Two-valued logics for naive truth theory

Abstract

It is part of the current wisdom that the Liar and similar semantic paradoxes can be taken care of by the use of certain non-classical
multivalued logics. In this paper I want to suggest that bivalent logic can do just as well. This is accomplished by using a non-deterministic matrix to define the negation connective. I show that the systems obtained in this way support a transparent truth predicate. The paper also contains some remarks on the conceptual interest of such systems.