The indispensabilty of mathematics

Cover......Page 1
Title Page......Page 5
Acknowledgments......Page 7
Contents......Page 9
1 Mathematics and Its Applications......Page 13
1.1 Realism and Anti-realism in Mathematics......Page 14
1.2.1 Introducing Indispensability Arguments......Page 18
1.2.2 The Quine/Putnam Indispensability Argument......Page 21
1.2.3 Other Indispensability Arguments......Page 25
1.3 The Road Ahead......Page 29
2.1 Introducing Naturalism......Page 33
2.2 Quinean Naturalism......Page 34
2.3 The Methodologies of Philosophy and Science......Page 38
2.3.1 The “Two Dogmas” Argument......Page 39
2.3.2 How Useful Is the Distinction?......Page 40
2.4 The Causal Version of Naturalism......Page 44
2.5 Holism......Page 45
2.6 The First Premise Revisited......Page 49
3 The Eleatic Principle......Page 51
3.1 The Inductive Argument......Page 53
3.2 The Epistemic Argument......Page 54
3.3 The Argument from Causal Explanation......Page 57
3.3.1 The Bending of Light......Page 59
3.3.2 Antipodal Weather Patterns......Page 61
3.3.3 The FitzGerald-Lorentz Contraction......Page 62
3.4 Causal Relevance......Page 63
3.5 Rejecting Inference to the Best Explanation......Page 65
3.5.1 Ellis\'s Argument......Page 66
3.5.2 Cartwright\'s Argument......Page 67
3.6.1 Balaguer\'s Fictionalism......Page 70
3.6.2 Azzouni\'s Challenge......Page 73
3.7 The Moral......Page 74
3.8 Recapitulation......Page 77
4 Field\'s Fictionalism......Page 79
4.1 The Science without Numbers Project......Page 80
4.1.1 Conservativeness......Page 82
4.1.2 Nominalisation......Page 84
4.2 What Is It to Be Indispensable?......Page 88
4.3 The Role of Confirmation Theory......Page 90
4.4.1 The Complex Numbers......Page 93
4.4.2 The Dirac Equation......Page 95
4.4.3 The Lorentz Transformations......Page 97
4.5 Review of Field\'s Fictionalism......Page 99
5.1.1 The Scientific Fictions Objection......Page 103
5.1.2 The Role of Mathematics in Science......Page 104
5.1.3 The Mathematical Practice Objection......Page 105
5.2 Maddy\'s Naturalism......Page 108
5.3 Defending the Indispensability Argument......Page 110
5.3.1 The Scientific Fictions Objection Revisited......Page 111
5.3.2 The Role of Mathematics in Science Revisited......Page 113
5.3.3 The Mathematical Practice Objection Revisited......Page 117
5.4 Review of Maddy\'s Objections......Page 123
6 The Empirical Nature of Mathematical Knowledge......Page 127
6.1 The Obviousness of Some Mathematical Truth......Page 128
6.2 The Unfalsiflability of Mathematics......Page 134
6.3.1 Contrastive Empiricism......Page 138
6.3.2 The Objection......Page 139
6.3.3 A Residual Worry......Page 144
6.4 Is Mathematics Contingent?......Page 146
6.4.1 What Is the Contingency Contingent On?......Page 148
6.4.2 The Argument from Insularity......Page 150
7 Conclusion......Page 153
7.1 What the Argument Doesn\'t Show......Page 154
7.2 The Benacerraf Challenges......Page 159
7.2.1 What Numbers Could Not Be......Page 160
7.2.2 Naturalising Mathematical Epistemology......Page 163
7.3 A Slippery Slope?......Page 167
Bibliography......Page 169
Index......Page 181