Book contents
- Kant’s Philosophy of Mathematics
- Kant’s Philosophy of Mathematics
- Copyright page
- Dedication
- Contents
- Contributors
- Acknowledgements
- Introduction
- Part I Roots
- Part II Method and Logic
- Part III Space and Geometry
- Part IV Arithmetic and Number
- 10 Arithmetic and the Conditions of Possible Experience
- 11 Kant’s Philosophy of Arithmetic
- 12 Kant on ‘Number’
- References to Works by Kant
- Bibliography
- Index
11 - Kant’s Philosophy of Arithmetic
An Outline of a New Approach
from Part IV - Arithmetic and Number
Published online by Cambridge University Press: 24 April 2020
- Kant’s Philosophy of Mathematics
- Kant’s Philosophy of Mathematics
- Copyright page
- Dedication
- Contents
- Contributors
- Acknowledgements
- Introduction
- Part I Roots
- Part II Method and Logic
- Part III Space and Geometry
- Part IV Arithmetic and Number
- 10 Arithmetic and the Conditions of Possible Experience
- 11 Kant’s Philosophy of Arithmetic
- 12 Kant on ‘Number’
- References to Works by Kant
- Bibliography
- Index
Summary
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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- Information
- Kant's Philosophy of Mathematics , pp. 248 - 266Publisher: Cambridge University PressPrint publication year: 2020