From Critique to Paradigm: Husserl’s Appropriation of Riemannian Geometry

This work offers a new interpretation of the intellectual dialogue between Edmund Husserl and Bernhard Riemann’s theory of manifolds, arguing that this relationship extends beyond mere influence to constitute a central structural inspiration of the project Husserl would later outline as pure logic in the Prolegomena to Pure Logic . The original contribution of this analysis is to demonstrate how Husserl’s engagement evolved from an initial critical opposition, centered on the accusation of a “vicious circle” in deriving Euclidean geometry, to the adoption of Riemann’s work as a crucial paradigmatic model for his own Doctrine of Manifolds ( Mannigfaltigkeitslehre ). The paper documents the overcoming of this critique, a turning point evidenced by Husserl’s distinction between the “pure categorial form” of the manifold and its “concretization” in phenomenal space. In doing so, Husserl found in the Riemannian separation between a manifold’s abstract topological structure and its metric the perfect model for his own distinction between the ideal form of a theory and its empirical content. Ultimately, we demonstrate how Husserl assimilated the structural potentials of Riemann’s mathematics to prefigure the three fundamental tasks of pure logic, therefore transforming a revolutionary mathematical structure into a primary paradigm for his transcendental theory of science.