An Introduction to the Philosophy of Mathematics
Department of Philosophy
University of Sydney
Sydney, NSW, Australia
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
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
Reviews and Critical Notices
- Archie, L.C. (2013) Choice.
- Ashbacher, C. (2014) Journal of Recreational Mathematics, 38(1): 50.
- Baron, S. (2014) Philosophy in Review, 34(1–2): 72–4.
- Cohnitz, D. (2015) Erkenntnis, forthcoming.
- Irvine, A. (2014) Philosophia Mathematica, 22(1): 124–5.
- Marquis, J. (2013) Mathematical Reviews, MR2985901.
- Pettigrew, R. (2013) Bulletin of Symbolic Logic, 19(3): 396–7.
- Soto, C. (2014) Crítica: Revista Hispanoamericana de Filosofía,, 46(138): 93–102.
- Wagner, C. (2013) Teaching Philosophy, 36(3): 316–20.
- Weber, Z. (2013) The Australasian Journal of Philosophy, 91(4): 828.