Burt C. Hopkins - The Problem of the Unity of a Manifold in the Development of Husserl’s Philosophy

Husserl’s account of the formal structure of a mathematical manifold doesn’t adequately distinguish the formality of ideal meanings from that of meanings that are formalized. Husserl’s use of the term “formal,” which refers to both ideal and formalized meanings, suggests that they share a common essential structure of “formality.” That they do not is an important implication of Husserl’s phenomenological analysis of the constitution of ideal—in the sense of “ideas in the Kantian sense”—and formalized—in the sense of symbolic mathematics—meanings. Two phenomenologically significant consequences follow. One, Husserl’s account of a mathematical manifold is problematical, because it has a dimension determined by a logical norm rather than a descriptively constituted eidos. Two, Husserl’s account of the constitution of the temporal foundation of the manifold that composes the stream of consciousness is determined by the appeal to eidetic structures whose formal conceptuality is mathematical rather than phenomenolo