Mathematics and Reality
by Leng, MaryFormat: Hardcover
Pub. Date: 2010-06-18
Publisher(s): Oxford University Press
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Summary
Mary Leng offers a defence of mathematical fictionalism, arguing that we have no reason to believe that there are any mathematical objects. In mounting this defence, she responds to the indispensability argument for the existence of mathematical objects, arguably the most pressing challenge that fictionalists must face. According to the indispensability argument, we ought to believe that there are such things as numbers, functions, and sets, since claims whose truth would require the existence of such things are indispensable in the formulation of our best scientific theories. In response to this argument, Leng offers an account of the role of mathematics in empirical science that does not assume that the mathematical hypotheses used in formulating our scientific theories are true. Book jacket.
Author Biography
Mary Leng is Lecturer in Philosophy at the University of Liverpool.
Table of Contents
| Introduction | p. 1 |
| Naturalism and Mathematics | p. 2 |
| A Note on Existence and Quantification | p. 13 |
| A Note on 'Abstract' | p. 18 |
| Naturalism and Ontology | p. 20 |
| Rejecting 'First Philosophy' | p. 21 |
| Naturalized Ontology | p. 36 |
| Naturalism and the Indispensability Argument | p. 44 |
| The Indispensability of Mathematics | p. 45 |
| Is Mathematics Dispensable? | p. 45 |
| Problems for Field's Programme | p. 50 |
| Accepting Indispensability | p. 70 |
| Naturalism and Mathematical Practice | p. 76 |
| Mathematical and Scientific Norms: A Conflict? | p. 78 |
| Reasons to Utter and Reasons to Believe | p. 82 |
| Against Recreational Mathematics | p. 90 |
| Naturalism and Scientific Practice | p. 100 |
| Scientific Confirmation and Mathematical Posits | p. 102 |
| Does the Indispensability Argument Conflict with Scientific Practice? | p. 110 |
| Cracks in the Argument: Ontological Commitment Revisited | p. 130 |
| Naturalized Ontology | p. 133 |
| Models and Idealizations | p. 135 |
| Does (Naturalized) Ontology Rest on a Mistake? | p. 138 |
| Explanation and Ontological Commitment | p. 151 |
| Mathematics and Make-Believe | p. 155 |
| An Anti-Realist Theory of Fiction | p. 156 |
| The Value of Make-Believe Representations | p. 167 |
| Mathematics as Fiction | p. 171 |
| Mathematical Fictionalism and Constructive Empiricism | p. 182 |
| Characterizing Nominalistic Content | p. 183 |
| Fictionalist vs. Constructive Empiricist Acceptance | p. 200 |
| Can We Merely Accept Our Theories? | p. 207 |
| Explaining the Success of Mathematics | p. 217 |
| Fictionalism and Inference to the Best Explanation | p. 218 |
| Is the Predictive Success of Fictionalist Science a Miracle? | p. 225 |
| Can Fictionalism Account for the Explanatory Power of Our Mathematical Hypotheses? | p. 241 |
| Fictionalism and Phase Space Theories | p. 249 |
| Conclusion | p. 253 |
| An Alternative Indispensability Argument | p. 255 |
| Anti-Platonism or Agnosticism? | p. 258 |
| Reviving a Dogma | p. 260 |
| References | p. 263 |
| Index | p. 271 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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