Indispensability and the problem of compatible explanations

Abstract

Alan Baker’s enhanced indispensability argument (EIA) supports mathematical platonism through the explanatory role of mathematics in science. Busch and Morrison defend nominalism by denying that scientific realists use inference to the best explanation (IBE) to directly establish ontological claims. In response to Busch and Morrison, I argue that nominalists can rebut the EIA while still accepting Baker’s form of IBE. Nominalists can plausibly require that defenders of the EIA establish the indispensability of a particular mathematical entity. Next, I argue that IBE cannot establish that any particular mathematical entity is indispensable. Mathematical entities do not compete with each other in the way physical unobservables do. This lack of competition enables alternative formulations of scientific explanations that use different, but compatible, mathematical entities. The compatibility of these explanations prevents IBE from establishing platonism.