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Synthese

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Why inference to the best explanation doesn’t secure empirical grounds for mathematical platonism

  • Kenneth Boyce
Article
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Abstract

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.

Keywords

Indispensability arguments Mathematical platonism Nominalism Inference to the best explanation Scientific realism Confirmation 

Notes

Compliance with ethical standards

Conflict of interest

The author declares that they have no conflict of interest.

Human and animal rights

The author did not conduct research involving human participants or animals.

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of MissouriColumbiaUSA

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