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Mathematical Philosophy?

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Part of the book series: The Philosophy of Science in a European Perspective ((PSEP,volume 4))

Abstract

This article reflects on the scope and limits of mathematical methods in philosophy.

This article is based on my inaugural lecture, which I gave in Bristol in December 2010. Thanks to Richard Pettigrew, Hannes Leitgeb, Neil Coleman, and Gregory Wheeler for valuable comments on earlier drafts of this article, and for stimulating conversations on the subject. Research for this article was partially supported by the AHRC project “Foundations of Structuralism” (AH/H001670/1).

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Notes

  1. 1.

    An alternative for the nominalist is to develop a fictionalist position concerning mathematical objects. (Thanks to Neil Coleman for pointing that out.) But here I assume that indispensability arguments justify adopting a realist line on the question of the existence of mathematical objects.

  2. 2.

    My former colleague Hannes Leitgeb emphasises that this is a valid objective of mathematical philosophy.

  3. 3.

    This point is emphasized in (Hansson 2000).

  4. 4.

    There is also the question who is meant with ‘our’ in this sentence. Experimental philosophers hold that many of the ‘intuitions’ on which analytical philosophy is built are generated by a quite unrepresentative sample of the population, and therefore suspect. I will leave this discussion aside here.

  5. 5.

    Frege also made this point (Frege 1879, introduction).

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Author information

Authors and Affiliations

  1. Department of Philosophy, University of Bristol, 43 Woodland Road, BS8 1UU, Bristol, UK

    Leon Horsten

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  1. Leon Horsten
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Correspondence to Leon Horsten .

Editor information

Editors and Affiliations

  1. Aarhus University, Ny Munkegade 1520, Aarhus, 8000, Denmark

    Hanne Andersen

  2. Inst. History & Foundations of Science, Utrecht University, Budapestlaan 6, Utrecht, 3584 CD, Netherlands

    Dennis Dieks

  3. , Faculty of Humanities, University of A Coruña, Dr. Vazquez Cabrera street, w/n, Ferrol, 15.403, Spain

    Wenceslao J. Gonzalez

  4. , Philosophy School of Social Science, University of Manchester, Manchester, M13 9PL, United Kingdom

    Thomas Uebel

  5. Centre Artificial Intelligence (CENTRA), Department of Computer Science, New University of Lisbon, Monte de Caparica, Lisbon, 2829-516, Portugal

    Gregory Wheeler

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Horsten, L. (2013). Mathematical Philosophy?. In: Andersen, H., Dieks, D., Gonzalez, W., Uebel, T., Wheeler, G. (eds) New Challenges to Philosophy of Science. The Philosophy of Science in a European Perspective, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5845-2_7

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