Hostname: page-component-848d4c4894-wzw2p Total loading time: 0 Render date: 2024-05-19T11:20:04.241Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.

References

Aristotle, , Categories. (As reprinted in Aristotle’s Categories and De Interpretatione. (trans.) J.L. Ackrill. Oxford: Oxford University Press, 1963. Pages 3-42.)Google Scholar
Bennett, Jonathon. (1966). Kant’s Analytic. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Hintikka, Jaakko. (1967). “Kant on the Mathematical Method.” The Monist 51; 352–375. (As reprinted in Kant Studies Today. Edited by Lewis White Beck. La Salle, IL: Open Court Press, 1969. Pages 117-140.)Google Scholar
Kant, Immauel. (1783). Prolegomena zu einer jeden Künftieen Metaphvsik. die als Wissensohaft wlrd auftreten Können. (As reprinted as Prolegomena to Any Future Metaphysics, (ed.) Lewis White Beck. New York: The Bobbs-Merrill Co., Inc., 1950.)Google Scholar
Kant, Immauel. (1787). Kritlk der reinen Vernunft. 2nd ed. Riga: Felix Hartknoch. (As reprinted Hamburg: Felix Meiner, 1956.)Google Scholar
Kant, Immauel. (1800). Vorlesungen Kants Über Logik. (ed.) G.B. Jäsche. (As reprinted as Logic. (trans.) Robert S. Hartman and Wolfgang Schwarz. New York: The Bobbs-Merrill Co., Inc., 1974.)Google Scholar
Kant, Immauel. (1968). Selected Pre-Critioal Writings and Correspondence with Beck , (trans.) G.B. Kerford and D.E. Waiford. Manchester: Manchester University Press.Google Scholar
Parsons, Charles. (1969). “Kant’s Philosophy of Arithmetic. In philosphy Science and Method. Edited by S. Morganbesser, P. Suppes, and M. White, New York: St. Martin’s Press. Pages 568-594.Google Scholar
Russell, Bertrand. (1919). Introduction to Mathematical Philosophy. L: George Allen and Unwin.Google Scholar
Wilson, Kirk Dallas (1975). “Kant on Intuition.” The Philosophical Quarterly 25: 247–265.CrossRefGoogle Scholar
Young, J. Michael (1982). “Kant on the Construction of Arithmetical Concepts.” Kant-Studien 73: 17–46.CrossRefGoogle Scholar