Dag Westerståhl: Carnap’s problem for intuitionistic propositional logic

Abstract

I will first give a brief background, with some examples, on ‘Carnap’s problem’: to what extent a consequence relation in a formal language fixes the meaning, relative to some given semantics, of the logical constants in that language. I then focus on intuitionistic propositional logic and show that it is ‘Carnap categorical’: the only interpretation of the connectives consistent with the usual intuitionistic consequence relation is the standard one. This holds relative to most well-known semantics with respect to which intuitionistic logic is sound and complete; among them Kripke semantics, Beth semantics, Dragalin semantics, and topological semantics. It also holds for algebraic semantics, although categoricity in that case is different in kind from categoricity relative to possible worlds style semantics. This is joint work with Haotian Tong.