Note 139 — Introductory material

With this, our deduction of projective Geometry from the à priori conceptual properties of a form of externality is completed. That such a form, when regarded as an independent thing, is self-contradictory, has been abundantly evident throughout the discussion. But the science of the form has been founded on the opposite way of regarding it: we have held it throughout to be a mere complex of relations, and have deduced its properties exclusively from this view of it. The many difficulties, in applying such an à priori deduction to intuitive space, and in explaining, as logical necessities, properties which appear as sensuous or intuitional data, must be postponed to Chapter IV. For the present, I wish to point out that projective Geometry is wholly à priori; that it deals with an object whose properties are logically deduced from its definition, not empirically discovered from data; that its definition, again, is founded on the possibility of experiencing diversity in relation, or multiplicity in unity; and that our whole science, therefore, is logically implied in, and deducible from, the possibility of such experience.