This paper attempts to show how the logical empiricists’ interpretation of the relation between geometry and reality emerges from a “collision” of mathematical traditions. Considering Riemann’s work as the initiator of a 19th century geometrical tradition, whose main protagonists were Helmholtz and Poincaré, the logical empiricists neglected the fact that Riemann’s revolutionary insight flourished instead in a non-geometrical tradition dominated by the works of Christoffel and Ricci-Curbastro roughly in the same years. I will argue that, in the attempt to interpret (...) general relativity as the last link of the chain Riemann–Helmholtz–Poincaré–Einstein, logical empiricists were led to argue that Einstein’s theory of gravitation mainly raised a problem of mathematical under-determination, i.e. the discovery that there are physical differences that cannot be expressed in the relevant mathematical structure of the theory. However, a historical reconstruction of the alternative Riemann–Christoffel–Ricci–Einstein line of evolution shows on the contrary that the main philosophical issue raised by Einstein’s theory was instead that of mathematical over-determination, i.e. the recognition of the presence of redundant mathematical differences that do not have any correspondence in physical reality. (shrink)

Robin Le Poidevin (2007) claims that we do form perceptual beliefs regarding order and duration based on our perception of events, but neither order nor duration are by themselves objects of perception. Temporal properties are discernible only when one first perceives their bearers, and temporal relations are discernible only when one first perceives their relata. The epistemic issue remains as to whether or not our perceptual beliefs about order and duration are formed on the causal basis of an event’s objective (...) order and duration. Le Poidevin raises this issue in the form of an epistemological puzzle of time perception, from which he derives the claim that the order and duration of events do not causally contribute to our perceptual beliefs about them. Since his view is motivated by a causal truthmaker principle for grounding knowledge, it also holds that perceptual beliefs about temporal features must be caused by the features themselves in order to count as knowledge. Given these theoretical commitments, there is a puzzle concerning how such perceptual beliefs could constitute knowledge of temporal properties. In response to Le Poidevin, I argue for an account according to which order and duration are objects of perception, causally contribute to our perceptual beliefs about them, and such beliefs are capable of counting as knowledge. I conclude by showing that, on my alternative account, the epistemological puzzle dissolves and his own solution to it fails. (shrink)