Jean Cavaillès in the legacy of Léon Brunschvicg: Mathematical philosophy and the problems of history

Résumé 0

Cavaillès᾽ conception of the history of mathematics stands in a close and contrasting relation with that of Brunschvicg, as explained in La Modalité du jugement (1897). The activity of scientific judgment was said there to be “mixed,” between judgments of interiority (ideal judgments) and judgments of exteriority (realistic judgments). The modality that corresponds to the “mixed” form of the historical activity of knowledge is that of the possible. Thus, a historical epistemology emerges, embedded in Kantian idealism that discards speculative idealism. Cavaillès᾽ conception of the creative necessity of the history of mathematics reduces the role of possibility and of the intellectual experience within this history. Cavaillès thus diverges from a master to whom Canguilhem’s philosophy of science may be seen as remaining closer. The recent history of mathematics, while paving the way for Kronecker᾽s revenge on the abstract set conceptions that inspired Cavaillès᾽ necessitarianism, leads us to a new appreciation of the radicalism he showed when diverging from Brunschvicg᾽s theory of the modality of judgment.