Restricting the T‐schema to solve the liar

Abstract

AbstractIf we want to retain classical logic and standard syntax in light of the liar, we are forced to restrict the T‐schema. The traditional philosophical justification for this is sentential – liar sentences somehow malfunction. But the standard formal way of implementing this is conditional, our T‐sentences tell us that if “p” does not malfunction, then “p” is true if and only if p. Recently Bacon and others have pointed out that conditional T‐restrictions like this flirt with incoherence. If we want to keep the “malfunction” motivation, our only other option is to non‐conditionally restrict the T‐schema, but Field and others have given powerful philosophical and technical arguments against this kind of approach. Here I argue that if we really take the philosophical motivation for restricting T‐sentences seriously, we can explain why conditional restrictions fail, answer Field's argument, and reason in a coherent way about truth using a non‐conditional restriction strategy. This cracks the door open for a fully classical response to the liar and related paradoxes. In closing, I argue that, when properly understood, this kind of “restriction” is not really a restriction at all. If this is right, then the holy grail of liar studies (classical logic, naïve truth, and standard syntax) may yet be attainable.