The French ‘Analysts’ and Peano’s Mathematical Logic: Couturat’s Remarques to Borel, Baire and Lebesgue

The historiographical categories ‘School of Peano’ and ‘Italian Mathematical Logic’ will be discussed, before illustrating the logical and foundational contributions by the Peanians included in the collective work Formulario di Matematica. The reception in France of these results will then be analysed, both at the level of research activity and in the context of teaching of real analysis (1883-1890). Particular attention will be paid to the role of L. Couturat in popularizing Peanian logic in the years 1896-1910, and to an emblematic episode: the debate in 1904 between Couturat, E. Borel, R. Baire and H. Lebesgue, regarding the possible use of Peano’s ideography within the Collection de monographies sur la théorie des fonctions. The implications of this story will be examined, focusing on how the destiny of the diffusion of mathematical logic in France was linked to Couturat’s cultural policies, which significantly conditioned the evolution of French research in the fields of philosophy and foundations of mathematics.