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

Part of the The Philosophy of Science in a European Perspective book series (PSEP, volume 5)


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.


Population Ecology Special Science Mathematical Explanation Fishery Statistic Methodological Reflection 
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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].


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

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

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