Sorin Bangu. The Applicability of Mathematics in Science: Indispensability and Ontology. Basingstoke: Palgrave Macmillan, 2012. ISBN 978-0-230-28520-0 (hbk). Pp. xiii + 252

Abstract

This is an interesting and important book. It is essential reading for anyone interested in indispensability arguments for mathematical entities and related debates tied to the role of mathematics in scientific discovery and explanation. Bangu's primary goals are to provide an improved version of an indispensability argument and to make clear the sort of naturalism and holism that it must assume. Along the way he argues that the way mathematics facilitates new discoveries in physics supports the claim that mathematics is indispensable. The book concludes with a discussion of mathematical explanation. Bangu presents four features that a mathematical explanation must have if it is to contribute to a successful inference to the best explanation argument for mathematical entities. He criticizes some examples that have been presented by others, but also develops his own case. In the end, then, we are left with a more thoroughly articulated case for why a naturalist who takes scientific practice seriously should also believe in mathematical entities.