Some problems for proof-theoretic semantics

Proof-theoretic semantics is an approach to logical semantics based on two ideas, of which the first is that the meaning of a logical connective can be explained by stipulating that some mode of inference, e.g., a natural deduction introduction or elimination rule, is permissible. The second idea is that the soundness of rules which are not stipulated outright may be deduced by some proof-theoretic argument from properties of the rules which are stipulated outright. I examine the first idea. My main conclusion is that the idea is more problematic, and requires more discussion, than has been generally realized. I mention five problems which will have to be overcome before the idea can be accepted as definitely viable.