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by: Ernest Nagel, James Newman, Douglas R. Hofstadter
List Price: $12.95Amazon.com's Price: $10.36 You Save: $2.59 (20%)Prices subject to change. Availability: Usually ships in 24 hours
Binding: Paperback
Dewey Decimal Number: 511
EAN: 9780814758373
ISBN: 0814758371
Label: NYU Press
Manufacturer: NYU Press
Number Of Items: 1
Number Of Pages: 129
Publication Date: October 01, 2008
Publisher: NYU Press
Release Date: October 01, 2008
Sales Rank: 128753
Studio: NYU Press
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Editorial Review:
Product Description:
A little masterpiece of exegesis.
Nature
An excellent non-technical account of the substance of Gödels celebrated paper.
Bulletin of the American Mathematical Society
In 1931 Kurt Gödel published his fundamental paper, 'On Formally Undecidable Propositions of Principia Mathematica and Related Systems.' This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences—perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as 'one of the greatest contributions to the sciences in recent times.'
However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.
Marking the 50th anniversary of the original publication of Gödel's Proof, New York University Press is proud to publish this special anniversary edition of one of its bestselling and most frequently translated books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.
Amazon.com Review:
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
Customer Reviews
Average Rating: 
Rating:  - A fine essay introducing the basic idea
Anyone interested in the foundation of modern math ought to be at least familiar with Godel. This is really a very readable short essay giving the general outline and the basic idea of this important proof. Even motivated high-school students will have no problem grasping it (assuming they leave their tv's and computer games long enough!)
Rating:  - Godel for people such as we (who are familiar with a little Theory of Numbrets)
I ran into Godel back in about 1955 in "Scientific American". I did not understand that. Now 53 years later, and with some more understanding of the theory of numbers, I find this work to be a magnificent opening into Godel's world. AS WOMDERFUL read!.
Rating: - A Simple Presentation of a Complex Topic
Godel's proof represents a milestone in mathematical and philosophical thought. This book, annotated by the remarkable Douglas Hofstadter, presents Godel's ideas in a language that's readily understandable by the educated layperson. It is clear, concise, and fascinating.
Rating: - Godel's incompleteness theorems explained in non-technical language
There is no question in my mind that the most misunderstood mathematical theorems of all time are Godel's incompleteness theorems. In essence, they state that no system powerful enough to do basic arithmetic is complete. Meaning that there will always be statements that are true in the system but that can never be proven in that system. These results have been seized upon by people with many different agendas and used to argue conclusions as significant as the existence of God and that human ... Read More
Rating: - how i understand Godel
Godel was able to construct a formula from the axioms of Principia Mathematica (PM, and related systems, due to Russell and Whitehead) that is (roughly) "There exists no proof for this formula". This IS the formula itself. now, we need to know if this is true or not. so we try to find a proof for it within PM. if it is possible to find the proof, that means the formula is correct. but the formula says you can't find it. if the proof cannot be found, that means the negation of the formula is correct, ... Read More
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