The culminating point of a first period under Alessandro Padoa’s and Bertrand Russell’s mixed influences in France lies in Jean Nicod’s philosophical essays. During a second period, Jacques Herbrand’s mathematical work blossoms. Before his early death, he had given his name to a fundamental theorem. Follows a period of debates among philosophers, mathematicians and physicists, stimulated in 1935 and 1937 by two congresses, totally or partially devoted to the philosophy of science, held in Paris. On that occasion, Paulette Février sketched a non-classical logic in which the existence of pairs of propositions that cannot be composed is postulated in order to set up Werner Heisenberg’s relations as principles. These ideas are developed by Jean-Louis Destouches to the point of describing how to build a unifying theory. The structuring of mathematical beings is the subject matter of Albert Lautman’s philosophical studies. The putative role of the notion of group in logic is examined. The notion of mathematical structure gives rise to two contributions: Marc Krasner generalizes Évariste Galois’ ideas, attributed to logic and extended to infinitary languages; Nicolas Bourbaki, taking into account the evolution of mathematics, designates under the term structure what we now call model.