Aristotle explains Whether and Plurality

One thing has one contrary. How is one opposed to the many? How is equal opposed to the big and the small?

“Whether” compares opposites. Opposites alone cannot be present together.

Therefore if “whether” is contrary to the more and the less, then it will be contrary to more things than one.

But if the unequal means the same as both the greater and the less together, the equal will be opposite to both (and the difficulty supports those who say the unequal is a ’two’), but it follows that one thing is contrary to two others, which is impossible.

Again, the equal is intermediate between the great and the small, but no contrariety is either observed to be intermediate, or, from its definition, can be so; for it would not be complete if it were intermediate between any two things, but rather it always has something intermediate between its own terms.

It is opposed either as negation or as privation.

It cannot be the negation or privation of one of the two; for why of the great rather than of the small?

Therefore, it is the privative negation of both. This is why ‘whether’ has reference to both.

There are always three cases. But it is not a necessary privation, for not everything which is not greater or less is equal, but only the things which are of such a nature as to have these attributes.

The equal is that which is neither great nor small but is naturally fitted to be either great or small. It is opposed to both as a privative negation (and therefore is also intermediate). That which is neither good nor bad is opposed to both, but has no name; for each of these has several meanings and the recipient subject is not one; but that which is neither white nor black has more claim to unity.

Yet even this has not one name, though the colours of which this negation is privatively predicated are in a way limited; for they must be either grey or yellow or something else of the kind. Therefore it is an incorrect criticism that is passed by those who think that all such phrases are used in the same way, so that that which is neither a shoe nor a hand would be intermediate between a shoe and a hand, since that which is neither good nor bad is intermediate between the good and the bad-as if there must be an intermediate in all cases.

But this does not necessarily follow. For the one phrase is a joint denial of opposites between which there is an intermediate and a certain natural interval; but between the other two there is no ‘difference’; for the things, the denials of which are combined, belong to different classes, so that the substratum is not one.