Mathematics, Metaphysics and Intuition in Kant

Dissertation, Harvard University (1996)

Emily Carson
McGill University
This thesis attempts to argue against an influential interpretation of Kant's philosophy of mathematics according to which the role of pure intuition is primarily logical. Kant's appeal to pure intuition, and consequently his belief in the synthetic character of mathematics, is, on this view, a result of the limitations of the logical resources available in his time. In contrast to this, a reading is presented of the development of Kant's philosophy of mathematics which emphasises a much richer philosophical role for intuition, beyond that of filling in deductive gaps in mathematical arguments. This role is largely determined by two factors: on the one hand, the epistemological gap in a traditional account of mathematical certainty, and on the other hand, the metaphysical worry raised by the followers of Leibniz and Wolff regarding the status of mathematics as a science consisting of truths. ;By appreciating how Kant's philosophy of mathematics developed against the background of what he saw as a conflict between the 'metaphysicians' and the 'mathematicians', we can see how the doctrine of pure intuition was required to fill the gaps in the account of the method and certainty of mathematics which Kant presents in the Prize Essay of 1764. This conflict takes its sharpest form between the monadists who uphold the metaphysical necessity of simple elements, and the geometers who uphold the infinite divisibility of space. In the Prize Essay Kant indirectly addresses this conflict by comparing the two disciplines. He asserts that the method of attaining certainty in mathematics is different from the method of metaphysics, and that as a result of this difference--primarily the different roles of definitions in each--mathematics is capable of a higher degree of certainty than metaphysics. He does not, however, explain this difference. Such an explanation seems particularly important in light of Kant's wish to secure geometry against the challenge of metaphysics. This thesis attempts to show that it is to provide such an explanation, to provide a philosophical grounding for the Prize Essay account, that Kant invokes the doctrine of pure intuition in his later account of mathematical knowledge
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