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IN HIS INAUGURAL DISSERTATION of 1770, Kant introduces the distinction between the faculties of sensibility and understanding. One consequence of this distinction is that it gives Kant the means to resolve some longstanding metaphysical disputes. If we keep straight the sources of our concepts and, in particular, don't make the mistake of imposing sensible conditions on the concepts of the understanding, we will avoid some of these disputes. What I want to emphasize in this paper is another important consequence which, I think, is less widely recognized, and that is the importance of this distinction for Kant's comparison of the methods of metaphysics and mathematics.
In his Prize Essay of 1764, Kant distinguishes mathematics and metaphysics with respect to their certainty and their methods. In particular, Kant claims that mathematics is capable of the highest degree of certainty and he argues that the imitation of mathematics by metaphysics leads only to error and confusion. I've argued elsewhere that Kant's comparison of mathematics and metaphysics in the Prize Essay raises a number of philosophical questions which are finally resolved only with the development of the notion of construction in pure intuition in the Critique of Pure Reason.1 In this paper, I want to consider an intermediate stage on the way to resolving the difficulties in the Prize Essay view. I want to show, first, how Kant's distinction between sensibility and intellect in the Inaugural Dissertation can be understood as arising-at least in part-out of the open questions faced by the comparison of metaphysics and mathematics in the Prize Essay. The key feature of that comparison which is left unexplained is why 'invention' is permissible in mathematics and not in philosophy. Why doesn't the arbitrary combination of concepts in mathematics lead to flights of fancy in that discipline as liant claims it does in metaphysics?
Understanding the distinction in the context of the Prize Essay comparison also requires that we take into consideration another concern of Kant's, and that is the dispute between the "mathematicians" and the "metaphysicians." The dispute was essentially over the respective roles and claims to knowledge of mathematics and metaphysics. In the Prize Essay, Kant clearly favors the results of the mathematicians over those of the metaphysicians, but it's not clear that this...