predicate of every subject every attribute and the negation of it indifferently. For it is absurd if of every subject its own negation is to be predicable, while the negation of something else which cannot be predicated of it is not predicable of it; for instance, if it is true to say of a man that he is not a man, evidently it is also true to say that he is not a trireme. If, then, the affirmative^[1] can be predicated, the negative must be predicable too; and if the affirmative is not predicable, the negative, at least, will be more predicable than {{Left sidenote|1008^a the negative of the subject itself. If, then, even the latter negative is predicable, the negative of 'trireme' will be also predicable; and, if this is predicable, the affirmative will be so too.—Those, then, who maintain this view are driven to this conclusion, and to the further conclusion that it is not necessary either to assert or to deny. For if it is true that a thing is man and not-man, evidently also it will be neither man nor not-man. For to the two assertions there answer two negations. And if the former^[2] is treated as a single proposition compounded out of two, the latter also is a single proposition opposite to the former.

Again, either the theory is true in all cases, and a thing is both white and not-white, and being and non-being, and all other contradictories are similarly compatible, or the theory is true of some statements and not of others. And if not of all, the exceptions will be contradictories of which admittedly only one is true; but if of all, again either the negation will be true wherever the assertion is, and the assertion true wherever the negation is, or the negation will be true where the assertion is, but the assertion not always true where the negation is. And (1) in the latter case there will be something which fixedly is not, and this will be an indisputable belief; and if non-being is indisputable and knowable, the opposite assertion will be more knowable. But (2) if what it is necessary to deny it is equally necessary to assert, it is either true or not true to separate the predicates and say, for instance, that a thing is white, and again that it is not-white. And if (a) it is