We cannot imagine two straight lines intersecting at two points even though they may do so. In this case our abilities to imagine depend upon our abilities to visualise.

T HE heart of Kant's views on the nature of mathematics is his thesis that the judgments of pure mathematics are synthetic a priori. Kant usually offers this as one thesis, but it is fruitful to regard it as consisting of two separate claims, a meta- physical subthesis and an epistemological ..