Des fondements vers l’avant. Sur la rationalité des mathématiques et des sciences formalisées

Abstract

Forward foundations. On the rationality of mathematics and of formalized sciences. — The failure of logicism for the question of foundations of mathematics invites us to consider this question under an epistemological point of view, in terms of rationality and not only of logic, and to extend it from mathematics to formalized sciences bearing on nature, such as physics, and even to scientific thought in general. One must take into account, in all cases, changes which correspond to conceptual constructions : they secure at the same time, afterwards, the well-foundedness of the theories which have prepared them ; consequently, we should admit as a general rule that rational foundations can only be obtained “forward”. These changes ask also the question of their conditions of possibility. We get the conclusion, for such changes to be possible and together with them enhancement of knowledge, that one must admit correlated transformations in the very forms of rationality, mathematical ones, physical ones and of scientific rationality in general.