Truth without standard models: some conceptual problems reloaded

Abstract

A theory of truth is usually demanded to be consistent, but w -consistency is less frequently requested. Recently, Yatabe has argued in favour of w-inconsistent first-order theories of truth, minimising their odd consequences. In view of this fact, in this paper, we present five arguments against w-inconsistent theories of truth. In order to bring out this point, we will focus on two very well-known w-inconsistent theories of truth: the classical theory of symmetric truth FS and the non-classical theory of naïve truth based on ᴌukasiewicz infinitely valued logic: PAᴌT.