Foundationalist mathematics attempts to describe physical continuity through a theory of the mathematical continuum.

The problem, as Wittgenstein sees it, is that mathematicians, especially foundationalists (e.g., set theorists), have sought to accommodate physical continuity by a theory that ‘describes’ the mathematical continuum (PR §171). When, for example, we think of continuous motion and the (mere) density of the rationals, we reason that if an object moves continuously from A to B, and it travels only the distances marked by “rational points”, then it must skip some distances (intervals, or points) not