In the philosophy of science, identity over time emerges as a central concern both as an ontological category in the interpretation of physical theories, and as an epistemological problem concerning the conditions of possibility of knowledge. In Reichenbach and subsequent writers on the problem of indistinguishable quantum particles we see the return of a contrast between Leibniz and Aquinas on the subject of individuation. The possibility of rejecting the principle of the identity of indiscernibles has certain logical difficulties, leading us inexorably from ontology into epistemology. For the epistemological problem we attend to the differences that emerged between the (neo-)Kantian and logical empiricist traditions, also saliently displayed in Reichenbach's writings. After examining the contrast between Kant's and Leibniz's conceptions of empirical knowledge, specifically with respect to the irreducibility of spatiotemporal determinations, we explore an application of a neo-Kantian view to the same problem of indistinguishable quantum particles.