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De la logique à l’arithmétique. Pourquoi des logiques et des mathématiques constructivistes?

Published online by Cambridge University Press:  22 March 2018

YVON GAUTHIER
YVON GAUTHIER*
Affiliation:
Université de Montréal
*
*<[email protected]>
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Abstract

In this article, I wish to discuss in an informal way the motivations and the motifs of the constructivist approach to logic and mathematics and by a natural extension to the general field of science, particularly theoretical physics. Foundational questions in those domains are not ruled by philosophical principles, but a critical philosophy of foundations could be the leitmotiv to the extent that it can be used as a criterion to decide between the theoretical options of scientific practices that are often oblivious to their own doctrinal presuppositions. My objective is to provide the justificatory reasons for a constructivist option or posture in the field of scientific knowledge.

Dans cet essai informel, je veux exposer les motivations et les motifs de l’approche constructiviste en logique et en mathématiques et, au-delà, dans le savoir scientifique en général et la physique théorique en particulier. Les questions fondationnelles dans ces domaines ne relèvent pas de la philosophie, mais la critique philosophique des fondements est ici un motif recteur ou un leitmotiv dans la mesure où elle départage les options théoriques d’une pratique scientifique souvent aveugle à ses propres présupposés doctrinaux. Il s’agit dès lors de la justification d’une option ou d’une posture philosophique critique dans le champ du savoir scientifique.

Keywords

logiquemathématiquesconstructivismearithmétiqueKronecker
Type
Original Article/Article original
Information
Dialogue: Canadian Philosophical Review / Revue canadienne de philosophie , Volume 57 , Issue 1 , March 2018 , pp. 1 - 28
Copyright
Copyright © Canadian Philosophical Association 2018 

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