Indispensability

Our best scientific theories explain a wide range of empirical phenomena, make accurate predictions, and are widely believed. Since many of these theories make ample use of mathematics, it is natural to see them as confirming its truth. Perhaps the use of mathematics in science even gives us reason to believe in the existence of abstract mathematical objects such as numbers and sets. These issues lie at the heart of the Indispensability Argument, to which this Element is devoted. The Element's first half traces the evolution of the Indispensability Argument from its origins in Quine and Putnam's works, taking in naturalism, confirmational holism, Field's program, and the use of idealisations in science along the way. Its second half examines the explanatory version of the Indispensability Argument, and focuses on several more recent versions of easy-road and hard-road fictionalism respectively. Cover Title page Copyright page Indispensability Contents 1 Introduction The Indispensability Argument 2 Naturalism and Holism 2.1 Methodological Naturalism 2.2 Maddy’s Second Philosophy 2.3 Confirmational Holism 3 Hard Road Nominalism: Field’s Program 3.1 Outline 3.2 Objections 4 An Objection from Scientific Practice 4.1 A Case Study 4.2 Do Scientists Literally Believe Mathematics? 5 The Enhanced Indispensability Argument 5.1 Moving Beyond the Quine–Putnam Indispensability Argument 5.2 The Enhanced Indispensability Argument The Enhanced Indispensability Argument (EIA) 5.3 The Role of Case Studies in Supporting EIA 5.4 The Audience for EIA 6 Easy Road Fictionalism 6.1 Narrowing the Easy Road 6.2 Nonexistent Entities Are Sometimes Explanatory 6.3 Restricting Inference to the Best Explanation 7 Hard Road Fictionalism 7.1 Three Grades of Hard Road Fictionalism 7.2 Nonmathematical Consequence-Preserving Hard Road Fictionalism 7.3 Mathematical Concept-Preserving Hard Road Fictionalism 7.4 Mathematical Theory-Preserving Hard Road Fictionalism 8 Conclusions References Acknowledgments