Parsimony, Ontological Commitment and the Import of Mathematics

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.