Advances in Proof-Theoretic Semantics

Description

This volume is the first ever collection devoted to the field of proof-theoretic semantics. Contributions address 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. The field of proof-theoretic semantics has existed for almost 50 years, but the term itself was proposed by Schroeder-Heister in the 1980s. Proof-theoretic semantics 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 presentations at the Second International Conference on Proof-Theoretic Semantics in Tübingen in 2013, where contributing authors were asked to provide a self-contained description and analysis 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. Front Matter....Pages i-vi Advances in Proof-Theoretic Semantics: Introduction....Pages 1-4 On the Relation Between Heyting’s and Gentzen’s Approaches to Meaning....Pages 5-25 Kreisel’s Theory of Constructions, the Kreisel-Goodman Paradox, and the Second Clause....Pages 27-63 On the Paths of Categories....Pages 65-77 Some Remarks on Proof-Theoretic Semantics....Pages 79-93 Categorical Harmony and Paradoxes in Proof-Theoretic Semantics....Pages 95-114 The Paradox of Knowability from an Intuitionistic Standpoint....Pages 115-137 Explicit Composition and Its Application in Proofs of Normalization....Pages 139-152 Towards a Proof-Theoretic Semantics of Equalities....Pages 153-160 On the Proof-Theoretic Foundations of Set Theory....Pages 161-171 A Strongly Differing Opinion on Proof-Theoretic Semantics?....Pages 173-188 Comments on an Opinion....Pages 189-193 On Dummett’s “Proof-Theoretic Justifications of Logical Laws”....Pages 195-210 Self-contradictory Reasoning....Pages 211-229 Completeness in Proof-Theoretic Semantics....Pages 231-251 Open Problems in Proof-Theoretic Semantics....Pages 253-283