Abstract:
Kant’s critical statements about the character and status of the axioms of geometry fail, on their own, to make clear his conception of the foundations of geometry. My aim in this talk is to provide an interpretation and analysis of Kant on the foundations of geometry that is sensitive to the mathematical and historical context of his remarks, as well as to the relation in which his theory of geometry stands to other of his philosophical commitments, such as his theory of sensibility. In the course of this discussion, I will propose how best to understand “ostensive construction”, the central explanatory notion of Kant’s theory of geometry.