Volume 43, 2008
Philosophy of Natural Sciences
Revision of Phenomenology for Mathematical Physics
Fundamental notions Husserl introduced in Ideen I, such as epochè, reality, and empty X as substrate, might be useful for elucidating how mathematical physics concepts are produced. However, this is obscured in the context of Husserl’s phenomenology itself. For this possibility, the author modifies Husserl’s fundamental notions introduced for pure phenomenology, which found all sciences on the absolute Ego. Subsequently, the author displaces Husserl's phenomenological notions toward the notions operating inside scientific activities themselves and shows this using a case study of the construction of noncommutative geometry. The perspective in Ideen I about geometry and mathematical physics includes points that are inappropriate to modern geometry and to modern physics, especially to noncommutative geometry and to quantum physics. The first point relates to the intuitive character of geometrical objects in Husserl. The second is linked to the notion of locality related to the notion of extension, by which Husserl characterizes the essence of physical things. The points show that the notion of empty X as a substrate, developed in “Phenomenology of Reason” in Ideen I, is helpful for considering the notions of physical reality and of geometrical space, especially reality in quantum physics and space in noncommutative geometry. The salient conclusions include the proposition that a
philosophical study of the relationship between the physical object X, which imparts a unity to what is given to sensibility, and the geometrical space X, which imparts a unity of sense to various mathematical operations, opens a reinterpretation of Husserl’s interpretation, supporting an epistemology of mathematical physics.