gz. A ‘this’ and a quantity are not the same, but the Platonists do not tell us how existing things in general are many, but how there are many quantities; for every number indicates a quantity and so does the unit. On the other hand, if a ‘this’ and a quantity are treated as the same, many contradictions follow.
470 Commentary
1087? 29. Tis odctas TaUTys, i.e. the dxivytos otcia which has been the subject of Book M (cf. 1076211), Aristotle has already at 1086 21 passed from the discussion of the Idea-numbers, which were the axivyntos ovata that the Platonists believed in, to the discussion of the first principles of the Idea-numbers, so that the transition now made is really not from the dxivyros otcia to its ‘principles but from one question about the principles to another. ‘This difficulty is correctly stated by Bz., but his proposal for its solution, the reading of dzopias for obaias, does not commend itself; Alexander read otcéas and inter- preted it as we have done. We have already seen (10868 21 n.) that there was an early divergence in the manuscripts as to where N should begin. It might be suggested that the original beginning was at 1086 21 (or 18), and that the present clause or the whole sentence was added by an early copyist who divided the books at this point and felt the lack of a formal introduction. But it seems more probable that 1086418 and 1087229 were two alternative transitions, both written by Aristotle, to the question of the principles of Idea-numbers, or in other words that 1086? 18—1087 25 is a fragment which does not really belong to the main structure of MN but was introduced by an early editor as dealing with the same subject.
In any case the distinction between M and N as dealing, the one with dxivnros ovata, the other with its first principles, is not well maintained ; we hear a good deal in M of the One and the indefinite dyad.
br. 1000’, i. €. dzroKeipevov TL
3. For the Méyos cf. Cas, 3> 24-27.
4. GN Erépa, i.e. GAN’ 4 apyn érépa.
ol 8€ krA. Aristotle proceeds to show (ll. 4-12) that the Platonists fall into the error (exposed in ® 36-» 4) of making contraries the first principles.
5. ot pév = (1, 9) 6 70 dvicoy Kai €v A€ywv. Plato is no doubt meant, since in M. 1081824 we have «lite domep 6 mpOrtos cimov e€ dviowr. Cf. Al. 796. 23.
6. ot 8€= (1. 8) 7G 8. The expression 7A9O0s seems to belong to Speusippus, cf. Z. 1028 21 n., M. 10859 n. In the light of the evi- dence there cited, we may ignore Alexander’s statement that it is the Pythagoreans (796. 32) or Pythagoras himself (ib. 34) that Aristotle is referring to. Xenocrates may possibly also have used the expression in this context (Plut. De An. Procr. ii. 1,2, 1012 Dk, cf, Aet. i. 3. 23).
12. Alexander reads dpv6ud Adyw & ov, and apparently takes the words to mean that the unequal, though in point of fact the same thing as the great and the small, has a different definition. But it seems more probable that the manuscript reading is right, and that
the meaning is: Plato treats the unequal (or the great and the small) as one and does not draw the distinction that though definable by a single definition it contains within itself a plurality, sc. the great and the small. This has more point in the context. Obviously contraries go in pairs, and Aristotle is confirming his statement that the Platonists make their first principles contraries by showing that for Plato the One and the-great-and-the-small are but /wo things. Aristotle himself in accordance with his usual misinterpretation of the great and small (cf. M. 108323 n.) insists on treating them as ¢hree (I. 14). This interpretation is rendered certain by comparison with 1088? r5.
12-13. GANG pv... daodiddacw: i. e., apart from the general error of making contraries the first principles, the Platonists describe the first principles or elements badly.
16, ot S€ 73 woAd Kai éXiyov. These thinkers are distinguished from those who posited the great and small, and, Plato being the chief of the latter thinkers (the doctrine is ascribed to him by name in A. 987» 20, 26, 988413, 26, Phys. 187217, 203215, 209? 35), the former must be disciples who modified the expression for the reason here assigned, viz. that the great and small was more fitted to serve as the principle of spatial magnitudes than of numbers. The other passages where the ‘many and few’ are referred to are 1088° 18, 1089? 12, A. 992° 16.
17-18. ot S¢. . . Td brepexov kai Td Gepexduevoy. Sext. Emp. p. 531 Bekker treats these as essential terms of the Pythagorean division of concepts, and Robin (p. 659) suggests that it may be ‘acousmatic’ Pythagoreans of the school of Hippasus that Aristotle has in mind; but the evidence is too vague to warrant any certain conclusion,
20, 21. Noyids appears to take two somewhat different shades of meaning according as it is used with dvoxepeias or with dzodeiéets. In the former case it means, as in I, 1005? 22 Aoyixads duoyepetas, LL. 1221>% tas cuxopartias Tas AoyiKds, very much what we mean by ‘quibbling’ (almost = coduotixal evoyAjoes De Int. 17*36). We may connect this with the definition of a NoyiKds Adyos as ek Wevdar, evddgwv d¢ (Top. 162 27). With dzodeiées the meaning seems rather to be ‘abstract’, cf. G. A. 747° 28 A€yw Aoyixiy (drdderEw) 81a TotTO, dre dow Kaborov paAAov, Toppwrépw TY oikeiwy éoTiv apxav.
24. Apelt’s proposal of xad for éx rests on the supposition that r7s dvados means the indefinite dyad, not, as it evidently does (cf. Al. 798. 14), the ideal Two. Cf. A. ggo? 20.
26. of 8... dvtiTOdacw. Alexander (798. 23) refers this view to ‘ other Pythagoreans ’(cf. 1. 6 n.),and with this we may compare Damasc. De Princ. c. 306 = Arist. fr. 15144 24 “ApiotoréAys O€ év Tots Apxutelois iotopel kat UvOaryopav “ dAdo” rv VAnv Kadciv. The latter statement is most improbable, since Aristotle in his preserved works never refers to the views of Pythagoras. But he may well have ascribed the view to certain Pythagoreans, and there may easily have been late Pytha- goreans, influenced by Platonism, who adopted such a view. Cf. Robin, pp. 650, 660.
27. ot dé wAAQos, cf. 1. 6 n.
472 Commentary
30. atr@. Alexander read avT@ (798. 34), and evidently takes erepov to be opposed td Tabr6, ‘the same’, and aro to aro, ‘the thing itself’, But in I. 105415 76 dAdo is opposed to ro Tair, and there is no trace in Aristotle of such a distinction between érepoy and dAdo; the two words are synonymous. Presumably one of the thinkers he is criticizing used the words 76 erepov and 70-rairo, another the words 70 aAXo and tavro.
BI. 8d€ns, i. e. riPavorntos, says Alexander. twos doéys is ‘something that can really be called an opinion’. Cf. the use of &dogos.
33. To 8 ev dtu pérpov onpatver. This is the strictest sense of ‘one’, I. 1052) 18, 1053 4
34. Tt €repov droxeiwevoy, something, different in each genus, which is the subject to which ‘one’ belongs as an attribute.
35. Sieots. Cf A. 1016” 22 n.
36. Bdows means the dipody—cf. schol. in Heph. p. 124 ed. West- phal Baous 8€ ear 70 éx S00 TodGV GrVETTHKOS, TOD ev Apoer TOD Oe Herer mrapadapBavopevov ; ib. p. 151 dexerae de (the iambic metre) év pev tH mpaitn Bdaoe tapBov kal o7rovociov.
1088?.2-3. 1d pev...ate®jow. Alexander explains (799. 21) that the finger is indivisible in efSos because it is not divided into fingers but into half-fingers, which are different in eidos from the finger; while the dieous is indivisible xara rHv alcOynow because it is the smallest sound— he means of course the smallest interval. This account of ‘indivisible in efSos’ is not a natural one, and does not agree with Aristotelian usage. In Aristotle the phrase seems to apply (1) to infimae species (B. 999? 3)3 (2) both to genera and to species, in virtue of the core of identity in each (A. 1016419; Aristotle says there dv advalperov 76 eloos Kata THY alobyow, So that Kad. TO eidos and Kara THY atoOnow is a distinction not always maintained); this seems to be the meaning also in I. 10522313 (3) to that which cannot be divided into parts different in kind from the whole (A. 1014# 27—this contrasts strongly with the meaning Alexander assigns)—i.e. to elements. In I. 1 the indivisible in quantity is opposed first to the indivisible in quality (1052” 35) and then to the indivisible in eidos (1053% 20, cf. De An. 430» 14), and the indivisible in «idos is evidently meant to be the same as the indivisible in quality. Further, xara ryv aicOyow, mpos THY ata O@yow is used in describing the indivisible in quantity (1053" 5, 23)- Evidently, then, 76 pev kata 76 €idos refers to év pev Tois qoLots TOLOY TL, and 76 dé mpos tiv aicOyow to ev dé Tots Toots tocov 7 (1. 1). The latter refers to quantitative units such as have been mentioned in 1087 34-37; the former to species and genera, which have con- ceptual unity (dv 4 vonows pia I, 1052430); of these, instances are given in ll, 9-14.
5. kat 6 dpwOyds ote mAHRGos pepetpnpevoy Kat APs pétpwr, cf. A.'1020*'13'n., Z. 10397 12 0.
6-8. 86...é. Sir T. Heath thinks (@%. Aath. i. 69) that this doctrine may be of Pythagorean origin. It appears in Nicom. J/nérod. Arithm, ii. 6. 3, 7. 3, and is implied by Euclid (£7. vii, Defs. 1, 2).
Q. ei immo. . . . dvOpwwos. Lines ro, 11 indicate that the ei clause should relate not to the measure but to the things measured, so that Bz.’s conjecture (which is confirmed to some extent by Alexander) seems necessary. Bywater’s proposal to excise 76 jérpov in |. 8 (J. of #. Xxxii, 111) does not meet the whole difficulty.
15-16, oi S€... prxpod, This is one of the passages which indicate that Plato used the phrase ‘indefinite dyad’, for 76 dviwov and 76 péeya kal puxpov are phrases characteristic of his doctrine. For similar passages cf. rogo> 32—109145, M. 1083” 23-36, and see Robin, Pp. 643-653.
15. Thy Sudda de. dé has its usual adversative force. The first clause states the unity of the dvicov, the second its twofold nature (cf. 1087” 9- 12), Thus Trendelenburg’s proposal to omit d¢ is unnecessary.
23. tav katnyopioy is loosely epexegetic of révtwv. The descrip- tion of relation as the least substantial of the categories is unique in Aristotle, but cf. 2. 1V. 1096? 21.
25. With et 7 €repoy there is no difficulty in supplying vAy éoriv.
29-35. There is no distinct kind of change which can be called change in respect of relation, as there is change in respect of substance, quality, quantity, and place. Change in respect of a relation is always due to change, in one of these other respects, of one of the relata. A thing may change in respect of a relation when z¢ does not change at all, but its correlative changes. This indicates, Aristotle observes, that relation is a superficial category. The statement that relation is the only category which has not a specific kind of change answering to it implies a list of categories including only substance, quality, quantity, place, relation. This precise list is not found else- where. But Aristotle probably has in mind a list of eight categories without kxetoOa. and éyew (which occur only in Cat, 1527, Top. 103 23), and omits wovy and wacyew as being practically equivalent to xivnors itself (cf. Phys, 22513 = K. 10684 14), and zoré because, while time is involved in-change, there is obviously no change which is merely in respect of time.
There is an excellent conspectus of the forms in which the list of categories appears in Aristotle, in Apelt, Beir. 2. Gesch. d. Gr. Phil. pp. 140, 141.
The subsidiary character of relation is nowhere stated in the Categories; this distinction between it and the other categories belongs more properly to metaphysics than to logic.
b6. kat Xwpls kal Gua, e.g. two is merely few, the largest number is merely many, but three is many relatively to two, few relatively to the other numbers.
8-11, «i S¢ 8)... pupa. The sentence is very difficult. Various solutions of the difficulty may be proposed: (1) The manuscript read-