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Logic, Epistemology, and the Unity of Science, p. 141-184

DOI: 10.1007/978-3-319-26506-3_5



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On the Computational Meaning of Axioms

Journal article published in 2014 by Alberto Naibo, Mattia Petrolo, Thomas Seiller ORCID
This paper is available in a repository.
This paper is available in a repository.

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An anti-realist theory of meaning suitable for both logical and proper axioms is investigated. As opposed to other anti-realist accounts, like Dummett-Prawitz verificationism, the standard framework of classical logic is not called into question. In particular, semantical features are not limited solely to inferential ones, but also computational aspects play an essential role in the process of determination of meaning. In order to deal with such computational aspects, a relaxation of syntax is shown to be 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where the objects of study are not typed objects like deductions, but rather untyped ones, in which formulas have been replaced by geometrical configurations.