Lisa A. Shabel. Mathematics in Kant's Critical Philosophy: Reflections on Mathematical Practice. Studies in Philosophy Outstanding Dissertations, Robert Nozick, ed. New York & London: Routledge, 2003. ISBN 0-415-93955-0. Pp. 178 [Book Review]

Philosophia Mathematica 15 (3):366-386 (2007)
  Copy   BIBTEX

Abstract

In this interesting and engaging book, Shabel offers an interpretation of Kant's philosophy of mathematics as expressed in his critical writings. Shabel's analysis is based on the insight that Kant's philosophical standpoint on mathematics cannot be understood without an investigation into his perception of mathematical practice in the seventeenth and eighteenth centuries. She aims to illuminate Kant's theory of the construction of concepts in pure intuition—the basis for his conclusion that mathematical knowledge is synthetic a priori. She does this through a contextualized interpretation of his notion of mathematical construction, which she argues can be approached by looking at Euclid's Elements and Christian Wolff's mathematical textbooks. The importance of the former for her interpretation is justified by the fact that nearly all of Kant's mathematical examples in the Critique are Euclidean propositions. The importance of the latter is revealed through the fact that Wolff's textbooks were not only widely read and representative of the state of elementary mathematics during Kant's time; Kant was also intimately familiar with them. During the thirty years prior to the publication of the Critique, he used the textbooks in the college-level introductory courses in mathematics and physics that he taught.In the introduction to her book, Shabel helpfully distinguishes her approach to Kant's philosophy of mathematics from that of previous commentators. She points out that most commentators assessed Kant's thoughts on mathematics in terms of the ‘supposedly devastating effects of the discovery of non-Euclidean geometry on his theory of space’.1 Bertrand Russell, for example, criticized Kant for his lack of a proper …

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 74,569

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Reflections On Kant’s Concept Of Space.Lisa Shabel - 2003 - Studies in History and Philosophy of Science Part A 34 (1):45-57.
Kant on the ‘Symbolic Construction' of Mathematical Concepts.Lisa Shabel - 1998 - Studies in History and Philosophy of Science Part A 29 (4):589-621.
Kant on Arithmetic, Algebra, and the Theory of Proportions.Daniel Sutherland - 2006 - Journal of the History of Philosophy 44 (4):533-558.
Mathematics, Metaphysics and Intuition in Kant.Emily Carson - 1996 - Dissertation, Harvard University
Redrawing Kant's Philosophy of Mathematics.Joshua M. Hall - 2013 - South African Journal of Philosophy 32 (3):235-247.
The Argument of Mathematics.Andrew Aberdein & Ian J. Dove (eds.) - 2013 - Dordrecht, Netherland: Springer.

Analytics

Added to PP
2017-02-21

Downloads
25 (#459,982)

6 months
1 (#418,924)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Lisa Shabel
Ohio State University

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references