On Logic And The Theory Of Science Jean Cavailles Jean Cavailles by Jean Cavailles [jean Cavailles] 9781733628105, 173362810X instant download after payment.

The preface and notice read more like dares than invitations to study On Logic and the Theory of Science. Gaston Bachelard hints at the challenges to come in his description of Cavaillès’s sentences as ‘often enigmatic in their concision’. The work’s editors were more frank when they presented the fruits of their original efforts in 1946. Apparently they considered authoring an introduction that might ‘shed some light on the background context of philosophical and mathematical culture which Cavaillès precisely wished to be taken for granted’. But they feared the result would be mere commentary. Instead, apart from filling in references, they presented the work without apparatus and with the conjecture that Cavaillès believed ‘those who did not make the effort to understand did not deserve to be enlightened’, a judgment all the more perplexing given that we are advised in the next paragraph that the problems raised in the pages to follow ‘cannot honestly receive any definitive solution’.

To reconstruct the mental space in which Cavaillès thought would require a complete study of the revolutions in logic and mathematics that shaped the first half of the twentieth century. Even so, obscurities would remain. There is something in On Logic and the Theory of Science to baffle everyone. Steeped in a philosophical formation at the crossroads of neo-Kantianism and phenomenology, Cavaillès brings to mathematics questions that are beyond the mathematician’s purview. And yet often he will make a mathematical allusion to illustrate a philosophical point, such as when he presents science as ‘a Riemannian volume, closed and yet without any exterior’. 

Our strategy has been less to resolve the enigmas of Cavaillès’s writing than to preserve them in English. As for the context required even to understand them as enigmas, it is at least plausible that Cavaillès could take some mathematical culture for granted on the part of his readership.