Indispensability Arguments and Mathematical Explanation in Science

The aim of this thesis is to find a way to undermine the indispensability argument for mathematical platonism. In chapter 1 I provide a brief survey of the indispensability argument, arguing that the explanatory indispensability argument is stronger than earlier forms of the argument. This is because it has less controversial premises, appealing neither to confirmational holism nor to a strong naturalism but rather to inference to the best explanation, a principle of inference which both sides in the indispensability debate are taken to accept. Hence I take the explanatory indispensability argument as my target. In chapter 2, I provide a more detailed account of the way in which inference to the best explanation, or IBE, is involved in the explanatory indispensability argument. I present two readings of the argument, rejecting the first reading and arguing that a second reading, which involves an instance of IBE, is the most plausible. Chapter 3 considers whether there are genuine cases of mathematical explanation in science, focusing on an explanation from evolutionary biology provided by Alan Baker. I draw on the biological literature to argue that there is some reason to doubt that Baker's explanation meets the conditions for a successful application of IBE. In chapter 4 I examine a number of restrictions on IBE recently suggested in the indispensability debate. Firstly, I argue that the indexing account suggests a reasonable restriction on IBE, but that proponents of the indexing account have not yet shown that this restriction is successful in undermining the explanatory indispensability argument. Secondly, I examine a restriction on IBE proposed by Pincock, arguing that this restriction is also unsuccessful in blocking the support of mathematical claims through IBE. Thirdly, I propose a restriction on IBE motivated by scientific practice and which, I argue, successfully undermines the explanatory indispensability argument.