Comment on "the undeniable effectiveness of mathematics in the special sciences"

Tim Raz

pp. 75-84

in: Dennis Dieks, Stephan Hartmann, Thomas Uebel, Marcel Weber, Maria C. Galavotti (eds), New directions in the philosophy of science, Berlin, Springer, 2014

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.

Cited authors

Colyvan Mark