Mathematics and Reality

Mary Leng

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

Mathematics and Reality

Mary Leng

Description

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

Mary Leng

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

Mathematics and Reality

Mary Leng

Author Information

Mary Leng, University of York

Mathematics and Reality

Mary Leng

Reviews and Awards

"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

"...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