Aristotle sums up his reasoning here as follows: "It would seem also that in saying the man is not a horse we should be either more or not less right than in saying he is not a man, so that we shall be right in saying that the same person is a horse; for it was assumed to be possible to make opposite statements equally truly. It follows then that the same person is a man and a horse, or any other animal. While, then, there is no proof of the axiom [the principle of non-contradiction] without qualification, there is a proof relatively to anyone who will make these suppositions. And perhaps if we had questioned Heraclitus himself in this way we might have forced him to confess that opposite statements can never be true of the same subjects”
(Metaphysics, Book VI, 3, 1062a25-31). See also Posterior Analytics, Book I, 2 (72a12).