Gödel's Proof

Ernest Nagel, James R. Newman, Douglas R. Hofstadter , Douglas R. Hofstadter

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English

New York University Press
01 October 2008

Philosophy; Mathematics & Sciences; Mathematical logic

"An accessible explanation of Kurt Gödel's groundbreaking work in mathematical logic

In 1931 Kurt Gödel published his fundamental paper, ""On Formally Undecidable Propositions of Principia Mathematica and Related Systems."" This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences—perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as ""one of the greatest contributions to the sciences in recent times.""

However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.

New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science."

By: Ernest Nagel, James R. Newman
Foreword by: Douglas R. Hofstadter, Douglas R. Hofstadter
Imprint: New York University Press
Country of Publication: United States
Edition: 50th Anniversary ed
Dimensions: Height: 203mm, Width: 127mm, Spine: 12mm
Weight: 181g
ISBN: 9780814758373
ISBN 10: 0814758371
Pages: 160
Publication Date: 01 October 2008
Audience: College/higher education , Professional and scholarly , Professional & Vocational , A / AS level , Further / Higher Education
Format: Paperback
Publisher's Status: Active

Contents Foreword to the New Edition by Douglas R. Hofstadter ix Acknowledgments xxiii i Introduction 1 ii The Problem of Consistency 7 iii Absolute Proofs of Consistency 25 iv The Systematic Codification of Formal Logic 37 v An Example of a Successful Absolute Proof of Consistency 45 vi The Idea of Mapping and Its Use in Mathematics 57 vii Godel's Proofs 68 a Godel numbering 68 b The arithmetization of meta-mathematics 80 c The heart of Godel's argument 92 viii Concluding Reflections 109 Appendix: Notes 114 Brief Bibliography 125 Index 127

KURT GODEL taught at Vienna University in the 1930s and then became a Professor in the Institute for Advanced Study at Princeton University. ERNEST NAGEL was John Dewey Professor of Philosophy at Columbia University. JAMES R. NEWMAN was the author of What is Science. DOUGLAS R. HOFSTADTER is College of Arts and Sciences Professor of Computer Science and Cognitive Science at Indiana University and author of the Pulitzer-prize winning Godel, Escher, Bach: An Eternal Golden Braid.

Reviews for Gödel's Proof

"""A little masterpiece of exegesis. Nature An excellent non-technical account of the substance of Gdels celebrated paper. Bulletin of the American Mathematical Society"