Philosophy of Mathematics
A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers

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.

1125101487
Philosophy of Mathematics
A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers

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.

26.95 In Stock
Philosophy of Mathematics

Philosophy of Mathematics

by Øystein Linnebo
Philosophy of Mathematics

Philosophy of Mathematics

by Øystein Linnebo

Paperback

$26.95 
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Overview

A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers

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.


Product Details

ISBN-13: 9780691202297
Publisher: Princeton University Press
Publication date: 03/24/2020
Series: Princeton Foundations of Contemporary Philosophy , #15
Pages: 216
Product dimensions: 5.50(w) x 8.50(h) x 0.60(d)

About the Author

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.

Table of Contents

Acknowledgments vii

Introduction l

Chapter 1 Mathematics as a Philosophical Challenge 4

Chapter 2 Frege's Logicism 21

Chapter 3 Formalism and Deductivism 38

Chapter 4 Hilbert's Program 56

Chapter 5 Intuitionism 73

Chapter 6 Empiricism about Mathematics 88

Chapter 7 Nominalism 101

Chapter 8 Mathematical Intuition 116

Chapter 9 Abstraction Reconsidered 126

Chapter 10 The Iterative Conception of Sets 139

Chapter 11 Structuralism 154

Chapter 12 The Quest for New Axioms 170

Concluding Remarks 183

Bibliography 189

Index 199

What People are Saying About This

From the Publisher

"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

"Thought-provoking."MAA Reviews

"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

"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

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