Validity in a dialetheist framework

Abstract

In this paper, we develop two theories of validity in a dialetheist framework, both based on Meadows (2014). The first one, LPV∗, has LP's consequence relation but the validity predicate of Meadows' fixed point construction. The second theory, DT (the one we favour), is defined in terms of its validity predicate. Therefore, in DT, the validity predicate and the consequence relation coincide. Moreover, this theory, unlike Meadows' VAL, is reflexive.