Louis Rougier’s reception of the Peano School

Résumé En

Among the numerous influences and reciprocal interactions between France and Italy at the beginning of the 20th century, it is interesting to investigate the complex case of Louis Rougier’s reception of Italian mathematical logic (including in particular the contributions by some members of the Peano school: Giuseppe Peano, Giovanni Vailati, Alessandro Padoa, and Mario Pieri). This paper aims to investigate the role and the influence of the Peano school on the inversion of this French tendency of philosophers to ignore logic and mathematics. My claim is that Rougier was not only personally interested in Italian mathematics and logic, and in particular in the innovations made by Peano and his school, but used it to support a project of renewal of French logic and scientific philosophy. Rougier recalls the contributions of the school to axiomatics and to mathematical logic, in order to criticize the standard teaching of logic in France, mainly based on syllogistic theory, as well as the view, still defended by his teacher Goblot in 1907, that mathematical proofs are largely based on intuition. For this purpose, any reference to Hilbert’s axiomatics would have sufficed. The reason why Rougier refers also to Peano and his entourage is related to a common interest in linguistics and in epistemology.