Federigo Enriques,Gaston Bachelard et Ferdinand Gonseth

The development and complexity of the debate about the conceptual structure of science in the XX^th century gave birth to a new discipline, the history of epistemology, with the aim of giving a critical history of our «epistemological heritage» with suitable methodologies of a historical and theoretical nature. A critical history of the philosophy of science on more «Wenden», besides the neo-positivistic and post-neo-positivistic ones; in Italy and France, in the first period of the XX^th century, developed a tradition of epistemological research in a neo-rationalistic sense with specific theoretical characteristics, particularly for the relevance assigned to the historicity of science. The Italian-French epistemology favored the study of the relationship between mathematical and physical thought, such as can be characterized as a really autonomous physical-mathematical epistemology; this different historical and epistemological approach, first elaborate by Federigo Enriques and then by Gaston Bachelard, Albert Lautman and Ferdinand Gonseth, allowed us to understand in the 30's the «implicit philosophy» in the works of Kurt Gödel and Hermann Weyl.