Godel's Proof: Amazon.ca: Ernest Nagel, James R. Newman, Douglas R. Hofstadter: Books

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Gödel's incompleteness theorem--which showed that any robust mathematical system contains statements that are true yet unprovable within the system--is an anomaly in 20th-century mathematics. Its conclusions are as strange as they are profound, but, unlike other recent theorems of comparable importance, grasping the main steps of the proof requires little more than high school algebra and a bit of patience. Ernest Nagel and James Newman's original text was one of the first (and best) to bring Gödel's ideas to a mass audience. With brevity and clarity, the volume described the historical context that made Gödel's theorem so paradigm-shattering. Where the first edition fell down, however, was in the guts of the proof itself; the brevity that served so well in defining the problem made their rendering of Gödel's solution so dense as to be nearly indigestible.

This reissuance of Nagel and Newman's classic has been vastly improved by the deft editing of Douglas Hofstadter, a protégé of Nagel's and himself a popularizer of Gödel's work. In the second edition, Hofstadter reworks significant sections of the book, clarifying and correcting here, adding necessary detail there. In the few instances in which his writing diverges from the spirit of the original, it is to emphasize the interplay between formal mathematical deduction and meta-mathematical reasoning--a subject explored in greater depth in Hofstadter's other delightful writings. --Clark Williams-Derry

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Customer Reviews

13 Reviews

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4 star:		(1)
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4.3 out of 5 stars (13 customer reviews)

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2 of 2 people found the following review helpful:

4.0 out of 5 stars Good attempt to explain the proof, May 23 2004

By A Customer

This review is from: Godel's Proof (Hardcover)

This was clearly one of the best attempts at explaining Godel's proof that I have seen, at least superficially speaking. As someone who just wanted to understand what the basic ideas are, I looked over various books and decided on this one because of its high rating. I gave it 4 stars because I was left feeling that there were several times when background knowledge of higher mathematics/logic was assumed and I think more could have been done to explain those parts on a level comprehensible to an interested layperson.

I think the attempt in the book is a good one, but I guess perhaps not enough is said about just how abstract these ideas are and how difficult it is to simply dive in (even with a good book) and expect to understand this proof fully.

I am going to try Godel, Escher, Bach, and Roger Penrose's Shadows of the Mind next, since I have heard that both of them also include explanations of Godel's theorem. But I now have a greater appreciation of why there will never be a "Godel's Proof for Dummies" book!

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5.0 out of 5 stars Half way through, great read, July 18 2011

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dp - See all my reviews

This review is from: Godel's Proof (Paperback)

I'm an aspiring mathematician/physicist with a strong interest in philosophy. Godel's theorems have always interested me, but I just haven't yet had a chance to study the mathematical logic necessary to understand them. While at the library to pick up a book to begin studying this very subject, I happened to see this book entitled "Godel's Proof". As it was short and purported to give a quick and somewhat general explanation of his work, I decided there couldn't be anything to lose in picking up this book.

I'm happy to say that I read half of it yesterday and am extremely excited to finish off the second half today. As many reviewers have said, this book isn't the rigorous exposition that a logician or mathematician may desire. However, as anyone who studies difficult subjects deeply knows, it is extremely useful to be given an understandable and simple outline of what you are about to embark on. This book (so far) is exactly that. It isn't so rigorous that you get bogged down in details of specific proofs, but it isn't so "dumbed down" that the explanation is devoid of any real meaning.

I recommend this book to anyone in my situation. Someone who would like a simple and understandable (but still valuable) overview of the subject as a precursor to deeper study.

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5.0 out of 5 stars Lucid & satisfying: Godel's Proof and modern logic, May 18 2004

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Stavros Macrakis (Cambridge, MA, USA) - See all my reviews
(REAL NAME)

This review is from: Godel's Proof (Paperback)

In 100 lucid and highly readable pages, presents the most important ideas of modern logic: axiomatisation (Euclid), formalization (Hilbert), metamathematical argumentation, consistency, completeness, etc., leading up to Godel's incompleteness result. Elementary from a technical point of view, but technical people should read it to get perspective. Non-technical people will appreciate its workmanlike, substantive exposition, in contrast to the mysticism, obfuscation, and cuteness of a "Godel, Escher, Bach". It is old (1958) and very incomplete (no set theory, no computability, no non-standard analysis, ...), but still essential reading.

(I wrote this review in 1998, but Amazon doesn't know I'm the same person as macrakis@alum.mit.edu.)

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Most recent customer reviews

5.0 out of 5 stars Don't be intimidated by the subject matter.
The greatest merit of this book is its ability to take a rather arcaic and complicated proof and successfully present it, in a concise and understandable manner, to a broad... Read more

Published on Jan 3 2004 by C. Goss

5.0 out of 5 stars Wish I'd read it first ...
I read Godel's paper in grad school. I wish I had read this first, because it lays out the structure of the argument clearly. Read more