Abstract

Some proponents of the indispensability argument for mathematical realism maintain that the empirical evidence that confirms our best scientific theories and explanations also confirms their pure mathematical components. I show that the falsity of this view follows from three highly plausible theses, two of which concern the nature of mathematical application and the other the nature of empirical confirmation. The first is that the background mathematical theories suitable for use in science are conservative in the sense outlined by Hartry Field. The second is that the empirical relevance of mathematical statements suitable for use in science is mediated by their non-mathematical consequences. The third is that statements receive additional empirical confirmation only by way of generating additional empirical expectations. Since each of these is a thesis we have good reason to endorse, my argument poses a challenge to anyone who argues that science affords empirical grounds for mathematical realism.