Advances in Proof-Theoretic Semantics

This volume covers, in the first ever book collection of its kind, the field of proof-theoretic semantics. The wide variety of researchers contributing to this volume cover topics including the systematics of introduction and elimination rules and proofs of normalization, the categorial characterization of deductions, the relation between Heyting's and Gentzen's approaches to meaning, knowability paradoxes, proof-theoretic foundations of set theory, Dummett's justification of logical laws, Kreisel's theory of constructions, paradoxical reasoning and the defence of model theory.§§Proof-theoretic semantics is a field that has been in existence for almost 50 years but the term itself was proposed by Schroeder-Heister in the 1980s. It explains the meaning of linguistic expressions in general and of logical constants in particular in terms of the notion of proof. This volume emerges from talks given at the Second International Conference on Proof-Theoretic Semantics in Tübingen in 2013, whereby contributing authors were asked to provide a self-contained description of a significant research question in this area. The contributions are representative of the field and should be of interest to logicians, philosophers and mathematicians alike.§§