Godel's Proof

Godel's Proof

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In 1931 Kurt Goedel 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. Goedel 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 Goedel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.

Marking the 50th anniversary of the original publication of Goedel's Proof, New York University Press is proud to publish this special anniversary edition of one of its bestselling and most frequently translated 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.
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Product details

  • Paperback | 160 pages
  • 124.46 x 195.58 x 12.7mm | 136.08g
  • New York University Press
  • New York, United States
  • English
  • Revised
  • Revised ed.
  • 0814758371
  • 9780814758373
  • 88,082

Review quote

"An excellent nontechnical account of the substance of Goedel's celebrated paper."

-American Mathematical Society "A little masterpiece of exegesis."

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About Ernest Nagel

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.
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Table of 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
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Rating details

3,685 ratings
4.14 out of 5 stars
5 42% (1,544)
4 37% (1,371)
3 15% (570)
2 4% (160)
1 1% (40)
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