Roy Cook, Dept. of Philosophy, University of Minnesota, Twin Cities—One of the most prominent challenges to the correctness of classical logic has been proposed by intuitionists, who object to the validity of excluded middle: P or not-P.

Intuitionists argue that not all instances of excluded middle are logically true, since (on their view) we have no logical guarantee that every sentence is either determinately true or determinately false. In this talk I will not argue against the intuitionist's claims, but instead argue that their focus on (the simple propositional version of) excluded middle is misguided. One of the primary advantages to adopting a non-classical logic strictly weaker than classical logic, such as intuitionistic logic, is that more theories are consistent in weaker logics, and hence adopting weaker logics gives us more choices for our theories. But it turns out that, in a very simple technical sense, (the propositional version of) excluded middle is irrelevant to such concerns.