10542 13-19. For the argument cf. I. 1003 22-34, Z. 1030” 10-12, K. 10612 18.
Unity and plurality ; identity ; likeness ; otherness ; difference ; contrariety (ch. 3).
1054220. The one and ¢he many are opposed in several senses—in one of them as the indivisible or undivided to the divisible or divided. The opposition is that of contrariety (involving as it does privation), not of contradiction nor of relation.
26. Unity is explained by reference to plurality, the indivisible by reference to the divisible, because the latter are more manifest to sense.
29. To the one belong the terms same, like, equal; to plurality the terms other, unlike, unequal. | Zhe same means (1) the same in number, (2) one both in definition and in number (in this sense you are the same with yourself), (3) one in definition (in this sense equal straight lines are the same—here equality is unity).
bg. Things are “ke, (1) if, not being absolutely the same (i.e. without difference in their composite substance), they are the same in form (e.g, the larger square is like the smaller), (2) if they have the same form and do not differ in degree, (3) if they have the same attribute in different degrees, (4) if they have more attributes, or more of the obvious attributes, the same than different.
13. Other and unizke have a similar variety of meaning. Other is (1) opposed to the same, so that everything is either the same as or other than everything else. It is used (2) if the matter and the defini- tion are not both one, and (3) as in mathematics.
18. Other is not the contradictory of the same ; things which are not are neither the same nor other, but simply ‘not the same’; things that ave are either the same or other.
23. Difference is different from otherness, The other need not be other in any particular respect, but the different must be different in some respect, so that there must be some identical thing in which the different things differ, i.e. either-genus or species. Things differ in genus if they have not a common matter and do not pass into each other (i.e. things that belong to different categories); in species, if they belong to the same genus.
31. Contraries are different, and contrariety is a kind of difference.
All contraries differ; they are not only other but some are other in genus, while others are in the same category and therefore in the same genus. We have distinguished elsewhere which things are the same or other in genus.
10542 23. at dvtiOécers tetpaxds. The four kinds of opposite are dvripacts, Tavaytia, TA mpds TL, TTEpaIs Kal eéis (A, 10184 20, cf. Cat. 11> 17).
24. Mate adoption of odre (A>) for todtwy gives an impossible sense, unless his suggested rearrangement of |. 25, otre ds dvtidacis ovre ds Ta mpos TL Acyopeva, evavtia ay ein, be adopted also. Alexander says (615. 2) émet d¢ ai dvriOéoes terpaxds, 7d ev Kal Ta TOAAG Hs TA evavrio GVTiKELTOL, Kal ovre OS TO. Tpos TL OvUTE as Eis Kat OTEpHoLS ovTE os KaTd- gacis kat drddacis. It is impossible to say exactly what he read ; he may be merely interpreting freely.
It seems better to keep the reading tovrwy, which gives a fair sense. ‘Since one of the terms “ divisible” and “indivisible” is privative, they must be contraries and not contradictory or relative terms.’ Aristotle should have said, in accordance with his fourfold division of opposites, ‘ since they are not privative, nor contradictory, nor relative, they must be contrary’; but privation and contrariety are not mutually exclusive. Contrariety is the extreme form of privation, the form in which the attribute present in the one term is entirely absent in the other (1055) 14, 26, I. 1004» 27, torr» 18). As Bz. remarks, a clause indicating that the privation is of the extreme type has to be supplied in sense after Odrepov.
26. héyerat points to the fact that ddva/perov is derived from dauperov. -dyAodrat points to the fact that the meaning of ‘ one’ or ‘ indivisible’ is explained by reference to ‘many’ or ‘ divisible’.
30. ev TH Starpécer Tay evavtiwy, cf. TD. 1004? 2 n.
g2. Other passages on the various senses of ‘the same’ are A. 9, Top. i. 4, Vv. 4. 133" 15 sqaq.
33-34. éva pev...atrd. Since this is opposed to unity of both definition and number (absolute identity, ll. 34, 35) and to unity of definition (the unity of the members of a species, ll. 35-» 3), Alexander must be right in explaining this first kind of unity as accidental unity, which is expounded at length in A. 1015 17-34.
be, Bz. was right in omitting rd before isoydévua; the word is actually omitted by A> as well as by Alexander.
tetpdywva, This word in Aristotle usually means ‘ square’ but here ‘quadrilateral’ (cf. De An. 414 31(?), Pl. Zim. 558, Crit. 118 c). Euclid distinguishes the two as terpéywvoy and rerpdrAevpov respec- tively. .
3-13. On the meanings of ‘like’ cf. A. 10188 15-18,
1g. 7 Aeuxdy. There is no trace in Alexander of the manuscript reading 7 xpvo@, which is in itself highly improbable. The balance of the sentence would lead one to expect something like 7 Nevxov, and
288 Commentary
Alexander probably read this ; his words are 6 dé xarrirepos TO dpy’pw Kata. TO mpoxetpor, olov TO Nevkdv. xpvod doubtless came in by ditto- graphy.
14-22. On the meanings of ‘other’ cf. A. 101849-1
14-18. Aristotle offers apparently three senses of ‘ ae *, but really the first clause gives a quite general statement of its meaning, and the other two give varieties. of this.
15. d&mav mpds Grav 7 tadTs } GAA. Aristotle’s remarks in ]]. 19-22 show that with this is to be understood the reservation doa Aéyerau €v kal év. ‘Other’ is the privative, not the contradictory, of ‘ the same’, and there are pairs of things (viz. ju évra) of which neither is predic- able.
17. ds Ta év Tors paPypatiKkois. This is to be understood as opposed to the sense of ‘ the same’ given in], 1.
18. 81a todro, i.e. because ‘other’ is the opposite of ‘the same’ (1. 15). Apelt (Betrdge, p. 220) thinks it refers forwards to 1. 19 od yap avripacis éort Tod radrod, but this is less probable, Christ’s view that dua rodro is spurious is quite unjustified.
22. Something like Apelt’s ré@uxe doa (cf. 1. 19) appears to be wanted instead of refuxds. I have printed the elided form, for which cf, Pl. Phil. 353 cvpBeBny jytv, Dem. 21. 120 oddé as ou’ Gduxo, &c.
23-31. On the meanings of ‘different’ cf. A. 10184 12-15.
26. dvdykn taitéd ti eivar @ Siapepouow. Aristotle means that if A and B are different, there must be a single statable respect in which they differ. If A differs from B in genus, B also differs from A in genus; if in species, then in species. He does not mean that they must have an attribute in common; this is not true in the extreme case, dawv ado oyna THS KaTnyopias.
28. The remark about yévos and yéveois is an interesting indication of the influence of biology on Aristotle’s logic. Cf. the account of yevos in A. 28.
29. olov dcwv ado oxfpa THs Katnyopias. In view of |. 35 (note) it seems that ofov = ‘i.e,’, not ‘e.g.’. Aristotle seems in this context to restrict the name ‘genus’ to the categories. Cf. A. 1016> 33 n.
31-32. 148° évaytia...t1s. Bz. points out that these words are out of place, since Aristotle is dealing in this chapter only with dvapopa and comes to évaytidrys Only in the next. The objection is sound, but with this sentence belongs the next. For rdvta yap diapépovra (or Suahépovra re) haiveras is meaningless if the subject be 7a duapéepovra, but significant if it be ra évavria. It seems better to treat 1054 31— 1055® 2 as a discussion of contraries which ought to have been super- seded by the fuller discussion in chapter 4 but was retained by the ex- cessive zeal of the original editor. For the meanings of ‘ contrary’ cf. A. 1018# 25-35.
34. If we read ra diahépovra for duadépovra with Alexander, or diahépovta Ti patverat, only the one sentence 7a 8’ évaytia xrA. need be regarded as out of place. But it seems better to retain the manuscript
reading. Alexander’s reading rayra yap ra Siahépovra paiverat kai taird is excluded by the fact that some things which are ‘ different ’, viz. those that are different in category, are in no respect rairdé. The point which Aristotle makes above and in ]. 35 is not that things that differ must be the same in some respect, but that there must be some one thing in which they differ. adyta yap dSiadepovra ti daiverar kal od povov érepa. 6vra. would be a preferable departure from the manuscripts (though Aristotle would probably have said tw rather than ri, cf. 1. 26); but no departure seems necessary.
35. év TH abt cvotorxia THs KaTnyopias, cf. A. 9864 23n. Here ‘contraries (or differents) which are in the same ‘line of predication’ are said to be in the same genus. In 1058 13 (the only other pas- sage in which ovorouxia ris Karyyopias is found) contraries in the same genus are said to be in the same ‘line of predication’. Thus ‘genus’ and ‘line of predication’ are coextensive terms. Now it seems natural to identify the ‘line of predication’ here with the ‘figure of predication ’ six lines earlier. It is surprising to find genus identified with category, but the identification is vouched for by A. 1016) 33 (where see note), 102412. Aristotle doubtless calls many classes which are not categories genera, but in the strict sense the categories are the only genera, since they are the only classes that are not species.
Thus Bz.’s suggestion that cvotoryia THs Katyyopias means one of the main divisions of a category, within which the same sort of predi- cate is found (thus the various predicates of number might be thought of as forming a ‘ column’ under the main predicates odd and even) falls to the ground.
avoroxia is used (enter alia) of a series of terms of which each is wider than that which comes under it (Am. Post. 66% 27, 35, 79° 7, 8, 80> 27, 812 21, 87> 6, 14), and each category is one cvororxia ris katyyopias in the sense that it forms a ‘ Porphyry’s tree’ of which the apex is the name of the category.
1055*2. év adda, A. 1024 9-16.
Contrariety (ch. 4).
1055* 3. Contrariety is maximum difference. This is clear; for, while things that differ in genus cannot pass into each other at all, con- traries are the starting-points and extremes in the passage into each other of things differing in speczes, and have the greatest interval between them. Now what is greatest in each class is complete (since there is no going beyond it), so that contrariety is complete difference, the meaning of ‘ complete’ varying with the meaning of ‘ contrary’.
1g. One thing cannot have more than one contrary, since (1) nothing can be more extreme than the extreme, nor can there be more than two extremes to the same interval, (2) contrariety is a difference, and difference is between two things.
290 Commentary
23. The truth of the other definitions of contrariety. follows: (1) the complete difference is the greatest difference, for () there is no difference between a thing and others ow/szde its genus, and (4) the complete difference is the greatest difference between a thing and others zmsede its genus. (2) The things that differ most in the same genus are contraries; so too are (3) the things that differ most in the same receptive material, and (4) the things falling under the same capacity that differ most,
83. Positive state and privation are the first contrariety—but only when the privation is complete. Other contraries are so called because they possess, produce, tend to produce, or are acquisitions or losses of these or of other contraries.
38. The kinds of opposition are contradiction, privation, con- trariety, relation. (1) Contradiction is not the same as contrariety since it does not admit of a mean while contrariety. does. (2) Priva- tion is a kind of contradiction, an incapacity which is determinate or involves the same subject which is capable of having the positive state. Hence, while contradiction has no mean, privation sometimes has ; everything is equal or of equal, but only that which could be equal must be either equal or wnegual.
bir. Since generation is from contrary to contrary, and is either from form or from privation, all contrariety is privation, though not all ptivation is contrariety since there are various forms of privation ; con- traries are the extremes from which change starts.