ISBN-10:
0814758169
ISBN-13:
9780814758168
Pub. Date:
04/01/2012
Publisher:
New York University Press
Godel's Proof / Edition 1

Godel's Proof / Edition 1

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Product Details

ISBN-13: 9780814758168
Publisher: New York University Press
Publication date: 04/01/2012
Edition description: Revised
Pages: 160
Sales rank: 972,629
Product dimensions: 5.00(w) x 8.00(h) x 0.60(d)

About the Author

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 Gödel, Escher, Bach: An Eternal Golden Braid.

Table of Contents

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

What People are Saying About This

From the Publisher

"A little masterpiece of exegesis."

-Nature,

"An excellent non-technical account of the substance of Gödel's celebrated paper."

-Bulletin of the American Mathematical Society

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Godel's Proof 4.8 out of 5 based on 0 ratings. 4 reviews.
Guest More than 1 year ago
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.
billmcn on LibraryThing 7 months ago
This is a non-formal, though still rigorous, presentation of the argument of Gödel's famous demonstration that will be accessible to anyone familiar with the basics of mathematical proof, logic, and number theory. By the end of the book, I acutally had the outline of Gödel's tricky self-referential argument all in my head at once, and though it faded quickly, I feel confident I could resurrect it with another reading. Nagel's description of the significance of the proof, as opposed to its mechanics, is less thorough, but that's a quibble. This slim book is a truly impressive feat of exposition.
Anonymous More than 1 year ago
Simply excellent. You will understand this "piece of jewell" (which is not a minor stuff concerning this theorem..)!!!
Guest More than 1 year ago
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.