CONSISTENCY AND THE THEORY OF TRUTH

Abstract

AbstractWhat is the logical strength of theories of truth? That is: If you take a theory${\cal T}$and add a theory of truth to it, how strong is the resulting theory, as compared to${\cal T}$? Once the question has been properly formulated, the answer turns out to be about as elegant as one could want: At least when${\cal T}$is finitely axiomatized theory, theories of truth act more or less as a kind of abstract consistency statement. To prove this result, however, we have to formulate truth-theories somewhat differently from how they have been and instead follow Tarski in ‘disentangling’ syntactic theories from object theories.