Formalization and Intuition in Husserl’s Raumbuch

Abstract

Husserl planned to deal with a philosophy of Euclidean geometry in the second and unpublished volume of the Philosophie der Arithmetik. Thus, after the publication of the first volume, he outlined an analytical/formal method that should have allowed a pure understanding of any spatial manifold. Nevertheless, dealing with the analytical geometry of Bernhard Riemann, he understood the limits of a pure formal approach. Therefore, he started investigating space representation from a psychological point of view, trying to detect those intuitions grounding geometrical concepts. Notwithstanding, Husserl abandoned this geometrizing space theory too because, in my view, it did not offer a plain explanation of the relations between geometry and space theory, material, and formal concepts. In this paper, I investigate the reasons why in his early studies Husserl wavered from a formalizing to an intuitive approach to the space problem.