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Godel's Proof

by Ernest Nagel and James R. Newman New York University Press
Pub Date:
10/2008
ISBN:
9780814758373
Format:
Pbk 160 pages
Price:
AU$28.99 NZ$30.43
Product Status: In Stock Now
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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.

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

'A little masterpiece of exegesis.' - Nature 'An excellent non-technical account of the substance of G Âdel's celebrated paper.' - Bulletin of the American Mathematical Society
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 G÷del, Escher, Bach: An Eternal Golden Braid.