Skip to main content
Log in

Mathematics and conceptual analysis

  • Original Paper
  • Published:
Synthese Aims and scope Submit manuscript

Abstract

Gödel argued that intuition has an important role to play in mathematical epistemology, and despite the infamy of his own position, this opinion still has much to recommend it. Intuitions and folk platitudes play a central role in philosophical enquiry too, and have recently been elevated to a central position in one project for understanding philosophical methodology: the so-called ‘Canberra Plan’. This philosophical role for intuitions suggests an analogous epistemology for some fundamental parts of mathematics, which casts a number of themes in recent philosophy of mathematics (concerning a priority and fictionalism, for example) in revealing new light.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Boolos G. (1971). The iterative conception of set. Journal of Philosophy 68, 215–232

    Article  Google Scholar 

  • Chalmers D. (1996). The conscious mind. New York, Oxford University Press

    Google Scholar 

  • Feigenson L., Carey S., Spelke E. (2002). Infant’s discrimination of number vs. continuous extent. Cognitive Psychology 44, 33–66

    Article  Google Scholar 

  • Field H. (1980). Science without numbers. Princeton, NJ, Princeton University Press

    Google Scholar 

  • Frege G. (1884). The foundations of arithmetic (translated by J. L. Austin). Oxford, Blackwell

    Google Scholar 

  • Gödel K. (1964). What is Cantor’s continuum problem?. In: Benacerraf P., Putnam H.(eds) Philosophy of mathematics: Selected readings. Cambridge, Cambridge University Press, pp. 470–485

    Google Scholar 

  • Jackson F. (1998). From metaphysics to ethics: A defence of conceptual analysis. Oxford, Oxford University Press

    Google Scholar 

  • Kitcher P. (1978). The plight of the platonist. Noûs 12, 119–136

    Article  Google Scholar 

  • Kitcher P. (1980). A priori knowledge. Philosophical Review 89, 3–23

    Article  Google Scholar 

  • Kripke S. (1980). Naming and necessity. Cambridge, MA, Harvard University Press

    Google Scholar 

  • Lakatos I. (1976). Proofs and refutations. Cambridge, Cambridge University Press

    Google Scholar 

  • Lewis D. (1970). How to define theoretical terms. Journal of Philosophy 67, 427–446

    Article  Google Scholar 

  • Lewis D. (1973). Counterfactuals. Oxford, Blackwell

    Google Scholar 

  • Maddy P. (1997). Naturalism in mathematics. Oxford, Oxford University Press

    Google Scholar 

  • McGee V. (1997). How we learn mathematical language. Philosophical Review 106, 35–68

    Article  Google Scholar 

  • Nolan, D. (1996). The credo of the Canberra planners. http://www.st-andrews.ac.uk/dpn/docs/ credo.htm.

  • Nolan, D. (forthcoming). Platitudes and analysis. In D. Braddon-Mitchell, & R. Nola (Eds.), Naturalism and analysis. Cambridge, MA: MIT Press.

  • O’Leary-Hawthorne J., Price H. (1996). How to stand up for non-cognitivists. Australasian Journal of Philosophy 74,275–292

    Article  Google Scholar 

  • Parsons C. (1995). Platonism and mathematical intuition in Kurt Gödel’s thought. Bulletin of Symbolic Logic 1, 44–74

    Article  Google Scholar 

  • Rosen G. (1990). Modal fictionalism. Mind 99, 327–354

    Article  Google Scholar 

  • Smith M. (1994) The moral problem. Oxford, Blackwell

    Google Scholar 

  • Soames S. (2004). Reference and description. Princeton, Princeton University Press

    Google Scholar 

  • Stalnaker R. C. (1978). Assertion. In Context and content (pp. 78–95). Oxford: Oxford University Press

  • Stalnaker R.C. (1996). Varieties of supervenience. Philosophical Perspectives 10, 221–242

    Google Scholar 

  • van Fraassen B.C. (1989). Laws and symmetry. Oxford, Oxford University Press

    Google Scholar 

  • Williamson T. (2006). Conceptual truth. Proceedings of the Aristotelian Society, Supplementary Volume, 80.

  • Yablo S. (2001). Go figure: A path through fictionalism. Midwest Studies in Philosophy 25, 72–102

    Article  Google Scholar 

  • Yablo S. (2005). The myth of the seven. In: Kalderon M.E.(ed) Fictionalism in metaphysics. Oxford, Oxford University Press, pp. 88–115

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Antony Eagle.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Eagle, A. Mathematics and conceptual analysis. Synthese 161, 67–88 (2008). https://doi.org/10.1007/s11229-006-9151-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11229-006-9151-8

Keywords

Navigation