I IntroductionAtMetaphysicsΓ 3, Aristotle argues that it belongs to a single discipline, which he callsfirst 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 tob34. 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...

In Book Γ of the Metaphysics Aristotle states and attempts to prove what he calls the basic principle of the science of being as being: the law of non‐contradiction. In this paper I defend an interpretation of his proof, inspired by Elizabeth Anscombe's 1961 essay in ‘Three Philosophers’, though some of its features were remarked on by Lukasiewicz in 1910, according to which Aristotle is proving this principle only for substance predicates, and that it is to be understood as the (...) basic principle of metaphysics rather than of logic. It is the principle that every substance has an essential nature, and if it is of the essential nature of x to be F then it cannot be of the essential nature of x to be not‐F since then x's being F and x's being not‐F would be the same. He puts it by saying that in such a case F and not‐F would ‘signify the same’ for x. Since they do not, x cannot be both. (shrink)