ISBN-10: 3319226851

ISBN-13: 9783319226859

This quantity is the 1st ever assortment dedicated to the sphere of proof-theoretic semantics. Contributions tackle themes together with the systematics of creation and removal principles and proofs of normalization, the categorial characterization of deductions, the relation among Heyting's and Gentzen's ways to which means, knowability paradoxes, proof-theoretic foundations of set concept, Dummett's justification of logical legislation, Kreisel's thought of structures, paradoxical reasoning, and the defence of version theory.

The box of proof-theoretic semantics has existed for nearly 50 years, however the time period itself was once proposed by means of Schroeder-Heister within the Eighties. Proof-theoretic semantics explains the that means of linguistic expressions generally and of logical constants specifically when it comes to the idea of facts. This quantity emerges from shows on the moment overseas convention on Proof-Theoretic Semantics in Tübingen in 2013, the place contributing authors have been requested to supply a self-contained description and research of an important learn query during this zone. The contributions are consultant of the sphere and will be of curiosity to logicians, philosophers, and mathematicians alike.

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**Extra resources for Advances in Proof-Theoretic Semantics**

**Example text**

Goodman [17, p. g. in the manner described in [22, Sect. 2]. But as Goodman makes free use of λ-notation throughout both of his expositions (apparently via such an abbreviation), it will be here simpler to assume that the system includes λβ instead of the rules which Goodman takes to axiomatize the combinators. Until Sect. 5, we will also suppress discussion of a number of other primitive notions and their corresponding axioms pertaining to the treatment of so-called “grasped domains” which are introduced in the formulation of T ω .

G. Gentzen [11, p. 167], Goodman [16, p. 7], Troelstra [45, p. 210], Dummett [7, Sect. 2], Fletcher [10, p. 81], and Tait [41, p. 221]. Kreisel’s Theory of Constructions, the Kreisel-Goodman Paradox … 33 not just a construction transforming arbitrary proofs of A into proofs of B in the sense of the original clause (P→ ) but rather a pair p, q consisting of such a construction together with another proof p which demonstrates that q has this property. The second-clause variants are formed by adding similar clauses to (P¬ ) and (P∀ ).

P∨ ) A proof of A ∨ B consists of a proof of A or a proof of B. (P→ ) A proof of A → B consists of a construction which transforms any proof of A into a proof of B. (P¬ ) A proof of ¬A consists of a construction which transforms any hypothetical proof of A into a proof of ⊥ (a contradiction). (P∀ ) A proof of ∀x A consists of a construction which transforms all c in the intended range of quantification into a proof of A(c). (P∃ ) A proof of ∃x A consists of an object c in the intended range of quantification together with a proof of A(c).

### Advances in Proof-Theoretic Semantics

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