Note 172 — Introductory material
Reading edition
I have now shown, I hope conclusively, that spherical space affords no objection to the apriority of my axiom. Any two points have one relation, their distance, which is independent of the rest of space, and this relation requires, as its measure, a curve uniquely determined by those two points. I might have taken the bull by the horns, and said: Two points can have no relation but what is given by lines which join them, and therefore, if they have a relation independent of the rest of space, there must be one line joining them which they completely determine. Thus James says[175]: