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# Incompleteness: The Proof and Paradox of Kurt Gödel (Great Discoveries)

KURT GODEL IS CONSIDERED the twentieth century's greatest mathematician. His monumental theorem of incompleteness overturned the prevailing conviction that the only true statements in math were those that could be proved. Inspired by Plato's philosophy of a higher reality, Godel demonstrated conclusively that there are in every formal system undeniably true statements that
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Paperback, 224 pages

Published
February 28th 2006
by W. W. Norton & Company
(first published 2005)

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## Community Reviews

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*Gödel, Escher, Bach*, and also in a video lecture, there’s hardly any biographical/personal information about the human behind the mathematician here to be found. That’s where Rebecca Goldstein jumps in. Her book focuses on the life of the “greatest logician since Aristotle”. About his time at the Vienna Circle (a.k.a. the Schlick-Group) in the ...more

*The more I think about language, the more it amazes me that people ever understand each other at all.*

Fucking Gödel.

The above (pictured with a rueful smile and head shake) succinctly summarizes my feelings for the incomparable Kurt Gödel—the greatest logician since Aristotle, as Rebecca Goldstein makes sure to iterate several times—the quiet and unassuming genius whose steel-trap mind could capture those ethereal abstract truths and convert them into human language constructs; who single-handedly ...more

This is a book that prefers to tell rather than show: Goldstein spends 160 pages telling the reader how amazing and important and revolutionary Göde ...more

We need to grasp Godel's theories accurately because we ...more

1 The book goes through thumbnail sketches of Godel's famous proofs and then a more involved version, but even after the more detailed explanation I still felt like I had only scratched the surface of it. Some of the things asserted about the process of Godel numbering seemed almost magical as a result. This is a tough balancing act for any popular take ...more

In this book Rebecca Goldstein sets out to explain Kurt Godel’s life, including his incompleteness theorems. She first sets the stage in an environmental context, both personal and mathematical. Then comes her explanation of Godel’s theorems. And finally, the later stages of his life.

The book starts our interestingly enough with the relationship between Einste ...more

Anyway, there are a number of things I did know about Gödel, but some things I did not. I remembered the Einstein-Gödel friendship, but I did not realize that his Incompleteness Proofs were taken the wrong way: that is, they w ...more

The description of Gödel’s proof was short and well written, but it was only about 25 pages. I can say I have less of a misunderstanding of the proof, but I can’t say I understood Goldstein’s explanation. If you’re looking for a good explanation, this probably isn’t ...more

The introduction is nice - she talks about the creation of the Institute for Advanced study in Princeton, and the unlikely friendship between Gödel and Einstein. Then she launches into a discussion of the Vienna Cir ...more

Perhaps it's narrow-minded of me, but I didn't really care too much about Gödel's upbringing and his (non-proof-based) philosophical views. It is good to cover early history in a biography, but the focus should have been on his incompleteness work. Goldstein spends far too much time on his philosophical views (to the point of feeling quite redundant to me) and how they contrasted with other leading thinkers of the time. I found her focus on this topic inexplicable ( ...more

Mar 27, 2010
Ken
rated it
really liked it
·
review of another edition

Shelves:
b-philosophy,
qa-mathematics

The mind of a mathematician must be a horrible place to be. It must also be a difficult thing to dissect, but Rebecca Goldstein did so fabulously. As is my preference for reading, I picked this book up for the biographical information, yet found myself studying the technical breakdown of the incompleteness theory. I don't know how well it set in my mind, but my curiosity was piqued. I will definitely look into it more.

One thing that bothered me a little, and I read this in another review as wel ...more

One thing that bothered me a little, and I read this in another review as wel ...more

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Rebecca Newberger Goldstein grew up in White Plains, New York, and graduated summa cum laude from Barnard College, receiving the Montague Prize for Excellence in Philosophy, and immediately went on to graduate work at Princeton University, receiving her Ph.D. in philosophy. While in graduate school she was awarded a National Science Foundation Fellowship and a Whiting Foundation Fellowship.

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## Other Books in the Series

Great Discoveries
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“The necessary incompleteness of even our formal systems of thought demonstrates that there is no nonshifting foundation on which any system rests. All truths — even those that had seemed so certain as to be immune to the very possibility of revision — are essentially manufactured. Indeed the very notion of the objectively true is a socially constructed myth. Our knowing minds are not embedded in truth. Rather the entire notion of truth is embedded in our minds, which are themselves the unwitting lackeys of organizational forms of influence.”
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“The secret of the demagogue is to appear as dumb as his audience so that these people can believe themselves as smart as he is.”
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