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Mathematics and Reality


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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

About the Author

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).


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 *
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 * 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 *

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