ABSTRACT
A mathematical and scientific enterprise, geometry is to be understood, therefore, as the exploration of the consequences of the principles and theorems of the mind’s pure form of spatial intuition. Geometry can be known a priori without reducing to mere tautology precisely because it is at the very basis of perception. For those 18th- and 19th-century scholars puzzling over the extradition of sensations and precepts from inside to outside, the German philosopher Immanuel Kant provided an influential proposal. The lesson learned from measuring objects that are rough and fragmented is at odds with what we had been led to presume from Isaac Newton’s and I. Kant’s notion of space as absolute. Contained within the parable of the man in the inner room is Kant’s thesis of space as a pure form of intuition. The proof lay with several metaphysical arguments based on the nature of space and one transcendental argument derived from the special character of Euclidean geometry.
