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SUBATOMIC INFERENCES: AN INFERENTIALIST SEMANTICS FOR ATOMICS, PREDICATES, AND NAMES

Part of: Other social and behavioral sciences (mathematical treatment) Proof theory and constructive mathematics

Published online by Cambridge University Press:  02 July 2021

KAI TANTER
KAI TANTER*
Affiliation:
MONASH UNIVERSITY SCHOOL OF PHILOSOPHICAL HISTORICAL AND INTERNATIONAL STUDIES MONASH UNIVERSITY CLAYTON, VIC 3800, AUSTRALIA
*
E-mail: [email protected]
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Abstract

Inferentialism is a theory in the philosophy of language which claims that the meanings of expressions are constituted by inferential roles or relations. Instead of a traditional model-theoretic semantics, it naturally lends itself to a proof-theoretic semantics, where meaning is understood in terms of inference rules with a proof system. Most work in proof-theoretic semantics has focused on logical constants, with comparatively little work on the semantics of non-logical vocabulary. Drawing on Robert Brandom’s notion of material inference and Greg Restall’s bilateralist interpretation of the multiple conclusion sequent calculus, I present a proof-theoretic semantics for atomic sentences and their constituent names and predicates. The resulting system has several interesting features: (1) the rules are harmonious and stable; (2) the rules create a structure analogous to familiar model-theoretic semantics; and (3) the semantics is compositional, in that the rules for atomic sentences are determined by those for their constituent names and predicates.

Keywords

proof-theoretic semanticsinferentialismbilateralismsub-atomic semantics

MSC classification

Primary: 03F03: Proof theory, general
Secondary: 91F20: Linguistics
Type
Research Article
Information
The Review of Symbolic Logic , Volume 16 , Issue 3 , September 2023 , pp. 672 - 699
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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