Thomas Ryckman's new book, The Reign of Relativity, represents a fundamental breakthrough in our understanding of the complex interrelationships between philosophy and mathematical physics in the first quarter of the twentieth century.1 Ryckman shows, in particular, that the philosophical significance of the general theory of relativity was by no means confined to its appropriation by logical empiricism, but extended far wider to embrace a variety of philosophical approaches under the general rubric of transcendental idealism. Most importantly, perhaps, Einstein's theory was subject to a profound effort at interpretation and development by the philosophically minded mathematician Hermann Weyl, working under the explicit inspiration of the transcendental phenomenological idealism of Edmund Husserl. Ryckman's book thus points in radically new directions for understanding twentieth-century philosophy more generally and, in particular, the much vexed question of the relationship between analytic and continental philosophical traditions.
Weyl's work on the general theory of relativity was framed, as Ryckman beautifully and illuminatingly shows, by Husserlian philosophy, and it involved, in particular, a deep investigation into the mathematical and philosophical foundations of geometry under the rubric of what Weyl called "purely infinitesimal geometry [rein infinitesimale Geometrie]"which, in turn, was intended to reflect the philosophical primacy of that which is directly and immediately presented to the ego in the phenomenological here-and-now. On this basis Weyl developed what he himself conceived as a constructive mathematical "essential analysis [Wesensanalyse]" of the nature of space (and of the nature of space-time), and he put this analysis to use in physics, as Ryckman also shows, in articulating, for the first time, the idea of a gauge transformation, which Weyl then applied in developing a unified geometrical theory of the gravitational and electro-magnetic fields. And, although this particular theory soon fell by the wayside in the further development of twentieth-century mathematical physics, Weyl's idea of a gauge transformation was eventually taken up-first by Weyl himself and then by others-in the development of field theory within quantum mechanics. Although the precise role and significance of Husserlian phenomenology in these later developments is not yet entirely clear, there is no doubt that Weyl's ambitious combination of mathematical, physical, and philosophical thinking provides a striking illustration of the wide-ranging intellectual fruitfulness of transcendental phenomenology.
Weyl's particular application of transcendental phenomenology to mathematical physics is very technical and difficult, and I will leave it to Ryckman himself to provide us with further illumination on this score. What I propose to do is to discuss some of the historical background and context against the background of which both Husserlian phenomenology and Weyl's work were articulated, so as to shed further light, in particular, on what I myself take to be some of the more important philosophical problems that arise here. This will lead to a somewhat different perspective than Ryckman's on the question of a phenomenological foundation for twentiethcentury mathematical physics-although I hope one that is complementary to rather than in conflict with Ryckman's work.
The problem of a transcendental foundation for mathematical physics begins, of course, with the work of Kant-who Husserl himself, in the Crisis, rightly takes to be the father of transcendental philosophy. For Kant, this project took the form of what he called a metaphysical foundation for Newtonian physics, in which the Newtonian concepts of absolute space, time, and motion were replaced by the schematized application of the pure concepts of the understanding to the pure intuitions of space and time. More specifically, the categories of substance, causality, and community resulted in what Kant understood as the fundamental laws of Newtonian mechanics-the conservation of the total quantity of matter, the law of inertia, and the equality of action and reaction-which, in turn, provided an a priori basis for a procedure of "time-determination" resulting in an empirical interpretation, as it were, of the concepts of absolute space, time, and motion within our experience of the physical world. …