“Models for Liars in Bradwardine's Theory of Truth,” pages 99–114 in Insolubles and Consequences: Essays in Honour of Stephen Read, edited by Catarina Dutilh Novaes and Ole Thomassen Hjortland, College Publications, 2012
According to Stephen Read, Thomas Bradwardine’s theory of truth provides an independently motivated solution to the paradoxes of truth, such as the liar. In a series of papers, I have discussed modal models for Read’s reconstruction of Bradwardine’s theory. In this paper, provide a hypersequent calculus for this theory, and I show that the cut rule is admissible in the hypersequent calculus.
(This paper is dedicated to Professor Stephen Read, whose work has been a profound influence on my own. His work on relevant logic, on proof theoretical harmony, on the logic of identity and on Thomas Brad- wardine’s theory of truth have been a rich source of insight, of stimulation and of provocation. In an attempt to both honour Stephen, and hopefully to give him some pleasure, I am going to attempt to cook up something original using some of the many and varied ingredients he has provided us. In this paper, I will mix and match ideas and techniques from Stephen’s papers on proof theory, on Bradwardine’s theory of truth, and on identity to offer a harmonious sequent system for a theory of truth inspired by Stephen Read’s recovery of the work of Thomas Bradwardine.)