Mathematics and Reality: Hardback: Mary Leng
- Oxford University Press

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A fresh approach to one of the oldest philosophical problems

Shows the special interest of mathematics as a case-study in metaphysics and epistemology

Considers mathematics not as an abstract discipline but in the context of its empirical success

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.

Readership:
Scholars and advanced students of philosophy and philosophy of science, as well as mathematicians with an interest in philosophy.

Mary Leng, University of York

"I also believe that this book has the potential to serve as a source of productive disagreement that would significantly advance the realismanti-realism debate in mathematics." - Jeffrey W. Roland, Mind

"...an original and valuable study, whose greatest merit is perhaps its ability to construct a well deveoped and rich philosophical framework to defend the intuitive idea that the success of mathematics in applications depends essentially on how things are with non-mathematical objects." - Davide Rizza The Philosophical Quarterly July 2011

"The book is sure to generate considerable discussion: 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 in debates for years to come. Mathematics and Reality belongs on the shelf of every philosopher of mathematics." - John P. Burgess, Philosophia Mathematica

"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

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

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