# Optimal representations and the Enhanced Indispensability Argument

- 382 Downloads

## 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 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.

## Keywords

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

### Acknowledgements

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.

## References

- Azzouni, J. (2004).
*Deflating existential consequence: A case for nominalism*. New York: Oxford University Press.Google Scholar - Baker, A. (2005). Are there genuine Mathematical Explanations of Physical Phenomena?
*Mind*,*114*, 223–238.CrossRefGoogle Scholar - Baker, A. (2009). Mathematical explanation in science.
*British Journal for the Philosophy of Science*,*60*, 611–633.CrossRefGoogle Scholar - Baker, A. (2016). Parsimony and inference to the best mathematical explanation.
*Synthese*,*193*, 333–350.CrossRefGoogle Scholar - Bangu, S. (2008). Inference to the best explanation and mathematical realism.
*Synthese*,*160*, 13–20.CrossRefGoogle Scholar - Bangu, S. (2012).
*The applicability of mathematics in science: Indispensability and ontology*. New York: Palgrave Macmillan.Google Scholar - Bueno, O. (2012). An easy road to nominalism.
*Mind, 121*(484), 967–982.Google Scholar - Bueno, O. (2016). An anti-realist account of the application of mathematics.
*Philosophical Studies*,*173*, 2591–2604.CrossRefGoogle Scholar - Bueno, O., & Colyvan, M. (2011). The inferential conception of the applicability of mathematics.
*Noûs*,*45*(2), 345–374.CrossRefGoogle Scholar - Bueno, O., & French, S. (2012). Can mathematics explain physical phenomena?
*British Journal for the Philosophy of Science*,*63*(1), 85–113.CrossRefGoogle Scholar - Colyvan, M. (2001).
*The indispensability of mathematics*. Oxford: Oxford University Press.CrossRefGoogle Scholar - Cooley, J. (2016)
*Magicicada.org*(consulted on Sept 2016)Google Scholar - Cox, T., & Carlton, C. (2003). A comment on gene introgression versus en masse cycle switching in the evolution of 13-year and 17-year life cycles in periodical cicadas.
*Evolution*,*57*(2), 428–432.CrossRefGoogle Scholar - Field, H. (1980).
*Science without Numbers: A defense of nominalism*. Princeton, NJ: Princeton University Press.Google Scholar - Franklin, J. (2014).
*An Aristotelian realist philosophy of mathematics. Mathematics as the science of quantity and structure*. Basingstoke, UK: Palgrave Macmillan.Google Scholar - Goles, E., Schulz, O., & Markus, M. (2001). Prime number selection of cycles in a predator–prey model.
*Complexity*,*6*, 33–38.CrossRefGoogle Scholar - Keas, M. (Forthcoming), Systematizing the theoretical virtues.
*Synthese*.Google Scholar - Kitcher, P. (1981). Explanatory unification.
*Philosophy of Science*,*48*(4), 507–531.CrossRefGoogle Scholar - Lange, M. (2013). What makes a mathematical explanation distinctively mathematical?
*British Journal for the Philosophy of Science*,*64*, 485–511.CrossRefGoogle Scholar - Lyon, A. (2011). Mathematical explanations of empirical facts, and mathematical realism.
*Australasian Journal of Philosophy*,*90*(3), 559–578.CrossRefGoogle Scholar - Matson, J. (2013).
*Deciphering the strange mathematics of Cicadas*. Berlin: Scientific American.Google Scholar - Melia, J. (2000). Weaseling away the indispensability argument.
*Mind, 109*(435), 455–479.Google Scholar - Orzack, S., & Sober, E. (2001).
*Adaptationism and optimality*. Cambridge: Cambridge University Press.CrossRefGoogle Scholar - Rice, C. (2015). Moving beyond causes: Optimality models and scientific explanation.
*Noûs*,*49*(3), 589–615.CrossRefGoogle Scholar - Rizza, D. (2011). Magicicada, mathematical explanation and mathematical realism.
*Erkenntnis*,*74*(1), 101–114.CrossRefGoogle Scholar - Saatsi, J. (2011). The Enhanced Indispensability Argument: Representational versus explanatory role of mathematics in science.
*British Journal for the Philosophy of Science*,*62*(1), 143–154.CrossRefGoogle Scholar - Weisberg, M. (2007). Three kinds of idealization.
*Journal of Philosophy*,*104*(12), 639–659.CrossRefGoogle Scholar - Weisberg, M. (2013).
*Simulation and similarity. Using models to understand the world*. Oxford: Oxford University Press.CrossRefGoogle Scholar - Yoshimura, J. (1997). The evolutionary origins of periodical cicadas during ice ages.
*The American Naturalist*,*149*(1), 112–124.CrossRefGoogle Scholar