From Phenomenology to the Philosophy of the Concept: Jean Cavailles as a Reader of Edmund Husserl

The article reconstructs Jean Cavailles's polemical engagement with Edmund Husserl's phenomenological philosophy of mathematics. I argue that Cavailles's encounter with Husserl clarifies the scope and ambition of Cavailles's philosophy of the concept by identifying three interrelated epistemological problems in Husserl's phenomenological method: (1) Cavailles 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, Cavailles's philosophy of mathematics is premised on a threefold affirmation designed to overcome these inadequacies. Cavailles 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 Cavailles's encounter with Husserl does not merely describe a polemical engagement with a rival philosophical position; it allows us to reconstruct Cavailles's own highly original contributions to the philosophy of mathematics.