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Customer Reviews

4.5 out of 5 stars
4.5 out of 5 stars

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on 27 June 1999
Simply magnificent. This book meets and exceeds the description on its back cover -- offering "any educated person with a taste for logic and philosophy the chance to satisfy his intellectual curiosity about a previously inaccessible subject." This book gives anyone with the interest and the motivation a solid, if not complete, understanding of the ideas underlying the proof. While it's true that someone very unfamiliar with mathematics (or, more importantly, with logic and mathematical thinking) would not get as much out of the book, it does a very good job of walking the reader through Gödel's complex but breathtakingly elegant reasoning. I wholeheartedly recommend this book.
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on 24 November 2004
For those interested, but uninitiated, in the philosophy of mathematics or mathematical philosophy should seriously consider reading this excellent introductory text. In a highly concise and lucid manner, the authors successfully explain the origins, development and details of Godel's proof and examine some of the wider implication of it.
It is not, however, particularly easy reading. Unlike reading a novel, it requires some effort to fully understand and grapple with the strange but intriguing concepts discussed. No background or logic necessary; technicalities are generally avoided.
All in all, outstanding. Well worth buying.
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on 16 June 1999
I Read this book in an afternoon. While this book covers many of Godels ideas, concepts, and systematically works throught the incompleteness theory, it does however lack the fine detail of the actual theorem. I recomend this book for those who wish to find out aout Godels Proof, without wanting the know the fine details.
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on 16 July 2008
This book by Nagel and Newman is a great classic, clever and suited to the intellectually curious who have not the patience (or talent) for the full syntax of mathematical logic.

Aside: It is a little misleading that Amazon, in their header, say "By Douglas R.Hofstadter, ..." as he wrote the preface only to this much later reprinted edition.
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on 10 December 2008
I have not read Godels paper, and it is unlikely I will, but I found this an eminently clear, readable and understandable (and, dare i say, enjoyable!) distillation.

And hopefully it has set me up for a second attempt at Hofstadter's Eternal Golden Braid :)
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on 9 January 2014
I have to go against the flow of reviews and give this 3. I am not a mathematician, but a computer scientist (who has worked with applied mathematics). I found Nagel and Newman's exposition of Gödel's theorems good to a point, but, despite several re-reads, the "click" of the elusive intuition didn't materialise.

I continued my search to understand Gödel and found a more intuiitive exposition in "Incompleteness" by Rebecca Goldstein. The key difference in Goldstein's exposition was to make clear the "diagonal lemma". Goldstein states that Gödel "didn't actually use it, but rather derived the particular case"; it does however convey the entrance of self-referentiality more clearly. Nagel and Newman's text does not mention the "diagonal lemma". I would recommend Goldstein's text to lay persons seeking an intuitive grasp of the incompleteness theorem.
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on 27 February 1997
This book, Godel's Proof, explains a complex subject in easy to understand language. It guides you through every step of the way, teaching all the information you need to understand the proof before it attempts to explain the proof itself. I found it to be very interesting. This is the only math book I have ever read of my own free will. I recomend this book to anyone who has a slight intrest in math or logic.
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on 13 September 2007
"Gödel's Proof" is a classic. Despite of being brief it doesn't sacrifice punctuality for length. There are no superfluous paragraphs in this book which leads the leader with steady but not lengthy steps to the understanding of the greatest leap taken in the field of Mathematical Logic. The text is not written in a technical style and even the few mathematical proofs found at the last chapters are indispensable for understanding the heard of Gödel's Proof.

Don't be confused from the mathematical title of this book and think that this book is written only for mathematicians. On the contrary I believe that the importance of this proof reaches every natural science because the language used from the majority of the these sciences is mathematics and therefore the characteristics of the language used to describe natural processes affects the epistemological foundations of the aforementioned natural sciences.

This unique textbook has also a lot to do with cognitive science and the way we think as human beings while trying to understand our natural environment. For this reason I consider "Gödel's Proof" as a wonderful book of cognitive science too. I truly recommend this book to anyone who want to take a deep dive in the big blue of what mathematics are and their connection with empirical reality. It is the best book to get a good feeling about Mathematical Logic and reasoning.
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on 5 June 2016
Halfway through it - it needs a lot of rereading and rethinking, but that is the nature of the subject matter. I feel that perhaps it needs a few more concrete examples of the various 'arithmetisation' processes which are inherent in the whole slightly potty world of mathematical logic and Godel. One juicy example of the pottiness. At one point we are shown the 'typographical' version of a theorem which involves the use of the following entry in a formula: s...s0, which means the s written out 'a' (an astronomical number) of times. You get a strong feeling that if any specific mention of 'a' to conveniently replace the ambiguous dots was used in this formula it would be a frightful blunder in that the whole thing would become some sort of circular argument. It makes you wonder...
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on 19 July 2014
A very brief but excellent conceptual summary of Godel's theorems that touches on some of the technicalities as well. It introduces some of the philosophical,mathematical and logical underpinning while capturing the general import of Godel's achievement.Obviously I wouldn't tackle the complex mathematical logic involved in the proofs themselves after reading just this book; for that a course in mathematical logic would be necessary and/or a more technically minded introduction.

If you want a good idea of what Godel theorems are about, this is a very good place to start.
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