Abstract

Perhaps the most powerful argument that has been made in favour of the view that some contradictions are true (dialetheism) is that it allows for a solution to the logical paradoxes which is immune to the well-known problem of revenge. The version of the view which would seem to have the best chance of avoiding the problem is a particularly thoroughgoing dialetheism, most prominently defended by Graham Priest, which takes paraconsistent set theory as its working metatheory. The purpose of this paper is to characterise a revenge problem for this thoroughgoing dialetheism, involving the notion of invalidity. I argue that the inconsistency of the metatheory commits dialetheists of this sort to accepting as contradictory, not only truth, but validity: in other words, some inference principles are both valid and invalid. I show that, depending on the details of the theory, all, or ‘almost all’ (in a sense to be explained), inference principles can be shown to be dialetheically invalid. I argue that this gives rise to a revenge problem for dialetheism, since it makes the notion of invalidity inexpressible for the dialetheist and deprives them of the ability to express crucial semantic claims about their theory.