Note 127 — Introductory material

The pure doctrine of extension, as constructed by Grassmann, need not be discussed—it included much empirical material, and was philosophically a failure. But his principles, I think, will enable us to prove that projective Geometry, abstractly interpreted, is the science which he foresaw, and deals with a matter which can be constructed by the pure intellect alone. If this be so, however, it must be observed that projective Geometry, for the moment, is rendered purely hypothetical[132]. All necessary truth, as Bradley has shown, is hypothetical[133], and asserts, primâ facie, only the ground on which rests the necessary connection of premisses and conclusion. If we construct a mere conception of externality, and thus abandon our actually given space, the result of our construction, until we return to something actually given, remains without existential import—if there be experienced externality, it asserts, then there must be a form of externality with such and such properties. That there must be experienced externality, Kant's first argument about space proves, I think, to those who admit experience of a world of diverse but interrelated things. But this is a question which belongs to the next Chapter.