The philosophical coming of age of science. Euler’s role in Cassirer’s early philosophy of space and time

Cassirer’s early philosophy of space and time, overshadowed by his later work on relativity, has been scarcely explored in the literature. This paper aims to bridge this gap. It argues that understanding Cassirer’s point of view requires acknowledging the pivotal role he attributed to the work of Leonhard Euler in the philosophical ‘coming of age’ of modern science. Against the Leibniz-Berkeley philosophical plea for the relativity of all motion, Euler objected that if Newton’s absolute space and time did not exist, the principle of inertia would be come meaningless and with it a scientific theory of motion. According to Cassirer, Kant took a step beyond Euler by shifting the focus from the existence of space and time as ‘things’ to their function as necessary ‘conditions’ of the possibility of mechanics. In the nineteenth century, it became clear that Newton’s absolute space and time entail more structure than necessary. Nevertheless, according to Cassirer, the Euler-Kant insight still holds: a geometric structure serving as an inertial structure is the condicio sine qua non of a coherent theory of motion, including general relativity. This paper concludes that Cassirer came close to defending a sort of ‘inertial functionalism’ dressed in neo-Kantian garb.