchus of Samos190-224.

^[681]: Not identical with that of the fixed stars, but having the same motion.

^[682]: i.e., revolves with its equator in the ecliptic.

^[683]: i.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.

^[684]: Not the same, but having the same motion.

^[685]: of 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.

^[686]: Aristotle is trying to establish a mechanical relation between the spheres, which Eudoxus and Callipus did not attempt to do.

^[687]: The moon.

^[688]: In sect. 11.

^[689]: 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.

^[690]: i.e., the movers of the spheres.

^[691]: See previous note.

^[692]: 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.

^[693]: The 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.

^[694]: 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.

^[695]: Cf. Aristot. Met. 2.3.1.

^[696]: e.g. the Egyptian deities. Zoomorphism in Greek religion is a doubtful quantity.

^[697]: 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.

^[698]: Cf. Aristot. Met. 9.8.18.

^[699]: If Mind is a potentiality, since a potentiality is of contraries, Mind may think that which is worst.

^[700]: i.e., beings composed of matter as well as form. Such beings are contrasted with the divine Mind, which is pure form.

^[701]: The 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.

^[702]: 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).

^[703]: Because there is an eternal substance, which is not derived from contraries (Aristot. Met. 12.6.1).

^[704]: Things are derived from a substrate as well (Aristot. Met. 12.2.1).

^[705]: See on Aristot. Met. 14.1.4.

^[706]: The Bad was identified with the unequal; cf. Aristot. Met. 1.6.10.

^[707]: See Aristot. Met. 12.7.10

^[708]: Cf. Aristot. Met. 1.4.3.

^[709]: Empedocles Fr. 17 (Diels), 18-20.

^[710]: Cf. Aristot. Met. 9.9.3.

^[711]: Motion presupposes a final cause, which was not what Anaxagoras meant by Mind. Cf. Aristot. Met. 1.7.5.

^[712]: Aristotle identifies the efficient cause, in a sense, with the final cause. Cf. Aristot. Met. 7.9.3.

^[713]: 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).

^[714]: Cf. Aristot. Met. 3.4.11-20.

^[715]: Cf. Aristot. Met. 12.2.2, 3.

^[716]: The Eleatics. Cf. Aristot. Met. 1.5.10-13.

^[717]: i.e., an efficient cause.

^[718]: 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.

^[719]: By assuming an eternal actual mover (Aristot. Met. 12.6.4).

^[720]: Cf.Aristot. Met. 8.6.

^[721]: Speusippus and his followers; cf. Aristot. Met. 7.2.4, Aristot. Met. 14.3.8.

^[722]: Hom. Il.2.204.

^[723]: The reference is presumably to Aristot. Physics 1.

^[724]: In Books 7-9.

^[725]: This was the orthodox Platonist view; cf. Aristot. Met. 1.6.4.

^[726]: Xenocrates and his followers.

^[727]: The Pythagoreans and Speusippus.

^[728]: Cf. Aristot. Met. 3.2.23-30.

^[729]: Aristot. Met. 3.2.23-27.

^[730]: i.e., in the natural order of development. Thus generation (γένεσις) is used in two different senses in this argument, which therefore becomes invalid (Bonitz).

^[731]: sect. 1-3 above.

^[732]: Aristot. Met. 12.7.6.

^[733]: Optics studies lines and harmonics numbers because these sciences are subordinate to geometry and arithmetic (Aristot. An. Post. 75b 15).

^[734]: Cf. Aristot. Met. 14.2.9, 10.

^[735]: i.e., potentially.

^[736]: Cf. Aristot. Met. 3.2.4.

^[737]: There is no obvious fulfilment of this promise.

^[738]: It 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.

^[739]: Cf. Aristot. Phys. 194a 20, Aristot. De Part. Anim. 642a 24.

^[740]: Cf. Aristot. Met. 1.5.2, 16.

^[741]: This 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.

^[742]: Cf. Introduction.

^[743]: With sect. 6-13 cf. Aristot. Met. 1.9.1-8, which are almost verbally the same. See Introduction.

^[744]: sect. 14, 15 have no counterpart in Book 1.

^[745]: 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.

^[746]: sc. in the definition or essence of Ideal man.

^[747]: i.e., being an idea will be a characteristic common to all ideas, and so must be itself an Idea.

^[748]: This chapter corresponds almost verbally to Aristot. Met. 1.9.9-15. Cf. note on Aristot. Met. 13.4.6.

^[749]: Plat. Phaedo 100d.

^[750]: This 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.

^[751]: The units.

^[752]: i.e., Ideal or natural.

^[753]: In Aristot. Met. 13.2.1-3.

^[754]: The Pythagorean number-atomist view; See Introduction.

^[755]: i.e., either all numbers are material elements of things, or some are and others are not.

^[756]: Cf. sect. 2.

^[757]: Cf. Aristot. Met. 1.6.4.

^[758]: Cf. Aristot. Met. 12.10.14.

^[759]: Cf. Aristot. Met. 13.8.9, 10, Aristot. Met. 14.3.15, Aristot. Met. 14.5.7, and see Introduction.

^[760]: Cf. 10ff., Aristot. Met. 13.1.4.

^[761]: Plato.

^[762]: i.e., the (semi-)Ideal lines, planes, etc. Cf. Aristot. Met. 1.9.30.

^[763]: Speusippus; cf. sect. 7 above.

^[764]: Xenocrates. For his belief in indivisible lines see Ritter and Preller 362. Aristotle ascribes the doctrine to Plato in Aristot. Met. 1.9.25.

^[765]: sect. 8.

^[766]: sc. the view of Xenocrates (cf. Aristot. Met. 13.8.8).

^[767]: Aristot. Met. 13.6.2, 3.

^[768]: 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.

^[769]: The Platonists.

^[770]: 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.

^[771]: i.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.

^[772]: This is a necessary implication of the theory of inaddible units (cf. Aristot. Met. 13.6.1, 2).

^[773]: 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).

^[774]: This is a corollary to the previous argument, and depends upon an identification of ones (including the Ideal One or Unity) with units.

^[775]: i.e., the Ideal One.

^[776]: This is of course not true of the natural numbers.

^[777]: i.e., 3 is produced by adding 1 to 2.

^[778]: Cf. sect. 18.

^[779]: 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.

^[780]: i.e., if numbers are not generated by addition, there must be Ideal (or natural) numbers.

^[781]: 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.

^[782]: i.e., it is only reasonable to suppose that other 5’s might be made up out of different combinations of the units.

^[783]: Cf. Introduction.

^[784]: In each case the other factor is the indeterminate dyad (cf. sect. 18).

^[785]: Which conflicts with the view under discussion.

^[786]: The implication seems to be, as Ross says, that the Platonists will refuse to admit that there is a number between 2 and 3.

^[787]: i.e., if numbers are specifically different. Cf. Aristot. Met. 13.6.1.

^[788]: sect. 2-4 above.

^[789]: i.e., the biggest number.

^[790]: 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.

^[791]: 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.

^[792]: Cf. Aristot. Met. 13.1.4.

^[793]: i.e., Speusippus recognized unity or the One as a formal principle, but admitted no other ideal numbers. Aristotle argues that this is inconsistent.

^[794]: Aristot. Met. 13.7.1-8.3.

^[795]: Cf. Aristot. Met. 13.6.7.

^[796]: See Introduction.

^[797]: This is proved in Aristot. De Gen. et. Corr. 315b 24-317a 17.

^[798]: See Introduction.

^[799]: Cf. Aristot. Met. 13.7.5 n. Aristotle is obviously referring to the two units in the Ideal 2.

^[800]: Cf. DieIs, Vorsokratiker 270. 18.

^[801]: Aristot. Met. 13.7.18.

^[802]: 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.

^[803]: i.e., as implying an actual infinite.

^[804]: i.e., as inconsistent with the conception of an Idea as a determining principle.

^[805]: Cf. Aristot. Met. 12.8.2. The Platonists derived this view from the Pythagoreans; see Introduction.

^[806]: Robin 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).

^[807]: Cf. Aristot. Met. 13.4.7, 8; Aristot. Met. 1.9.2, 3.

^[808]: 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.

^[809]: 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.

^[810]: 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.

^[811]: Cf. Aristot. Met. 7.10, 11.

^[812]: Aristotle 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.

^[813]: Perhaps the Atomists; but cf. Aristot. Met. 1.8.3, 4.

^[814]: If 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.

^[815]: Cf. Aristot. Met. 13.7.5.

^[816]: Cf. Aristot. Met. 13.6.10.

^[817]: Cf. Aristot. Met. 3.4.34, Aristot. Met. 14.3.9.

^[818]: The reference is probably to Speusippus; Plato and Xenocrates did not believe in points (Aristot. Met. 1.9.25, Aristot. Met. 13.5.10 n).

^[819]: Aristotle again identifies the indeterminate dyad with the number 2.

^[820]: sc. of the elements of number.

^[821]: sc. but from an indivisible part of plurality—which is not a plurality but a unity.

^[822]: i.e., to say that number is derived from plurality is to say that number is derived from number—which explains nothing.

^[823]: sc. which plurality has been shown to be.