Toward a ‘Form-Intuition’: Mathematical Objectité in French Epistemology from Cavaillès to Pradelle

This paper contributes to broader philosophical debates on objectité, understood as the mode of being and constitution of mathematical objects. It reconstructs the development of French mathematical epistemology – from Jean Cavaillès to Dominique Pradelle – through an examination of the relation between intuition and the constitution of mathematical objectité. Against Kantian approaches, which ground the possibility of mathematical knowledge in the pure forms of sensible intuition, and logicist approaches developed by Gottlob Frege and Bertrand Russell, which reduce them to formal structures, the paper advances the concept of form-intuition: a mode of intuition immanent to formal operations themselves. Drawing on a transformation of Edmund Husserl’s notion of categorial intuition, it argues that mathematical objects emerge through the dynamic interplay between symbolic practices and their internal organization. Analyses of Cavaillès, Jules Vuillemin, and Pradelle show that objectité is neither given in immediate intuition nor secured by formal systems but produced through structured practices. By reinterpreting Leibniz’s project of mathesis universalis as a theory of formal generation, the paper proposes a practice-based account of objectité that extends beyond mathematics and offers a new perspective on the relation between form, intuition, and knowledge.