Proof-Theoretic Semantics. Schroeder-Heister, P. In The Stanford Encyclopedia of Philosophy. Metaphysics Research Lab, Stanford University, Winter 2016 edition, 2016. ![Proof-Theoretic Semantics [link]](https://bibbase.org/img/filetypes/link.svg "link")
Paper abstract bibtex Proof-theoretic semantics is an alternative to truth-conditionsemantics. It is based on the fundamental assumption that the centralnotion in terms of which meanings are assigned to certain expressionsof our language, in particular to logical constants, is that ofproof rather than truth. In this senseproof-theoretic semantics is semantics in terms of proof .Proof-theoretic semantics also means the semantics of proofs,i.e., the semantics of entities which describe how we arrive at certainassertions given certain assumptions. Both aspects of proof-theoreticsemantics can be intertwined, i.e. the semantics of proofs is itselfoften given in terms of proofs., Proof-theoretic semantics has several roots, the most specific onebeing Gentzen's remarks that the introduction rules in hiscalculus of natural deduction define the meanings of logical constants,while the elimination rules can be obtained as a consequence of thisdefinition (see section 2.2.1). Morebroadly, it belongs to what Prawitz called general prooftheory (see section 1.1). Even morebroadly, it is part of the tradition according to which the meaning ofa term should be explained by reference to the way it is usedin our language., Within philosophy, proof-theoretic semantics has mostly figuredunder the heading “theory of meaning”. This terminologyfollows Dummett, who claimed that the theory of meaning is the basis oftheoretical philosophy, a view which he attributed to Frege. The term“proof-theoretic semantics” was proposed bySchroeder-Heister (1991; used already in 1987 lectures in Stockholm) in order not to leave the term“semantics” to denotationalism alone—after all,“semantics” is the standard term for investigations dealingwith the meaning of linguistic expressions. Furthermore, unlike“theory of meaning”, the term “proof-theoreticsemantics” covers philosophical and technical aspects likewise.In 1999, the first conference with this title took place inTübingen.
@incollection{schroeder-heister_proof-theoretic_2016,
edition = {Winter 2016},
title = {Proof-{Theoretic} {Semantics}},
url = {https://plato.stanford.edu/archives/win2016/entries/proof-theoretic-semantics/},
abstract = {Proof-theoretic semantics is an alternative to truth-conditionsemantics. It is based on the fundamental assumption that the centralnotion in terms of which meanings are assigned to certain expressionsof our language, in particular to logical constants, is that ofproof rather than truth. In this senseproof-theoretic semantics is semantics in terms of proof .Proof-theoretic semantics also means the semantics of proofs,i.e., the semantics of entities which describe how we arrive at certainassertions given certain assumptions. Both aspects of proof-theoreticsemantics can be intertwined, i.e. the semantics of proofs is itselfoften given in terms of proofs., Proof-theoretic semantics has several roots, the most specific onebeing Gentzen's remarks that the introduction rules in hiscalculus of natural deduction define the meanings of logical constants,while the elimination rules can be obtained as a consequence of thisdefinition (see section 2.2.1). Morebroadly, it belongs to what Prawitz called general prooftheory (see section 1.1). Even morebroadly, it is part of the tradition according to which the meaning ofa term should be explained by reference to the way it is usedin our language., Within philosophy, proof-theoretic semantics has mostly figuredunder the heading “theory of meaning”. This terminologyfollows Dummett, who claimed that the theory of meaning is the basis oftheoretical philosophy, a view which he attributed to Frege. The term“proof-theoretic semantics” was proposed bySchroeder-Heister (1991; used already in 1987 lectures in Stockholm) in order not to leave the term“semantics” to denotationalism alone—after all,“semantics” is the standard term for investigations dealingwith the meaning of linguistic expressions. Furthermore, unlike“theory of meaning”, the term “proof-theoreticsemantics” covers philosophical and technical aspects likewise.In 1999, the first conference with this title took place inTübingen.},
urldate = {2017-03-30},
booktitle = {The {Stanford} {Encyclopedia} of {Philosophy}},
publisher = {Metaphysics Research Lab, Stanford University},
author = {Schroeder-Heister, Peter},
editor = {Zalta, Edward N.},
year = {2016},
keywords = {Curry's paradox, Hilbert, David: program in the foundations of mathematics, Russell's paradox, category theory, connectives: sentence connectives in formal logic, logic, history of: intuitionistic logic, logic: classical, logic: intuitionistic, logic: linear, logic: substructural, logical constants, mathematics, philosophy of: intuitionism, paradoxes: and contemporary logic, proof theory: development of, realism: challenges to metaphysical, self-reference, truth: revision theory of, type theory},
}
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