, Volume 196, Issue 1, pp 247–263 | Cite as

Optimal representations and the Enhanced Indispensability Argument

  • Manuel BarrantesEmail author


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 defend the EIA. 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.


Enhanced Indispensability Argument Mathematical explanations Optimal representations Magicicadas Mathematical Platonism Theoretical virtues 



I would like to thank Paul Humphreys for his comments on several versions of this paper. The final version also benefited from helpful discussions with Otávio Bueno, James Cargile, and Juan Durán, and the comments of two anonymous reviewers.


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© Springer Nature B.V. 2017

Authors and Affiliations

  1. 1.University of VirginiaCharlottesvilleUSA

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