Gödel's Proof Revised Edition

by Ernest Nagel (Author), James Newman (Author), Douglas R. Hofstadter (Editor, Foreword)

98 customer reviews

ISBN-13: 978-0814758373

ISBN-10: 0814758371

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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.

Marking the 50th anniversary of the original publication of Gödel'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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Editorial Reviews

Review

"A little masterpiece of exegesis."

-Nature

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

-American Mathematical Society

About the Author

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

Product details

Paperback: 160 pages
Publisher: NYU Press; Revised edition (October 1, 2008)
Language: English
ISBN-10: 0814758371
ISBN-13: 978-0814758373
Product Dimensions: 5 x 0.4 x 8 inches
Shipping Weight: 4.8 ounces (View shipping rates and policies)
Average Customer Review: 98 customer reviews
Amazon Best Sellers Rank: #68,907 in Books (See Top 100 in Books)
- #21 in Books > Science & Math > Mathematics > Pure Mathematics > Logic
- #60 in Books > Science & Math > Mathematics > History
- #997 in Books > Textbooks > Science & Mathematics > Mathematics

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As promised, a complete though not thorough explanation of Godel's incompleteness theorem

September 18, 2016

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Overall, I very much enjoyed this book. It was as promised, a complete, though not thorough explanation of Godel's incompleteness theorem.

While it did use mathematical syntax throughout the book, it was all in the context of what was necessary for the explanation (and in many cases the mathematical symbols are easier to parse than the written explanation, however usually both are provided). Furthermore, tables are often shown throughout the book to further reinforce concepts.

As someone with an engineering rather than formal mathematics background, I found the book overall quite easy to follow. That is not to say that there weren't a few pages for which I needed to re-read several times, or that I would jump backwards in the book to reacquire the context of what was being explained, but it seemed like the book chose the right trade offs overall.

It is worth noting that the book is quite a quick read. I imagine most people would get through it in a little over a couple of hours. Yet the length of the book feels right. It manages to gloss over the right areas, while not affecting the subsequent explanations negatively.

6 people found this helpful

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Roberto Rigolin F Lopes

Consistency implies incompleteness

November 28, 2017

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We are in 1931, some clever people like Hilbert, Russell and Whitehead have been trying to put mathematics on solid foundations. But a young guy called Gödel just constructed a proof stating that all consistent systems are incomplete. Then if mathematics has no contradictions (consistent), it cannot be composed by theorems (incomplete). Therefore, it is impossible to validate mathematics using mathematics. Damn, this kid just shocked the whole scientific community. How on earth someone proof that ALL consistent systems within the whole universe of possible systems are incomplete? This book will give you some clues. If you want to see and hear it, read GEB by Douglas Hofstadter.

4 people found this helpful

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Gregory W. Pappas

This is an excellent book that makes one of the most difficult subjects ...

March 18, 2016

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This is an excellent book that makes one of the most difficult subjects to truly understand accessible to someone that has some understanding of number theory. Kurt Godel's Incompleteness Theory is a monument to human thinking on a level equal to Albert Einstein's Theory of Relativity which is only fitting because Einstein was a great admirer and friend of Godel. It is an excellent explanation of the limits that exist of formalized mathematics with respect to the fundamental foundation of number theory.

Ernest Nagel's Godel's Proof could and should be made into a high level college course.

7 people found this helpful

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Amazon Customer

April 21, 2018

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Personally, I think the author did good job as he has tried to explain this very complex topic in relatively simple words. However, this book is intented for somebody already acquainted with mathematics, mainly with basic of mathematical (or formal) logic. The author describes mainly the topic itself, only sometimes he deals with historical backdrop. So, I would not recommend this book to somebody interested in history of science.
The book is divided to two main parts. In the first one (chapters 1 to 6) the author brings introduction to terms like a "consistency" and "completeness" in logic and he desribes methods how to prove that some formal system is consistent or complete. The author is also talking about some logical paradoxes. Then some necessary information about mapping in maths is provided. The second part of the book (namely chapter 7) contains Godel's proof itself. Since the proof is not very simple, the author fisrtly introduces some other auxiliary theorems. Finnaly, the proof is coined and explained in "natural" language. I highly appreciated many footnotes sheding more light on, at first glance, not very clear terms and statements.
To sum up, the book is worth reading and I think that everybody either using advanced maths in day-to-day working or dealing with computer sciences should read this book.

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Read This Instead of Gödel, Escher, Bach

January 2, 2014

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This book is simple, short, and to the point. It explains the project of Principia Mathematica, the idea of building mathematics as an extension of logic. It also explains the difference between mathematics and metamathematics, how consistency and completeness are proven logically, and how Gödel encoded the metamatematics in Principia into mathematical statements. It then explains how Gödel used this encoding to weave a paradox into the system, showing that it is incomplete.

The problem with GEB is that it explains Gödel's proof, but then uses the majority of its pages to advance a philosophical view that human thought is nothing more than computation (one that has been, in my opinion, thoroughly refuted by John Searle). This book sticks to its topic: Gödel's proof and its mathematical implications. It does not stray into speculative philosophy, venturing beyond what Gödel's theorem actually proved.

In short, this book is everything that GEB is not. It is simple, to the point, relatively easy to understand, and sticks to the topic at hand.

16 people found this helpful

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Allowed Me To Understand

August 21, 2016

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This book allowed me to understand Godel's proof and its implications. This surprised me and I would imagine even more surprise the professors to attempted to teach me the elements of mathematics. The book is written in an open and accessible style that enabled me to understand the work. I would recommend this book to anyone who wants to understand the often cited but understood by few theorem

One person found this helpful

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