Jean Cavailles in the Legacy of Leon Brunschvicg: mathematical philosophy and history problems

Cavailles. conception of the history of mathematics stands in a close and contrasted relation with Brunschvicg.s one, as explained in La Modalite du jugement (1897). The activity of scientific judgment was said there "mixed" between judgments of interiority (ideal judgments) and judgments of exteriority (realist ones). The modality which corresponds to the "mixed" form of the activity of knowledge is that of the possible. Hence a historical epistemology, which claims a Kantian idealist fatherhood and discards speculative idealism. Cavailles. conception of the creative necessity in the history of mathematics reduces the role of possibility and of intellectual adventure in this history. Cavailles thus diverges from a master to whom Canguilhem may be seen as remaining closer in his own philosophy of science. The recent history of mathematics, while preparing Kronecker's revenge on the abstract set conceptions which inspired Cavailles. necessitarism, leads us to a new appreciation of the radicalism he showed when diverging from Brunschvicg's theory of the modality of judgment.