 This is not the place for an adequate answer to this question, if indeed one is possible. For much of the 20th century, the accepted answer was that of Ernst Mach: Newton lived in an age “deficient in epistemological critique.” He was therefore unable to draw the conclusion that these dynamically indistinguishable spaces must be equivalent in every meaningful sense, so that no one of them deserves even in principle to be designated as “absolute space.” Yet even those whom the 20th century credited with more sophisticated epistemological views, such as Leibniz, evidently had difficulties understanding force and inertia in a Galilei-invariant way, despite a philosophical commitment to relativity. We may plausibly suppose that it was difficult to abandon the intuitive association of force or motion with velocity in space. It must also have been difficult, in the mathematical context of Newton’s time, to conceive of an equivalence-class structure as the fundamental spatio-temporal framework. It required a level of abstraction that became possible only with the extraordinary development of mathematics, especially of a more abstract view of geometry, that took place in the 19th century. Newton’s arguments established, for the assumptions of classical dynamics, the need for a dynamical space-time structure beyond the kinematical structure required to represent changes of relative position over time. But absolute space, with its superfluous elements, was the only such structure imagined for the next two centuries. It was accepted as the only realistic alternative to theories with no dynamical structure at all. There was as yet no notion of a structure that expressed all and only what was required by the dynamical laws. Euler, for example, in a penetrating critique of Leibnizian relationalism (1748), argued that the laws of motion require a notion of sameness of direction in space, and of uniform motion with respect to time. The truth of the laws of motion—which, for Euler, were more securely established than any principle of metaphysics—could not, therefore, be reconciled with any account of space and time as merely ideal. But he did not see the possibility of separating true acceleration and rotation from true velocity with respect to absolute space. 