"Kant on Mathematical Definitions and Construction (In Response to Rationalist Critics)"
Abstract: Kant’s view of definition is important for his philosophy of mathematics. In texts that originated as defenses of his Critical philosophy against rationalist objections, he makes especially clear that mathematical concepts are grasped through definitions in a way that makes possible the use of construction in mathematics (which distinguishes the mathematical method from that of philosophy). But at the same time that Kant suggests that definitions somehow incorporate constructions, he discusses examples of mathematical concepts whose definitions have undergone change. This seems to concede to his rationalist critics that mathematical judgments could be rendered analytic, specifically by incorporating the constructions that prove them into the definitions of the concepts. I will argue that it is less important for Kant to deny that mathematical judgments can be extracted from the definitions of concepts than to uphold a role for sensible representation in acquiring mathematical knowledge.
Katherine Laura Dunlop is a Professor at the University of Texas, Austin.
