Kant's Philosophy of Geometry—On the Road to a Final Assessment

摘要

The paper attempts to summarize the debate on Kant’s philosophy of geometry and to offer a restricted area of mathematical practice for which Kant’s philosophy would be a reasonable account. Geometrical theories can be characterized using Wittgenstein’s notion of pictorial form. Kant’s philosophy of geometry can be interpreted as a reconstruction of geometry based on one of these forms — the projective form. If this is correct, Kant’s philosophy is a reasonable reconstruction of such theories as projective geometry; and not only as they were practiced in Kant’s time, but also as architects use them today.