An Introduction to the Philosophy of Mathematics

by Mark Colyvan

Department of Philosophy
University of Sydney
Sydney, NSW, Australia

Publication Details

Publisher: Cambridge University Press, Cambridge
Publication Date: June 2012
Pages: x + 188
ISBN: 978-0-521-82602-0 (hardback); 978-0-521-53341-6 (paperback)
Cover illustration: Detail of the 100th non-trivial zero of the Riemann zeta function (image courtesy of Tibor Majlath).

You can purchase a copy of this book from Cambridge University Press or from Amazon.


An Introduction to the Philosophy of Mathematics is part of the Cambridge Introduction to Philosophy series of undergraduate text books. This introduction to the philosophy of mathematics focuses on contemporary debates in an important and central area of philosophy. The reader is taken on a fascinating and entertaining journey through some intriguing mathematical and philosophical territory. Topics include the realism/anti-realism debate in mathematics, mathematical explanation, the limits of mathematics, the significance of mathematical notation, inconsistent mathematics, and the applications of mathematics. Each chapter has a number of discussion questions and recommended further reading from both the contemporary literature and older sources. Very little mathematical background is assumed, and all of the mathematics encountered is clearly introduced and explained using a wide variety of examples. The book is suitable for an undergraduate course in philosophy of mathematics and, more widely, for anyone interested in philosophy and mathematics.


1. Mathematics and Its Philosophy
2. The Limits of Mathematics
3. Plato's Heaven
4. Fiction, Metaphor, and Partial Truths
5. Mathematical Explanation
6. The Applicability of Mathematics
7. Who's Afraid of Inconsistent Mathematics?
8. A Rose by any Other Name
9. Desert Island Theorems

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