Timothy Clarke

Aristotle thinks that the Platonic theory of Forms is vulnerable to the Third Man regress. According to Alexander of Aphrodisias, the regress arises from the conjunction of three Platonist claims, which I label ‘Exemplification’, ‘Similarity’, and ‘Distinctness’. It is clear why, taken together, these three claims generate an infinite regress of Forms. What is not clear is why Aristotle thinks that a Platonist should have to accept each of the claims. My answer begins from the fact that, in Metaphysics A and M, Aristotle mentions the Third Man as a consequence, not of positing Forms, but of certain ways of arguing for Forms. By working out what these arguments are likely to have been, we can understand why he took the Platonist to have been committed to all three claims, and thus why he saw the Third Man as a serious difficulty.

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.