Talk:Gödel's incompleteness theorems

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I think that when I created this earlier (effing rollback) I did call it theory but wp uses theorem. SJGsjg 20:16, 15 September 2007 (EDT)

Number theory[edit]

I thought the theorem applied to ZFC set theory. - π 22:33, 28 March 2010 (UTC)

It applies to all theories, including ZFC set theory, which include arithmetic. (Provided that they are formalized in the appropriate way.) There are other theorems which apply specifically to set theory, such as the theorems that the axiom of choice and the continuum hypothesis can neither be proved nor disproved. I'll see if I can add a line or to the article which clarifies that. Thanks. TomS TDotO (talk) 10:07, 29 March 2010 (UTC)

Multiplication?[edit]

I always thought induction (or in ZFC, replacement and specification) was the big "gotcha" in this, since it's impossible to express in first-order logic, so you're left with statements that can't be finitely defined. Sake Fueled (talk) 13:07, 22 October 2011 (UTC)

Godel Unknotted[edit]

You might want to check out my refutation of Godel's Incompleteness Theorem at: Godel Unknotted. It's kind of interesting. — Unsigned, by: 208.83.126.102 / talk / contribs 19:51, 7 April 2015‎ (UTC)

Ugh, the formatting on that wiki was just too awful. I know this sounds immature, but the way the text was structured undermined my ability to take it seriously. If you weren't claiming to refute one of the most famous theorems in mathematics, I'd probably have made more effort to try to figure out what you were saying, but as it stands, I just couldn't bring myself to try. Is that unfair? ikanreed You probably didn't deserve that 19:59, 7 April 2015 (UTC)
Given as none of the brand new notation is defined, I'd call that an acceptable request for clarity. Like that is so unreadable I don't even know WHICH of the two you're claiming to refute. PacWalker 20:04, 7 April 2015 (UTC)
This may be of use. PacWalker 20:05, 7 April 2015 (UTC)
I'm hoping (or maybe !hoping) this is just an artifact of your formatting, but does the final "look what I did!" read something like
( \lnot (A \leftrightarrow B)) \leftrightarrow (A \nleftrightarrow B)
^this? PacWalker 20:21, 7 April 2015 (UTC)
Gödel would have scratched his head and then demolished the argument. Sorte Slyngel (talk) 18:14, 10 December 2015 (UTC)

Gödel and God[edit]

Someone with a better understanding of Gödel's theorems may have come across something like: Gödel says there are unprovable but true theorems, hence any logical discussion of God is futile. (Yes, this has been stated, but I saw it so long ago, that I can't remember where.) So that would mean that God is an improvable theorem in an arithmetical system. Is it worthwhile to mention this in the article? Cheers Sorte Slyngel (talk) 20:36, 9 December 2015 (UTC)

I added a paragraph, though honestly this argument is so out there that my first reaction was "what, seriously?" - LucidFox (talk) 08:13, 10 December 2015 (UTC)
Thanks for taking care of that. I saw this argument so long ago that I've forgotten where, but my reaction was precisely the same as yours - that is WTF. But there is nothing so far out, that somebody doesn't claim it as truth. :-) Sorte Slyngel (talk) 18:08, 10 December 2015 (UTC)

Gödel and the constitution[edit]

From a mention in a magazine I was reading, came to [1] - with a link to the pdf. What was the flaw? Anna Livia (talk) 00:41, 17 December 2018 (UTC)

That is an excellent question, @Anna Livia. I ran into this story while reading a book about Albert Einstein a while ago. I searched for further information on what Godel thought was a flaw in the U.S. Constitution so serious the U.S. herself could become a dictatorship. I never succeeded. :-( Nerd (talk) 01:28, 17 December 2018 (UTC)
To clarify - the article mentioned G's comment - I looked for a link suitable for RW.
Given that KG was Austrian and into incompleteness (albeit of a different kind), and it was 'the time of the bellicose dictators' - could it have been that the US constitution did not provide a sufficiency of methods for containing or removing a President who was becoming dictatorial but #superficially# remaining within the apparent spirit of the constitution.
Should this exchange be copied over to the US Constitution talk page? Anna Livia (talk) 10:56, 17 December 2018 (UTC)
@Anna Livia Good idea! Please do! Nerd (talk) 16:25, 19 December 2018 (UTC)
'Category of occasions where it is best to ask first - if you rearrange/clarify on the UCS page. Anna Livia (talk) 23:47, 19 December 2018 (UTC)