Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Øystein Linnebo, one of the world’s leading scholars on the subject, introduces all of the classical approaches to the field as well as more specialized issues, including mathematical intuition, potential infinity, and the search for new mathematical axioms. Sophisticated but clear and approachable, this is an essential book for all students and teachers of philosophy and of mathematics.
Øystein Linnebo is professor of philosophy at the University of Oslo. He is the author of Thin Objects: An Abstractionist Account and the coauthor (with Salvatore Florio) of The Many and the One: A Philosophical Study.
- Acknowledgments
- Introduction
- CHAPTER ONE
- Mathematics as a Philosophical Challenge
- CHAPTER TWO
- Frege’s Logicism
- CHAPTER THREE
- Formalism and Deductivism
- CHAPTER FOUR
- Hilbert’s Program
- CHAPTER FIVE
- Intuitionism
- CHAPTER SIX
- Empiricism about Mathematics
- CHAPTER SEVEN
- Nominalism
- CHAPTER EIGHT
- Mathematical Intuition
- CHAPTER NINE
- Abstraction Reconsidered
- CHAPTER TEN
- The Iterative Conception of Sets
- CHAPTER ELEVEN
- Structuralism
- CHAPTER TWELVE
- The Quest for New Axioms
- Concluding Remarks
- Bibliography
- Index
"Excellent. . . . [A]n exceptionally well-informed, very readable and clear introduction to the subject. If you are looking for an entry point into the extensive philosophical literature on the nature of mathematics, look no further."—A. C. Paseau, Mathematical Gazette
"Provides a nice lay of the land for anyone interested in contemporary philosophy of mathematics."—Gregory Lavers, Philosophia Mathematica
"Clear, concise, and well written. . . . [T]his is an excellent introduction to the philosophy of mathematics and should be seriously considered by any individual interested in the subject."—Choice
"Thought-provoking."—MAA Reviews
"This is an excellent introduction to the philosophy of mathematics, with clear and careful coverage of both traditional topics and cutting-edge contemporary debates."—Roy T. Cook, University of Minnesota
