A New Conditional for Naive Truth Theory

Abstract

In this paper a logic suitable for reasoning disquotationally about truth, ${\mathsf{TJK}}^{+}$, is presented and shown to have a standard model. This work improves on Hartry Field’s recent results establishing consistency and $\omega$-consistency of truth theories with strong conditional logics. A novel method utilizing the Banach fixed point theorem for contracting functions on complete metric spaces is invoked, and the resulting logic is shown to validate a number of principles which existing revision theoretic methods have so far failed to provide.