Überconsistent Logics and Dialetheism

Graham Priest, a world-renowned logician and philosopher, is Distinguished Professor of Philosophy at The Graduate Center, City University of New York, Boyce Gibson Professor Emeritus at the University of Melbourne, and International Research Fellow at the Ruhr University of Bochum. He is known for his work on non-classical logic, metaphysics, the history of philosophy, and Buddhist philosophy.  He has published over 300 articles—in nearly every major philosophy and logic journal—and eight books—mostly with Oxford University Press.

For many decades now, logics which permit inconsistent but non-trivial theories have been investigated and discussed. However, of recent years, we have seen the recognition that there are logics which not only permit contradictions, but which deliver contradictions: the logical truths are themselves inconsistent. As yet, they have no standard name as far as I know. Let uscall them überconsistent logics. Dialetheism is the view that some contradictions are true. It might well be thought that these logics which delivercontradictory logical truths provide a slam dunk for dialetheism. After all, as Quine puts it, ‘if sheer logic is not conclusive, what is?’ Matters are notthat straightforward, however. This talk is an initial investigation of the relationship between überconsistent logics and dialetheism. In the first part of the talk I give the appropriate background for the discussion. In the second I discuss how three well known überconsistent logics bear on the matter of dialetheism.