8-5. The point here is: how can there be this plurality of Ones, if at the same time, as Plato says, number or plurality is generated only by the union of One with an indefinite dyad? Plurality, which is said to involve a material principle, breaks out even in the formal principle.
3. Taira modkdd, For the absence of the article cf. Xen. Az. iv. 7. 5 dAlyous TovTous avOpwrovs, Lys. 7. 10 téOvnKe Tada tpia érn, and Kihner, Grech. Gramm. § 465 Anm. 6a.
5. Trendelenburg remarks that here it is only ‘One and az indefi- nite dyad’, not ¢he indefinite dyad, that is ascribed to Plato. But this is probably unimportant. Cf, M. 1081% 14 n.
éxeivov. Aristotle has previously said of zpadro: (10g90” 32), but clearly has had Plato in his mind.
7. & Xiwvidou paxpds AMdyos. The scholiast on Eur. Phoen. 215 quotes a verse from Simonides of Amorgos :
ri radra bud paxpOv Adywy avedpap.ov ;
N, 3. 1cgo> 26 — 10918 15 483
But Aristotle seems to point to some more striking phrase or passage than this; further, he never refers by name to Simonides of Amorgos, and often to Simonides of Ceos, so that we need not doubt that the latter is meant. Alexander says that in the "Araxro. Simonides represented the sort of story that a slave will tell to cover his failure in some duty (fr, 189 Bergk.). Cf het, 141523. Perhaps the reference is to a mime like those of Sophron and Epicharmus; cf. Schneidewin in RA. Mus. vii. 460-463. We may compare Eur. /pA. in Aul. 313 paxpors de doddos dy déyers Adyovs. Antisthenes con- temptuously called definition a paxpos Aoyos (H. 1043? 25). ‘
10. The great and the small cannot (Aristotle maintains) produce any number save 2 and its powers, since it is dvoroids (M. 1082 14, 1083» 35). In order to derive other numbers the Platonists had to use (contrary to their own principles) addition as well as multiplication (M. 1084* 4).
(B) Adsurdity of ascribing generation to the numbers tf these are thought of as eternal (ch. 3. 10918 12—4. 10g1* 29).
12. It is absurd to ascribe generation to eternal things, as the Pythagoreans certainly do. They say that when the One had been put together the nearest part of the unlimited began to be drawn and limited by the limit.
18, But the discussion of these thinkers is more appropriate to physics ; we are seeking the principles of wnmovadle things.
1091° 23. They say the odd is not generated, implying that the even is, viz. from the equalization of the great and the small. These, then, must previously have been unequal, so that the account is meant to be historical, and not merely logical.
1091* 12-29. Bz. points out the connexion between this passage and 1088 14-35. — Aristotle there showed that eternal things cannot be constructed out of elements. Here he shows that the Pythagoreans and Platonists actually proposed to explain the generation of eternal things.
15-18. This is one of the comparatively few passages which throw light on the general Pythagorean cosmology. Aristotle’s suggestions as to the mode of composition of 76 & (i.e. the spatially extended first unit, M. 1080 20-21 n,) are not necessarily based on any- thing the Pythagoreans had said; they might be merely derisive con- jectures of his own, like his suggestions about the constitution of the Platonic numbers in 10g2* 21 ff. (where owépya occurs again, ib, 32). But in one respect he uses the Pythagorean terminology, for xpo.ds is doubtless used in the Pythagorean sense of ‘surface’ (De Sensu
Tia
484 Commentary
439" 30). Aristotle is here referring to the Pythagorean generation of solids by fluxion from planes, of planes from lines, and of lines from points. Again, his reference to seed probably implies that some Pythagoreans thought of the generation of numbers as akin to that of living things. For the conception of the ‘ nearest parts of the infinite ’ being ‘ drawn and limited by the limit’ (here apparently = the One) cf. Anatol. p. 30 Heib. (Diels, Vors. 112. 1) rv povaduuny diow “Eorias tporov ev péow idptoba, Philol. fr. 7 Diels 75 aparov dppoobev, 7d ev, év TO. peow. Tas opaipas éotia Kadcira, fr. 17 6 KOopos eis eoTiv, jptato Sé yiyvecOar ard Tod pécov. The ‘infinite’ is the air (Phys. 2048 31), mvedpa (213” 23), or mvon (Stob. Lvl. i, 18. 1 b = Diels 276. 43),—things not distinguished in the early period of Pythagorean- ism (cf. Anaximenes). The One is thought of as being in the centre of a shapeless mass of air or vapour and gradually introducing shape and limit into it, working from within outwards. The ‘drawing in’ is further described as ‘ breathing’, and the wind or void drawn in is said to keep the units apart (Phys. 213° 24). ‘This is’,as Prof. Burnet remarks (Z. G. P. §53), ‘a very primitive way of describing the nature of discrete quantity’. It will be observed that the Pythagoreans are trying to describe at one moment the formation of the number system and that of the physical universe, which is just what on their principles they were bound to do. The number One is identified with the central fire, as two was with the earth and seven with the sun,
15-17. &s... O07. For similar tautology cf. Znd. Ar. 538” 33-39.
19. éferdfew tu wept picews. There is much to be said for Bywater’s proposal e&erdlew év rn rept picews.
Aristotle discusses the Pythagorean cosmology in such passages as Phys. iii. 4, De Caelo ii. 2, 9, 13.
23-29. Though so far Aristotle has mentioned only the Pytha- goreans (I. 13), he now proceeds to argue that the Platonic account of the origination of things from the principles is chronological, not merely logical. For their failure to give any account of the production of odd number cf. A. 98734n. It is hard to believe that they seriously denied the derivativeness of odd numbers. Zeller supposes that it was only the first odd number (3) that they treated as ungenerated, as it is their original (zpérov) generation of even number that is referred to in 1. 243 if they assumed the number 3 without generating it, they might be said to deny the derivativeness of odd number, though they gave a derivation for odd numbers other than 3. Syrianus’ explana- tion is probably the correct one—viz. that the Platonists were speaking ‘symbolically’; ‘likening odd number to the gods, they naturally say it is ungenerated, while, taking even number as analogous to things that have matter in them, they call it generated and liken it to a dyad ; but none the less they derive the series of even and odd numbers from the same principles’; i.e. they described the odd numbers as un- generated because they likened them to the One, the principle of pure form, and the even numbers as generated because they likened them to the indefinite dyad, the principle of matter and change.
28. o6 tod Oewpioa evexev. Alexander tells us (819. 37) that Aristotle is here attacking Xenocrates’ interpretation of Plato; for this cf. De Caelo 279 32 280% 2, which the Greek commentators interpret as referring to Xenocrates. A similar interpretation of the Platonic Yoxoyovia as logical, not temporal, was offered by Xenocrates and Crantor (Plut. Az. Procr. 3. 1013).
From Procl. 7 Lucid. ed. Friedlein, p. 77. 15—78. 8, we may infer that Speusippus is also referred to.
(C) Relation between the first principles and the good (ch. 4. 10918 29—5. 1092 21).
2g. It is a difficult question whether the good and the beautiful are among the first principles or are later.
33. The cosmologists seem to agree with some moderns who treat them as later owing to the objection which confronts those who make the One a first principle; but the objection is not to the ascribing of goodness as an attribute to the principle, but to making the One actually the constituent element in things.
b4. Similarly the cosmologists say that not the first beings—Night, Ouranos, Chaos, Ocean—but Zeus rules the world ;
8. but those whose treatment is not purely mythical, such as Pherecydes and the Magi, identify the first generator and the best, as do Empedocles and Anaxagoras. Of the believers in unchangeable substances some identify the One with the good, but make oneness its essence.
16. It is strange if itis not as being good that self-sufficiency and eternality belong to the primary being; but truly they belong to it just because it is good. The first principle, then, is good.
20. But that this good principle should be the One, or an element of numbers, is impossible. Difficulties arise (to avoid which some make the One the principle of mathematical number only) :
25. (1) Each unit becomes essentially a good, and we get too many goods.
26. (2) Every Form becomes essentially a good. But if there are Forms only of goods, the Forms are not substances ; while if there are Forms also of substances, all animals, plants, &c., will be goods.
gt. (3) The contrary element will be the bad itself. One thinker avoided describing the One as good, just because it would follow that plurality was bad. Others accept the identification of the unequal with the bad.
486 Commentary
35. It follows that (a) all things partake of the bad except the One ; (8) the numbers share it in a purer form than the spatial magnitudes ; (y) the bad is the place of the good and shares and desires in that which destroys it; (8) the bad is the potentially good.
1092? 5. These conclusions follow from treating (1) every prin- ciple as an element, (2) the contraries~as principles, (3) the One as first principle, (4) the numbers as the primary substances, self-sub- sistent, and Forms.
g. If, as we have seen, it is impossible either to put or not to put the good among the first principles, evidently the account of the first principles must be wrong. It is wrong, too, to argue that because living things come from something indefinite and undeveloped, the first principles of all things must be undeveloped; the undeveloped seed comes from a fully developed parent.
17. Again, it is absurd to make place simultaneous in origin with the mathematical solids (for they are not anywhere), and to say that they must be somewhere without saying what their place is.
IOQI* 29—1092° 17. The relation of the good to the dpxai, and the views of Speusippus and the Pythagoreans about it, have already been briefly discussed in A. 1072 30 ff.
30. ebmopyjoaytt émtipnow, ‘a reproach to any one who makes light of it’.
ZI. dmopiav pév. The d¢ clause does not come till » 16.
32. otov Bouddpeba Adyew adits TS dyabdy. Cf. note at beginning of Book M.
33. mapa pev yép. The d¢ clause does not come till » 13.
34. Tdv Oeoddywv. Though Aristotle uses Geodoyixy as a Synonym for first philosophy, GeoAdyo. never means, in his works, anything but the cosmologists, such as Homer and Hesiod, as opposed to the ducukot ; cf. B. 10004 9, A. 1071» 27, 1075 26. So Geodroyia Meleor. 353% 35, Geodoyeiy A. 983” 29.
tov viv tioiv refers, as A. 1072» 31 shows, to the Pythagoreans and Speusippus.
37. Aristotle does not specify what the dvoyépeua was which Spet- sippus tried to avoid. He must mean that Speusippus, observing that Plato (who is meant by évou in 1), through treating the One as first principle and regarding it as good (cf. A. 988% 14), fell into diffi- culties (such as those which Aristotle points out passzm), tries to avoid them, not, as he should have done, by ceasing to regard the abstract One as first principle, but by ceasing to regard the first principle as good.
be, Two mistakes are here ascribed to Plato: (1) he regarded the One as a first principle, (2) he regarded it as that sort of principle which is an actual constituent element in ils product, viz.in number. A fuller
list of the mistakes involved is given in 1092°6: (1) he makes every first principle an element, (2) he treats contraries as first principles, (3) he makes the One a first principle, (4) he treats the numbers as the first substances, separately existent, and Forms. For the differ- ence between element and first principle cf. A. 1, 3, Z. 1041 31, A. 1070> 25.
4. of... womnTat of dpxator = of Geodoyor * 34.