Truth within Proof-Theoretic Semantics

Truth plays an important role in our everyday discourse. However, the philosophical study of truth has proven challenging.

The semantics of truth is complicated both by questions of the nature of truth and by the paradoxes naïve theories generate. Traditional views about truth hold that a statement is true if it corresponds to reality.

These views require positing a correspondence relation between reality on the one hand and language on the other; spelling out the details of such an account has fallen prey to vicious circle arguments and other accusations of triviality.

Deflationism about truth, in contrast, assumes that the meaning of “true” can be explained with reference only to its linguistic and logical role.

As such, it is natural to try and clarify the content of deflationism by offering an inferentialist explanation of deflationism. Proof-theoretic semantics brings precision to inferentialism.

Hence, if the truth predicate can be given a proof-theoretic semantics, we will finally be able to state precisely what deflationism amounts to.

The main objective of this project is to assess to what extent proof-theoretic semantics is compatible with the deflationist conception of truth and to deploy proof-theoretic semantics in elucidating what it means for truth to be a metaphysically light notion. This is important because it has been argued that no proof-theoretic semantics can be given to truth.

However, the argument is based on a naïve, classical, inflationary notion of truth. Deflationism opens up a non-classical, non- naïve approach to truth. There is no research on whether proof-theoretic semantics is compatible with this approach to truth.

This project will provide a proof-theoretic semantics for deflationary truth, focusing on intuitionistic and intermediate logics, and thereby give strong support to deflationism and clarify its implications and contents.