Proponents of the explanatory indispensability argument for mathematical platonism maintain that claims about mathematical entities play an essential explanatory role in some of our best scientific explanations. They infer that the existence of mathematical entities is supported by way of inference to the best explanation from empirical phenomena and therefore that there are the same sort of empirical grounds for believing in mathematical entities as there are for believing in concrete unobservables such as quarks. I object that this inference depends on a false view of how abductive considerations mediate the transfer of empirical support. More specifically, I argue that even if inference to the best explanation is cogent, and claims about mathematical entities play an essential explanatory role in some of our best scientific explanations, it doesn’t follow that the empirical phenomena that license those explanations also provide empirical support for the claim that mathematical entities exist.
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For a general overview of such arguments see (Colyvan 2015).
See (Field 1980) for an influential challenge to this claim.
For a similar point see (Morrison 2012, pp. 265–266).
For a historically and philosophically informative discussion of the role that Brownian motion played in convincing the scientific community of the reality of atoms see (Maddy 1997, pp. 133–157).
See (Colyvan 2001, pp. 76–86) for an argument that the sense in which mathematics may be regarded as “indispensable” to our best scientific theories is best understood in terms of its contributions to those theories’ explanatory virtues.
Or in Baker’s (2009, p. 613) own wording, it is an example of a case in which “mathematical objects play an indispensable explanatory role in science.”
An argument along these lines from the cogency of IBE to a principle like Explanatory Consequence is discussed by Morrison (2012, pp. 274–275).
For helpful comments on previous drafts, I would like to thank Mark Balaguer, Sarah Boyce, Lindsay Brainard, Matt Duncan, Luke Kallberg, various anonymous referees, and the audience members of numerous venues in which I presented previous versions of this paper. I would also like to thank the University of Missouri Research Board and the University of Missouri Philosophy Department for the generous provision of a research leave that allowed me to focus on this project.
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Boyce, K. Why inference to the best explanation doesn’t secure empirical grounds for mathematical platonism. Synthese 198, 583–595 (2021). https://doi.org/10.1007/s11229-018-02043-2
- Indispensability arguments
- Mathematical platonism
- Inference to the best explanation
- Scientific realism