Reformulating an Argument of Aristotle’s against Contradictions

Abstract

Aristotle put forward a number of arguments against contradictions being true, in Metaphysics. However, many of them share a common flaw; the opponent in the debate (a dialetheist) can accept both the conclusion, and its negation. My aim will be to reformulate one argument, the Anscombe/Cresswell argument, to eliminate this flaw. I do so by exploiting modern developments in dialethic theory. I turn the argument into a non-question-begging reductio by exploiting the fact that a reductio can be to absurdity but not contradiction, and can conclude in the rejection of what lead to it (in this case, a contradiction). I also respond to a number of other objections to this argument, exploring the possibility that there is a good argument that keeps to the spirit of the original. I conclude that there is such an argument, but one that is only about very specific contradictions.