 A cornerstone of Reichenbach’s logical analysis of the theory of general relativity is the thesis of “the relativity of geometry”, that an arbitrary geometry may be ascribed to spacetime (holding constant the underlying topology) if the laws of physics are correspondingly modified through the introduction of “universal forces”. This particular argument for metric conventionalism has generated substantial controversy on its own, but is better understood through an account of its genesis in Reichenbach’s early neo-Kantianism. Independently of that genesis, the thesis becomes the paradigmatic illustration of Reichenbach’s broad methodological claim that conventional or definitional elements—“coordinative definitions” associating mathematical concepts of the physical theory with “elements of physical reality”—are a necessary condition for empirical cognition in the mathematical sciences of nature. At the same time, Reichenbach’s thesis of metrical conventionalism is part and parcel of an audacious program of epistemological reductionism regarding spacetime structures. This was first attempted in his “constructive axiomatization” (1924) of the theory of relativity on the basis of “elementary matters of fact” (Elementartatbestande) regarding the observable behavior of lights rays, and rods and clocks. Here, and in the more widely read treatment (1928), metrical properties of spacetime are deemed less fundamental than topological ones, while the latter are derived from the concept of time ordering. But time order in turn is reduced to that of causal order and so the whole edifice of structures of spacetime is considered epistemologically derivative, resting upon ultimately basic empirical facts about causal order and a prohibition against action-at-a-distance. The end point of Reichenbach’s epistemological analysis of the foundations of spacetime theory is then “the causal theory of time”, a type of relational theory of time that assumes the validity of the causal principle of action-by-contact (Nahewirkungsprinzip).