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.
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.
