Who Needs a Proof of the Principle of Non-Contradiction?

The topic of this paper is Aristotle’s ‘proof by refutation’ of the Principle of Non-Contradiction (Metaphysics Γ 4, 1006a11–1007a20). I consider a worry which has often been raised in connection with this proof. The worry is that, faced with an opponent who is prepared to tolerate contradictions, the argument is dialectically powerless: it is incapable of getting them to abandon their position. In reply, I argue that the proof needs to be seen in its proper context, that is, as part of Aristotle’s response to an opponent who demands a demonstration of the principle. This allows us to clarify the purpose of the argument and answer the worry about its effectiveness.