, Volume 160, Issue 1, pp 13–20 | Cite as

Inference to the best explanation and mathematical realism

  • Sorin Ioan BanguEmail author
Original Paper


Arguing for mathematical realism on the basis of Field’s explanationist version of the Quine–Putnam Indispensability argument, Alan Baker has recently claimed to have found an instance of a genuine mathematical explanation of a physical phenomenon. While I agree that Baker presents a very interesting example in which mathematics plays an essential explanatory role, I show that this example, and the argument built upon it, begs the question against the mathematical nominalist.


Mathematics Explanation Realism Nominalism 


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  1. Baker A. (2005). Are there genuine mathematical explanations of physical phenomena?. Mind 114:223–237CrossRefGoogle Scholar
  2. Balaguer M. (1998). Platonism and anti-platonism in mathematics. Oxford University Press, OxfordGoogle Scholar
  3. Cartwright N. (1983). How the laws of physics lie. Oxford University Press, OxfordGoogle Scholar
  4. Colyvan M. (2001). The indispensability of mathematics. Oxford University Press, OxfordGoogle Scholar
  5. Colyvan M. (2002). Mathematics and aesthetic considerations in science. Mind 111:69–78CrossRefGoogle Scholar
  6. Field H. (1980). Science without numbers. Princeton University Press, PrincetonGoogle Scholar
  7. Field H. (1989). Realism, mathematics and modality. Blackwell, OxfordGoogle Scholar
  8. Leng M. (2005). Mathematical explanations. In: Cellucci C., Gillies D. (eds) Mathematical reasoning and heuristics. King’s College Publications, London, pp. 167–189Google Scholar
  9. Maddy P. (1997). Naturalism in mathematics. Clarendon Press, OxfordGoogle Scholar
  10. Melia J. (2002). Response to Colyvan. Mind 111:75–79CrossRefGoogle Scholar
  11. Putnam, H. (1971). Philosophy of logic. Reprinted in Mathematics matter and method: Philosophical papers (Vol. 1, 2nd ed., pp. 323–357). Cambridge: Cambridge University Press (1979).Google Scholar
  12. Putnam, H. (1979). What is Mathematical Truth’ in Mathematics Matter and Method: Philosophical Papers (Vol. 1, 2nd ed., pp. 60–78). Cambridge: Cambridge University Press.Google Scholar
  13. Quine W.V. (1981). Theories and things. Harvard University Press, Cambridge, MAGoogle Scholar
  14. Resnik, M. (1995). Scientific vs mathematical realism: The indispensability argument. Philosophia Mathematica (3), 3/2, 166–174Google Scholar
  15. Steiner M. (1978a). Mathematics, explanation and scientific knowledge. Noûs 12:17–28CrossRefGoogle Scholar
  16. Steiner M. (1978b). Mathematical explanation. Philosophical Studies 34:135–151CrossRefGoogle Scholar
  17. Van Fraassen B. (1980). The scientific image. Clarendon Press, OxfordGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of TorontoTorontoCanada

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