On the computational meaning of axioms

Alberto Naibo, Mattia Petrolo, Thomas Seiller

Abstract

This paper investigates an anti-realist theory of meaning suitable for both logical and proper axioms. Unlike other anti-realist accounts such as Dummett–Prawitz verificationism, the standard framework of classical logic is not called into question. This account also admits semantic features beyond the inferential ones: computational aspects play an essential role in the determination of meaning. To deal with these computational aspects, a relaxation of syntax is necessary. This leads to a general kind of proof theory, where the objects of study are not typed objects like deductions, but rather untyped ones, in which formulas are replaced by geometrical configurations.

Original languageEnglish
Title of host publicationEpistemology, knowledge and the impact of interaction
EditorsJuan Redmond, Olga Pombo Martins, Ángel Nepomuceno Fernández
Number of pages44
PublisherSpringer
Publication date2016
Pages141-184
Chapter5
ISBN (Print)978-3-319-26504-9
ISBN (Electronic)978-3-319-26506-3
DOIs
Publication statusPublished - 2016
SeriesLogic, Epistemology, and the Unity of Science
Volume38
ISSN2214-9775

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