Parsimony, Ontological Commitment and the Import of Mathematics

  • Daniele MolininiEmail author
Part of the Boston Studies in the Philosophy and History of Science book series (BSPS, volume 334)


In a recent paper Alan Baker has argued for the thesis that the use of a stronger mathematical apparatus in optimization explanations can reduce our concrete ontological commitment, and this results in an increase of explanatory power. The import of this thesis in the context of the Enhanced Indispensability Argument is significant because it sheds light on how the Inference to the Best Explanation principle, on which the Enhanced Indispensability Argument crucially depends, may work at the level of concrete and mathematical posits in scientific explanations. In this paper I examine Baker’s position and I argue that, although the employment of additional mathematical resources in some explanations can enhance explanatory power, it is highly controversial that Baker’s example of cicadas can have a strong import in the platonism vs nominalism debate. I conclude with a general discussion of the way in which a stronger mathematical apparatus may sometimes lead to an increase of explanatory power.



I wish to thank the organizers of the Second FilMat Conference and the members of the audience for useful discussion of this paper. I benefitted immensely from suggestions from Marco Panza, Matteo Morganti, Mauro Dorato, Marc Lange, Davide Vecchi, Stathis Psillos, Andrea Sereni, Michèle Friend, Pierluigi Graziani, Achille Varzi, Francesca Poggiolesi, Mary Leng, Luca Incurvati, Andrew Arana, Josephine Salverda, Claudio Ternullo and Giorgio Venturi. I would also like to thank an anonymous referee for his helpful comments.


  1. Baker, A. 2003. Quantitative parsimony and explanatory power. The British Journal for the Philosophy of Science 54(2): 245–259.CrossRefGoogle Scholar
  2. Baker, A. 2005. Are there genuine mathematical explanations of physical phenomena? Mind 114: 223–238.CrossRefGoogle Scholar
  3. Baker, A. 2009. Mathematical explanation in science. British Journal of Philosophy of Science 60: 611–633.CrossRefGoogle Scholar
  4. Baker, A. 2016. Parsimony and inference to the best mathematical explanation. Synthese 193(2): 333–350.CrossRefGoogle Scholar
  5. Baker, A. 2017a. Mathematics and explanatory generality. Philosophia Mathematica 25(2): 194–209Google Scholar
  6. Baker, A. 2017b. Mathematical spandrels. Australasian Journal of Philosophy 95(4): 779–793.CrossRefGoogle Scholar
  7. Behncke, H. 2000. Periodical cicadas. Journal of Mathematical Biology 40(5): 413–431.CrossRefGoogle Scholar
  8. Busch, J., and J. Morrison. 2016. Should scientific realists be platonists? Synthese 193(2): 435–449.CrossRefGoogle Scholar
  9. Colyvan, M. 2001. The indispensability of mathematics. New York: Oxford University Press.CrossRefGoogle Scholar
  10. Cox, R.T., and C.E. Carlton. 1998. A commentary on prime numbers and life cycles of periodical cicadas. The American Naturalist 152(1): 162–164.CrossRefGoogle Scholar
  11. Grant, P.R. 2005. The priming of periodical cicada life cycles. Trends in Ecology & Evolution 20(4): 169–174.CrossRefGoogle Scholar
  12. Hoppensteadt, F., and J. Keller. 1976. Synchronization of periodical cicada emergences. Science 194(4262): 335–337.CrossRefGoogle Scholar
  13. Hunt, J. 2016. Indispensability and the problem of compatible explanations. Synthese 193(2): 451–467.CrossRefGoogle Scholar
  14. Ito, H., S. Kakishima, T. Uehara, S. Morita, T. Koyama, T. Sota, J.R. Cooley, and J. Yoshimura. 2015. Evolution of periodicity in periodical cicadas. Scientific Reports 5: 14094 EP.Google Scholar
  15. Karabulut, H. 2006. The physical meaning of lagrange multipliers. European Journal of Physics 27(4): 709.CrossRefGoogle Scholar
  16. Koenig, W.D., and A.M. Liebhold. 2013. Avian predation pressure as a potential driver of periodical cicada cycle length. The American Naturalist 181(1): 145–149.CrossRefGoogle Scholar
  17. Kon, R. 2012. Permanence induced by life-cycle resonances: The periodical cicada problem. Journal of Biological Dynamics 6(2): 855–890.CrossRefGoogle Scholar
  18. Lange, M. 2013. What makes a scientific explanation distinctively mathematical? The British Journal for the Philosophy of Science 64(3): 485–511.CrossRefGoogle Scholar
  19. Lehmann-Ziebarth, N., P.P. Heideman, R.A. Shapiro, S.L. Stoddart, C.C.L. Hsiao, G.R. Stephenson, P.A. Milewski, and A.R. Ives. 2005. Evolution of periodicity in periodical cicadas. Ecology 86(12): 3200–3211.CrossRefGoogle Scholar
  20. Lewis, D. 1973. Counterfactuals. Oxford: Basil Blackwell.Google Scholar
  21. Liggins, D. 2016. Grounding and the indispensability argument. Synthese 193(2): 531–548.CrossRefGoogle Scholar
  22. Maier, C.T. 1985. Brood vi of 17-year periodical cicadas, magicicada spp. (hemiptera: Cicadidae): New evidence from connecticut, the hypothetical 4-year deceleration, and the status of the brood. Journal of the New York Entomological Society 93(2): 1019–1026.Google Scholar
  23. Marlatt, C.L. 1907. The periodical cicada. Washington, DC: U.S. Department of Agriculture, Bureau of Entomology.CrossRefGoogle Scholar
  24. Marshall, D.C. 2001. Periodical cicada (homoptera: Cicadidae) life-cycle variations, the historical emergence record, and the geographic stability of brood distributions. Annals of the Entomological Society of America 94(3): 386–399.CrossRefGoogle Scholar
  25. Marshall, D.C., J.R. Cooley, and C. Simon. (2003). Holocene climate shifts, life-cycle plasticity, and speciation in periodical cicadas: A reply to cox and carlton. Evolution 57(2): 433–437.CrossRefGoogle Scholar
  26. May, R.M. 1979. Periodical cicadas. Nature 277(5695): 347–349.CrossRefGoogle Scholar
  27. Molinini, D., F. Pataut, and A. Sereni. 2016. Indispensability and explanation: An overview and introduction. Synthese 193(2): 317–332.CrossRefGoogle Scholar
  28. Nariai, Y., S. Hayashi, S. Morita, Y. Umemura, K.-I. Tainaka, T. Sota, J.R. Cooley, and J. Yoshimura. 2011. Life cycle replacement by gene introduction under an Allee effect in periodical cicadas. PLOS ONE 6(4): 1–7.CrossRefGoogle Scholar
  29. Nolan, D. 1997. Quantitative parsimony. The British Journal for the Philosophy of Science 48(3): 329–343.CrossRefGoogle Scholar
  30. Pincock, C. 2012. Mathematics and scientific representation. New York: Oxford University Press.CrossRefGoogle Scholar
  31. Psillos, S. 2009. Knowing the structure of nature. Basingstoke: Palgrave Macmillan.CrossRefGoogle Scholar
  32. Van Fraassen, B.C. 1989. Laws and symmetry. Oxford: Clarendon Press.CrossRefGoogle Scholar
  33. Webb, G. 2001. The prime number periodical cicada problem. Discrete and Continuous Dynamical Systems – Series B 1(3):387–399.CrossRefGoogle Scholar
  34. Yoshimura, J. 1997. The evolutionary origins of periodical cicadas during ice ages. The American Naturalist 149(1): 112–124.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Centre for Philosophy of SciencesUniversity of LisbonLisbonPortugal

Personalised recommendations