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Inference to the best explanation and mathematical realism


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.

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  • Baker A. (2005). Are there genuine mathematical explanations of physical phenomena?. Mind 114:223–237

    Article  Google Scholar 

  • Balaguer M. (1998). Platonism and anti-platonism in mathematics. Oxford University Press, Oxford

    Google Scholar 

  • Cartwright N. (1983). How the laws of physics lie. Oxford University Press, Oxford

    Google Scholar 

  • Colyvan M. (2001). The indispensability of mathematics. Oxford University Press, Oxford

    Google Scholar 

  • Colyvan M. (2002). Mathematics and aesthetic considerations in science. Mind 111:69–78

    Article  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • Leng M. (2005). Mathematical explanations. In: Cellucci C., Gillies D. (eds) Mathematical reasoning and heuristics. King’s College Publications, London, pp. 167–189

    Google Scholar 

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

    Google Scholar 

  • Melia J. (2002). Response to Colyvan. Mind 111:75–79

    Article  Google Scholar 

  • 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).

  • 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.

  • Quine W.V. (1981). Theories and things. Harvard University Press, Cambridge, MA

    Google Scholar 

  • Resnik, M. (1995). Scientific vs mathematical realism: The indispensability argument. Philosophia Mathematica (3), 3/2, 166–174

    Google Scholar 

  • Steiner M. (1978a). Mathematics, explanation and scientific knowledge. Noûs 12:17–28

    Article  Google Scholar 

  • Steiner M. (1978b). Mathematical explanation. Philosophical Studies 34:135–151

    Article  Google Scholar 

  • Van Fraassen B. (1980). The scientific image. Clarendon Press, Oxford

    Google Scholar 

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Correspondence to Sorin Ioan Bangu.

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Bangu, S.I. Inference to the best explanation and mathematical realism. Synthese 160, 13–20 (2008).

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