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Description
Table of contents
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 toprovide 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.
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 toprovide 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.
- Cover
- Frontmatter
- Advances in Proof-Theoretic Semantics: Introduction
- On the Relation Between Heyting’s and Gentzen’s Approaches to Meaning
- Kreisel’s Theory of Constructions, the Kreisel-Goodman Paradox, and the Second Clause
- On the Paths of Categories
- Some Remarks on Proof-Theoretic Semantics
- Categorical Harmony and Paradoxes in Proof-Theoretic Semantics
- The Paradox of Knowability from an Intuitionistic Standpoint
- Explicit Composition and Its Application in Proofs of Normalization
- Towards a Proof-Theoretic Semantics of Equalities
- On the Proof-Theoretic Foundations of Set Theory
- A Strongly Differing Opinion on Proof-Theoretic Semantics?
- Comments on an Opinion
- On Dummett’s “Proof-Theoretic Justifications of Logical Laws”
- Self-contradictory Reasoning
- Completeness in Proof-Theoretic Semantics
- Open Problems in Proof-Theoretic Semantics