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. (shrink)

I IntroductionAt Metaphysics Γ 3, Aristotle argues that it belongs to a single discipline, which he calls first philosophy, to investigate both substance and a special class of claims which includes among its members the principle of non-contradiction. At Γ 4, after insisting that the PNC is, strictly speaking, indemonstrable, he sets forth a series of sketches of refutative arguments intended to show how it can, nonetheless, be substantiated. Traditionally, his main refutative argument has been taken to be embedded in (...) the passage which runs from 1006a31 to b34. In that passage, he tries to show that anyone who denies the PNC and who can then be led, by means of an artfully arranged series of questions, to agree to a few seemingly modest theses about the signification of expressions of a certain type — which Aristotle illustrates with the general term ‘man’ — is thereby logically committed to the following modal claim: ‘It is necessary, then, if it is true to say that something is a man, that it be a bipedal animal'. (shrink)

While defending the principle of non-contradiction in Metaphysics 4, Aristotle argues that the Measure Doctrine of Protagoras is equivalent to the claim that all contradictions are true; given all appearances are true (as the Protagorean maintains), anytime people disagree we get a true contradiction. This argument seems clearly invalid: nothing guarantees that actual disagreement occurs over every matter of fact. The argument in fact works perfectly, I propose, because the Protagorean view falls prey to a version of Fitch's “paradox” of (...) knowability. The proposed reading shows how Aristotle treats the Protagorean view at issue as an epistemic theory of truth distinct from the mere claim that all appearances are true (which other opponents put forward on different grounds) and reveals Aristotle's underlying concern with the modal collapse of possibility into actuality. The revised Protagorean view Aristotle confronts in a subsequent chapter is furthermore best understood as an attempt to avoid this Fitch-style result. (shrink)