Godel's Proof / Edition 1

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"In 1931 Kurt Godel disrupted some of the fundamental assumptions underlying mathematics and logic with the publication of his revolutionary paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." Ironically, few mathematicians of the time were able to understand the young scholar's complex proof, and the full importance of this work was largely overlooked for many years. Godel was at last recognized by his peers and presented with the first Albert Einstein Award in 1951 for achievement in the natural sciences - the highest honor of its kind in the United States. The award committee, which included Albert Einstein and J. Robert Oppenheimer, described his work as "one of the greatest contributions to the sciences in recent times."" In Godel's Proof, Ernest Nagel and James Newman provide a readable and non-technical explanation for both scholars and non-specialists of the main ideas and broad implications of Godel's discovery. First published in 1958 and in print continuously in ten languages, this highly popular, seminal work offers every educated person with an interest in mathematics, logic, and philosophy the opportunity to understand a previously difficult and inaccessible subject.
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Editorial Reviews

From the Publisher
"An excellent nontechnical account of the substance of Gödel's celebrated paper."

-American Mathematical Society

"A little masterpiece of exegesis."


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Product Details

  • ISBN-13: 9780814758168
  • Publisher: New York University Press
  • Publication date: 4/1/2012
  • Edition description: Revised
  • Edition number: 1
  • Pages: 160
  • Sales rank: 828,943
  • Product dimensions: 5.18 (w) x 8.22 (h) x 0.60 (d)

Meet the Author

James R. Newman was the author of What is Science.

Ernest Nagel was John Dewey Professor of Philosophy at Columbia University.

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 Gödel, Escher, Bach: An Eternal Golden Braid.

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Table of Contents

Foreword to the New Edition by Douglas R. Hofstadter
I Introduction
II The Problem of Consistency
III Absolute Proofs of Consistency
IV The Systematic Codification of Formal Logic
V An Example of a Successful Absolute Proof of Consistency
VI The Idea of Mapping and Its Use in Mathematics
VII Gödel’s Proofs
A Gödel Numbering
B The Arithmetization of Meta-Mathematics
C The Heart of Gödel’s Argument
VIII Concluding Reflections
Appendix: Notes
Brief Bibliography

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Customer Reviews

Average Rating 4.5
( 3 )
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Sort by: Showing all of 3 Customer Reviews
  • Anonymous

    Posted April 15, 2002

    Great Book !!!

    Great introductory book on Godel´s incompletness theorem. Starts with a clear explanation about how simple axioms become theorems and some of the problems associated with consitency. Next it will guide you through the requirements to grasp Godel´s proof and at the end it will provide a clear explanation on the subject. It will even explain what mathematical formality is all about. Don´t worry about your mathematical background the authors do a great job on explaining everything as simple as possible. Once I started reading I couldn´t stop. I recommend reading it before the formal paper written by Godel itself.

    2 out of 2 people found this review helpful.

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  • Anonymous

    Posted February 10, 2002

    Clear and concise

    This book does the best job of explaining a fundamentally opaque subject matter clearly and concisely to the lay reader, especially with the new footnotes added in by Douglas Hofstadter in this editione. i highly recommend this title to those interested in the fundamentals of mathematics, logic, or computer science.

    1 out of 2 people found this review helpful.

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  • Anonymous

    Posted January 5, 2014

    You must read it!!

    Simply excellent. You will understand this "piece of jewell" (which is not a minor stuff concerning this theorem..)!!!

    Was this review helpful? Yes  No   Report this review
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