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Science and mathematics: the scope and limits of mathematical fictionalism

Mary Leng: Mathematics and reality. Oxford: Oxford University Press, 2010, x+278pp, £39.00 HB

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Notes

  1. I have benefitted from Lavers (2010) and Burgess (2010).

  2. Over the course of this (relatively brief) history, there has been a gradual change of terminology from nominalism to fictionalism to describe positions, such as Leng’s, that hold that (most) core mathematical claims are false because the entities they refer to do not exist.

  3. One source of confusion is that we do sometimes use the term “explain” in cases where we are really describing. For example, I may explain where Naples is by referring to Italy as a boot.

  4. For a good summary of Yablo’s views see Yablo (2005).

  5. e.g. “[T]he supposed acausality of mathematical objects … [renders] the fictionalist’s proposed attitude of acceptance more plausible than the constructive empiricist alternative” (201).

  6. There is also arguably a fifth formulation of MND, where the MND claim is about “one’s ability to adopt, reasonably, the methods and expectations of modern science” (204).

  7. For further discussion, see Baker (2003).

  8. See Colyvan (1998) for a discussion of various problems with the Eleatic Principle.

  9. “[T]he regularities that actually hold between non-mathematical objects might reasonably be expected to agree with the predictions of our mathematically stated empirical theories even if it is supposed that those theories have things completely wrong about the relations they posit to hold between the mathematical and non-mathematical objects they posit. After all, according to the fictionalist there may, for all we can know, be no mathematical objects …” (233–234).

  10. Quotations in the first paragraph are from Blanchard (2002, 48).

  11. Except perhaps the mathematics of the research frontier. We can bracket such cases, as they arise in virtue of the speculative nature of the research frontier.

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Authors and Affiliations

  1. University of Missouri, 438 Strickland Hall, Columbia, MO, 65211-4160, USA

    Christopher Pincock

  2. Department of Philosophy, Swarthmore College, Swarthmore, PA, 19081, USA

    Alan Baker

  3. Wadham College, Oxford, OX1 3PN, UK

    Alexander Paseau

  4. Department of Philosophy, University of York, Heslington, York, YO10 5DD, UK

    Mary Leng

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  1. Christopher Pincock
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  2. Alan Baker
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  4. Mary Leng
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Correspondence to Christopher Pincock.

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Pincock, C., Baker, A., Paseau, A. et al. Science and mathematics: the scope and limits of mathematical fictionalism. Metascience 21, 269–294 (2012). https://doi.org/10.1007/s11016-011-9640-3

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