Advertisement

Comment on “The Undeniable Effectiveness of Mathematics in the Special Sciences”

Chapter
  • 1.4k Downloads
Part of the The Philosophy of Science in a European Perspective book series (PSEP, volume 5)

Abstract

In this paper, I critically discuss two of Mark Colyvan’s case studies. After a short exposition of Colyvan’s program, I first comment on the Lotka-Volterra predator-prey model. I agree with Colyvan’s thesis that mathematical models in population ecology can be explanatory. The historical fathers of mathematical population ecology anticipated this thesis. However, the issue of idealization is not sufficiently emphasized; Volterra’s discussion of the predator-prey model shows that he was acutely aware of the problem of idealization. As to the second case, I point out that the explanation of the structure of the bee’s honeycomb, based on the mathematical honeycomb conjecture, is not a scientific explanation at all.

Keywords

Population Ecology Special Science Mathematical Explanation Fishery Statistic Methodological Reflection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

I thank Mark Colyvan, Michael Esfeld and Raphael Scholl for useful comments on earlier drafts of this paper. Parts of Sects. 3 and 4 are based on joint work with Raphael Scholl and the paper (Scholl and Räz 2013). This work was supported by the Swiss National Science Foundation, [100018-140201/1].

References

  1. Batterman, R.W. 2010. On the explanatory role of mathematics in empirical science. The British Journal for the Philosophy of Science 61: 1–25.CrossRefGoogle Scholar
  2. Cartwright, N. 1983. How the laws of physics lie. Oxford: Oxford University Press.CrossRefGoogle Scholar
  3. Fejes Tóth, L. 1964. What the bees know and what they do not know. Bulletin AMS 70: 468–81.CrossRefGoogle Scholar
  4. Frigg, R., and S. Hartmann. 2012. Models in science. http://plato.stanford.edu/entries/models-science/.
  5. Lyon, A., and M. Colyvan. 2008. The explanatory power of phase spaces. Philosophia Mathematica 16(2): 227–243.CrossRefGoogle Scholar
  6. Räz, T. 2013. On the application of the honeycomb conjecture to the Bee’s honeycomb. Philosophia Mathematica 21: 351–360.CrossRefGoogle Scholar
  7. Scholl, R., and T. Räz. 2013. Modeling causal structures. European Journal for Philosophy of Science 3(1): 115–132.CrossRefGoogle Scholar
  8. Volterra, V. 1928. Variations and fluctuations of the number of individuals in animal species living together. Journal du Conseil International pour l’Exploration de la Mer 3(1): 3–51.CrossRefGoogle Scholar
  9. Volterra, V., and U. D’Ancona. 1935. Les associations biologiques au point de vue mathématique. Paris: Hermann.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of Lausanne, Quartier UNIL-DorignyLausanneSwitzerland

Personalised recommendations