In Treatise 1.2, Of the ideas of space and time, Hume examines our ideas of spatial extension and temporal duration, our ideas of geometric equality, straightness, flatness, and mathematical point, and our ideas of a vacuum and of time without change. Hume does not, however, restrict his attention to these ideas; he also draws conclusions about space and time themselves. He argues that space and time are not infinitely divisible, that their smallest parts must be occupied, and that as a consequence there is no vacuum or interval of time without change. His treatments of matters beyond the scope of the section's title have received harsh criticism. His conclusions have seemed contrary to mathematics and physics. His method of arguing - applying features of our mere ideas of space and time to space and time themselves - has seemed philosophically inept. The apparent success of these criticisms has led to widespread neglect of this part of Hume's work.

The neglect is unfortunate. In Of the ideas of space and time Hume gives important characterizations of the skeptical approach that will be developed in the rest of the Treatise. When that approach is better understood, the force of Hume’s arguments concerning space and time can be appreciated, and the influential criticisms of them can be seen to miss the mark.