“Attraper le geste et pouvoir continuer. For a new kind of mathematical constructivism”

This article proposes a new form of mathematical constructivism grounded in the notion of gesture, understood as a synthetic act embedded in a tradition and justified by its successful continuation. Starting from Maurizio Ferraris’s critique of postmodernism and his call for a minimal realism, the paper argues that Ferraris’s position remains tied to Kant’s legacy, particularly to Kantian mathematical constructivism and its analytic–synthetic framework. By revisiting Kant’s account of the construction of mathematical objects, the article shows how the unicity of space and time ultimately imposes a crypto-analytic scheme that restricts creativity and discovery. As an alternative, the paper turns to Jean Cavaillès’s conception of mathematics as an experimental activity, in which mathematical objects are inseparable from the gestures that generate them. Drawing on subsequent developments in French philosophy of mathematics, especially in the works of Gilles Châtelet and Giuseppe Longo, the article extends the notion of gesture beyond mathematics to scientific and ordinary experience. It concludes by defending a Peircean metaphysical realism, fully a posteriori and processual, in which ontology and epistemology remain distinct yet deeply intertwined, and in which knowledge is understood as the ongoing synthesis of meaning through historically situated gestures.