Note 117 — Introductory material

In accordance with this procedure, then, let us define our points as the terms of spatial relations, regarding whatever is not a point as a relation between points. What, on this view, must our points be taken to be? Obviously, if extension is mere relativity, they must be taken to contain no extension; but if they are to supply the terms for spatial relations, e.g. for straight lines, these relations must exhibit them as the terms of the figures they relate. In other words, since what can really be taken, without contradiction, as the term of a spatial relation, is unextended, we must take, as the term to be used in Geometry, where we cannot go outside space, the least spatial thing which Geometry can deal with, the thing which, though in space, contains no space; and this thing we define as the point[127].