Why Priest's reassurance is not reassuring

Abstract

In the service of paraconsistent (indeed, ‘dialetheic’) theories, Graham Priest has long advanced a non-monotonic logic (viz., MiLP) as our ‘universal logic’ (at least for standard connectives), one that enjoys the familiar logic LP as its monotonic core [10, Chs 16, 19]. In this paper, I show that MiLP faces a dilemma: either it is (plainly) unsuitable as a universal logic or its role as a ‘universal logic’ (indeed, its role full stop) is a mystery. While familiarity with the basic ideas of dialetheism [4, 10] is assumed, formal details of the target logics are relegated to an appendix; the basic problem is evident without them.