Ce que le neuroconstructivisme a apporté au débat philosophique sur les fondements des mathématiques

International audience ; In recent decades, experts in cognitive neuroscience have been multiplying experimental studies to identify brain cells, biological, psychological and physiological phenomena involved in the mathematical construction process. According to the results of these experimental studies, number and space would have their origin in mental representations linked to brain structures inherited from biological evolution, but also to relationships that brain structures seem to maintain with the sensory and motor data of the sensitive world, without forgetting the epigenetic influence that takes place during the postnatal individual evolution. By interpreting the foundations of mathematics by neural mechanisms, phylogenetic (innate) predispositions and the epigenetic influence that takes place during ontogenetic evolution, cognitive neuroscience implicitly affirms that mathematics is the work of a human construction.However, during the previous century, Poincaré's mathematical constructivism, admitting that the construction of mathematics cannot be done in the margins of the human mind and experience, has continued to serve as a repulsive on the part of inveterate defenders of logical-formalist theories. In arithmetic first, Poincaré, opposed to the logicism that wants numbers to be considered pre-existing entities to man, showed that the construction of numbers (integer and real) is based on an interactivity between intuition and experience. In geometry, after the birth of non-Euclidean geometries, Poincaré, refusing to consider this branch of mathematics as an a priori science, and opposing the idea that axiomatics could constitute the only foundation of geometry, presented a psycho-physiological approach to geometry where he showed that the visual, muscular, tactile and vestibular sensations that accompany our movements (or movements) constitute the foundations of geometry. We could bring Poincaré's mathematical constructivism closer to the neuroconstructivism advocated by cognitive neuroscience, ...