Carnap, Categoricity, and Commas

The commas between the premises in an inference from ψ ₁,… ,ψ ₙ ψ 1 , … , ψ n to φ φ are normally treated as conjunctions. This is fine, except when we investigate to what extent a consequence relation, or a set of inference rules, fixes the meaning of the logical constants (Carnap’s Categoricity Problem): it then in effect constitutes a bias in favor of the standard interpretation of ∧ . I look at what happens to the categoricity of some sublogics of classical propositional logic if we avoid that bias by requiring that there be exactly one premise. This binary format is also common in the literature. It turns out that intuitionistic logic loses its categoricity, whereas classical logic keeps it. I also consider Holliday’s fundamental logic, Goldblatt’s orthologic, and some other related logics.