Page - 110 - in The Complete Aristotle

everything is equal or is not equal. Further the expressions ‘it is a not-white log’ and ‘it is not a white log’ do not imply one another’s truth. For if ‘it is a not-white log’, it must be a log: but that which is not a white log need not be a log at all. Therefore it is clear that ‘it is not-good’ is not the denial of ‘it is good’. If then every single statement may truly be said to be either an affirmation or a negation, if it is not a negation clearly it must in a sense be an affirmation. But every affirmation has a corresponding negation. The negation then of ‘it is not-good’ is ‘it is not not-good’. The relation of these statements to one another is as follows. Let A stand for ‘to be good’, B for ‘not to be good’, let C stand for ‘to be not-good’ and be placed under B, and let D stand for not to be not-good’ and be placed under A. Then either A or B will belong to everything, but they will never belong to the same thing; and either C or D will belong to everything, but they will never belong to the same thing. And B must belong to everything to which C belongs. For if it is true to say ‘it is a not-white’, it is true also to say ‘it is not white’: for it is impossible that a thing should simultaneously be white and be not-white, or be a not-white log and be a white log; consequently if the affirmation does not belong, the denial must belong. But C does not always belong to B: for what is not a log at all, cannot be a not-white log either. On the other hand D belongs to everything to which A belongs. For either C or D belongs to everything to which A belongs. But since a thing cannot be simultaneously not-white and white, D must belong to everything to which A belongs. For of that which is white it is true to say that it is not not-white. But A is not true of all D. For of that which is not a log at all it is not true to say A, viz. that it is a white log. Consequently D is true, but A is not true, i.e. that it is a white log. It is clear also that A and C cannot together belong to the same thing, and that B and D may possibly belong to the same thing. Privative terms are similarly related positive ter terms respect of this arrangement. Let A stand for ‘equal’, B for ‘not equal’, C for ‘unequal’, D for ‘not unequal’. In many things also, to some of which something belongs which does not belong to others, the negation may be true in a similar way, viz. that all are not white or that each is not white, while that each is not-white or all are not- white is false. Similarly also ‘every animal is not-white’ is not the negation of ‘every animal is white’ (for both are false): the proper negation is ‘every animal is not white’. Since it is clear that ‘it is not-white’ and ‘it is not white’ mean different things, and one is an affirmation, the other a denial, it is evident that the method of proving each cannot be the same, e.g. that whatever is an animal is not white or may not be white, and that it is true to call it not-white; for this means that it is not-white. But we may prove that it is true to call it white or not-white in the same way for both are proved 110