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Structures, fictions, and the explanatory epistemology of mathematics in science

Christopher Pincock: Mathematics and scientific representation. New York: Oxford University Press, 2012, 330pp, $65.00 HB

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Notes

  1. Thus, fictionalists are committed to saying that counterfactuals can be true even if there are no abstract objects (and they will presumably also want to say that they can be true even if there are no non-actual possible worlds). I have defended this view elsewhere (2010), but I obviously can’t get into this here.

  2. To say that the mathematical realm is plenitudinous is (roughly) to say that there are as many abstract mathematical objects as there could be. There are numerous arguments for the claim that plenitudinous versions of platonism are superior to non-plenitudinous versions. I can’t get into this here, but see my (1998).

  3. I would like to thank Chris Pincock for comments on an earlier draft of this paper.

  4. Pincock talks in terms of “confirming a representation” and this must be, I take it, a shortcut for the idea that we confirm certain claims about the world made on the basis of representing it in a certain way.

  5. Pincock credits Wilholt (2004, 287) with discovering this example, who in turn found about it in a conversation with Haim Gaifman (private communication).

  6. My positions in this section reflect the views I articulated in a recent book on the IA, argument which I take to support a non-platonistic form of realism in ontology (See Bangu 2012).

  7. There are other problematic aspects of Pincock’s discussion, but there is no space to present them here. A central one is the absence of a thorough examination of the role of confirmational holism within the IA, and thus a reaction to Maddy’s (1997) objections. It seems to me they have to be addressed even if one defends only the “realism-in-truth-value” version of the argument.

  8. Hylton (2007) offers more details on Quine’s reasons for preferring first-order logic.

  9. See Landry (2012) for a recent overview as well as many references to earlier work.

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Authors and Affiliations

  1. Department of Philosophy, California State University, 5151 State University Drive, Los Angeles, CA, 90032, USA

    Mark Balaguer

  2. Department of Philosophy, University of California, 1238 Social Sciences and Humanities Building, Davis, CA, 95616-8673, USA

    Elaine Landry

  3. Philosophy Department, University of Bergen, 314A Sydnesplass 12/13, 5007, Bergen, Norway

    Sorin Bangu

  4. Department of Philosophy, Ohio State University, 350 University Hall, 230 N Oval Mall, Columbus, OH, USA

    Christopher Pincock

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  1. Mark Balaguer
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  2. Elaine Landry
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  3. Sorin Bangu
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  4. Christopher Pincock
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Correspondence to Mark Balaguer.

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Balaguer, M., Landry, E., Bangu, S. et al. Structures, fictions, and the explanatory epistemology of mathematics in science. Metascience 22, 247–273 (2013). https://doi.org/10.1007/s11016-013-9781-7

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  • DOI: https://doi.org/10.1007/s11016-013-9781-7

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