SOME PROBLEMS FOR PROOF-THEORETIC SEMANTICS
William R. Stirton · The Philosophical Quarterly · 2007
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.