History and becoming of science in Jean Cavaillès

Abstract

This paper is focused on Cavaillès’ theory of science and his peculiar epistemology. In order to understand the position of Cavaillès concerning the becoming of mathematics, it is necessary to start from the way he utilizes the historical method inherited from Brunschvicg. In Cavaillès’ works, historical analysis is not reduced to a mere reconstruction of the past, but is regarded as an instrument to find the necessity that characterizes the movement of science. This movement is originated by the tensions between a necessary internal push and historical contingency, and it goes at its own pace, being determined by nothing else but the mathematics itself. Therefore, Cavaillès also states the failure of all foundational projects and  affirms the complete autonomy of the becoming of mathematics, which develops as a dialectic unforeseeable concatenation of concepts.