Abstract

Background

Let me introduce you to a simple experiment with your imagination. First pick any two objects in your visual field that lie apart from one another, and then imagine a straight line between them. Now notice that the straight line must be in some space, though not in the same space as those two objects you picked initially. It must be in some space, because it is between them and so it bears a spatial relation to them; yet it is not in the same space as they are, because it is not really ‘out there’ as they are. The space where geometrical objects like the straight line you just imagined arise might be called pure space as opposed to visual space (i.e. the space we perceive by sight) or physical space (i.e. the space that scientific theories like general relativity describe). The fundamental idea of Kant's philosophy of geometry is that Euclidean geometry is the science of pure space.