Note 180 — Introductory material

In the present chapter, we have to discuss two questions which, though scarcely geometrical, are of fundamental importance to the theory of Geometry propounded above. The first of these questions is this: What relation can a purely logical and deductive proof, like that from the nature of a form of externality, bear to an experienced subject-matter such as space? You have merely framed a general conception, I may be told, containing space as a particular species, and you have then shown, what should have been obvious from the beginning, that this general conception contained some of the attributes of space. But what ground does this give for regarding these attributes as à priori? The conception Mammal has some of the attributes of a horse; but are these attributes therefore à priori adjectives of the horse? The answer to this obvious objection is so difficult, and involves so much general philosophy, that I have kept it for a final chapter, in order not to interrupt the argument on specially geometrical topics.