Contents -- 1 Mathematics and Its Applications -- 1.1 Realism and Anti-realism in Mathematics -- 1.2 Indispensability Arguments -- 1.3 The Road Ahead -- 2 The Quinean Backdrop -- 2.1 Introducing Naturalism -- 2.2 Quinean Naturalism -- 2.3 The Methodologies of Philosophy and Science -- 2.4 The Causal Version of Naturalism -- 2.5 Holism -- 2.6 The First Premise Revisited -- 3 The Eleatic Principle -- 3.1 The Inductive Argument -- 3.2 The Epistemic Argument -- 3.3 The Argument from Causal Explanation -- 3.4 Causal Relevance -- 3.5 Rejecting Inference to the Best Explanation -- 3.6 The Content of Scientific Theories -- 3.7 The Moral -- 3.8 Recapitulation -- 4 Field's Fictionalism -- 4.1 The Science without Numbers Project -- 4.2 What Is It to Be Indispensable? -- 4.3 The Role of Confirmation Theory -- 4.4 The Role of Mathematics in Physical Theories -- 4.5 Review of Field's Fictionalism -- 5 Maddy's Objections -- 5.1 The Objections -- 5.2 Maddy's Naturalism -- 5.3 Defending the Indispensability Argument -- 5.4 Review of Maddy's Objections -- 6 The Empirical Nature of Mathematical Knowledge -- 6.1 The Obviousness of Some Mathematical Truth -- 6.2 The Unfalsifiability of Mathematics -- 6.3 The Sober Objection -- 6.4 Is Mathematics Contingent? -- 7 Conclusion -- 7.1 What the Argument Doesn't Show -- 7.2 The Benacerraf Challenges -- 7.3 A Slippery Slope? -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z.