Mathematical Explanation in Science

Inspired by indispensability arguments originating from Quine, mathematical realists such as Alan Baker argue that since mathematics plays a key explanatory role in our best scientific theories, then the very same reasons which convince us to be scientific realists should lead us to be mathematical realists as well. Baker's enhanced indispensability arguments (EIA) makes use of inference to the best explanation (IBE) to deliver the realist conclusion. Mathematical nominalists have resisted this argument by asserting that there is no such thing as a genuine mathematical explanation (GME) where the mathematics is playing an indispensable explanatory role. In this dissertation I will argue that the nominalist is incorrect and that GMEs do, in fact, exist. My methodology will be to develop a set of criteria that clearly defines a GME which the nominalist would gladly accept. From there, a new example of a GME will be advanced that satisfies all of the criteria. To solidify this result, I will show that Strevens' kairetic account of scientific explanation clearly points to mathematics playing an indispensable explanatory role in our supposed examples of GME. While this all bodes well for mathematical realism, I will further argue that the EIA still does not lead to mathematical realism. Baker assumes that using IBE to infer the existence of mathematical objects is unproblematic. I will challenge this assumption, and without IBE the EIA does not deliver. By no means does this result block the realist project. Ultimately, I believe that freeing ourselves from the yoke of traditional indispensability arguments and focussing on how it is that mathematics can explain physical facts explain will advance the realist position even further.Ph.D