Philosophy of Mathematics in the Twentieth Century: Selected Essays

Philosophy of Mathematics in the Twentieth Century: Selected Essays

by Charles Parsons


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In this illuminating collection, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the course of the past century.

Parsons begins with a discussion of the Kantian legacy in the work of L. E. J. Brouwer, David Hilbert, and Paul Bernays, shedding light on how Bernays revised his philosophy after his collaboration with Hilbert. He considers Hermann Weyl's idea of a "vicious circle" in the foundations of mathematics, a radical claim that elicited many challenges. Turning to Kurt Gödel, whose incompleteness theorem transformed debate on the foundations of mathematics and brought mathematical logic to maturity, Parsons discusses his essay on Bertrand Russell's mathematical logic—Gödel's first mature philosophical statement and an avowal of his Platonistic view.

Philosophy of Mathematics in the Twentieth Century insightfully treats the contributions of figures the author knew personally: W. V. Quine, Hilary Putnam, Hao Wang, and William Tait. Quine's early work on ontology is explored, as is his nominalistic view of predication and his use of the genetic method of explanation in the late work The Roots of Reference. Parsons attempts to tease out Putnam's views on existence and ontology, especially in relation to logic and mathematics. Wang's contributions to subjects ranging from the concept of set, minds, and machines to the interpretation of Gödel are examined, as are Tait's axiomatic conception of mathematics, his minimalist realism, and his thoughts on historical figures.

Product Details

ISBN-13: 9780674728066
Publisher: Harvard
Publication date: 03/17/2014
Pages: 368
Product dimensions: 6.40(w) x 9.40(h) x 1.20(d)

About the Author

Charles Parsons is Edgar Pierce Professor of Philosophy, Emeritus, at Harvard University.

Table of Contents

Preface ix

Introduction 1

Part I Some Mathematicians as Philosophers

1 The Kantian Legacy in Twentieth-Century Foundations of Mathematics 11

2 Realism and the Debate on Impredicativity, 1917-1944 40

Postscript to Essay 2 62

3 Paul Bernays' Later Philosophy of Mathematics 67

4 Kurt Gödel 93

5 Gödel's "Russell's Mathematical Logic" 103

Postscript to Essay 5 123

6 Quine and Gödel on Analyticity 127

Postscript to Essay 6 147

7 Platonism and Mathematical Intuition in Kurt Godel's Thought 153

Postscript to Essay 7 188

Part II Contemporaries

8 Quine's Nominalism 199

9 Genetic Explanation in The Roots of Reference 220

10 Hao Wang as Philosopher and Interpreter of Gödel 243

11 Putnam on Existence and Ontology 267

12 William Tait's Philosophy of Mathematics 290

Bibliography 321

Copyright Acknowledgments 343

Index 345

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