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The Enhanced Indispensability Argument, the Circularity Problem, and the Interpretability Strategy

Heylen, Jan and Tump, Lars Arthur (2019) The Enhanced Indispensability Argument, the Circularity Problem, and the Interpretability Strategy. [Preprint]

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Abstract

Within the context of the Quine-Putnam indispensability argument, one discussion about the status of mathematics is concerned with the `Enhanced Indispensability Argument', which makes explicit in what way mathematics is supposed to be indispensable in science, namely explanatory. If there are genuine mathematical explanations of empirical phenomena, an argument for mathematical platonism could be extracted by using inference to the best explanation. The best explanation of the primeness of the life cycles of Periodical Cicadas is genuinely mathematical, according to Baker (2005, 2009). Furthermore, the result is then also used to strengthen the platonist position (e.g. Baker 2017a). We pick up the circularity problem brought up by Leng (2005) and Bangu (2008). We will argue that Baker's attempt to solve this problem fails, if Hume's Principle is analytic. We will also provide the opponent of the Enhanced Indispensability Argument with the so-called 'interpretability strategy', which can be used to come up with alternative explanations in case Hume's Principle is non-analytic.
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Item Type: Preprint
Creators:
CreatorsEmailORCID
Heylen, Janjan.heylen@kuleuven.be0000-0002-2809-3320
Tump, Lars Arthurlarsarthur.tump@kuleuven.be0000-0002-2790-3045
Additional Information: Accepted by Synthese
Keywords: indispensability; mathematical explanation; platonism; nominalism; Frege Arithmetic; Hume's Principle; relative interpretation
Subjects: Specific Sciences > Mathematics > Ontology
Depositing User: Dr. Jan Heylen
Date Deposited: 21 May 2019 16:04
Last Modified: 21 May 2019 16:04
Item ID: 16033
Subjects: Specific Sciences > Mathematics > Ontology
Date: 2019
URI: http://philsci-archive.pitt.edu/id/eprint/16033

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