Abstract: As we have seen, Kant claims that we have innate intuitions of time and space, and that these produce in us knowledge about arithmetic and geometry. In Kant, there is no real distinction between geometry as a study of formal relations within a theory and the study of the structure of physical space. This distinction is more recent than Kant. It is, however, an important distinction. Pure mathematics is the study of abstract structures. The natural sciences apply mathematical theories to actual physical systems.