white things; each number is many because it consists of ones and is measured by one, and as opposed to one, not to few.
25. In this sense two is many ; it is not many in the sense of being a plurality which is superior either relatively or absolutely. It is few absolutely, since it is the first inferior plurality (hence Anaxagoras was wrong in saying ‘all things were together, infinite in multitude and in smallness—by which he meant fewness—, for they were not infinite in fewness), since fewness is constituted not by one but by two.
32. One and many in numbers are opposed, then, as measure to the measurable, and these are opposed as things that are per accidens relative. A may be relative to B (1) as being its contrary, or (2) be- cause B is relative to A (in which indirect sense ‘knowledge’ is relative to ‘knowable ’).
10571. One may be fewer than some other things; it does not follow that it is few.
2. Plurality isthe genus of number; number is plurality measurable by one. One and number are opposed not as contraries but as some relative terms have been said to be opposed, viz. as measure to measurable; hence not everything that is one is a number.
7. Knowledge might be thought to be related to the knowable as measure to the measured, but in fact, while all knowledge is knowable, not everything knowable is knowledge; in a sense knowledge is measured by the knowable.
12. Plurality is contrary neither to few (many being contrary to few as superior to inferior plurality), nor in every way to one. In one way it is contrary to one, because it is divisible while the one is indivisible ; in another it is merely relative to it, as knowledge is to the knowable, if many means number and one the measure of number.
10565. ddiyov 7% ddiyo. This does not mean ‘little or few’. édtyov means ‘few” as well as dAéya, and is used only because of the awkwardness of using the plural as a predicate of ro €v. On the other hand zod% and zoAAa are used with a distinction of meaning, ‘much’ and ‘many’, |. 12.
II. kal 6 dv 4 woAd Kal TohAd, Kat TO TWoAAG odd. This clause is introduced to confirm the premise just stated, that woAv and éAtyov are varieties of plurality; Aristotle confirms this by remarking that (apart from the case of fluids) what is zodv is woAAd, in which the plural case shows that a plurality is in question.
12. ci py TL... edopiotw, ‘unless indeed there is a difference in an easily moulded continuum’, viz. a fluid, to which ‘much’ but not ‘many’ is applicable. Alexander reads dopiorw, and takes this to refer to liquid; this is possible, since fluid is referred to in De Gen. et
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Corr. 329 30 aS TO dopiorov oikeiw dpw, eddopiorov dv (what has no definite boundary of its own, and readily takes the shape of its re- ceptacle), but not probable, since fluid is often referred to as eddépurrov simpliciter (De Caelo 313° 8, De Gen. et Corr. 328° 14, Meteor. 3607 23, 381) 20),
14. ddN’ lows xtd. Aristotle begins” here.his discussion of the difficulties stated in ll. 5-14. The vital point in his solution of the difficulties is the distinction (Il. 16-20) between two senses of ‘many’ —the sense of ‘superior plurality’, in which it is opposed to ‘few’, and the sense of ‘number’, in which it is opposed to ‘one’, and opposed not as its contrary but as its correlative. Thus (1) the first difficulty (Il. 5, 6) disappears. Though many is opposed to one and to few, it does not follow that one is few, for it is many in different senses that is opposed to one and to few. (2) The second difficulty (Il. 6-10) disappears. We cannot say ‘two is many and therefore one is few’, for two is not many in the sense in which many is opposed to few (i. e. in the sense that there is a plurality which is smaller and which may be called few), but only in the sense in which many is opposed to one. (3) The third difficulty (ll. 10-14) disappears. For one of the premises of the argument, viz. that one is few, has now been shown to be untrue.
21, 22. Jaeger is no doubt right in treating kat 15 petpytév as a gloss on kal Ta prepeTpnweva, Suggested by jerpyrds in]. 23. Besides this he reads a colon after Aevkd, inserts dorep before ra peyerpypeva, and a comma after pérpov. This produces a neat sentence, but is (I think) an unnecessary departure from the evidence. It is just possible to retain xal 7d petpyntov if we abolish the full stop after it. “For we say one or many as though one said one and ones or white thing and white things; and things measured—in relation to their measure—and the measurable and multiples are spoken of in the same
? way. 25. TAHO0s Exov brepoxhy i meds TL 7 GwAQs, a plurality greater than some other, or than any other.
26. adda mpdrtov, sc. tAHO0s éorw.
28. dméotn, ‘left the subject’, cf. Zop. 1079, Phys. 191” 10, £. WV. 11659 35.
gO. eer... “kal ddtyétyt” makes specific the criticism stated generally in the previous clause. ‘Anaxagoras should not have been content to say ‘all things were together, infinite both in multitude and in smallness”; he ought to have said “and in fewness”.’ od yap dzreipa is then added somewhat elliptically. ‘And thus the error of his view becomes apparent ; for things cannot be infinite in fewness.’ Aristotle thinks that when Anaxagoras said xal 7AO0s Kal opixpdryra (fr. 1) he meant to be mentioning opposites; and the opposite of multitude is not smallness but fewness. Anaxagoras meant, as a matter of fact, what he said, that things were infinitely many and infinitely small, in the sense that everything however small included yet smaller parts. If he had meant that they were infinitely few, Aristotle’s objection
(od yap azeipa) that things cannot be infinitely few, since there is an absolute few, viz., two, would have been sound. After od« 6p0ds aaréory we might have expected ddd’ de, but for similar instances of d¢ cf. K. 10612 23, De An. 409» 28, Pol. 13267 12.
The meaning of the passage has been well brought out by Prof. A. A. Bowman in Class, Rev. xxx. 42-44.
31-32. émel 7d GAtyovy . . . SUo evidently refers back to |. 27 diya & amd@s ra dv0 xrX. Christ is right in treating the intervening words as parenthetical, but his excision of ov« in ]. 28 is indefensible.
There is a further difficulty in the present passage. Knowledge is said (1. 36) to be relative to the known in the sense that something else (the known) is relative to 27, But in A. 15 the known was said to be relative to knowledge in this sense; cf.1057% 7-12. There the known, here knowledge is made the term which is really absolute and only incidentally relative. The two statements are to be reconciled as follows: The term ‘knowledge’ is prior to the term ‘knowable’, since knowable = possible object of knowledge. But the thing which is knowable is prior to the knowledge of it, since there can be a know- able which is not known but there cannot be knowledge which is not ot something knowable. Cf. 1057 4-12.
1057* 3. Eott yap dprOuss wAHO0S Evi petpytoy, cf. A. 10207 13 n.
8. For drodidwow, ‘turns out’, cf. Ax. Post. 99°30, Meteor. 363° 11, A. A. 585> 32, 58622, G. A. 72278.
g-12. The sentence is difficult; the alleged fact (ovpBaive dé) is surprising in itself, and does not stand in a proper antithesis to what ‘one might suppose’ (d0€ere wey yap dv). The expression is loose, but the point (if the reading be right) seems to be this: Knowledge might be thought to be the measure of the knowable (a free render- ing of Protagoras’ maxim), but in point of fact, while all knowledge must be knowable, not all that is knowable is actually known or knowledge. The point is stated more accurately in Caf. 7» 22-35, where as here the relation of the knowable to knowledge is dis- tinguished from the relation of a genuine zpos ru term to its correlative. Cf. 1053 31-35. The doctrine of the identity of knowledge with its object (De An. 430% 4, &c.), to which Alexander and Bz. refer, does not seem to be relevant.
I suspect, however, that we should read émuornunv pev tacay émt- OTHTOU civan TO dé emvaTNTOV py TaV TPds emcaTHpyy, ‘that all knowledge is
298 Commentary
of a knowable, but not all the knowable is relative to actual knowledge’. This agrees better with Caz. 7 29 émuoryrod ev yap pm dvTos obk EoTW exioTHpn (ovdevds yap éorat ereornpn), emiornpns dé pr ovons ovdev KWATEL €TLOTHTOV €iVaL, OLOV Kal 6 TOD KUKAOV TETPAyOVLT [LOS elye éoTw emloTyrToV, ETLOTHN [LEV AVTOD OVK EoTW OvdETW, AvTOS BE emLOTNTOY EoT'.
14-17. From one point of view number is contrary to the one, because they have contrary attributes, being respectively divisible and indivisible; but from another point of view they are related not as contraries but with the sort of relation that knowledge has to the knowable, being respectively number (i.e. the measurable) and mea- sure. The distinction drawn in 105635 between évavria and the other kind of zpés 7: thus reappears in this sentence ; the meaning is brought out better by deleting the comma after 7. in 1. 16. It seems clear that the subject of 7 (1. 16) is not as Alexander and Bz, suppose » érotnun but 7d 7AROos, and that 76 & & pérpov, not ro 8 ev Kat /€rpov, is to be read.
The nature of intermediates (ch. 7).
105718. Intermediates must be compounded out of contraries ; for (1) they are always in the same genus as the extremes, since (a) they are that into which things must change before they reach the ex- tremes, and (4) it is not possible to change from one genus into another except per accidens, e. g. from a colour to a shape.
30. But (2) (a) all intermediates are between opposites (for it is only between these, fer se, that change can take place); and (4), of opposites, (i) contradictories admit of no mean (contradiction being between opposites one of which must be true of every subject) ; while (ii) relative terms that are not contrary have no mean because they are not in the same genus. Intermediates must therefore be between coniraries.
b2. (3) They must therefore be composed of these contraries. For the contraries must either fall within one genus or not. (a) If they do, so that there is something prior to the contraries, the differentiae that make the contrary species will be prior contraries ; for the species consist of the genus + the differentiae.
12, The intermediates will be composed of the genus + certain differentiae, which will not be the first contraries (otherwise every colour would be either white or black), but are intermediate between them.
19. Thus we have to consider first, of what are composed the inter- mediates between (4) contraries that are no/ in the same genus; for the things in the same genus must be composed of terms that do not
involve the genus as an element in them, or else be incomposite. Contraries are not compounded of one another, and are therefore starting-points ; of the intermediates ad/ or mone are compounded out of the contraries. Now from the contraries there arises somedhing such that change reaches it before it reaches the contraries (for there must be something that is less than the one and more than the other). Therefore all the o/her intermediates also are composite ; for that which has a quality in a higher degree than A and in a lower degree than B must be compounded of A and B.
29. But since there is nothing homogeneous with the contraries and prior to them, all intermediates must be compounded of the contraries, and therefore the lower terms, whether contraries or intermediates, will be compounded of the first contraries. Clearly, then, all intermediates are (1) in the same genus, (2) between contraries, and (3) compounded out of the contraries.
Chapters 7-10 are for some unknown reason not commented on by Alexander.
1057°18. kat éviwy €otw, i.e. in the great majority of cases; there are some contraries, however, like odd and even, straight and crooked, which admit of no mean (1055> 24).