Logic and the Liar Paradox

Abstract

AbstractThe Liar and related paradoxes create a prima facie conflict between two equally important principles of classical logic—the Law of the Excluded Middle (LEM) and the Law of Non-Contradiction (LNC). Dialetheists such as Graham Priest and JC Beall solve the paradoxes by accepting the negations of some instances of the LNC and rejecting classical logic in favor of a “paraconsistent” logical framework in which contradictions do not entail every conclusion. Hartry Field advocates the mirror image of this solution, rejecting certain instances of the LEM and thus rejecting classical logic in favor of a “paracomplete” framework in which not every LEM instance is entailed by every premise. Some paradox-solvers, eager to avoid either of these amputations of classical logic, reject paradoxical instances of the T-Schema. This is an easy way out, but the search for an adequate solution is best conducted elsewhere. The rest of the book will be spent on the project of resisting the paraconsistent and paracomplete solutions to the paradoxes and finally proposing a positive solution that retains classical logic without sacrificing the T-Schema.KeywordsParadoxesRevengeDialetheismParaconsistentParacompleteT-SchemaBivalence