Gareth Young

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.

The purpose of this book is to present unpublished papers at the cutting edge of research on dialetheism and to reflect recent work on the applications of the theory. It includes contributions from some of the most respected scholars in the field, as well as from young, up-and-coming philosophers working on dialetheism. Moving from the fringes of philosophy to become a main player in debates concerning truth and the logical paradoxes, dialetheism has thrived since the publication of Graham Priest’s In Contradiction, and several of the papers find their roots in a conference on dialetheism held in Glasgow to mark the 25th anniversary of Priest’s book. The content presented here demonstrates the considerable body of work produced in this field in recent years. With a broad focus, this book also addresses the applications of dialetheism outside the more familiar area of the logical paradoxes, and includes pieces discussing the application of dialetheism in metaphysics, philosophy of language, and philosophy of mind.