Institute of Information Science, Academia Sinica

Fitch’s paradox of knowability shows that, given plausible modal and epistemic principles, the axiom that all truths are knowable implies that all truths are known. Fitch’s paradox is typically discussed in the context of classical and intuitionistic logic. In this paper, we consider Fitch’s paradox in a range of non-classical logics, including relevant logics, Łukasiewicz logics, HYPE, and sub-intuitionistic logics. We show that some forms of the paradox hold in the non-classical logics, while others do not. (This is joint work with Branden Fitelson.)