Mathematics and Reality

Paperback | April 1, 2013

byMary Leng

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Mary Leng offers a defense of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (andtherefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at least approximately) true. But since claims whose truth wouldrequire the existence of mathematical objects are indispensable in formulating our best empirical theories, it follows that we have good reason to believe in the mathematical objects posited by those mathematical theories used in empirical science, and therefore to believe that the mathematicaltheories utilized in empirical science are true. Previous responses to the indispensability argument have focussed on arguing that mathematical assumptions can be dispensed with in formulating our empirical theories. Leng, by contrast, offers an account of the role of mathematics in empirical science according to which the successful use ofmathematics in formulating our empirical theories need not rely on the truth of the mathematics utilized.

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Mary Leng offers a defense of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (andtherefore for the existence of the mathematica...

Mary Leng is Lecturer in Philosophy at the University of Liverpool. She previously held a research fellowship at St John's College, Cambridge (2002-2006), and visiting fellowships at the University of California at Irvine (2001) and the Peter Wall Institute for Advanced Study at the University of British Columbia (2003). Her primary r...
Format:PaperbackDimensions:290 pages, 9.21 × 6.14 × 0.68 inPublished:April 1, 2013Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:019967468X

ISBN - 13:9780199674688

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Table of Contents

1. Introduction2. Naturalism and Ontology3. The Indispensability of Mathematics4. Naturalism and Mathematical Practice5. Naturalism and Scientific Practice6. Naturalized Ontology7. Mathematics and Make-Believe8. Mathematical Fictionalism and Constructive Empiricism9. Explaining the Success of Mathematics10. Conclusion

Editorial Reviews

"as the most substantial work on nominalism to appear for a decade or so, it demands a prompt response from the antinominalist side if the issue is not to go by default, and as the earliest large-scale treatment of an important type of position, it is likely to be the point of departure indebates for years to come ... belongs on the shelf of every philosopher of mathematics." --Philosophia Mathematica