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Why Inference to the Best Explanation Doesn’t Secure Empirical Grounds for Mathematical Platonism

Kenneth, Boyce (2018) Why Inference to the Best Explanation Doesn’t Secure Empirical Grounds for Mathematical Platonism. [Preprint]

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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.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Kenneth, Boyceboyceka@missouri.edu0000-0002-6783-3352
Keywords: indispensability arguments; mathematical platonism; nominalism; inference to the best explanation; scientific realism; confirmation
Subjects: Specific Sciences > Mathematics > Applicability
Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > Ontology
Specific Sciences > Mathematics
Depositing User: Dr. Kenneth Boyce
Date Deposited: 30 Nov 2018 16:58
Last Modified: 30 Nov 2018 16:58
Item ID: 15402
Subjects: Specific Sciences > Mathematics > Applicability
Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > Ontology
Specific Sciences > Mathematics
Date: November 2018
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/15402

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