Description
Book SynopsisMary 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
Trade ReviewMathematics 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 *
Table of Contents1. 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
