The Subjectivity of Space

Abstract

Much of what we have said about time holds mutatis mutandis for space. Here too it is necessary to distinguish between the spatial as intuitively representable extension and the spatial as a system for ordering natural objects, achieved with the aid of pure concepts. This system can be realized in a manner quite analogous to the arrangements of objects in the time sequence, the only difference being that what is now involved is not a one-dimensional continuum but a three-dimensional one. As we noted above (Part I, § 67), one of the most significant accomplishments, epistemolog-ically, of modern mathematics was to establish the fundamental difference between geometry as a system of pure judgments and concepts in which all that matters are mutual logical relations, and geometry as the system of intuitive spatial structures and their relationships, with which these concepts and judgments are correlated. The first system corresponds with the second in every respect, of course. But it is fully independent of the latter in that it need not in any way be conceived of as a description of the laws that govern the intuitive geometrical structures. As we saw, this was proved by the fact that the very same geometrical propositions can be given an intuitive content in the most diverse ways.