Why Priest’s reassurance is not reassuring

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. 1 LP and MiLP: the basic picture The logic LP (for ‘logic of paradox’) offers many virtues in philosophy, most notably for underwriting theories subject to paradox (e.g., truth, properties, etc).1 But LP is also a notoriously weak logic. Example: LP never sanctions the inference from {¬A,A ∨ B} to B. This inference goes wrong where A is a glut (and, hence, A ∧ ¬A true) and B untrue. LP guards against that threat. But one might think that for just that reason a subtler, more liberal logic is required – one that sanctions the inference of q from {¬p, p ∨ q} in case