Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Good weasel hunting

Abstract

The ‘indispensability argument’ for the existence of mathematical objects appeals to the role mathematics plays in science. In a series of publications, Joseph Melia has offered a distinctive reply to the indispensability argument. The purpose of this paper is to clarify Melia’s response to the indispensability argument and to advise Melia and his critics on how best to carry forward the debate. We will begin by presenting Melia’s response and diagnosing some recent misunderstandings of it. Then we will discuss four avenues for replying to Melia. We will argue that the three replies pursued in the literature so far are unpromising. We will then propose one new reply that is much more powerful, and—in the light of this—advise participants in the debate where to focus their energies.

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

References

  1. Audi, P. (2012). Grounding: Towards a theory of the in-virtue-of relation. Journal of Philosophy, 109, 685–711.

  2. Azzouni, J. (2004). Deflating existential consequence: A case for nominalism. New York: Oxford University Press.

  3. Azzouni, J. (2009). Evading truth commitments: The problem reanalyzed. Logique & Analyse, 206, 139–176.

  4. Baker, A. (2005). Are there genuine mathematical explanations of physical phenomena? Mind, 114, 223–238.

  5. Baker, A. (2009). Mathematical explanation in science. British Journal for the Philosophy of Science, 60, 611–633.

  6. Balaguer, M. (1998). Platonism and anti-platonism in mathematics. New York: Oxford University Press.

  7. Balaguer, M. (2011). Fictionalism in the philosophy of mathematics. In E. N. Zalta (Ed.) Stanford encyclopedia of philosophy (Fall 2011 ed.). URL http://plato.stanford.edu/archives/fall2011/entries/fictionalism-mathematics/

  8. Bangu, S. (2012). The applicability of mathematics in science: Indispensability and ontology. New York: Palgrave Macmillan.

  9. Colyvan, M. (2001). The indispensability of mathematics. New York: Oxford University Press.

  10. Colyvan, M. (2010). There is no easy road to nominalism. Mind, 119, 285–306.

  11. Colyvan, M. (2012). Road work ahead: heavy machinery on the easy road. Mind, 121, 1031–1046.

  12. Crane, T. (1990). An alleged analogy between numbers and propositions. Analysis, 50, 224–230.

  13. Daly, C., & Langford, S. (2009). Mathematical explanation and indispensability arguments. Philosophical Quarterly, 59, 641–658.

  14. Field, H. (1980). Science without numbers: A defence of nominalism. Oxford: Blackwell.

  15. Field, H. (1989). Realism, mathematics and modality. Oxford: Blackwell.

  16. Glymour, C. (1980). Theory and evidence. Princeton: Princeton University Press.

  17. Jackson, F., & Pettit, P. (1990). Program explanation: A general perspective. Analysis, 50, 107–117.

  18. Knowles, R. forthcoming. Heavy duty platonism. Erkenntnis.

  19. Leng, M. (2010). Mathematics and reality. Oxford: Oxford University Press.

  20. Liggins, D. (2008). Quine, Putnam, and the “Quine-Putnam indispensability argument”. Erkenntnis, 68, 113–127.

  21. Liggins, D. (2012). Weaseling and the content of science. Mind, 121, 997–1005.

  22. Liggins, D. (2014). Abstract expressionism and the communication problem. British Journal for the Philosophy of Science, 65, 599–620.

  23. Lyon, A., & Colyvan, M. (2008). The explanatory power of phase spaces. Philosophia Mathematica, 16, 227–243.

  24. Lyon, A. (2012). Mathematical explanations of empirical facts, and mathematical realism. Australasian Journal of Philosophy, 90, 559–578.

  25. MacBride, F. (1999). Listening to fictions: A study of Fieldian nominalism. British Journal for the Philosophy of Science, 50, 431–455.

  26. Maddy, P. (2005). Three forms of naturalism. In S. Shapiro (Ed.), The Oxford handbook of philosophy of mathematics and logic (pp. 437–459). New York: Oxford University Press.

  27. Marcus, R. (2014). The holistic presumptions of the indispensability argument. Synthese, 191, 3575–3594.

  28. Melia, J. (1992). An alleged disanalogy between numbers and propositions. Analysis, 52, 46–48.

  29. Melia, J. (1995). On what there’s not. Analysis, 55, 223–229.

  30. Melia, J. (1998). Field’s programme: Some interference. Analysis, 58, 63–71.

  31. Melia, J. (2000). Weaseling away the indispensability argument. Mind, 109, 455–479.

  32. Melia, J. (2002). Response to Colyvan. Mind, 111, 75–78.

  33. Melia, J. (2003). Review of Colyvan’s The indispensability of mathematics. Metascience, 12, 55–58.

  34. Melia, J. (2008). A world of concrete particulars. Oxford Studies in Metaphysics, 4, 99–124.

  35. Melia, J. (2011). Response to Daly and Langford. Mind, 119, 1117–1121.

  36. Morrison, J. (2012). Evidential holism and indispensability arguments. Erkenntnis, 76, 263–278.

  37. Morrison, M. (2007). Spin: All is not what it seems. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics, 38, 529–557.

  38. Penrose, R. (1990). The emperor’s new mind: Concerning computers, minds, and the laws of physics. London: Vintage.

  39. Pincock, C. (2007). A role for mathematics in the physical sciences. Noûs, 41, 253–275.

  40. Pincock, C. (2012). Mathematics and scientific representation. New York: Oxford University Press.

  41. Raley, Y. (2012). Why the weasel fails. Philosophia Mathematica, 20, 339–345.

  42. Resnik, M. (1997). Mathematics as a science of patterns. New York: Oxford University Press.

  43. Rizza, D. (2011). Magicicada, mathematical explanation, and mathematical realism. Erkenntnis, 74, 101–114.

  44. Rosen, G. (1994). What is constructive empiricism? Philosophical Studies, 74, 143–178.

  45. Saatsi, J. (2011). The enhanced indispensability argument: Representational versus explanatory role of mathematics in science. British Journal for the Philosophy of Science, 62, 143–154.

  46. Saatsi, J. (2012). Mathematics and program explanations. Australasian Journal of Philosophy, 90, 579–584.

  47. Saatsi, J. forthcoming. On the ‘indispensable explanatory role’ of mathematics. Mind.

  48. Scott, M., & Brown, P. (2012). Pragmatic antirealism: a new antirealist strategy. Philosophical Studies, 161, 349–366.

  49. Sober, E. (1993). Mathematics and indispensability. Philosophical Review, 102, 35–57.

  50. Stalnaker, R. (1978). Assertion. Syntax and Semantics, 9, 315–332.

  51. Stanley, J. (2001). Hermeneutic fictionalism. Midwest Studies in Philosophy, 25, 36–71.

  52. Turner, J. (2011). Review of Yablo’s Things: Philosophical Papers (Vol. 2). URL http://ndpr.nd.edu/news/25473-things-philosophical-papers-volume-2/.

  53. Walton, K. L. (1993). Metaphor and prop-oriented make-believe. European Journal of Philosophy, 1, 39–57.

  54. Yablo, S. (2000). A paradox of existence. In A. Everett & T. Hofweber (Eds.), Empty names, fiction and the puzzles of non-existence (pp. 275–312). Stanford: CSLI Publications.

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

  56. Yablo, S. (2002). Abstract objects: A case study. Philosophical Issues, 12, 220–240.

Download references

Acknowledgments

We would like to thank Chris Daly, Joe Morrison, Leo Tarasov, and two anonymous referees for their comments on earlier drafts. Rob Knowles gratefully acknowledges the award of a Jacobsen Studentship by the Royal Institute of Philosophy, which supported the work presented here.

Author information

Correspondence to David Liggins.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Knowles, R., Liggins, D. Good weasel hunting. Synthese 192, 3397–3412 (2015). https://doi.org/10.1007/s11229-015-0711-7

Download citation

Keywords

  • Weaseling
  • Nominalism
  • Fictionalism
  • Melia
  • Heavy duty platonism