Philosophia Mathematica 4 (1):18-41 (1996)

In this expository article one of the contributions of Jean Cavailles to the philosophy of mathematics is presented: the analysis of ‘mathematical experience’. The place of Cavailles on the logico-philosophical scene of the 30s and 40s is sketched. I propose a partial interpretation of Cavailles's epistemological program of so-called ‘conceptual dialectics’: mathematical holism, duality principles, the notion of formal contents, and the specific temporal structure of conceptual dynamics. The structure of mathematical abstraction is analysed in terms of its complementary dimensions: paradigmatic generalization (domain extension, descriptive definitions, creative role of the symbolism...) and thematic reflexivity of concepts (promotion of operations to objects of a higher type).
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DOI 10.1093/philmat/4.1.18
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Domain Extension and the Philosophy of Mathematics.Kenneth Manders - 1989 - Journal of Philosophy 86 (10):553-562.
La Logique de Husserl.Suzanne Bachelard - 1958 - Philosophy and Phenomenological Research 19 (1):126-127.
Das Kontinuum.H. Weyl - 1960 - Journal of Symbolic Logic 25 (3):282-284.

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