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Godel's Proof (Routledge Classics), by Ernest Nagel, James R. Newman
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'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.
- Sales Rank: #1390138 in eBooks
- Published on: 2012-12-06
- Released on: 2012-12-06
- Format: Kindle eBook
Review
'Nagel and Newman accomplish the wondrous task of clarifying the argumentative outline of Kurt Godel's celebrated logic bomb.' – The Guardian
Most helpful customer reviews
3 of 3 people found the following review helpful.
Godel's incompleteness theorem, clearly explained
By Andres C. Salama
Gödel's incompleteness theorem remains one of the most quoted, yet most misunderstood work in mathematics of the last century. Many non mathematicians had used the theorem (without understanding it, of course), to "prove" just about everything (generally it's been used to imply the limits of science, or stuff to that effect). The theorem, though, hardly implies that. This short book, written some 50 years ago, remains probably the best explanation of Godel's work available to the layman. The book starts explaining the background to Godel's theorem, as mathematicians such as Hilbert and Russell sought the axiomatization of mathematics. Godel's work, of course, proved that to be impossible. The book then proceeds to explain the theorem itself, as clearly as it possibly can (though I have to say that, as a non expert, the Gödel numbering scheme seems a like a trick to me, a sleight of hand. Yet, what do I know about this?). Overall, a great book about a much misunderstood work.
0 of 0 people found the following review helpful.
A VERY HELPFUL SUMMARY OF GÖDEL's "INCOMPLETENESS THEORUM," AND OTHER WORK
By Steven H Propp
An introduction to this 1958 book states, "Here is the first book to present a readable explanation to both scholars and non-specialists of the main ideas, the broad implications of Gödel's proof. It offers any educated person with a taste for logic and philosophy the chance to satisfy his intellectual curiosity about a previously inaccessible subject."
The Introduction adds, "he proved that it is impossible to establish the internal logical consistency of a very large class of deductive systems... unless one adopts principles of reasoning so complex that their internal consistency is as open to doubt as that of the systems themselves. In the light of these conclusions, no final systematization of many important areas of mathematics is attainable, and no absolutely impeccable guarantee can be given that many significant branches of mathematical thought are entirely free from internal contradiction." (Pg. 6)
The authors point out, "Until recently it was taken as a matter of course that a complete set of axioms for any given branch of mathematics can be assembled. In particular, mathematicians believed that the set proposed for arithmetic in the past was in fact complete, or, at worst, could be made complete simply by adding a finite number of axioms to the original list. The discovery that this will not work is one of Gödel's major achievements." (Pg. 56)
They summarize, "he showed that it is impossible to give a meta-mathematical proof of the consistency of a system comprehensive enough to contain the whole or arithmetic---unless the proof itself employs rules of inference in certain essential respects different from the Transformation Rules used in deriving theorems within the system... if the proof is not finitistic, it does not realize the aims of Hilbert's original program; and Gödel's argument makes it unlikely that a finitistic proof of the consistency of arithmetic can be given." (Pg. 58)
They suggest in the book's conclusion, "In the light of these circumstances, whether an all-inclusive definition of mathematical or logical truth can be devised, and whether, as Gödel himself appears to believe, only a thoroughgoing philosophical 'realism' of the ancient Platonic type can supply an adequate definition, are problems still under debate and too difficult for further consideration here." (Pg. 99)
For those hesitant to work their way through Gödel's On Formally Undecidable Propositions of Principia Mathematica and Related Systems, this book is an excellent alternative.
0 of 0 people found the following review helpful.
Five Stars
By Brichu
Book in a very good condition
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