Communication Dans Un Congrès Année : 2024

Axiomatic definitions in the Peano School

Résumé

Based on a detailed analysis of the different types and uses of definitions made by Peano (by axioms, by abstraction, by operators, conditional, ...) and by some of the collaborators to the Formulario (Vailati, Pieri, Burali-Forti, Vacca, Padoa), it will be claimed that the adequacy of definitions is not a question that can be established independently of an analysis of the mathematical practice in which the definitions are used. The definition of a mathematical concept must be analyzed also in the light of the definitions of other concepts that might be derived from it, and the adequacy evaluated for all definitions altogether. Based on an original reading of Peano’s axiomatics, the paper will provide examples to support the idea that the choice of the most appropriate definition is not only a logical-philosophical question (based on syntactic criteria or metatheoretical criteria) but also a mathematical choice related to the objectives the mathematician has while trying to solve a specific problem and to the consideration of an axiomatic theory as a whole.

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Dates et versions

halshs-04860037 , version 1 (14-01-2025)

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  • HAL Id : halshs-04860037 , version 1

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Paola Cantu. Axiomatic definitions in the Peano School. The Lesson of Peano and Russell. Logical Tools for the Computational Approach to Legal Theory, Sep 2024, Genova, Italy. ⟨halshs-04860037⟩
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