Title: Updates on Carnap’s Problem

Abstract

Carnap’s Problem, as Denis Bonnay and I understand it, is to what extent a consequence relation in some logical language fixes the meaning of the logical constants in that language. One thought in the background is that people can have fairly robust intuitions about ´what follows from what’ without having clear ideas about logicality, so it is of some interest to see if and how the former determines the latter. I will give an overview of what has been achieved in this area so far, concerning classical first-order logic, logics with generalized quantifiers, and modal logic. Then I end with some partial results on Carnap’s Problem for intuitionistic propositional logic (this is joint work with my student Haotian Tong).