Aristotle, Metaphysics

[1056a] [1] 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 theory¹ 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"; [20] 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;