Godel's Proof (Routledge Classics) 3rd Edition, Kindle Edition
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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.
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- ASIN : B00AZ4RE1E
- Publisher : Routledge; 3rd edition (December 6, 2012)
- Publication date : December 6, 2012
- Language : English
- File size : 508 KB
- Simultaneous device usage : Up to 4 simultaneous devices, per publisher limits
- Text-to-Speech : Enabled
- Screen Reader : Supported
- Enhanced typesetting : Enabled
- X-Ray : Not Enabled
- Word Wise : Enabled
- Print length : 104 pages
- Lending : Not Enabled
- Best Sellers Rank: #1,870,962 in Kindle Store (See Top 100 in Kindle Store)
- Customer Reviews:
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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.
Top reviews from other countries
Dennoch reicht die Schärfe der Darstellung nicht zu einer lückenlosen Beweisskizze aus, so dass der Leser das Buch eher als eine Hinführung anstatt einer Einführung sehen muss.
Das E-Book bietet leider einen schlechten Mathematik-Satz, was aber wohl dem Stand der Technik geschuldet ist. Wer hier keine Kompromisse eingehen will, greift besser zur gedruckten Ausgabe.