17. This can be proved by induction. Every contrariety has a privation as one of its terms, but there are various kinds of priva- tion; it sometimes means mere privation, sometimes privation at a particular time or in a particular part, or complete privation. Some of these kinds admit of a mean (a man need not be either good or bad), others do not (a number must be either odd or even), Again, some have a determinate subject, others have not.
26. Thus it is clear that one of two contraries is always privative. It is enough to show this of the summa genera of contraries, e. g. of one and many ; the rest are reducible to these.
1055" 17-19. moddax@s S€. .. attots is explained by ll. 24-33. Contraries may be defined as ra wAciorov diadépovra, as ra ev Taito yever TAcicrov Suadepovra, as Ta ev Tare dextcKG wAciorov Siadépovra, Or as Ta t7d THY airnv Svvapw rrclcTov diaepovra, and ‘ complete differ- ence’ will mean the maximum difference possible in each of these cases.
23. Bz. takes this to be an instance of dare 7” apodos7; but that is
le 4emO55® 17 — 105553 291
rarely found unless the protasis has been so long that the structure of the sentence has been to some extent forgotten. It is better to take oAws Te ei ori KTA. as Subordinate to davepdv (éorw). ‘And, to put the matter generally, this (that one thing has not more than one con- trary) is evident if contrariety is difference, and difference—and there- fore complete difference—is between two things.’
23-33. The kinds of contrary mentioned in A. 10184 25-35 are:
(1) 7a py dwvard dua TO atTd rapeiven TOV SiadepdvTwv Kara. yéevos,
(2) ra wAciorov Siadépovta Tov év TO adTa yever (= 1055 27),
(3) Ta wrciorov Siahépovra Tov év TatTed SexTiKG ( = 10558 29),
(4) Ta mAciorov Siahepovra trav brd THY adryy Svvapw ( = 1055% 31).
I agrees with A in the last three kinds, but excludes the first (1055 26). In I the genus is conceived as a summum genus (105429). Nothing can pass from one genus to another (1054 29, 10579 26); naturally therefore there cannot be contrary genera or contraries in different genera. In A and elsewhere genus is treated more loosely, and virtue and vice can be treated as contrary genera ( Zop. 123» 14-16).
26-27. Serta yap... peytoty. ‘For it has been shown that in relation to things outside its genus a thing has no difference, while with regard to things within one genus the complete difference is the greatest.’ It is impossible to make consistent Aristotle’s various statements in these chapters about difference. In chapter 3 difference in genus was freely recognized, and in its extremest form, viz. differ- ence of category (105429, 35). So too in this chapter (1055 6). Yet here he says that there is no such thing as difference between a thing and something else outside its genus. Two explanations might be offered. (1) Aristotle may mean that if X and Y are in different genera they should not be said to have a difference, but the genera should. If this had been his meaning, however, he would probably have taken the trouble to state it clearly. (2) It may be that while he uses diapéeperv, Sudhopov in a sense almost (not quite, cf. 1054 25) as wide as their everyday sense, he uses duadopa in the technical sense which it bears in his logic, viz..= a differentiation of a genus. This seems more likely.
It is not clear where the proof referred to in d€8exra. has been given. Presumably in]. 6. Things in different genera may be called dvadépovra, but since there is no passage from one to the other there is no definite measurable interval, no dcapopa, between them.
bg. Privation, we are told by Aristotle, is a kind of contradiction, and contrariety is a kind of privation. Zeller objects that when the conception of privation is cleared up it is seen to fall either under con- tradiction or under contrariety. This objection I have dealt with in notes on A. 1022) 22-24, 24-31. An. Post. 73% 21, to which he refers, in no way proves his point; it rather suggests that contrariety reduces itself either to privation or to contradiction. The general position is this; Contradiction is the relation between two proposi-
292 Commentary
tions of the type ‘Ais B’,‘Ais not B’. Privation is the condition of a subject capable of being B (let us call it A>) when it in any degree fails to be B. Contrariety is the relation between two condi- tions of A», that in which it is fully B and that in which it is not B at all. Thus contradiction includes privation as a particular case, and privation includes contrariety as a particular case.
4. % yap Td G8uvatovy bdws éxew. The application of a privative term to a subject which is quite incapable of having the positive pre- dicate is improper. In such a case it is only the contradictory term that should be applied. Strictly therefore Aristotle should not have included this as a case of privation (as he does both here and in A. 1022623), since privation is cuverAnppévg TO Sexrixd, i.e. implies that the subject could have the positive predicate, and is duopirbeioa, i.e. limited to such a subject. Aristotle is here taking account of the fact that terms like ‘blind’, though properly applicable only to animals, are in ordinary language sometimes applied to other things.
7. év Gddows, A. 22.
Q. otepnoews Sé tos Eotwv, i.e. in the case of all proper privations, as distinguished from the improper cases referred to in 1. 4 (note). For the possibility of an intermediate between ééis and orépyors cf. Cat. 13? 3 (seeing and blind), K. 10614 21 (just and unjust).
22. 7 7T@ kupiw, ‘or in the dominant part’. Alexander aptly illus- trates this by saying that a man might be called dyeup if he had no right hand.
25. Bz. argues that the fact that some positive terms (like odd and even) have a determinate subject to which they are appropriate, while others (like good and bad) have none but may be applied in any category, is the reason why the former do not admit of a middle while the latter do. He therefore reads 67 for the manuscript év. Alexander gives the same general interpretation, and probably also read 6ru (624. 12). But it seems clear that this is not the reason why good and bad admit of a middle. Take Aristotle’s favourite instance of privation, ‘blind’, which has a determinate subject, viz. animals ; there are inter- mediates between ‘seeing’ in the full sense and ‘blind’ in the full sense. Distinctions such as are suggested by 7% wore 7 &v tut, olov av é€v 7Aukia Twi 7 TS Kupiw, 7 avTy are applicable to good and bad but not to odd and even, and this is the reason why the former admit of a middle and the latter donot. ér ra pv xrX. raises a fresh point, the point of the proper application of privative terms, already mentioned in 1. 4.
The opposition of ‘ equal’ to ‘ greater’ and ‘ less’ (ch. 5).
105530. If one thing has only one contrary, how is one opposed to many, or equal to greater and smaller? ‘ Whether’ always implies opposition ; we ask ‘ whether it is white or black’, ‘ whether it is white
or not white’, but not ‘ whether it is a man or white’. When we state alternatives between which there is no apparent opposition, as in ‘whether Cleon came, or Socrates’, we imply that they are incom- patible ; if they are compatible the question would be absurd and another opposition would take its place, ‘whether both came, or only one of the two’.
10562 3. Now we ask ‘ whether it is greater, less, or equal’; what is the implied opposition of equal to the other terms? It is not con- trary either to one or to both, for (1) it is not contrary to one any more than to the other ; (2) it is contrary to unequal, so that it would have more than one contrary. If unequal is equivalent to greater and smaller together, equal would be opposed to both, but it would still have two contraries, which is impossible. (3) Equal is between great and small, but a contrariety cannot be intermediate, or it would not be complete.
15. The opposition must therefore be either contradiction or priva- tion. ‘ Equal’ is not the contradiction or privation of either extreme more than of the other ; therefore it is the privative contradiction of both. Hence it is never stated as alternative to one of them alone.
20. It is not a necessary privation, for not everything that is neither greater nor less is equal, but only that which could be greater or less. It is the privative contradiction of both, and therefore intermediate between them.
24. What is neither good nor bad is opposed to both but has no name, since the terms are ambiguous and have no one appropriate subject-matter. Even what is neither white nor black has no one name, though the colours of which ‘ neither white nor black ’ is pre- dicated are limited.
30. Therefore it is not fair to object that if what is neither good nor bad is between the two, there will always be an intermediate
etween two terms, e.g. what is neither a shoe nor a hand will be be- tween the two. The one is a joint contradiction of opposites between which there is an intermediate and an interval; between the other two terms there is no difference since they belong to different genera.
1055° 34. && imo8écews, i.e. on the assumption that the person who came must have been either Cleon or Socrates.
36.. GAN’ otk... . yévet ToOTo, i.e. this is not the necessary disjunction of any class.
GAA Kal TodTo éxeiPev EdpAuber, ‘but even the use of “ whether” in such a question as “ whether Cleon or Socrates came” is derived from its proper use in which the alternatives stated are opposite’.
204 Commentary
1056" 1-2. «i 8¢... dvtiGeow, ‘but if they could be true together, even so the question falls none the less into an antithesis’.
8-11. ‘If “the unequal’: means the same as both (the greater and the less), then the equal would be opposed to both, but this means (in spite of the fact that we have now one word “unequal” to denote both) that one thing is contrary to two others; which is impossible.
10. tots doKxouct Td dyicoy Sudda eivor, the Platonists, cf. N.
1087) 4, - 15. Having shown that the opposition is not that of contrariety, Aristotle infers that it is ether contradiction or prtvation (the fourth kind of opposition, that of relation, it evidently cannot be, since the equal is in that sense opposed not to the unequal but tothe equal). It is disconcerting to find him, immediately after, saying that it is przvalzve contradiction, But in truth contradiction and privation are not mutually exclusive. Equal and greater-or-smaller are not strictly con- tradictory, for neither is true of non-quanta. But they are privatively contradictory, i.e. contradictory (so that both cannot be true and one must be true) when predicated of any subject in a certain genus, the genus of quanta. dddacis orepytixy amounts to the same thing as OTEpHOts. Cr 1055» 3n.
26. modax&s yap héyetat Exdtepov, the good and the bad are found in every category, Z. 1. 1096 19.
35. The best sense is got by translating ‘for the one is a joint negation of opposites’. guvamddacrs is predicate, and 7% is attracted to its gender.
DI. tav 8 otk gots Stapopd, according to the account of difference in 1054 23—1055% 2.
The opposition of ‘one’ to ‘many’ (ch. 6).
1056 3. A-similar question may be asked about one and many. If many is opposed to one absolutely, difficulties follow: (1) One will be few, because many is opposed to few; (2) two will be many and therefore one will be few, since it can only be in opposition to one that two is many; (3) woAv and éA‘yor are in plurality what long and. short are in length, and what is much is many and what is many is much (unless fluids are an exception), so that the few will be a plurality, and therefore one will be a plurality.
14. The truth is that the many are also called much, but the meaning of the two terms is different; water may be much but is not many. But many is applicable to all things that are discrete, and means (1) a plurality which is absolutely or relatively superior, as opposed to few, but also (2) number, as opposed to one. The opposi- tion of one to many is like that of one to ones or of white thing to.