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Synthesis, Sensibility, and Kant’s Philosophy of Mathematics

Published online by Cambridge University Press:  31 January 2023

Carol A. Van Kirk
Carol A. Van Kirk*
Affiliation:
Ohio University, Athens
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Extract

Kant’s philosophy of mathematics presents two fundamental problems of interpretation: (1) Kant claims that mathematical truths or “judgments” are synthetic a priori; and (2) Kant maintains that intuition is required for generating and/or understanding mathematical statements. Both of these problems arise for us because of developments in mathematics since Kant. In particular, the axiomatization of geometry--Kant’s paradigm of mathematical thinking--has made it seem to some commentators as, for example, Russell, that both (1) and (2) are false (Russell 1919, p. 145).2 If virtually all of mathematics, including geometry, is axiomatizable, it would seem that mathematics results in analytic judgments that are totally independent of sensibility, the source, according to Kant, of intuition. In this paper I will address both of these difficulties. I shall argue that Kant’s understanding of both “synthetic” and “intuition” make his position immune to these criticisms.

Type
Part II. History and Philosophy of Science
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1986 , Issue 1: Volume One: Contributed Papers 1986 , 1986 , pp. 135 - 144
Copyright
Copyright © Philosophy of Science Association 1986

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Footnotes

1

I gratefully acknowledge helpful discussion from my colleagues in the Philosophy Department at Ohio University and also from the members of the Philosophy Department at Michigan State University. The comments made by Dr. Cynthia Hampton and Dr. Rhoda Kotzln were especially useful.

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