Note 171 — Introductory material

This, however, is mere speculation. I come now to the pièce de résistance of my argument. The ambiguity in spherical space arose, as we saw, from a relation of magnitude to the rest of space—such a relation being unaltered by a motion of the two points, and therefore falling outside our introductory reasoning. But what is this relation of magnitude? Simply a relation of the distance between the two points to a distance given in the nature of the space in question. It follows that such a relation presupposes a measure of distance, and need not, therefore, be contemplated in any argument which deals with the à priori requisites for the possibility of definite distances[174].