In studying Kant I am running into a problem. Kant refers to pure geometry as only having objective reality under the condition that it refers only to objects of the senses (Prolegomena, Note I). If Kant is speaking of pure geometry, then he must be talking about a priori intuitions, but objects of the senses seem to imply the sensing of objects in the world, or at least their outer appearances, which is a posteriori. So which is it, a priori pure geometry, or a posteriori objects of the senses?
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I was also confused by this when I read it many years ago. I eventually decided that he meant that geometry is about space, and space is how objects of the senses are related to one another.– David GudemanMar 21 at 17:14
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1The same productive imagination that synthesizes objects from the manifold of sensation in perception also synthesizes pure intuitions in geometry. As a result, the former conform to the latter and we get synthetic a priori. But it also means that geometric concepts that pure intuitions attach to can only apply to objects of experience, the sensible objects, and not, say, to noumena.– ConifoldMar 22 at 0:09
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1This is really numerous ardent kantian readers’ confusion which in its another more well known problem formulation is akin to ”is visual geometric epistem true and deepest a priori form of understanding of human mind/intelligence? If not, what else we should thank for…– Double KnotMar 22 at 18:24
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