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Incompleteness: The Proof and Paradox of Kurt Gödel

(Great Discoveries)

3.99  ·  Rating details ·  1,399 ratings  ·  140 reviews
"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, Incompleteness indelibly portrays the tortured genius whose vision rocked the stability of mathematical reasoning—and brought him to the edge of madness.
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Paperback, 224 pages
Published February 17th 2006 by W. W. Norton Company (first published 2005)
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BlackOxford
Dec 07, 2018 rated it really liked it
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 quan
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Matt
I’ve always been fascinated by Kurt Gödel and his incompleteness theorems. While Douglas Hofstadter did a fine job in explaining the latter in his book 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 th ...more
Szplug
Jan 21, 2011 rated it really liked it
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
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Brad Lyerla
Nov 18, 2013 rated it it was amazing  ·  review of another edition
INCOMPLETENESS is an excellent book about an intellectually elusive subject. Kurt Godel's fame was established by his proof of something called "the Incompleteness Theorem." His proof employed formal logic to establish a basic truth about mathematics. Namely, that in closed systems, there will be true statements that cannot be proved. Until Godel's proof, many leading mathematicians assumed the opposite was true. This is a challenging subject to write about, but Goldstein makes it easily accessi ...more
K York
Mar 20, 2013 rated it really liked it
Shelves: philosophy
What a wonderful book. Goldstein not only lays out Godel's famous theorems in relatively understandable terms for the layman (an accomplishment in itself,) but provides an original, funny, and lucid account of the intellectual atmosphere in which these theorems arose. She discussed Godel's relation to the Logical Positivists and Formalists, which sheds great light upon the meaning of his discoveries. She also dispels the postmodernists mythologies about what Godel's theorems mean. In addition, s ...more
Stephie Williams
Apr 30, 2014 rated it liked it
I may have read this book previously, but I could not remember doing so. This review replaces the very short review I had previously made.

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
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Matthew
Jul 13, 2008 rated it it was ok
Shelves: real-worldy
Suck it, postmodernists.
Jeff
Jan 11, 2018 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
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Collin Winter
"Incompleteness" is less about Gödel's actual incompleteness theorems -- the proofs and their specific mathematical legacy -- than it is about the philosophical environment those theorems were developed in. Put another way, this is a book less about Gödel and more about Gödel and Wittgenstein, or perhaps more accurately, about Wittgenstein and Gödel.

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
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Davin
Apr 23, 2007 rated it liked it
Well written and a good picture of Godel, his work, philosophy and the times he lived in. There would be more starts up there but for 2 reasons:

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
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Keith Akers
May 21, 2010 rated it really liked it
This is a great book to learn more about "Goedel's Proof" (actually two proofs, or actually three proofs if you count his Ph. D. thesis on predicate calculus). The incompleteness of mathematics is an astounding concept -- it's so astounding, that you are left breathless, not even sure what the whole thing means. Does this mean that God exists? Actually, Goedel himself toyed with variations of the ontological proof. The incompleteness of mathematics is just really hard to wrap your brain around; ...more
Rossdavidh
Jun 08, 2014 rated it liked it  ·  review of another edition
Shelves: purple
David Foster Wallace (RIP) once referred to Kurt Goedel, the subject of this book, as mathematics' Prince of Darkness. Douglas Hofstadter gave his Incompleteness Theorems (1 and 2) a central role in his book “Goedel, Escher, Bach”. Goedel's ideas are so central to 20th century thinking that it is likely that Einstein (for many years until his death Goedel's closest friend) was the only person he ever met who he was not, eventually, to become more famous and influential than (for example Wittgens ...more
Bakunin
Jun 28, 2019 rated it really liked it
Rebeccca Goldstein is an American philosopher and writer. This book managed to dive into who Gödel was and what his views on mathematics really meant. I was intrigued by this myth of a man; a man who seemed only to get more quiet as he grew older. He never seemed to argue against the popular trends of the day yet was quite certain of his own opinion. In fact the last great philosopher he admired was Leibniz. I was interested in how Gödel was formed as a person and given his infamous secrecy this ...more
Domhnall
Apr 24, 2016 rated it it was amazing
Shelves: philosophy
This book is succinct, accessible and well constructed. Godel's Incompleteness Theorems are so significant in the history of ideas that it is essential to have a decent grasp of just what they are and why they mattered and this book supplies that need for general readers. It gives a good enough explanation of Godel's findings and deals with the reactions of other major names to his theories, which sheds interesting light on their work too.

We need to grasp Godel's theories accurately because we
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Megan Lawson
Aug 04, 2018 rated it it was ok
I very much enjoyed the second half of this book - in which there was a discussion (though I wish more mathematically and logically minded) of Godel's Incompleteness Theorems as well as stories of his life and interactions at Princeton.

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
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Liquidlasagna
Jun 30, 2020 rated it did not like it
Amazon Review

Bad history, bad math

Pretentious and sloppy, filled with mistakes and repetitions. See the AMS review on-line for some details. Terrible.

And shame on S. Pinker and B. Greene for their glowing cover reviews. Were they swayed by the adoring references to them in the text?

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Review from someone at Stanford

Goldstein bases her story of the development of the incompleteness theorems on the supposed fact that – in contrast to the views of the Vienna Circle – Gödel was already a confirmed P
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Jr
Mar 15, 2018 rated it it was ok
Seems to have a major misconception.

I got it as a gift and picked it up to see if I wanted to read. Actually, based on the subject I thought I might want to recommend to a book club I am part of because it's a subject I am very interested in and would make for a good discussion.

However, diving in at chapter ii (which is well into the book) there was a discussion about postulates (or axioms) and intuition. That axioms are necessary for a mathematical system because you need a foundation to build
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Brett
Apr 16, 2014 rated it liked it  ·  review of another edition
This book is serviceable in being a readable introduction to Gödel's famous proofs and a general (very general) understanding of the intellectual and historical circumstances within which it grew. While I do not have the capabilities to judge whether she provides a completely faithful representation of Gödel and his proofs, it is within my power to deem her handling of Wittgenstein, whom she spends a great deal of pages discussing, to be sorely unsympathetic, uncharitable, and misrepresentative. ...more
Greg Talbot
Focuses largely on the man, Kurt Godel, not so much the implications of the incompleteess theorem.

No doubt, Kurt Godel lived an interesting life. He was in the exemplary Vienna Circle, friends with Einstein, and is generally considered one of the most important mathematicians of the 20th century. However, his inwardness, strangeness and general disinterest in human connection does not make for a particularly interesting story.

If you're interested in the ideas of Godel, I don't think this is the
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Christopher
May 01, 2013 rated it it was ok
This book attempted to be a biography, a history of an idea, and a history of an intellectual time all at the once, and it passed with average colors. This is the kind of book where nothing went terribly wrong, but nothing went terribly right either. So while I don't really have any major problems with it, it remains stubbornly "OK."

Also note: Godel really needed to read some Chesterton, even though he would have hated it.
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Peter Flom
Sep 02, 2012 rated it it was amazing
Shelves: math
This is a great book about a strange and brilliant man. It's hard to think of a writer better qualified to write it than Rebecca Goldstein. Full review: http://www.allvoices.com/contributed-... ...more
Brian
Feb 17, 2013 rated it it was ok
I respect the book more than I like it. It does clarify some of the issues of the Incopmleteness theorem, but there's still much ambiguity and technicality here.

Also, I didn't feel for Godel. He needed to get out more.
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Jafar
Mar 15, 2007 rated it really liked it
A great book about this most genius mathematical mind of the last 100 years. Rebecca Goldstein actually provides a simplified version of the proof of the Incompleteness Theorem.
Rob
Feb 27, 2009 rated it liked it  ·  review of another edition
A persuasive interpretation of Godel as mathematical Platonist rather than as harbinger of modernist anxiety.
Jonathan Fretheim
Mar 31, 2011 rated it liked it
Gödel died a paranoid and lonely man. This book is a bummer.
Daniel S
Dec 30, 2013 rated it really liked it
Shelves: favorites
Sad at the end. So sad.
Micah
Feb 14, 2016 rated it it was amazing
This book is perfectly balanced between the historical and analytical. The last line in the book was worth all the effort and shoots the book up several layers of appreciation.
Abdullah Başaran
Such a disorderly depiction of Gödel's life and theorems. Old-school hilarity and weird citation style that needs further ado. ...more
Dylan Siebert
Jan 18, 2021 rated it liked it
I wanted to rate this book higher than I did, but I had to admit that that was because of the subject matter rather than the writing itself. Kurt Gödel, said to be the greatest mathematician of the twentieth century, the greatest logician since Aristotle, and the dearest intellectual companion of Albert Einstein, published his famous incompleteness theorems in 1931, when he was twenty-four years old. These two related proofs effectively ended one major field of mathematical endeavour and opened ...more
Gabriel
Abandoned it, actually. Dense reading, maybe next time I get it back
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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.

After e
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