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# Incompleteness: The Proof and Paradox of Kurt Gödel

## (Great Discoveries)

by

"A gem…An unforgettable account of one of the great moments in the history of human thought." —Steven Pinker

Probing the life and work of Kurt Gödel,

Probing the life and work of Kurt Gödel,

*Incompleteness*indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.## Get A Copy

Paperback, 224 pages

Published
February 17th 2006
by W. W. Norton Company
(first published 2005)

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## Community Reviews

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Start your review of Incompleteness: The Proof and Paradox of Kurt Gödel (Great Discoveries)

**Gödel’s Riposte to Augustine**

I find an unexpected comfort in Gödel’s Proof of Incompleteness in mathematics - essentially that we have no good reason to believe that even arithmetic has a solid logical foundation. To me the implication is that no matter how much we learn, we will still be wrong. Not because we don’t know everything, but because what we do know is fundamentally uncertain. We are not unsure only about mathematics. Physics for example will always exhibit paradoxes like those of ...more

*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

Quite possibly the young ...more

Jan 11, 2018
Jeff
rated it
liked it
·
review of another edition

Recommends it for:
Gödel-girls-and-boys

I'm going to reread the sections specifically about Gödel's incompleteness theorems because i'd really like to be able to speak about them without misrepresenting them one of these days. You could call it a New Year resolution if you wanted to.

I don't know how to rate this book because i'm so incapable of rating Goldstein's ability to convey the mathematical ideas. I can say that i thought i read many sentences more than once ... but in completely different sections of the book, as if the editor ...more

I don't know how to rate this book because i'm so incapable of rating Goldstein's ability to convey the mathematical ideas. I can say that i thought i read many sentences more than once ... but in completely different sections of the book, as if the editor ...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 ...more

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

However I did not enjoy the first half of the book much at all. It felt like it was a 150 page set up to what the philosophical world was like that Godel was walking into. I didn't need that and didn't feel like it did much to move along my understanding of Godel ...more

Nov 09, 2018
Eric
rated it
really liked it
·
review of another edition

Shelves:
non-fiction,
biography-autobiography

What a fascinating and under appreciated man.

What makes the book really enjoyable are the themes that the author skillfully builds on throughout the ...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 ...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

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

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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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“Einstein’s and Gödel’s metaconvictions were addressed to the question of whether their respective fields are descriptions of an objective reality—existing independent of our thinking of it—or, rather, are subjective human projections, socially shared intellectual constructs.”
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1 likes

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