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On the computational meaning of axioms

Alberto Naibo , Mattia Petrolo, Thomas Seiller

pp. 141-184

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.

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Full citation:

Naibo, A. , Petrolo, M. , Seiller, T. (2016)., On the computational meaning of axioms, in J. Redmond, O. Martins & Ã. Fernández (eds.), Epistemology, knowledge and the impact of interaction, Dordrecht, Springer, pp. 141-184.

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