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Reviews elsewhere on the web:
Danny Yee
American Mathematical Society (pdf)
Garret Wilson

Ernest Nagel and James R Newman

Godel's proof

Gödel's incompleteness theorem has a reputation of being mysterious and difficult to understand. In Gödel's Proof Ernest Nagel and James R Newman give a clear explanation of the basics of the proof. They explain the background to the proof and in particular the search for a way of proving consistency of a system of axioms. They then exhibit a system where such a proof is possible - the propostional calculus. The book continues with chapters on the concept of mapping in mathematics, and on Gödel numbering, finishing off with the proof of the incompleteness theorem itself.

I did have some misgivings about the book. I felt that some examples of proofs from axioms would have helped the reader to understand what was going on. Also the book doesn't mention Gödel's β function, which I consider to be the most innovative part of the proof - how you code for 'and so on..' when your system doesn't include such a concept. In summary, the book would be useful for those wishing to get a clear idea of Gödel's theorem without getting too technical, and to go further than what is given in most popular treatments of the subject, but it doesn't go that much further than such treatments.

See also:Gödel's incompleteness theorem project

Product Description

'Nagel and Newman accomplish the wondrous task of clarifying the argumentative outline of Kurt Godel's celebrated logic bomb.' – The Guardian

In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of physicist Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system. The importance of Godel's Proof rests upon its radical implications and has echoed throughout many fields, from maths to science to philosophy, computer design, artificial intelligence, even religion and psychology. While others such as Douglas Hofstadter and Roger Penrose have published bestsellers based on Godel’s theorem, this is the first book to present a readable explanation to both scholars and non-specialists alike. A gripping combination of science and accessibility, Godel’s Proof by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and philosophy the chance to satisfy their intellectual curiosity.

Kurt Godel (1906 – 1978) Born in Brunn, he was a colleague of physicist Albert Einstein and professor at the Institute for Advanced Study in Princeton, N.J.