Section 5

Since one thing has one contrary, it might be asked in what sense unity is opposed to plurality, and the equal to the great and to the small. For if we always use the word whether in an antithesis—e.g., whether it is white or black, or whether it is white or not (but we do not ask whether it is a man or white, unless we are proceeding upon some assumption, and asking, for instance, whether it was Cleon who came or Socrates.

This is not a necessary disjunction in any class of things, but is derived from the use in the case of opposites—for it is only opposites that cannot be true at the same time—and we have this same use here in the question which of the two came? for if both alternatives were possible, the question would be absurd; but even so the question falls into an antithesis: that of one or many—i.e., whether both came, or one)—

if, then, the question whether is always concerned with opposites, and we can ask whether it is greater or smaller, or equal, what is the nature of the antithesis between equal and greater or smaller? It is contrary neither to one only, nor to both: for (a) it is no more contrary to the greater than to the smaller; (b) equal is contrary to unequal, and thus it will be contrary to more than one thing;

(c) if unequal means the same as both greater and smaller at the same time, equal must still be opposed to them both: This difficulty supports the theory 1 that the unequal is a duality. But the result is that one thing is contrary to two; which is impossible.

Further, it is apparent that equal is intermediate between great and small, but it is not apparent that any contrariety is intermediate, nor can it be, by definition; for it could not be complete if it were the intermediate of something, but rather it always has something intermediate between itself and the other extreme.

It remains, then, that it is opposed either as negation or as privation. Now it cannot be so opposed to one of the two, for it is no more opposed to the great than to the small.

Therefore it is a privative negation of both. For this reason we say whether with reference to both, and not to one of the two—e.g., whether it is greater or equal, or whether it is equal or smaller; there are always three alternatives. But it is not a necessary privation; for not everything is equal which is not greater or smaller, but only things which would naturally have these attributes.

The equal, then, is that which is neither great nor small, but would naturally be either great or small; and it is opposed to both as a privative negation, and therefore is intermediate between them. And that which is neither good nor bad is opposed to both, but it has no name (for each of these terms has several meanings, and there is no one material which is receptive of both); that which is neither white nor black is better entitled to a name,

although even this has no single name, but the colors of which this negation is privatively predicated are to a certain extent limited; for it must be either grey or buff or something similar.

Therefore those persons are wrong in their criticism who imagine that all terms are used analogously, so that that which is neither a shoe nor a hand will be intermediate between shoe and hand, because that which is neither good nor bad is intermediate between good and bad—as though there must be an intermediate in all cases; but this does not necessarily follow.

For the one is a joint negation of opposites where there is an intermediate and a natural interval; but in the other case there is no question of difference, since the joint negation applies to things which are in different genera, and therefore the substrate is not one. 2