The Scientific Implications of Epistemology: Weyl and Husserl

Abstract

The title of this article refers to the subtitle of the section “Subject and Object” of the major work of Hermann Weyl. We can immediately remark the surprising order of the terms: should we not expect from a man of science that he preferably discuss the epistemological implications of science? Using epistemology as the vector of scientific thought, Weyl examines how, under the pressure of an issue inherent in science, the classical philosophical doctrine of the subjectivity of sensible qualities eventually rooted out any trace of intuition in the now purely symbolic representation of the objective world. The precedence of epistemology over physics could be justified by this conceptual revolution initiated by special relativity: physics is now geometry in action. Through gradual improvement geometrical concepts have become more and more involved in phenomena taking place in physical space-time: geometry is not only ontologically rooted in the real through its ability to produce semantic universals (curvatures, manifolds, groups, connections, etc.), but, besides, it is actively involved in its becoming by the fact that its symmetry principles have a constitutive action. In short, while mathematics is still in Galileo’s physics only a language appropriate to the study of nature, a remarkable ontological extension of the founding project of mathematical physics led to a deep upheaval of its sense: the means of knowledge cannot be separated from the knowledge of the objects themselves.

Translated from French by Pascale Pelletier, revised by the author.