Antirealist Truth

Until now, antirealists have offered sketches of a theory of truth, at best. In this paper, we present an antirealist theory of truth in some formal detail. We show that the theory is able to deal satisfactorily with the problems that are standardly taken to beset antirealism. According to antirealists, there is an intimate connection between truth and human cognitive capacities which holds by conceptual necessity. While antirealists differ about the exact nature of the connection, no antirealist disputes its conceptual necessity; it distinguishes the antirealist conception of truth from a realist one accompanied by some methodological view to the effect that, by natural selection perhaps, or maybe just by good fortune, our epistemic powers happen to be so attuned to the world we inhabit that there exist no truths which are beyond our ken in principle. So far antirealists have proposed constraints to be met by antirealist theories of truth, and even a sporadic “informal elucidation” of antirealist truth (Putnam [1981:56]), but an antirealist theory of truth, comparable, if only just remotely, in formal precision to Tarski’s [1956] theory of truth, for instance, is still glaringly missing from the literature. Williamson [2006] seems right to castigate antirealists for, so far at least, failing to offer anything going beyond amerely programmatic sketch of their position. In this paper, we aim to address this lack by taking at least some first steps towards defining a formally precise antirealist theory of truth for a language. The adequacy conditions for an antirealist theory of truth are partly the same as those for a realist theory of truth: The theory should be both materially and formally adequate in Tarski’s sense. That is, the truth predicate, as defined by the theory, should satisfy the disquotational schema and it should be paradox-free. In addition it should not entail what one might call quasi-paradoxes, that is, consistent but intuitively absurd claims, such as—to mention a famous example—the claim that all truths are known. Furthermore, the theory should validate our core intuitions about truth as much as possible. For instance, it should make most, and preferably all, sentences we pretheoretically regard as being truth-valued come out as such. Likewise, it should entail certain