A Note on the Unprovability of Consistency in Formal Theories of Truth

Why is it that even strong formal theories of truth fail to prove their own consistency? Although Field (Mind, 115, 459, 2006) has addressed this question for many theories of truth, I argue that there is an important and attractive class of theories of truth that he omitted in his analysis. Such theories cannot prove that all their axioms are true, though unlike many of the cases Field considers, they do not prove that any of their axioms are false or that any of their rules of inference are not truth preserving. I argue that it is the fact that such theories are not finitely axiomatizable that stops them from proving their own consistency.