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Optimal Representations and the Enhanced Indispensability Argument

Barrantes, Manuel (2017) Optimal Representations and the Enhanced Indispensability Argument. [Preprint]

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Abstract

The Enhanced Indispensability Argument (EIA) appeals to the existence of Mathematical Explanations of Physical Phenomena (MEPPs) to justify mathematical Platonism, following the principle of Inference to the Best Explanation. In this paper, I examine one example of a MEPP —the explanation of the 13-year and 17-year life cycle of magicicadas— and argue that this case cannot be used to justify mathematical Platonism. I then generalize my analysis of the cicada case to other MEPPs, and show that these explanations rely on what I will call ‘optimal representations’, which are representations that capture all that is relevant to explain a physical phenomenon at a specified level of description. In the end, because the role of mathematics in MEPPs is ultimately representational, they cannot be used to support mathematical Platonism. I finish the paper by addressing the claim, advanced by many EIA defendants, that quantification over mathematical objects results in explanations that have more theoretical virtues, especially that they are more general and modally stronger than alternative explanations. I will show that the EIA cannot be successfully defended by appealing to these notions.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Barrantes, Manuelmb3cs@virginia.edu0000-0002-7997-5948
Keywords: Enhanced Indispensability Argument; mathematical explanations; optimal representations; magicicadas; mathematical necessity; mathematical Platonism.
Subjects: Specific Sciences > Mathematics > Applicability
Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > Ontology
General Issues > Explanation
Specific Sciences > Mathematics
General Issues > Models and Idealization
General Issues > Realism/Anti-realism
Depositing User: Mr. Manuel Barrantes
Date Deposited: 18 Jun 2017 13:27
Last Modified: 18 Jun 2017 13:27
Item ID: 13126
Subjects: Specific Sciences > Mathematics > Applicability
Specific Sciences > Mathematics > Explanation
Specific Sciences > Mathematics > Ontology
General Issues > Explanation
Specific Sciences > Mathematics
General Issues > Models and Idealization
General Issues > Realism/Anti-realism
Date: 2017
URI: https://philsci-archive-dev.library.pitt.edu/id/eprint/13126

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