Aristotle, Metaphysics

[1006a] [1] and say that it is possible to hold this view. Many even of the physicists adopt this theory. But we have just assumed that it is impossible at once to be and not to be, and by this means we have proved that this is the most certain of all principles.Some, indeed, demand to have the law proved, but this is because they lack education¹; for it shows lack of education not to know of what we should require proof, and of what we should not. For it is quite impossible that everything should have a proof; the process would go on to infinity, so that even so there would be no proof.² If on the other hand there are some things of which no proof need be sought, they cannot say what principle they think to be more self-evident. Even in the case of this law, however, we can demonstrate the impossibility by refutation, if only our opponent makes some statement. If he makes none, it is absurd to seek for an argument against one who has no arguments of his own about anything, in so far as he has none; for such a person, in so far as he is such, is really no better than a vegetable.And I say that proof by refutation differs from simple proof in that he who attempts to prove might seem to beg the fundamental question, whereas if the discussion is provoked thus by someone else, refutation and not proof will result.The starting-point for all such discussions is not the claim that he should state that something is or is not so [20] (because this might be supposed to be a begging of the question), but that he should say something significant both to himself and to another (this is essential if any argument is to follow; for otherwise such a person cannot reason either with himself or with another);and if this is granted, demonstration will be possible, for there will be something already defined. But the person responsible is not he who demonstrates but he who acquiesces; for though he disowns reason he acquiesces to reason. Moreover, he who makes such an admission as this has admitted the truth of something apart from demonstration [so that not everything will be "so and not so"].

Thus in the first place it is obvious that this at any rate is true: that the term "to be" or "not to be" has a definite meaning; so that not everything can be "so and not so." Again, if "man" has one meaning, let this be "two-footed animal."By "has one meaning" I mean this: if X means "man," then if anything is a man, its humanity will consist in being X. And it makes no difference even if it be said that "man" has several meanings, provided that they are limited in number;