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Mathematics and Reality Mary Leng (University of York)

Mathematics and Reality By Mary Leng (University of York)

Mathematics and Reality by Mary Leng (University of York)


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Summary

Mary Leng defends a philosophical account of the nature of mathematics which views it as a kind of fiction (albeit an extremely useful fiction). On this view, the claims of our ordinary mathematical theories are more closely analogous to utterances made in the context of storytelling than to utterances whose aim is to assert literal truths.

Mathematics and Reality Summary

Mathematics and Reality by Mary Leng (University of York)

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 (and therefore 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 would require 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 mathematical theories 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 of mathematics in formulating our empirical theories need not rely on the truth of the mathematics utilized.

Mathematics and Reality Reviews

Mathematics and Reality is to be recommended highly ... it presents a distinctive new version of fictionalism to throw into the contemporary mix that will repay close attention by all philosophers of mathematics. * Alan Weir, British Journal for the Philosophy of Science *
this book has the potential to serve as a source of productive disagreement that would significantly advance the realism-anti-realism debate in mathematics. * Jeffrey W. Rowland, Mind *

About Mary Leng (University of York)

Mary Leng is Lecturer in Philosophy at the University of York. 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 research interests are in the Philosophy of Mathematics and Logic, and the Philosophy of Science. She is the co-editor (with Alexander Paseau and Michael Potter) of Mathematical Knowledge (Oxford: OUP, 2007).

Table of Contents

1. Introduction ; 2. Naturalism and Ontology ; 3. The Indispensability of Mathematics ; 4. Naturalism and Mathematical Practice ; 5. Naturalism and Scientific Practice ; 6. Naturalized Ontology ; 7. Mathematics and Make-Believe ; 8. Mathematical Fictionalism and Constructive Empiricism ; 9. Explaining the Success of Mathematics ; 10. Conclusion

Additional information

NLS9780199674688
9780199674688
019967468X
Mathematics and Reality by Mary Leng (University of York)
New
Paperback
Oxford University Press
2013-03-21
290
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
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