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An Outline of a New Approach
from Part IV - Arithmetic and Number
Published online by Cambridge University Press: 24 April 2020
The last half century has seen great advances in our understanding of Kant’s philosophy of mathematics, but we have not yet arrived at a satisfactory interpretation of Kant’s philosophy of arithmetic. In fact, it will be argued that on a key point – whether Kant’s understanding of number is fundamentally cardinal or ordinal – we face a standstill in which competing interpretations appear to have equal support. A new approach is needed in order to overcome this standstill and adjudicate between interpretations. This paper does not argue for a particular interpretation; instead, it outlines what that new approach requires, one that I believe will deepen our understanding of Kant’s philosophy of arithmetic and permit a more nuanced account.
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