Much light has been thrown on the date of Bks. M and N relatively to one another and to the rest. of the MJefaphysics, by Jaeger’s researches in his Arzsto/eles, pp. 181-199, 212-215. BookM, with its clear distinction between the doctrines of Plato, Speusippus, and Xenocrates, belongs to a later period than the criticism of the ideal theory in Book A. The original ideal theory is now for Aristotle somewhat out of date, and he is content to reproduce in chs. 4, 5 what he has said about it in A. 9; his efforts are now turned towards the discussion of mathematical and ideal numbers and magnitudes. The discussion is completed by 10862 15, and he ends, as he does occa- sionally elsewhere (Jaeger refers to the end of A and of £. J. ix), with a literary quotation (1086417). The final sentence (ib. 18-21) is difficult to construe, and perhaps its last words are missing, as might easily happen at the end of a book. Syrianus tells us that some manuscripts made M end at this point.
In M. 1086 21-32 we have a preface which Jaeger (187-189) has shown to be a doublet of that at the beginning of M (1076* 8-32). The latter is much the more elaborate. It mentions, besides Ideas and numbers, the spatial magnitudes (I. 18); it distinguishes the views of Plato, Speusippus, and Xenocrates (ll. 19-22). It treats the dis- cussion of the original ideal theory as a minor matter, sufficiently discussed in the ééwrepuxot Adyou (Il. 26-29).
In trying to find a date for the section M. 10864 21-end, Jaeger concentrates on 1086? 16-19. It is not clear that he is right in supposing that when Aristotle says BovAdwefa he must mean, as in A. 990” 9, 11, 16, 18, 23, 991» 7, B. 997? 3, 1002» 14, ‘we Platonists ’. But it is at any rate possible to interpret the passage as an argumenium ad hominem directed against Platonists from a Platonic standpoint.
What is more convincing is that, while in 1086% 21-24 Aristotle says of the views of the materialists merely that they have been discussed in the P&ysics, and are inappropriate to the present dis- cussion, in 1076 8-10 he says that the matter of sensible things has been discussed in the Physics, and their actuality (or form) has been discussed Jater. I.e., M. zuz/—1086* 18 presupposes, while M. 1086* 21—/in. does not, the discussions of ZH®. The one version presupposes only AB; the other belongs to the time when Aristotle had worked the greater part of the JJefaphysics more or less into a single whole. (Jaeger, 212-215.)
Rst 1076" 9 407
Jaeger concludes that M. 1086* 21—end belongs to the same early period as AB, i.e. to Aristotle’s stay at Assos in 348-345 B.c. It is only natural, then, that this brief section contains more references to AB than the whole of Z—A (1086 34, » 2, 15).
But in N. 1091*32, otov BovddcucOa A€yew abtd Td dyabdv Kal 7d apiorov, Aristotle certainly treats himself as a Platonist. N, then, also belongs to the Assos period; and, since Xenocrates was Aristotle’s companion at Assos, it is only natural that, while M criticizes him frequently and sharply (e.g. 1083) 2 xe(purra A€yerau 5 tplros tpdros), N criticizes him only in passing (1088> 28-35, r1ogo? 20-32), Further, the preface in M. 9 undertakes to examine the views of those who hold that the elements (1) of Ideas or (2) of mathematical numbers are the elements of all things. The theory of Ideas is treated of in M. 1086 32—end. N begins with a reference to the wide-spread doctrine that the elements of all things are contraries, but soon (1087> 4) settles down to discuss the view that unity and plurality or the equal and the unequal are the elements at once of mathematical number and of all things; and to this theory (that of Speusippus, already mentioned in the preface, M. 1086 29) and the kindred theory of the Pythagoreans, the rest of N is for the most part devoted. M. 1068# 21—N. end thus forms a whole, and a whole earlier than M beginning—1086? 18.
Two supposed kinds of immaterial substance to be discussed— mathematical objects and Ideas (ch, 1. 1076% 8-32).
107628. We have discussed elsewhere the substance of sensible things; we have now to consider whether there is apart from these an unchangeable eternal substance. First we must sift the opinions of others on the question.
16, Some hold that mathematical objects are substances; others hold that the Ideas are. Some believe in both, some identify them, some believe only in the mathematical objects.
22. We will discuss (I) mathematical objects, asking no further questions about them but simply whether they exist, and if so, how; (II) the Ideas (briefly); (III) and chiefly, whether the substances and principles of things are numbers and Ideas.
107629. év pev TH pebd8m... Ans no doubt refers to Phys. i. dotepoy is referred by Alexander to PAys. ii, and by Bz. to the latter part of the PAysics. But neither of these can be described strictly as discussing ‘substance according to actuality’, i.e. form. The posi- tion of pev.and d¢ shows that vorepov dé does not refer to the Physics,
408 Commentary
and the part of Aristotle’s works which best answers to the description is Me. ZH®. Bz.’s interpretation is partly actuated by the wish to show that MN do not presuppose the central part of the Mef/aphyszcs.
Cf. Introduction, pp. xviii f.
12, mp@tov, Alexander’s notion that zparov means ‘with special care’ cannot be accepted. ap@rov must-refer to time. A positive statement of Aristotle’s-doctrine of ‘unchangeable and eternal sub- stance’ was meant to follow. But this cannot be identified with A, which seems to be an earlier and separate work.
15. tot... Sucxepaivwpev. The order of the words is curious, the object being to throw into prominence the opposition between kowov and idia. ‘And that if some doctrine is common to us and them, we may not on that account be privately dissatisfied with our- selves’ For the expression cf. A. 984% 29.
1g. ot pév, sc. Plato and his most orthodox followers, cf. A. 987? 14- 18.
20-21. ot S€... €repor S€ tives. Alexander ascribes to Xenocrates (745. 32) and also to Speusippus (782. 32) the belief in mathematical number only ; in 766.8 he ascribes to both Speusippus and Xenocrates the identification of ideal and mathematical number, and to some of the Pythagoreans the belief in mathematical number only. We may safely infer that he knew little or nothing about the matter. A com- parison of Z. 1028 21-24, where Speusippus is mentioned by name, with A. 1075” 37—1076%3 and N. rogo» 13-20 makes it evident that it was Speusippus who rejected the Ideas and believed in mathematical number only. Asc. (379. 17) thinks it was Xenocrates who identified ideal number with mathematical, and this is strongly confirmed by the reference in 1080) 29 (where see note) to the well-known Xenocratean doctrine of indivisible lines. oi 8€, then, means Xenocrates, érepou dé twes the Pythagoreans and Speusippus, Cf. Introduction, pp. Ixxi- Ixxvi. Aristotle omits the fourth possible view, ascribed to dAXos tis in ro8oP 21, the view that ideal number exists but not mathematical.
22. ™p@Tov pév, chs. 2, 3.
26. émeita, chs. 4, 5.
27. amdds, ‘simply, without elaboration’. Cf. Pol. 1341> 38 i 8 Aéeyopev THv Kéilapow, viv pev ards, tadkw F ev Tois rept zownTiKAs €podpev capecrepov.
écov vopwou xdpiv, ‘as far as the accepted manner of treatment re- quires ’"—and it requires some discussion of all views held by thinkers of repute. Cf. betas evexa, dicts causa, Diphilus Zuypago. fr. 2. 13 ovdev 7p0€ws Trovel yap otros GAN’ dcov vopou (Xépiy, and Pol. 1341» 31 vov d€ vopukds SueAwpev, TOYS TUTrOUS LOVOY EiTOVTES TEPL AUTOV.
28, tv é&wtepikay Adyov. The meaning of this phrase has been repeatedly discussed; the following discussions in particular may be mentioned: Bernays, Dialoge des Aristoteles, 29-93; Zeller, Phil. der Griechen, Il. 2. (ed. 4) 112-126; Grant, Lthics of Arist. i, App. B; Grote, Aris/olle; ed. 3, 44-53 ; Diels in Sttzungsb. der Berl, Akad. 1883. 477-494; Susemihl in Meue Jahrb. fiir Philol. 1884. 265-277;
M. I. 10767 12-28 409
Susemihl and Hicks, Politics of Arist. 561-565. The other references to the éfwrepuxol Aoyou in the Aristotelian Corpus are as follows : LYS: 2x7? 3° mpOtov O& KadGs exer Suarophoat wept avrod (i.e. xpovov) Kal dua Tay eEwrepiKOv Aoyov.
E. NV. 1102 26 Aéyerou de wep aris (i, @ yoxiis) kal ev TOUS egurept- Kos Adyous d dpxovvTws evi, Kat xXpynoreov avrots’ otoy TO pev aoyov avTHS elvat, TO O€ Adyov exov.
EN. 11.40% 2 €repov 0 eat Toinos Kal Tpagis (miaTEvomev O€ mepl avrOv Kal. Tots elurepixois Aédyots).
L, £1217» 20 76 eivan ideay pu povov dyaGod GdXA. Kal dddov 6 drovodv Aeyerau AoyiKds Kal KevOs' emréoxerrar O€ TOAAOIS Tept adrod TpdTats Kal ev Tois e€wrepikors Adyous Kal ev Tols Kata pirocodiay.
LY. E. 1218 32 rdvra dh téayaGa 7 exrds } ev Woyy, Kal TovTwv atpe- TWTEPA TA ev TH Woy, Kabdrrep SiarpovpeOa Kal ev ToIs eEwrepiKots Ad-yots.
Pol. 1278» 30 adda. py Kal THs dpyis ye TOs Aeyouevous Tpdrous padiov dieAciv’ Kal yap ev Tois eEwrepixois Adyous OvopiLouca epi adtOv ToAAGKIS.
Pol, 1323? 21 vouicavras odv ikavOs roAAd A€yeoOar Kal TOV ev TOIS eEwrepixois Adyous wept THs dpiorys Cwfjs, kal viv xpyoréov avrois.
With these references may be compared the following, in which similar phrases are used: De Caelo 249% 30 év rots éyxu«Alos pidoco- gypact, L. NV. 1096* 3 ey rots éyxucAlous, De An. 407” 29 rots ev Kowo yvomevors Novos.
Bernays tries to show that in all these passages except the first the reference is to Aristotle’s dialogues, which were ‘ exoteric’, i.e. were published in a fuller sense than the works in which the references occur. In other words Bernays accepts the distinction, which had certainly become current by the time of Cicero, between the exoteric and the acroamatic works of Aristotle. It may be admitted that all the subjects in question were probably treated of in Aristotle’s dialogues, or in other lost works of his which were published in the full sense. Thus (to take the present passage and the first passage from the Hudemian Ethics) it is certain that Aristotle criticized the Ideas in the dialogue De Philo- sophia and in the works De Jdets and De Bono; he may also have dealt with them, as Bernays suggests, in the dialogues De Justitia, Sophistes, and Politicus, But the meaning of Aéyou in the Physics passage, as the preposition S:¢ shows, is not ‘books’ but ‘arguments’, and w7o in the present passage suggests the same, in view of the frequent tendency in Greek to treat ‘the argument’ as if it were a person, as in Aikowos Adyos and "Adiucos Adyos, 6 Adyos aipée, and many other examples quoted by Diels. By a comparison of Pol. 1323% 21-35 with Z. VV. 1098» 9-18 (dealing with the same subject) Diels shows beyond a doubt that by ra ey rots eCwrepiKois doyors IN 13234 22 Aristotle means the same as he does by ra Aeydpeva in 1098? 10, i.e. that in that passage at least é€. A\dyo. means ‘ discussions not pecu- liar to the Peripatetic school’. This is probably its meaning in the other passages also. ‘The precise shade of meaning may differ in the different passages ; in some the reference is to Academic doctrines, in others to discussions or distinctions which were familiar to cultivated
410 Commentary
Athenians of no particular philosophical school. In the present pas- sage the reference probably is to attacks on the Ideas by Antisthenes and by sophists like Polyxenus, the inventor of the ‘third man’ argu- ment against the Ideas (cf. A. 990 17n.). Diels’s conclusions do not seem to have been refuted by Jaeger’s argument in Ar/stofeles, 254- 270. Jaeger thinks the present reference isto the De Philosophia. 29-32. €r B€ .. . oxéfis. A further reason for brevity in the second part of the treatise, the discussion of the Ideas simplictter. The third and main part of the treatise (rév wAefw Adyov) must finish by throwing light on the second problem (xpos éxe(vny Set riv oKépuy amavtav), So that the second discussion need not itself be elaborate. 30. dray émickoT@pev, chs. 6-9.
I. Maruematicat Opjects (ch. 1. 10762 32—3. 1078) 6).
1076? 32. If they exist, they must exist either (A) in sensible things, in the way maintained by certain thinkers, or (B) separate from sensible things, or (C) in some other way.
Mathematical objects cannot exist as distinct substances (ch. 2).
10762 38. (A) We have shown (cf. B. 998% 7-19) that mathematical objects cannot be 2% sensible things; (1) because two solids cannot be in the same place, (2) because it would follow that the other powers and characteristics of things must also be immanent.