The effects of concatenation: Jean Cavaillès and mathematical philosophy

This dissertation proposes an interpretation of the positive doctrine in Jean Cavailles’s (19031944) essay On Logic and the Theory of Science [LTS] (1947). It is structured by a joint focus on Cavailles’s work as a historian of mathematics and on the received ‘rationalist’ history of philosophy with which the essay is in polemic. The first two chapters of the dissertation are genealogical, and give an account of how the concerns that will become central to LTS emerged through Cavailles’s epistemological research. In Chapter I, I offer an extended analysis of the way in which Cavailles engaged with the debate around ‘effective’ mathematics as it ran from the period of the French analysts (Borel, Lebesgue) through to the formation of modern mathematical logic and proof theory. In Chapter II, I proceed to a reconstruction of how Cavailles attempted to theorise the programmatic stakes of this earlier period of epistemological practice through the outlines of a philosophy of ‘mathematical experience’. In Chapter III, I offer an analysis of LTS orientated around Cavailles’s use of the term ‘concatenation [enchaînement]’ to describe the movement specific to the history of mathematics, and from this his assertion that the ‘nature of the intelligible’ is that it ‘cannot be all at once [d’un seul coup]’. The main objective of the dissertation is to show how this doctrine, which is explicitly stated in the vocabulary of Cartesian and post-Cartesian treatises on method, emerges from the ambition to develop what I call a theory of mathematical time, and to situate this programme in a broader history of theories of the necessarily successive character of thought.