The fundamental discussion of non-contradiction by Aristotle is in Met, Book IV:
[1005b] it is impossible for the same
man at the same time to believe the same thing to be and not to be; for if a man
were mistaken in this point he would have contrary opinions at the same time.
For it is impossible that there should be demonstration of absolutely everything; there would be an infinite regress, so that there would still be no demonstration. But if there are things of which one should not demand demonstration, these persons cannot say what principle they regard as more indemonstrable than the present one.
[1006a] We can, however, demonstrate negatively even that this view is impossible, if our opponent will only say something; and if he says nothing, it is absurd to
attempt to reason with one who will not reason about anything, in so far as he
refuses to reason. [...] The starting-point for all such arguments is not the
demand that our opponent shall say that something either is or is not (for this one might perhaps take to be assuming what is at issue), but that he shall say something which is significant both for himself and for another; for this is necessary, if he really is to say anything. For, if he means nothing, such a man will not be capable of reasoning, either with himself or with another.