Talk:Kurt Gödel
Was Kurt really Austrian-born? I think this will always be problematic. You could probably also say he was Czech-born or Austro-Hungarian-born. As far as I know Brunn was at that time part of Austria which was in turn part of the Austrian-Hungarian empire. I'm not sure how Czech or Austrian the parents of Kurt were (or considered themselves) but the fact that he was sent to a German-speaking school may be a hint. Anyway, if you think you have good arguments to change this, please do. :-)
-- Jan Hidders July 10 2001
I don't know German very well but is Der Herr Warum correct ?
--Kpjas
I speak a little German, (I watched a lot of Sesamstrasse as a child :-)) and it is certainly correct. You can check for yourself:
-- JanHidders
What is Goedel Number ? Taw
A Goedel numbering is a scheme (with certain nice properties) which associates logical formulas with numbers, so that instead of talking about strings like "(phi or psi) -> tau " you could talk about numbers that prepresent them instead. Once a particular Goedel numbering is fixed, a Goedel number of a particular logical formula/statement is the natural number that represents it according to the numbering. Why? --AV
Because some page on wiki (Light Bulb Jokes) has link named Goedel Number that points to Kurt Godel page. Taw
The links would best point to Gödel's incompleteness theorem where the concept is explained. Or we could write a separate article. --AxelBoldt
I'd support a separate article, it will make linking easier, and sometime somebody may want to talk about Godel numbers without getting into the whole incompleteness theorem. Perhaps the Godel Number page could just be a semi-short definition with links to Kurt Godel, and to the Incompleteness theorem, that way if there are other uses for Godel numbers than the proof of the incompleteness theorem we could have links to those pages as well. It certianly seems like there should be other uses for Godel numbers, but this is not my area and I don't really know anything about them... MRC
You're right, there're other uses, although they may be too advanced for Wikipedia. I agree that it should be a (short) article on its own. --AV
- It also implies that a computer can never be programmed to answer all mathematical questions.
I'm not sure this is the case. It implies that you cannot choose a formal system and then simply work out all its consequences, and as a result get the answer to all mathematical questions -- thus it proves that one potential way of a computer answering all mathematical questions doesn't work. But in the general case it's an open question whether computers are in principle capable of more or less intelligence than humans, and so this can only be said conclusively if either the AI question is resolved, or it is shown that it is in principle impossible to answer all mathematical questions (whether the answering is done by a human, computer, or something else). Delirium 04:07 1 Jul 2003 (UTC)
It's misleading. 'Answering all mathematical questions' is like running through a recursively enumerable set - can be done if you have an infinite supply of CPU cycles and don't mind waiting infinitely long.
Charles Matthews 04:37 1 Jul 2003 (UTC)
I have removed the sentence Charles Matthews objects to but not because it is wrong. The far more general point is true. The theorem does not only imply that computers cannot answer all mathematical questions; it implies people cannot either and, more than that, it implies that some mathematical questions are unanswerable. The sentence I have removed was written by someone who does not fully understand this theorem. Godel is often trotted out to support an anti-AI point of view, I suspect that that is what has happened here.
Psb777 09:44, 10 Feb 2004 (UTC)
- I respectfully disagree. The remark is IMO correct and relevant and therefore should stay. What the motives were of the one who wrote it is simply irrelevant. In fact, it could very well have been me that put it there, and I hold no such view. Removing correct information from an article in Wikipedia requires more justification than that. -- Jan Hidders 17:30, 12 Feb 2004 (UTC)
You would be right if the "correct" thing I removed was not just a small part of the truth. But I said it was not wrong which is not quite the same thing as saying correct. There are a lot of consequences of Godel's theorems, the interpretation I removed was not wrong but it was misleading. Why are not all the consequences of the theorem listed? [Because there are pages for the theorems!] Why this one (sub-)consequence? If the comment goes back then the general point must be what is replaced, not one that is needlessly computer specific. Paul Beardsell 07:16, 13 Feb 2004 (UTC)
- I don't agree that it is needlessly computer specific, and I would argue that it is the most important consequence from which almost all other consequences follow. In fact, it is essentially equivalent with the first theorem, so calling it "a small part of the truth" is, well, a bit misleading :-). Moreover, it illustrates why this is such an interesting theorem, so it certainly has its place there. If you don't like how it is worded, then by all means reword it, if you think it is too specific then make it more general, but removing statements from Wikipedia should always be done with the greatest care. So, since we have to stick to NPOV I will put it back and reword it a little so it reflects a bit more your point of view, even though I in fact disagree. Let me know if you find this unacceptable. -- Jan Hidders 10:28, 13 Feb 2004 (UTC)
I like your new wording. What part of it do you disagree with? And I'm being needlessly argumentative, now that you have crafted wording with which I agree, but in what way is the statement "It also implies that a computer can never be programmed to answer all mathematical questions" not computer specific? And, this quesion from interest only, do you think that the brain is capable of evaluating a super set of the algorithms which a computer can evaluate? Paul Beardsell 14:23, 13 Feb 2004 (UTC)
- Good, I'm happy you like the new wording. What I myself don't like about it, is that it now is a bit academic and abstract. The answer to your last question is "extremely unlikely and without any evidence whatsoever". However, I don't think there is a definitive proof that shows that a human brain or all humanity as a collective cannot do noncomputable things. -- Jan Hidders 13:05, 14 Feb 2004 (UTC)