Thursday, September 25, 2003

But Before I Go, Kant's Own Defense of Formal Space, Which I Should Have Found Earlier

"Space, represented as object (as we are required to do in geometry), contains more than mere form of intuition; it also contains combination of the manifold, given according to the form of sensibility, in an intuitive representation, so that the form of intuition gives only a manifold, the formal intuition gives unity of representation. In the Aesthetic I have treated this unity as belonging merely to sensibility, simply in order to emphasize that it precedes any concept, although, as a matter of fact, it presupposes a synthesis which does not belong to the senses but through which all concepts of space and time first become possible. For since by its means (in that the understanding determines the sensibility) space and time are first given as intuitions, the unity of this a priori intuition belongs to space and time, and not to the concept of the understanding."

All of which is to say, that space as an object is not the same as formal space. The space which we derive from experience, from observation, is still only the occasion of the intuition of space, not the creator of it. Space as object is in fact Riemann's "three-fold extensive magnitude". And for such an object formal space does not suffice. "It requires a synthesis which does not belong to the senses"; said synthesis can only be the transcendental apperception.

If people would just read the footnotes, they'd not have misread Kant, to their and Geometry's detriment. And if I'd read the footnote, I might've avoided posting my Defense.