Harmony and Paradox Intensional Aspects of Proof-Theoretic Semantics

This open access book investigates the role played by identity of proofs in proof-theoretic semantics. It develops a conception of proof-theoretic semantics as primarily concerned with the relationship between proofs (understood as abstract entities) and derivations (the linguistic representations o...

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Hlavní autor: Tranchini, Luca
Médium: E-kniha
Jazyk:angličtina
Vydáno: Cham Springer Nature 2024
Springer International Publishing
Springer International Publishing AG
Vydání:1
Edice:Trends in Logic
Témata:
canonicity harmony
Computer science
Computing and Information Technology
harmony via reductions and expansions
Higher-level rules
Hyperintensionality
Identity of proofs
Inferentialism
Jacinto and Read’s GE-stability
Mathematical foundations
Mathematical logic
Mathematical theory of computation
Mathematics
Mathematics and Science
Meaning of logical constants
Normalization
Paradox and proof-theory
Paradoxes as non-denoting derivations
PHILOSOPHY
Philosophy and Religion
Philosophy: logic
Prawitz-Tennant analysis of paradoxes
Proof theory and meaning
Proof-theoretic harmony
Proof-theoretic semantics
proofs as constructions
PSH-inversion and harmony
relative priority of correctness and validity
Sense and denotation
subformula
Topics in philosophy
ISBN:3031469216, 9783031469213, 3031469208, 9783031469206
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Popis
Shrnutí:This open access book investigates the role played by identity of proofs in proof-theoretic semantics. It develops a conception of proof-theoretic semantics as primarily concerned with the relationship between proofs (understood as abstract entities) and derivations (the linguistic representations of proofs). It demonstrates that identity of proof is a key both to clarify some —still not wholly understood— notions at the core of proof-theoretic semantics, such as harmony; and to broaden the range of the phenomena which can be analyzed using the tools of this semantic paradigm, so as to include for instance paradoxes. The volume covers topics such as the philosophical significance of different criteria of identity of proofs, and adequacy conditions for an intensional account of the notion of harmony. The author also examines the Prawitz-Tennant analysis of paradoxes by investigating on the one hand the prospectsof turning it into a theory of meaning for paradoxical languages, and on the other hand two distinct kinds of phenomena, first observed by Crabbe and Ekman, showing that the Tennant-Prawitz criterion for paradoxicality overgenerates. This volume is of interest to scholars in formal and philosophical logic.
ISBN:3031469216
9783031469213
3031469208
9783031469206
DOI:10.1007/978-3-031-46921-3