Gödel's Proof

noufalibrahim · 2022-11-14 · Original thread

A few of them.

1. This book made all the patchwork ideas I had about the incompleteness theorem fall into place and click while I was doing my bachelors https://www.amazon.in/Godels-Proof-Ernest-Nagel/dp/081475837...

2. This similarly solidified a lot of patchwork ideas I had about money https://www.amazon.com/Money-Unauthorized-Biography-Coinage-...

3. This didn't make the topic click but it shed light on the entire landscape after which anything I read on unicode made sense and filled up my mental map of the whole area https://www.joelonsoftware.com/2003/10/08/the-absolute-minim...

alok-g · 2021-06-17 · Original thread

Does either (claims to) explain the proof itself in it's full glory? I had read "Godel's Proof" by Ernest Nagel et al [1] and it fell short.

[1] https://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/08147583...

eindiran · 2020-07-14 · Original thread

For a detailed perspective on how the proof works, I highly recommend Ernest Nagel and James Newman's book Gödel's Proof [0], mentioned in the article. Alternatively, Gödel Escher Bach by Douglas Hofstader is a classic which serves as a great (and more accessible) introduction to the proof [1].

[0] https://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/081...

[1] https://www.amazon.com/G%C3%B6del-Escher-Bach-Eternal-Golden...

wellpast · 2019-09-04 · Original thread

Here's a good adjacent read that I thought was a much clearer and relatively accessible tour through the Proof - https://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/081... - it's more of a pamphlet than a book, really.

undershirt · 2018-10-01 · Original thread

I couldn't make it through GEB, but I read a good concise explanation in a book called Godel's Proof: https://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/081...

mindcrime · 2018-07-13 · Original thread

A few recommedations:

1. Black Like Me - John Howard Griffin - https://en.wikipedia.org/wiki/Black_Like_Me

2. More Matrix and Philosophy - William Irwin (ed) - https://www.amazon.com/More-Matrix-Philosophy-Revolutions-Re...

3. Godel, Escher, Bach: An Eternal Golden Braid - Douglas Hofstadter - https://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach

4. The New Jim Crow - Michelle Alexander - https://en.wikipedia.org/wiki/The_New_Jim_Crow

5. Capitalism: The Unknown Ideal - Ayn Rand - https://www.amazon.com/dp/0451147952/ref=sspa_dk_detail_4?ps...

6. The Fountainhead - Ayn Rand - https://en.wikipedia.org/wiki/The_Fountainhead

7. The Book of Why: The New Science of Cause and Effect - Judea Pearl - https://www.amazon.com/Book-Why-Science-Cause-Effect/dp/0465...

8. The Education of Millionaires - Michael Ellsberg - https://www.amazon.com/Education-Millionaires-Everything-Col...

9. The Silent Corner, The Whispering Room, and The Crooked Staircase - Dean Koontz - http://www.deankoontz.com/book-series/jane-hawk

10. Godel's Proof - Ernest Nagel & James Newman - https://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/081...

11. After Dark - Haruki Murakami - https://www.goodreads.com/book/show/17803.After_Dark

pvg · 2018-07-05 · Original thread

https://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/08147583...

Can be read in a couple of hours and you'll know as much about Goedel's work as any GEB reader. Nowadays even comes with a Hofstadter intro but no bulk or talking animals.

rintakumpu · 2018-02-20 · Original thread

I'd highly recommend "Gödel's Proof" by Ernest Nagel and James Newman (https://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/081...). It'll probably require a bit of patience to go through, but should be fairly accessible to reader without an extensive mathematics background.

simondedalus · 2016-10-21 · Original thread

I don't mean to be rude, but this objection only seems handwave-y if you don't understand Gödel's proofs (common), or you have some refutation of them (obviously uncommon, but definitely interesting).

This is a good not-too-technical but not-condescending explanation https://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/081... (it does get into the technical details; it just doesn't go line by line as you would if you wanted to recreate the proofs).

As long as you have the expressive power of Peano arithmetic (which all programming languages ought to, and definitely all proof systems ought to), you can find a Gödel sentence in the system and thus prove that it can't prove, of itself, "x is consistent".

It's worth looking into, if only for the enjoyment.

agentultra · 2013-12-18 · Original thread

I always found the study of logic to be very interesting. What I highly recommend reading first, however, is a layman's introduction to Gödel's Incompleteness Theorem [1]. The essential idea is, much like the conclusion in this article, that axioms are chosen and theorems are proven within the systems they create. The caveat is that no system can be proven to be complete.

[1] http://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/081475837...

giardini · 2013-10-24 · Original thread

GEB was a considerable waste of time and contributed nothing to my understanding of intelligence or AI. The time would have been be better spent elsewhere.

If you want to understand Godel's proofs then I recommend the book "Godel's Proof" by Ernest Nagel and James R. Newman:

http://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/081475837...

Instead of Hofstadter's GEB, read some of his papers, e.g., "Analogy as the Core of Cognition" http://prelectur.stanford.edu/lecturers/hofstadter/analogy.h...

But there are others who have focused longer on analogy, e.g., George Lakoff:

"Metaphors we Live by"

http://www.amazon.com/Metaphors-We-Live-George-Lakoff/dp/022...

"Where Mathematics Come From: How The Embodied Mind Brings Mathematics Into Being":

http://www.amazon.com/Where-Mathematics-Come-Embodied-Brings...

"Women, Fire, and Dangerous Things"

http://www.amazon.com/Women-Fire-Dangerous-Things-Lakoff/dp/...

jfb · 2013-09-30 · Original thread

For anyone looking for a brief, accessible explanation of the proof itself, I cannot recommend the Nagel and Newman [1] highly enough.

[1] http://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/081475837...

wicknicks · 2013-08-09 · Original thread

Oh wow! This is a great write up on Godel's work. Anybody who even vaguely cares about fundamentals of computer science should definitely give it a read, and if possible a thorough read.

Slightly related: Although a more technical/deeper discussion, but the book "Godel's Proof"[1] by Nagel and Newman is a very approachable text in this domain, and explains many aspects of the incompleteness theorems.

[1] http://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/0814...

alok-g · 2013-06-24 · Original thread

After reading the book, would I have some understanding of the actual proof, or learn mostly the historical context around it?

Note: I have felt deceived after reading Godel's Proof [1] since the authors claimed in the preface to have given an outline of the complete proof in the last chapter but did not (it was grossly incomplete). I am still indebted to the book though for teaching me how to think about pure mathematics.

[1] http://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/0814...

brown9-2 · 2012-06-24 · Original thread

Thanks for the recommendation, this sounds fascinating. By any chance have you also read "Godel's Proof" by Ernest Nagel and James Newman? http://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/0814... It sounds very similar in scope.

jstclair · 2012-01-22 · Original thread

Haven't read that one, but I try to re-read Nagel and Newman's at least once a year: http://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/081475837...

One thing I love about N&N is that it's short (160 pages) and the paperback is cheap ($7.65) so that I have no compunctions in lending it out.

giardini · 2011-12-28 · Original thread

GEB is a very large book with a small message. I do not recommend it. It is mostly an accumulation of the observations of metaphors and analogies by the author. Yes, I read the book but I found it very disappointing.

If you want to learn about Goedel's work then instead read a book that is much shorter and to the point:

"Godel's Proof by Ernest Nagel

http://www.amazon.com/Gödels-Proof-Ernest-Nagel/dp/081475837...

nkassis · 2010-11-27 · Original thread

You're doing exactly what you need to do, you are putting extra effort into it.

My feeling is the "bad" cs grads usually did not put in that extra effort. Reading GEB is rarely a required par of any CS degree but reading it is an incredibly useful thing in my view. It's a thick book and takes commitment to read.

Side note: Check out this book (http://www.amazon.com/G%C3%B6dels-Proof-Ernest-Nagel/dp/0814...) on Godel's proof. It's been updated by Doug Hofstadter the author of GEB. I found it pretty good. Read it slowly, two three time if needed. It will make sense.

emacdona · 2008-09-10 · Original thread

I read this little gem over the summer: Godel's Proof (http://www.amazon.com/Godels-Proof-Ernest-Nagel/dp/081475837...)

At 160 pages, it's the ideal size to carry with you everywhere you go. All summer long, any time I had an extra half an hour, I would take it out and read/re-read a chapter.

ISBN: 0814758371