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Mathematical Explanation and the Biological Optimality Fallacy

Published online by Cambridge University Press:  01 January 2022

Samantha Wakil  and
James Justus
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Abstract

Pure mathematics can play an indispensable role explaining empirical phenomena if recent accounts of insect evolution are correct. In particular, the prime life cycles of cicadas and the geometric structure of honeycombs are taken to undergird an inference to the best explanation about mathematical entities. Neither example supports this inference or the mathematical realism it is intended to establish. Both incorrectly assume that facts about mathematical optimality drove selection for the respective traits and explain why they exist. We show how this problem can be avoided, identify limitations of explanatory indispensability arguments, and attempt to clarify the nature of mathematical explanation.

Type
Explanation
Information
Philosophy of Science , Volume 84 , Issue 5 , December 2017 , pp. 916 - 930
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

For helpful feedback, thanks to Alan Baker, Mark Colyvan, Marc Lange, Elliott Sober, and audiences at the Philosophy of Science Association Meeting (Atlanta, 2016), Nordic Network for Philosophy of Science (Estonia, 2016), the University of Florida, and Florida State University.

References

Baker, A. 2005. “Are There Genuine Mathematical Explanations of Physical Phenomena?” Mind 114:223–38.CrossRefGoogle Scholar
Baker, A. 2009. “Mathematical Explanation in Science.” British Journal for Philosophy of Science 60:611–33.CrossRefGoogle Scholar
Baker, A. 2016. “Parsimony and Inference to the Best Mathematical Explanation.” Synthese 193:333–50.CrossRefGoogle Scholar
Baker, A. 2017. “Mathematics and Explanatory Generality.” Philosophia Mathematica 25 (2): 194–209.Google Scholar
Baker, A., and Colyvan, M. 2011. “Indexing and Mathematical Explanation.” Philosophia Mathematica 19:323–34.CrossRefGoogle Scholar
Borror, D., Long, D. De, and Triplehorn, C. 1981. An Introduction to the Study of Insects. 5th ed. Philadelphia: Saunders College.Google Scholar
Brinkmann, V., ed. 2007. Gods in Color-Painted Sculpture of Classical Antiquity. Munich: Biering & Brinkmann.Google Scholar
Colyvan, M. 2012. An Introduction to the Philosophy of Mathematics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Daly, C., and Langford, S. 2009. “Mathematical Explanation and Indispensability Arguments.” Philosophical Quarterly 59:641–58.CrossRefGoogle Scholar
Field, H. 1989. Realism, Mathematics, and Modality. Oxford: Blackwell.Google Scholar
Gould, S., and Lewontin, R. 1979. “The Spandrels of San Marco and the Panglossian Paradigm: A Critique of the Adaptationist Programme.” Proceedings of the Royal Society of London B 205:581–98.Google Scholar
Grant, P. 2005. “The Priming of Periodical Cicada Life Cycles.” Trends in Ecology and Evolution 20:169–74.CrossRefGoogle ScholarPubMed
Hales, T. 2001. “The Honeycomb Conjecture.” Discrete and Computational Geometry 25:1–22.CrossRefGoogle Scholar
Hepburn, H., Pirk, C., and Duangphakdee, O. 2014. Honeybee Nests: Composition, Structure, Function. Berlin: Springer.CrossRefGoogle Scholar
Karihaloo, B., Zhang, K., and Wang, J. 2013. “Honeybee Combs: How the Circular Cells Transform into Rounded Hexagons.” Journal of the Royal Society Interface 10 (86). doi:10.1098/rsif.2013.0299.CrossRefGoogle ScholarPubMed
Koenig, W., and Liebhold, A. 2013. “Avian Predation Pressure as a Potential Driver of Periodical Cicada Cycle Length.” American Naturalist 181:145–49.CrossRefGoogle ScholarPubMed
Lange, M. 2013. “What Makes a Scientific Explanation Distinctively Mathematical?” British Journal for Philosophy of Science 64:485–511.CrossRefGoogle Scholar
Lehmann-Ziebarth, N., Heideman, P., Shapiro, R., Stoddart, S., Hsiao, C., Stephenson, G., Milewski, P., and Ives, A. 2005. “Evolution of Periodicity in Periodical Cicadas.” Ecology 86:3200–3211. doi:10.1890/04-1615.CrossRefGoogle Scholar
Lyon, A., and Colyvan, M. 2008. “The Explanatory Power of Phase Spaces.” Philosophia Mathematica 16:227–43.Google Scholar
Maddy, P. 1992. “Indispensability and Practice.” Journal of Philosophy 89:275–89.CrossRefGoogle Scholar
Marshall, D., Cooley, J., and Hill, K. 2011. “Developmental Plasticity of Life-Cycle Length in the Thirteen-Year Periodical Cicada (Hemiptera: Cicadidae).” Annals of the Entomological Society of America 104:443–50.CrossRefGoogle Scholar
Moran, P. A. P. 1962. The Statistical Processes of Evolutionary Theory. Oxford: Clarendon.Google Scholar
Räz, T. 2013. “On the Application of the Honeycomb Conjecture to the Bee’s Honeycomb.” Philosophia Mathematica 21:351–60.CrossRefGoogle Scholar
Saatsi, J. 2011. “The Enhanced Indispensability Argument: Representational versus Explanatory Role of Mathematics in Science.” British Journal for Philosophy of Science 62:143–54.CrossRefGoogle Scholar
Saatsi, J. 2017. “Dynamical Systems Theory and Explanatory Indispensability.” Philosophy of Science, in this issue.CrossRefGoogle Scholar
Sober, E. 1993. “Mathematics and Indispensability.” Philosophical Review 102:35–57.CrossRefGoogle Scholar
Sober, E. 2000. Philosophy of Biology. 2nd ed. Boulder, CO: Westview.Google Scholar
Tóth, F. 1964. “What the Bees Know and What They Do Not Know.” Bulletin of the American Mathematical Society 70:468–81.CrossRefGoogle Scholar
van Fraassen, B. 1989. Laws and Symmetry. Oxford: Oxford University Press.CrossRefGoogle Scholar
Williams, K., and Simon, C. 1995. “The Ecology, Behavior, and Evolution of Periodical Cicadas.” Annual Review of Entomology 40:269–95.CrossRefGoogle Scholar