"I do not believe that there exists anything in external bodies for exciting tastes, smells, and sounds, etc. except size, shape, quantity, and motion." (Galileo Galilei, On Motion, p.48) When Galileo proposed his doctrine of subject and object and the distinction between primary and secondary qualities, he established the scientific prejudgement that the concept of space is of something geometrical and not differentiated qualitatively.

Newtonian "absolute space" was based on a realist conception of mathematics (see Jammer p. 95) To Newton, mathematics, particularly geometry, is not a purely hypothetical system of propositions...instead geometry is nothing but a special branch of mechanics. Newton's first law of motion, which links change in motion with force requires an absolute (or inertial?) framework. It requires a distinction between absolute motion and relative motion and links force to a change in absolute motion. For example, as the train pulls away from the station, the station may appear to be moving and it can be said that the station is in relative motion to the train, but the force is acting upon the train, and it is the train that is accelerating absolutely. Newton tried to establish an absolute frame of reference for the universe defined in relation to its center of gravity. (not necessarily identical with the sun) Absolute spatial movement and position could then be measured in relation to that point.

But is geometry an empirical or ideal activity? For Cassirer, the most radical removal of geometry from experience had already occurred with Euclid, which was already based on figures that are removed from all possibility of experiment. Not only the idealizations of point, line, and plane, but the idea of similar triangles, whose differences are considered inconsequential or fortuitous, and that become identified as "the same" mark an immense step away form ordinary perception.