Article ID: CBB543609928

From Phenomenology to the Philosophy of the Concept: Jean Cavaillès as a Reader of Edmund Husserl (2020)

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The article reconstructs Jean Cavaillès’s polemical engagement with Edmund Husserl’s phenomenological philosophy of mathematics. I argue that Cavaillès’s encounter with Husserl clarifies the scope and ambition of Cavaillès’s philosophy of the concept by identifying three interrelated epistemological problems in Husserl’s phenomenological method: (1) Cavaillès claims that Husserl denies a proper content to mathematics by reducing mathematics to logic. (2) This reduction obliges Husserl, in turn, to mischaracterize the significance of the history of mathematics for the philosophy of mathematics. (3) Finally, Husserl’s phenomenology distorts the nature of mathematical experience. Accordingly, Cavaillès’s philosophy of mathematics is premised on a threefold affirmation designed to overcome these inadequacies. Cavaillès claims that mathematics is an autonomous field of conceptual production that cannot be reduced to logical, psychological, or phenomenological descriptions of conceptual genesis. Two important corollaries follow: the history of mathematics must guide the philosophy of mathematics, and mathematical experience itself must be described according to the mechanisms of a novel theory of mathematical abstraction. In what follows, I demonstrate that Cavaillès’s encounter with Husserl does not merely describe a polemical engagement with a rival philosophical position; it allows us to reconstruct Cavaillès’s own highly original contributions to the philosophy of mathematics.

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Authors & Contributors
Mensch, James Richard
Weiler, Michael
Husserl, Edmund
Matjus, Ülo
Gimbel, Steven
Elliott, Brian
Journals
Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics
Studies in History and Philosophy of Science
Almagest
History of Psychiatry
Circumscribere: International Journal for the History of Science
Transversal: International Journal for the Historiography of Science
Publishers
Pennsylvania State University Press
Kluwer Academic
Routledge
Edwin Mellen Press
Boston University
Southern Illinois University at Carbondale
Concepts
Phenomenology
Epistemology
Philosophy
Philosophy of mathematics
Philosophy of science
Psychology
People
Husserl, Edmund
Heidegger, Martin
Peirce, Charles Sanders
Descartes, René
Reichenbach, Hans
Bachelard, Gaston
Time Periods
20th century, early
20th century
19th century
Places
France
Paris (France)
Germany
Europe
China
Institutions
Axiom
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