Hume’s Treatise, Book I, Part II, contains perplexing arguments against the infinite divisibility of space (and time) and the exactitude of geometry. We can attain a charitable reading of these difficult arguments by appreciating that they are guided by Hume’s phenomenological model of apprehension, and that this model (unlike Husserl’s for example) is intended to be sensible as opposed to intellectual. From the point of view of pure mathematics, Hume’s assumptions about the infinite may appear as crude misunderstandings of the continuum. However, once we see that phenomenological apprehension, for Hume, must always be of bounded, discrete, sensible particulars, we can explain not only Hume’s arguments against infinite divisibility but also the privileged role he assigns to arithmetic (the mathematics of discrete quantity) and to one-to-one correspondence between discrete units as the ultimate standard of exactitude.