Godel's Proof / Edition 1by Ernest Nagel, James R. Newman, Douglas R. Hofstadter
Pub. Date: 04/01/2012
Publisher: New York University Press
"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… See more details below
"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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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
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
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Most Helpful Customer Reviews
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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.
Simply excellent. You will understand this "piece of jewell" (which is not a minor stuff concerning this theorem..)!!!
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.