Talk:Gödel's incompleteness theorems
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)
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)
- 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)
Gödel and God
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)
Gödel and the constitution
- 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)