Harmony and Paradox
Intensional Aspects of Proof-Theoretic Semantics
Luca Tranchini
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Springer International Publishing
Geisteswissenschaften, Kunst, Musik / Allgemeines, Lexika
Beschreibung
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.
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Schlagwörter
Sense and denotation, Higher-level rules, Jacinto and Read’s GE-stability, Meaning of logical constants, PSH-inversion and harmony, harmony via reductions and expansions, Hyperintensionality, Inferentialism, Open Access, Proof-theoretic semantics, Paradoxes as non-denoting derivations, Normalization, subformula, canonicity harmony, relative priority of correctness and validity, Identity of proofs, Proof theory and meaning, proofs as constructions, Prawitz-Tennant analysis of paradoxes, Paradox and proof-theory, Proof-theoretic harmony