I am a Professor at the Department of History and Philosophy of Science of the University of Paris (formerly Paris 7), a member of SPHERE (CNRS, UMR 7219) and head of the Groupe de Recherche en Philosophie des mathématiques (PhilMath).
My work pertains to epistemology, logic and philosophy of language, all construed in connection with mathematics.
My HDR dissertation endeavors to extend, to context-sensitivity, the Russellian correspondence between the logical constants (the logical articulations of ordinary language) and the fundamentals of mathematics. Context-sensitivity is the fact that the semantic content of what is uttered generally depends on the context of utterance (a fact of which indexicals are an elementary example). My dissertation claims that context-sensitivity does not sound the death knell of Russell’s correspondence, but constitutes a reason to deepen it.
I have been interested in possible applications, in logic, of parts of traditional mathematics (differential geometry, homotopy theory, descent theory) which have hitherto received little attention within logic. I also have done work about Kantian themes and about early analytic philosophy (Frege, Russell, Wittgenstein, Carnap).
My PhD dissertation was about the general problem of the connection established (since Kant onward) between universality and necessity (all universal truths and all necessary truths being the same ones). I challenged that connection and worked toward analyzing both concepts independently of each other.