An Introduction to the Philosophy of Mathematics

by Mark Colyvan

Overview

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, including such topics as 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.

Product Details

ISBN-13:	9781139411189
Publisher:	Cambridge University Press
Publication date:	06/14/2012
Series:	Cambridge Introductions to Philosophy
Sold by:	Barnes & Noble
Format:	eBook
File size:	777 KB

About the Author

Mark Colyvan is Professor of Philosophy and Director of the Sydney Centre for the Foundations of Science at the University of Sydney. He is the co-author (with Lev Ginzburg) of Ecological Orbits: How Planets Move and Populations Grow (2004) and author of The Indispensability of Mathematics (2001).

Table of Contents

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. Epilogue: desert island theorems.

Editorial Reviews

"...Colyvan's introduction eschews a historically based, comprehensive survey. His final chapter contains a brief description of 20 selected mathematical theorems of philosophical interest. This skillfully written work, including liberal use of analogy and extensive exercises and recommended readings, is a stimulating introduction to some of the most discussed topics in contemporary philosophy of mathematics. Accessible to undergraduates with a background in mathematical logic... Highly recommended..."
—L.C. Archie, Lander University, CHOICE


"The present book is like a warm breeze after a cold winter in the rarefied atmosphere of the philosophy of mathematics.... The book is very well written and a pleasure to read. The chapters are short, clear and well structured.... include a list of discussion questions and recommended readings at the end of each chapter. ...it is a wonderful initiative.... I would not hesitate to use this book in an advanced undergraduate class in the philosophy of mathematics.... the philosophical discussions are always clear, provocative and stimulating. One of the challenges an instructor will face by adopting this book will undoubtedly be to contain the desire of students to discuss in depth some of the issues presented and to curb their enthusiasm and desire to know more or find answers to the questions."
—Jean-Pierre Marquis, Mathematical Reviews

From the Publisher