, Volume 190, Issue 12, pp 2413–2427

A Truthmaker Indispensability Argument



Recently, nominalists have made a case against the Quine–Putnam indispensability argument for mathematical Platonism by taking issue with Quine’s criterion of ontological commitment. In this paper I propose and defend an indispensability argument founded on an alternative criterion of ontological commitment: that advocated by David Armstrong. By defending such an argument I place the burden back onto the nominalist to defend her favourite criterion of ontological commitment and, furthermore, show that criterion cannot be used to formulate a plausible form of the indispensability argument.


Indispensability Ontological commitment Platonism Nominalism Truthmakers 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Armstrong D. (2004) Truth and truthmakers. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  2. Azzouni J. (1997) Thick epistemic access: Distinguishing the mathematical from the empirical. Journal of Philosophy 94(9): 472–484CrossRefGoogle Scholar
  3. Azzouni J. (2004) Deflating existential consequence: A case for nominalism. Oxford University Press, New YorkCrossRefGoogle Scholar
  4. Baker A. (2005) Are there genuine mathematical explanations of physical phenomena?. Mind 114(454): 223–238CrossRefGoogle Scholar
  5. Beebee H., Dodd J. (2005) Introduction. In: Beebee H., Dodd J. (eds) Truthmakers: The contemporary debate. Oxford University Press, Oxford, pp 1–16CrossRefGoogle Scholar
  6. Benacerraf P. (1973) Mathematical truth. The Journal of Philosophy 70(19): 661–679CrossRefGoogle Scholar
  7. Bigelow J. (1988) The reality of numbers: A physicalist’s philosophy of mathematics. Oxford University Press, OxfordGoogle Scholar
  8. Cameron R. (2008a) Truthmaker and ontological commitment: Or how to deal with complex objects and mathematical ontology without getting into trouble. Philosophical Studies 140(1): 1–18CrossRefGoogle Scholar
  9. Cameron R. (2008b) Turtles all the way down: Regress, priority and fundamentality in metaphysics. The Philosophical Quarterly 58(230): 1–14Google Scholar
  10. Cameron R. (2010) Necessity and triviality. The Australasian Journal of Philosophy 88(3): 401–415CrossRefGoogle Scholar
  11. Colyvan M. (1998) Is Platonism a bad bet?. The Australasian Journal of Philosophy 76(1): 115–119CrossRefGoogle Scholar
  12. Colyvan M. (2000) Conceptual contingency and abstract existence. The Philosophical Quarterly 50(198): 87–91CrossRefGoogle Scholar
  13. Colyvan M. (2001) The indispensability of mathematics. Oxford University Press, New YorkCrossRefGoogle Scholar
  14. Colyvan M. (2005) Ontological independence as the mark of the real. Philosophia Mathematica 13(2): 216–225CrossRefGoogle Scholar
  15. Colyvan M. (2010) There is no easy road to nominalism. Mind 119(474): 285–306CrossRefGoogle Scholar
  16. Dyke H. (2008) Metaphysics and the representational fallacy. Routledge, New YorkGoogle Scholar
  17. Field H. (1980) Science without numbers. Princeton University Press, Princeton, NJGoogle Scholar
  18. Field H. (1985) On conservativeness and incompleteness. The Journal of Philosophy 82(5): 239–260CrossRefGoogle Scholar
  19. Field H. (1993) The conceptual contingency of mathematical objects. Mind 102(406): 285–299CrossRefGoogle Scholar
  20. Gregory D. (2001) Smith on truthmakers. Australasian Journal of Philosophy 79(3): 422–427CrossRefGoogle Scholar
  21. Hale R., Wright C. (1992) Nominalism and the contingency of abstract objects. Journal of Philosophy 89(3): 111–135CrossRefGoogle Scholar
  22. Hale R., Wright C. (1994) A reductio ad surdurm? Field on the contingency of mathematical objects. Mind 103(410): 169–184CrossRefGoogle Scholar
  23. Heil J. (2003) From an ontological point of view. Oxford University Press, OxfordCrossRefGoogle Scholar
  24. Leng M. (2010) Mathematics and reality. Oxford University Press, OxfordCrossRefGoogle Scholar
  25. Liggins D. (2005) Truthmakers and explanation. In: Beebee H., Dodd J. (eds) Truthmakers: The contemporary debate. Oxford University Press, Oxford, pp 105–115CrossRefGoogle Scholar
  26. Maddy P. (1992) Indispensability and practice. The Journal of Philosophy 89(6): 275–289CrossRefGoogle Scholar
  27. Maddy, P. (1996). Ontological commitment: Between Quine and Duhem. Nous, 30, Supplement: Philosophical Perspectives, 10, Metaphysics, 317–341.Google Scholar
  28. McFetridge I. (1990) Truth, correspondence, explanation and knowledge. In: Haldane J., Scruton R. (eds) Logical necessity and other essays. Aristotelian Society, London, p 53Google Scholar
  29. Melia J. (1998) On “On what there is”. Pacific Philosophical Quarterly 79(1): 1–18CrossRefGoogle Scholar
  30. Melia J. (2000) Weaseling away the indispensability argument. Mind 109(435): 455–480CrossRefGoogle Scholar
  31. Melia J. (2002) Response to Colyvan. Mind 111(441): 75–79CrossRefGoogle Scholar
  32. Melia J. (2006) The conservativeness of mathematics. Analysis 66(3): 202–208CrossRefGoogle Scholar
  33. Miller K. (2010) The nature of mathematical objects: modality and minimalism. In: Hazlett A. (ed) New waves in metaphysics. Palgrave Macmillan, Basingstoke, pp 199–218Google Scholar
  34. Merricks T. (2007) Truth and ontology. Oxford University Press, New YorkCrossRefGoogle Scholar
  35. Molnar G. (2000) Truthmakers for negative truths. Australasian Journal of Philosophy 78(1): 72–76CrossRefGoogle Scholar
  36. Putnam, H. (1979a). Philosophy of logic. In Mathematics matter and method: Philosophical papers (pp. 323–357). Cambridge: Cambridge University Press.Google Scholar
  37. Putnam H. (1979b) What Is Mathematical Truth?. In: Putnam H. (ed) Mathematics matter and method: Philosophical papers. Cambridge University Press, Cambridge, pp 60–78CrossRefGoogle Scholar
  38. Quine W. (1948) On what there is. The Review of Metaphysics 2(5): 21–38Google Scholar
  39. Quine W. (1951) Main trends in recent philosophy: Two dogmas of empiricism. Philosophical Review 60(1): 20–43CrossRefGoogle Scholar
  40. Quine W. V. O. (1960) Word and object. MIT Press, Cambridge, MAGoogle Scholar
  41. Resnik M. D. (1995) Scientific vs mathematical realism: The indispensability argument. Philosophia Mathematica 3(2): 166–174CrossRefGoogle Scholar
  42. Restall G. (1996) Truthmakers, entailment and necessity. Australasian Journal of Philosophy 74(2): 331–340CrossRefGoogle Scholar
  43. Schaffer J. (2008) Truthmaker commitments. Philosophical Studies 141(1): 7–19CrossRefGoogle Scholar
  44. Shapiro S. (1983) Conservativeness and incompleteness. The Journal of Philosophy 80(9): 521–531CrossRefGoogle Scholar
  45. Smith B. (2002) Truthmaker realism: Response to Gregory. Australasian Journal of Philosophy 80(2): 231–234CrossRefGoogle Scholar
  46. Yablo S. (1998) Does ontology rest on a mistake?. Aristotelian Society, Supplementary Volume 72: 229–261CrossRefGoogle Scholar
  47. Yablo S. (2002) Abstract objects: A case study. Philosophical Issues 12: 220–240CrossRefGoogle Scholar
  48. Yablo S. (2009) Must existence-Questions have answers?. In: Chalmers D., Manley D., Wasserman R. (eds) Metametaphysics: New essays on the foundations of ontology. Oxford University Press, OxfordGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.School of Philosophical and Historical EnquiryUniversity of SydneySydneyAustralia

Personalised recommendations