Hostname: page-component-7dd5485656-zklqj Total loading time: 0 Render date: 2025-10-30T19:38:29.912Z Has data issue: false hasContentIssue false
  • English
  • Français

A SECOND PHILOSOPHY OF ARITHMETIC

Published online by Cambridge University Press:  08 November 2013

PENELOPE MADDY
PENELOPE MADDY*
Affiliation:
University of California
*
*DEPARTMENT OF LOGIC AND PHILOSOPHY OF SCIENCE, UNIVERSITY OF CALIFORNIA, IRVINE, CA 92697 E-mail: pjmaddy@uci.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper outlines a second-philosophical account of arithmetic that places it on a distinctive ground between those of logic and set theory.

Information

Type
Research Article
Information
The Review of Symbolic Logic , Volume 7 , Issue 2 , June 2014 , pp. 222 - 249
Copyright
Copyright © Association for Symbolic Logic 2013 

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.)

Article purchase

Temporarily unavailable

References

BIBLIOGRAPHY

Allison, H. (2004). Kant’s Transcendental Idealism (revised and enlarged edition). New Haven, CT: Yale University Press.CrossRefGoogle Scholar
Benacerraf, P. (1973). Mathematical truth. Reprinted in Benacerraf, P., and Putnam, H., editors. Philosophy of Mathematics (second edition). Cambridge, UK: Cambridge University Press, pp. 403–420.Google Scholar
Bloom, P. (2000). How Children Learn the Meanings of Words. Cambridge, MA: MIT Press.Google Scholar
Carey, S. (2009). The Origin of Concepts. New York, NY: Oxford University Press.Google Scholar
Friedman, M. (1992). Kant and the Exact Sciences. Cambridge, MA: Harvard University Press.Google Scholar
Gardner, S. (1999). Kant and the Critique of Pure Reason. London, UK: Routledge.Google Scholar
Hamkins, J. A Question for the Mathematics Oracle, 2011. Available from: http://jdh.hamkins.org/files/2012/09/A-question-for-the-math-oracle.pdf. Unpublished.Google Scholar
Hauser, M., Chomsky, N., & Fitch, W. T. (2002). The faculty of language: What is it, who has it, and how did it evolve? Science, 298, 1569–1579.Google Scholar
Kant, I. (1997). Critique of Pure Reason, Guyer, P., and Wood, A., editors, (Cambridge, UK: Cambridge University Press).Google Scholar
Koellner, P. Comment on Woodin [RI], 2011. Available from: http://logic.harvard.edu/EFI_Woodin_comments.pdf. Unpublished.Google Scholar
Ladyman, J., & Ross, D. (2007). Every Thing Must Go. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
Longuenesse, B. (1998). Kant and the Capacity to Judge. Princeton, NJ: Princeton University Press.Google Scholar
Maddy, P. (1988). Believing the axioms. Journal of Symbolic Logic, 53, 481–511, 736–764.CrossRefGoogle Scholar
Maddy, P. (1990). Realism in Mathematics. Oxford, UK: Oxford University Press.Google Scholar
Maddy, P. (1997). Naturalism in Mathematics. Oxford, UK: Oxford University Press.Google Scholar
Maddy, P. (2007). Second Philosophy. Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
Maddy, P. (2008). How applied mathematics became pure. Review of Symbolic Logic, 1, 16–41.CrossRefGoogle Scholar
Maddy, P. (2011). Defending the Axioms. Oxford, UK: Oxford University Press.Google Scholar
Maddy, P. (2011a). Naturalism, transcendentalism and therapy. In Smith, J., and Sullivan, P., editors. Transcendental Philosophy and Naturalism. Oxford, UK: Oxford University Press, pp. 120–156.CrossRefGoogle Scholar
Maddy, P. (2011b). Naturalism and common sense. Analytic Philosophy, 52, 2–34.Google Scholar
Maddy, P. (2014). A second philosophy of logic. In Rush, P., editor. The Metaphysics of Logic (to appear). Cambridge, UK: Cambridge University Press.Google Scholar
Maddy, P. (2013). The Logical Must. Unpublished manuscript.Google Scholar
McCarty, D. C. (2005). Intuitionism in mathematics. In Shapiro, S., editor. Oxford Handbook of Philosophy of Mathematics and Logic. New York, NY: Oxford University Press, pp. 356–386.CrossRefGoogle Scholar
Papineau, D. (2009). Naturalism. In Zalta, E. N., editor. The Stanford Encyclopedia of Philosophy (Spring 2009 edition). Available from: http://plato.stanford.edu/archives/spr2009/entries/naturalism/.Google Scholar
Parsons, C. (1969). Kant’s philosophy of arithmetic. In Posy, C., editor. Kant’s Philosophy of Mathematics. Dordrecht, Netherlands: Kluwer Academic Publishers, pp. 43–79.Google Scholar
Parsons, C. (1983). Mathematics in Philosophy. Ithaca, NY: Cornell University Press.Google Scholar
Parsons, C. (1984). Arithmetic and the categories. In Posy, C., editor. Kant’s Philosophy of Mathematics. Dordrecht, Netherlands: Kluwer Academic Publishers, pp. 135–158.Google Scholar
Parsons, C. (2012). Postscript. In his From Kant to Husserl. Cambridge, MA: Harvard University Press, pp. 100–114.Google Scholar
Posy, C., editor. (1992). Kant’s Philosophy of Mathematics. Dordrecht, Netherlands: Kluwer Academic Publishers.Google Scholar
Rohloff, W. (2007). Kantian intuition and applicability, chapter 2 of his Kant and Frege on the A Priori Applicability of Mathematics. PhD Dissertation, Department of Logic and Philosophy of Science, University of California, Irvine.Google Scholar
Tait, W. (1981). Finitism. Reprinted in his The Provenance of Pure Reason. New York, NY: Oxford University Press, 2005, pp. 21–42.Google Scholar
Tritton, D. J. (1988). Physical Fluid Dynamics (second edition). Oxford: Oxford University Press.Google Scholar
Wilson, M. (2006). Wandering Significance. Oxford: Oxford University Press.Google Scholar
Woodin, H. (1998). The tower of Hanoi. In Dales, H., and Oliveri, G., editors. Truth in Mathematics. Oxford: Oxford University Press, pp. 329–351.Google Scholar
Woodin, H. (RI). The realm of the infinite. Available from: http://logic.harvard.edu/EFI_Woodin_TheRealmOfTheInfinite.pdf.Google Scholar
Zermelo, E. (1930). On boundary numbers and domains of sets. Reprinted in his Collected Works, Ebbinghaus, H.-D., and Kanamori, A., editors. (E. de Pellegrin, trans.) Berlin: Springer, 2010, pp. 400–431.Google Scholar