Mathematics and Reality

by Leng, Mary

• ISBN13: 9780199280797
• ISBN10: 0199280797
• Format: Hardcover
• Copyright: 2010-06-18
• Publisher: Oxford University Press

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
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