Lectures on the Philosophy of Mathematics

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An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice.

In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.
Preface xvii
About the Author xix
1 Numbers 1
2 Rigor 53
3 Infinity 87
4 Geometry 119
5 Proof 157
6 Computability 193
7 Incompleteness 225
8 Set Theory 225
Bibliography 303
Notation Index 315
Subject Index 319
Joel David Hamkins is Professor of Logic at Oxford University and Sir Peter Strawson Fellow in Philosophy at University College, Oxford. The author of Proof and the Art of Mathematics (MIT Press), he is the creator of the popular blog Mathematics and Philosophy of the Infinite. He is a prominent contributor to MathOverflow, where he has posted more than 1,000 mathematical arguments.

About

An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice.

In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

Table of Contents

Preface xvii
About the Author xix
1 Numbers 1
2 Rigor 53
3 Infinity 87
4 Geometry 119
5 Proof 157
6 Computability 193
7 Incompleteness 225
8 Set Theory 225
Bibliography 303
Notation Index 315
Subject Index 319

Author

Joel David Hamkins is Professor of Logic at Oxford University and Sir Peter Strawson Fellow in Philosophy at University College, Oxford. The author of Proof and the Art of Mathematics (MIT Press), he is the creator of the popular blog Mathematics and Philosophy of the Infinite. He is a prominent contributor to MathOverflow, where he has posted more than 1,000 mathematical arguments.

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