ABSTRACT
Mathematics plays a prominent role in the theories of the constitutive elements of science. The indispensability argument in the philosophy of mathematics is used by some to argue for Platonism by claiming that the use of abstract entities of mathematics in successful empirical theory can only be explained by the existence of the abstract entities. Theories of the constitutive elements in science would most naturally be seen as rejecting Quine's confirmational holism and holding that mathematics is sui generis and a priori. Mathematics will be tinkered with less frequently than experimental hypotheses, becoming relatively a priori, that is, more likely to be taken for granted. Surveying the literature on the applicability of mathematics, author concludes that how one answers the indispensability argument does not affect author's argument on the role of the constitutive element in science. Like Sober, Susan Vineberg argues that the extension of scientific realism to mathematical entities is a nonsequitur.
