Kant’s Transcendental Method and His Theory of Mathematics

Abstract

This paper has a dual aim. On the one hand, it is a part of a larger attempt to understand the nature of Kant’s ideas of transcendental method and transcendental knowledge and their implications, for instance, the question as to what the objects of transcendental knowledge are. On the other hand, I am outlining once again what I take to be the true argumentative structure of Kant’s doctrines of the mathematical method, space, time, and the forms of inner and outer sense. The link between the two is that on my interpretation Kant’s theory of mathematics offers an excellent example of the applications of his transcendental method. Moreover, after having recently defended my construal of Kant’s views on mathematical reasoning and their foundation on historical and textual grounds, it may be in order to try to vindicate it in another way, to wit, by relating it to the overall nature of Kant’s philosophy, including his idea of transcendental knowledge. I suspect that this may be a better way of convincing my colleagues than nitty-gritty analyses of Kantian texts. At the same time, this approach offers me a chance of indicating some of the consequences of my results concerning Kant’s theory of mathematics for the rest of his philosophy. It turns out that the observations we can make in pursuing this line of thought have also interesting consequences for our contemporary thought in the philosophy of logic and mathematics.