Gestures, Peirce, and the French philosophy of mathematics

Abstract

The idea of ‘gesture’ is present in the philosophical world in various forms. All of them might find an important theoretical grounding in pragmatist philosophy, if we combine pragmatism with some French philosophies of mathematics and read it as a way out of the Kantian philosophy of representation. The paper uses the insights of Jean Cavailles (1903-1944) to set out the problem of the weakness of the epistemic Kantian defense of mathematical and logical thought. Cavailles rejected the possible amendments to Kant’s explanation provided by both Husserl and Bolzano and their heirs. He used the word ‘gesture’ in order to explain the activity of mathematicians who have to act synthetically, following rules, with some physical representation, and being aware of the possibility of failure. Cavailles conceived the use of gesture as an alternative to the Heidegerian idea of event defended by Albert Lautman. The paper then follows the idea of gesture in the French philosophy of mathematics of Gilles Châtelet and Giuseppe Longo. Finally, the paper illustrates how Peirce’s study of Existential Graphs and the main insights of pragmatism complete Cavailles’s idea by giving to gestures a phenomenological and semiotic structure. The pragmatist philosophy of gesture is thus a new way of overthrowing Kant’s philosophy of representation without surrendering to irrationalism.