This book provides an accessible, critical introduction to the three main approaches that dominated work in the philosophy of mathematics during the twentieth century: logicism, intuitionism and formalism.

Alexander George is Associate Professor of Philosophy at Amherst College. He is editor of Reflections on Chomsky (1989) Western State Terrorism (1991) and Mathematics and Mind (1994).

Daniel J. Velleman is Professor of Mathematics at Amherst College. He is author of How to Prove It: A Structured Approach (1994) and co-author of Which Way Did the Bicycle Go? And Other Intriguing Mathematical Mysteries (with Joseph Konhauser and Stan Wagon, 1996).