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Fondements des mathématiques: introduction à une philosophie constructiviste

Montréal: Presses de l'Université de Montréal (1976)

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  1. Théorie des modèles, de la simulation et représentation scientifique chez Mario Bunge.Jean Robillard - 2022 - Mεtascience: Discours Général Scientifique 2:45-73.
    On entend généralement par « théorie des modèles » autant la métamathématique (ou sémantique formelle) que la sémantique des modèles des sciences non formelles. Cet article a pour objet la théorie des modèles scientifiques que Mario Bunge a développée dans Method, Models and Matter (1973). J’y analyse l’intégration théorique qu’opère Bunge des sciences formelles et des sciences expérimentales ou observationnelles, laquelle prend appui sur sa philosophie des sciences. Je la compare sommairement à la théorie des modèles de Gilles-Gaston Granger dans (...)
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  • INVENTING LOGIC: THE LÖWENHEIM-SKOLEM THEOREM AND FIRST- AND SECOND-ORDER LOGIC.Valérie Lynn Therrien - 2012 - Pensées Canadiennes 10.
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  • Nicolas Bourbaki and the concept of mathematical structure.Leo Corry - 1992 - Synthese 92 (3):315 - 348.
    In the present article two possible meanings of the term mathematical structure are discussed: a formal and a nonformal one. It is claimed that contemporary mathematics is structural only in the nonformal sense of the term. Bourbaki's definition of structure is presented as one among several attempts to elucidate the meaning of that nonformal idea by developing a formal theory which allegedly accounts for it. It is shown that Bourbaki's concept of structure was, from a mathematical point of view, a (...)
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  • La descente infinie, l’induction transfinie et le tiers exclu.Yvon Gauthier - 2009 - Dialogue 48 (1):1.
    ABSTRACT: It is argued that the equivalence, which is usually postulated to hold between infinite descent and transfinite induction in the foundations of arithmetic uses the law of excluded middle through the use of a double negation on the infinite set of natural numbers and therefore cannot be admitted in intuitionistic logic and mathematics, and a fortiori in more radical constructivist foundational schemes. Moreover it is shown that the infinite descent used in Dedekind-Peano arithmetic does not correspond to the infinite (...)
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