LESSON 7

Opposition of the Equal to the Large and the Small

  Chapter 5: 1055b 30-1056b 2

             857. But since one thing has one contrary, someone might raise the question how the one is opposed to the many, and how the equal is opposed to the large and the small.

             858. For we always use the term whether antithetically, for example, whether it is white or black, or whether it is white or not white. But we do not ask whether it is white or man, unless we are basing our inquiry on an assumption, asking, for example, whether it was Cleon or Socrates that came; but this is not a necessary antithesis in any one class of things. Yet even this manner of speaking came from that used in the case of opposites; for opposites alone cannot exist at the same time. And this manner of speaking is used even in asking the question which of the two came. For if it were possible that both might have come at the same time, the question would be absurd; but even if it were possible, the question would still fall in some way into an antithesis, namely, of the one or the many, for example, whether both came, or one of the two.

             859. If, then, the question whether something is such and such always has to do with opposites, and one can ask whether it is larger or smaller or equal, there is some opposition between these and the equal. For it is not contrary to one alone or to both; for why should it be contrary to the larger rather than to the smaller?

             860. Again, the equal is contrary to the unequal. Hence it will be contrary to more things than one. But if unequal signifies the same thing as both of these together, it will be opposed to both.

             861. And this difficulty supports those who say that the unequal is a duality.

             862. But it follows that one thing is contrary to two; yet this is impossible.

             863. Further, the equal seems to be an intermediate between the large and the small; but no contrariety seems to be intermediate, nor is this possible from its definition; for it would not be complete if it were intermediate between any two things, but rather it always has something intermediate between itself and the other term.

             864. It follows, then, that it is opposed either as a negation or as a privation. Now it cannot be opposed as a negation or a privation of one of the two; for why should it be opposed to the large rather than to the small? Therefore it is the privative negation of both. And for this reason whether is used of both, but not of one of the two; for example, whether it is larger or equal, or whether it is equal or smaller; but there are always three things.

             865. But it is not necessarily a privation; for not everything that is not larger or smaller is equal, but this is true of those things which are naturally capable of having these attributes. Hence the equal is what is neither large nor small but is naturally capable of being large or small; and it is opposed to both as a privative negation.

             866. And for this reason it is also an intermediate. And what is neither good nor evil is opposed to both but is unnamed; for each of these terms is used in many senses, and their subject is not one; but more so what is neither white nor black. And neither is this said to be one thing, although the colors of which this privative negation is predicated are limited; for it must be either gray or red or some other such color.

             867. Hence the criticism of those people is not right who think that all terms are used in a similar way, so that if there is something which is neither a shoe nor a hand, it will be intermediate between the two, since what is neither good nor evil is intermediate between what is good and what is evil, as though there were an intermediate in all cases. But this does not necessarily follow. For one term of opposition is the joint negation of things that are opposed, between which there is some intermediate and there is naturally some distance. But between other things there is no difference, for those things of which there are joint negations belong to a different genus. Hence their subject is not one.

COMMENTARY

             2059. After having shown what contrariety is, here the Philosopher settles certain difficulties concerning the points established above. In regard to this he does two things. First (857:C 2059), he raises the difficulties; and second (858:C 2060), he solves them ("For we always").

             Now the difficulties (857) stem from the statement that one thing has one contrary; and this appears to be wrong in the case of a twofold opposition. For while the many are opposed to the one, the few are opposed to the many. And similarly the equal also seems to be opposed to two things, namely, to the large and to the small. Hence the difficulty arises as to how these things are opposed. For if they are opposed according to contrariety, then the statement which was made seems to be false, namely, that one thing has one contrary.

             2060. For we always (858).

             Then he deals with the foregoing difficulties; and, first, he examines the difficulty about the opposition between the equal and the large and the small. Second (868:C 2075), he discusses the difficulty about the opposition between the one and the many ("And one might").

             In regard to the first he does two things. First, he argues the question dialectically. Second (864:C 2066), he establishes the truth about this question ("It follows").

             In regard to the first he does two things. First, he argues on one side of the question in order to show that the equal is contrary to the large and to the small. Second (862:C 2064), he argues on the opposite side of the question ("But it follows").

             In regard to the first he gives three arguments. In the first of these he does two things. First, he clarifies a presupposition of the argument by stating that we always use the term whether in reference to opposites; for example, when we ask whether a thing is white or black, which are opposed as contraries; and whether it is white or not white, which are opposed as contradictories. But we do not ask whether a thing is a man or white, unless we assume that something cannot be both a man and white. We then ask whether it is a man or white, just as we ask whether that is Cleon or Socrates coming, on the assumption that both are not coming at the same time. But this manner of asking about things which are not opposites does not pertain to any class of things by necessity but only by supposition. This is so because we use the term whether only of opposites by necessity, but of other things only by supposition; for only things which are opposed by nature are incapable of coexisting. And this is undoubtedly true if each part of the disjunction "whether Socrates or Cleon is coming" is not true at the same time, because, if it were possible that both of them might be coming at the same time, the above question would be absurd. And if it is true that both cannot be coming at the same time, then the above question involves the opposition between the one and the many. For it is necessary to ask whether Socrates and Cleon are both coming or only one of them. And this question involves the opposition between the one and the many. And if it is assumed that one of them is coming, then the question takes the form, whether Socrates or Cleon is coming.

             2061. If, then, the question (859).

             From the proposition which has now been made clear the argument proceeds as follows: those who ask questions concerning opposites use the term whether, as has been mentioned above. But we use this term in the case of the equal, the large and the small; for we ask whether one thing is more or less than or equal to another. Hence there is some kind of opposition between the equal and the large and the small. But it cannot be said that the equal is contrary to either the large or the small, because there is no reason why it should be contrary to the large rather than to the small. And again, according to what has been said before, it does not seem that it is contrary to both, because one thing has one contrary.

             2062. Again, the equal (860).

             He now gives the second argument, which runs thus: the equal is contrary to the unequal. But the unequal signifies something belonging to both the large and the small. Therefore the equal is contrary to both.

             2063. And this difficulty (861).

             Then he gives the third argument, and this is based on the opinion of Pythagoras, who attributed inequality and otherness to the number two and to any even number, and identity to an odd number. And the reason is that the equal is opposed to the unequal; but the unequal is proper to the number two; therefore the equal is contrary to the number two.

             2064. But it follows (862).

             Next, he gives two arguments for the opposite opinion. The first is as follows: the large and the small are two things. Therefore, if the equal is contrary to the large and to the small, one is contrary to two. This is impossible, as has been shown above (861:C 2063).

             2065. Further, the equal (863).

             He now gives the second argument, which runs thus: there is no contrariety between an intermediate and its extremes. This is apparent to the senses, and it is also made clear from the definition of contrariety, because it is complete difference. But whatever is intermediate between any two things is not completely different from either of them, because extremes differ from each other more than from an intermediate. Thus it follows that there is no contrariety between an intermediate and its extremes. But contrariety pertains rather to things which have some intermediate between them. Now the equal seems to be the intermediate between the large and the small. Therefore the equal is not contrary to the large and to the small.

             2066. It follows, then (864).

             Here he establishes the truth about this question; and in regard to this he does three things. First, he shows that the equal is opposed to the large and to the small in a way different from that of contrariety; and he draws this conclusion from the arguments given above on each side of the question. For the first set of arguments showed that the equal is opposed to the large and to the small, whereas the second showed that it is not contrary to them. It follows, then, that it is opposed to them by some other type of opposition. And after having rejected the type of opposition according to which the equal is referred to the unequal but not to the large and the small, it follows that the equal is opposed to the large and to the small either as their negation or as their privation.

             2067. He shows in two ways that in the latter type of opposition the equal is opposed to both of the others (the large and the small) and not merely to one of them. First, he says that there is no reason why the equal should be the negation or the privation of the large rather than of the small, or vice versa. Hence it must be the negation or the privation of both.

             2068. He also makes this clear by an example, saying that, since the equal is opposed to both, then when we are making inquiries about the equal we use the term whether of both and not merely of one; for we do not ask whether one thing is more than or equal to another, or whether it is equal to or less than another. But we always give three alternatives, namely, whether it is more than or less than or equal to it.

             2069. But it is not necessarily (865).

             Second, he indicates the type of opposition by which the equal is opposed to the large and to the small. He says that the particle not, which is contained in the notion of the equal when we say that the equal is what is neither more nor less, does not designate a negation pure and simple but necessarily designates a privation; for a negation pure and simple refers to anything to which its own opposite affirmation does not apply; and this does not occur in the case proposed. For we do not say that everything which is not more or less is equal, but we say this only of those things which are capable of being more or less.

             2070. Hence the notion of equality amounts to this, that the equal is what is neither large nor small, but is naturally capable of being either large or small, just as other privations are defined. Thus it is evident that the equal is opposed to both the large and the small as a privative negation.

             2071. And for this reason (866).

             Third, in concluding his discussion between the large and the small; and he shows that the equal is intermediate in regard to this he does two things. First, he draws his thesis as the conclusion of the foregoing argument. For since it has been said that the equal is what is neither large nor small but is naturally capable of being the one or the other, then anything that is related to contraries in this way is intermediate between them, just as what is neither good nor evil is opposed to both and is intermediate between them. Hence it follows that the equal is intermediate between the large and the small. But there is this difference between the two cases: what is neither large nor small has a name, for it is called the equal, whereas what is neither good nor evil does not have a name.

             2072. The reason for this is that sometimes both of the privations of two contraries coincide in some one definite term; and then there is only one intermediate, and it can easily be given a name, as the equal. For by the fact that a thing has one and the same quantity it is neither more nor less. But sometimes the term under which both of the privations of the contraries fall is used in several senses, and there is not merely one subject of both of the privations taken together; and then it does not have one name but either remains completely unnamed, like what is neither good nor evil, and this occurs in a number of ways; or it has various names, like what is neither white nor black; for this is not some one thing. But there are certain undetermined colors of which the aforesaid privative negation is used; for what is neither white nor black must be either gray or yellow or some such color.

             2073. Hence the criticism (867).

             Then he rejects the criticism which some men offered against the view that what is neither good nor evil is an intermediate between good and evil. For they said that it would be possible on the same grounds to posit an intermediate between any two things whatsoever. Hence he says that, in view of the explanation that things having an intermediate by the negation of both extremes as indicated require a subject capable of being either extreme, it is clear that the doctrine of such an intermediate is unjustly criticized by those who think that the same could therefore be said in all cases (say, that between a shoe and a hand there is something which is neither a shoe nor a hand) because what is neither good nor evil is intermediate between good and evil, since for this reason there would be an intermediate between all things.

             2074. But this is not necessarily the case, because this combination of negations which constitute an intermediate belongs to opposites having some intermediate, between which, as the extremes of one genus, there is one distance. But the other things which they adduce, such as a shoe and a hand, do not have such a difference between them that they belong to one distance; because the things of which they are the combined negations belong to a different genus. Negations of this kind, then, do not have one subject; and it is not possible to posit an intermediate between such things.