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Contents 1 Goethe's Criticisms of Newton 2 statement of theorem 3 birth 4 Der Herr Warum 5 Goedel Number 6 Computer vs Computable 7 Pronunciation 8 Brno or Brünn? Or both? 9 greatest logicians of all time? 10 On psychological disorder 11 NPOV violation removed 12 The constitutional loophole 13 What Religion was Godel? 14 Asperger's Syndrome 15 I plan to add citations to the biographical information 16 Editing needed 17 Timeline 1938 to 1940 and the consistency results for AC and CH 18 Gödel citizenship hearing -- explaining my edit 19 Interesting work 20 Inconsistency 21 Structural cleanup 22 "Dangerous knowledge" show 23 Pronunciation of Kurt

[edit] Goethe's Criticisms of Newton

it says in his biography that he studied Goethe's criticisms of Newton. I thought some would find it useful to know the specific Criticisms of Newton Goethe constructed at such sites as http://rsc.anu.edu.au/rscnews/year1998/aug98/auggoethe.html and this book http://www.amazon.com/exec/obidos/ASIN/0521531322/thegermawayandmo

this is a very fascinating aspect of Godel that has been largely overlooked. A great scholar should create a wikipedia entry on these criticisms and then link this part of Godel's bio to it.

see the article Theory of Colours. —Preceding unsigned comment added by 207.241.238.233 (talk) 03:39, 28 November 2007 (UTC)

[edit] statement of theorem

"any self-consistent axiomatic system powerful enough to describe integer arithmetic will allow for propositions about integers that can neither be proven nor disproven from the axioms. "

integers, or natural numbers? Gödel's incompleteness theorem says natural numbers.

-- John Joseph Bachir 23 sept 2004 (after taking a formal language and automata exam...)

[edit] birth

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

[edit] Der Herr Warum

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:

• http://www.math.ucla.edu/~rfioresi/hc41/Goedel.html
• http://www.math.twsu.edu/history/Men/godel.html

-- JanHidders

[edit] Goedel Number

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

[edit] Computer vs Computable

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)

There isn't a definitive proof that there isn't reincarnation either. Paul Beardsell 01:04, 16 Feb 2004 (UTC)

There is however definitive proof that this discussion is over, if ever it started. ;-) Remember that Wikipedia is not a discussion forum and contributions should be made in the spirit of cooperation. Trying to lure people into little debates is usually not very productive. Good luck with your other contributions to Wikipedia. -- Jan Hidders 23:45, 16 Feb 2004 (UTC)

This page is the discussion forum for the article. Paul Beardsell 23:11, 17 Feb 2004 (UTC)

---

I am disappointed that the discussion has not continued. Upon reflection I agree with Jan Hidders that his new wording is academic and abstract. We have gone from something which was partially correct and perfectly understandable albeit misleading to something which is correct but jargon. I intend to replace the current text as follows. This removes the perceived anti-AI slant whilst maintaining readability. I propose we define computable and to do so elsewhere - and I hope the link I have used is considered adequate.

Comment to Aleph4 march 21 Thanks for your prompt reaction. I was prepared to wait four weeks for the first reader. The word ‘specific’ in my text seems to be misleading. So please omit it. The n in Gödels Z(n), itself not a symbol of System P, stands there for any positiv whole number out of the infinite sequence 0, f0, ff0, fff0, ...... etc. Another error that I just see in my text lies in my description of the number representations: evidently, the symbols f have to be put in front of the symbol 0 (zero) and not x ! Sorry, I must have slept! The symbol y in Gödels Z(y) however is a symbol of the System P, it stands there quite for itself, not for anything else, and, again I have to correct myself, its Gödel-number in Gödels paper is 19, my 13 comes from the Nagel-Newman booklet, from where I anyway assumed the way of writing the formulae to get them on a single line of typing. Yours Ginomadeira

Then: It also implies that a computer can never be programmed to answer all mathematical questions

Currently: It also implies that the set of truths about natural numbers is not recursively enumerable, which means that there is no algorithm that can enumerate all these mathematical truths.

New: It also implies that not all mathematical questions are computable.

Paul Beardsell 03:34, 22 Feb 2004 (UTC)

I do not see any meaning in It also implies that not all mathematical questions are computable. How can a question be computable?

There are two ways (well ... infinitely many really) of phrasing the incompleteness theorem:

1. There is no axiom system that generates all mathematical truths.
2. There is no computer program that lists all mathematical truths.

Of course the two are equivalent, but the equivalence is itself an interesting fact. The first of these is already in the article: These theorems ended a hundred years of attempts to establish a definitive set of axioms to put the whole of mathematics on an axiomatic basis... Why not use the sentence It also implies that a computer can never be programmed to answer all mathematical questions for the second? Aleph4 00:30, 11 Feb 2005 (UTC)

[edit] Pronunciation

This so-called English pronunciation IS nonsense. RickK | Talk 07:32, 19 Mar 2004 (UTC)

OK, but how does one pronounce Goedel? Is it more gurdel than girdel? Paul Beardsell 08:18, 19 Mar 2004 (UTC)

There is no "r" sound in Gödel. There may be none in "gurdel" or "girdel" either for Paul Beardsell but there will be for many English speakers. Informal pronunciation guides like this are problematic, though I understand the need for conveying the sound of the "ö". BrendanH 11:37, 31 Mar 2004 (UTC)

In the absence of a change, I have edited the pronunciation guide. However, I feel my version and the previous version are both worse than nothing. Mine is too fussy, the previous version is simply wrong (because it does not work for many English speakers). Someone should delete both. BrendanH 11:15, Apr 8, 2004 (UTC)

Ok, I deleted both :-) linking to the 'rhotic' page was a nice idea, but apart from still not yielding the correct pronounciation it's also quite unwieldy (AC, 23:04, 9 Apr 2004)

This is all very interesting but I am at a loss: How does one pronounce "Go:dl"? Is that supposed to be SAMPA? Paul Beardsell 15:13, 10 Apr 2004 (UTC)

The correct pronounciation can be heard here. Curiously enough, there are two different pronounciations of which only the one labeled '...godels01.wav' (watch your browser's status bar) comes reasonably close (AC, 16:59, 18 Apr 2004)

---

If it were provable it would be wrong, so one could prove wrong statements in this system.

Is some punctuation missing here ?

Shyamal 11:12, 8 Apr 2004 (UTC)

There is an often-repeated story about Godel's US citizenship interview, during which he began to describe the loophole he had found in the US Constitution, whereby the USA could be (legally) transformed into a dictatorship.

See for example this post from sci.math

1. Is it worth making some mention of this curious biographical detail in the article?

2. Is it recorded anywhere just what this "loophole" was? I have seen the anecdote in a number of different versions, but never any indication of how Godel's discovery was supposed to work.

User:Stuart Presnell

It's very important to view Godel's fears within a historical context, which the author of the entry failed to provide. Godel had just witnessed Nazi Germany be transformed from a functional democracy into a hated dictatorship; and they gained their power partly because of a loophole in the German Constitution that made the Nazi takeover legal on paper, if not in practice.

Godel may have been an eccentric person, but he wasn't just being an eccentric. He'd just seen one country (legally) transformed into a dictatorship. He had no reason to assume it couldn't happen again. Warning the judge about it probably sounded like his civic duty as a potential citizen.

[edit] Brno or Brünn? Or both?

Where was Gödel born?

1. Brno
2. Brünn, now Brno
3. In a city which is now (2005) known as Brno in the English-speaking world, but which in his time (at least by him and his family) was called "Brünn".

I think that (1) is misleading, and (3) is too verbose, so I prefer (2), which really is an abbreviation for (3). Please do not remove "Brünn" without explaining it here. -- Aleph4 23:40, 9 Apr 2005 (UTC)

In fact the only misleading proposal is (2) suggesting nonexistent renaming from Brünn to Brno. He was born in the city called Brno in Czech and Brünn in German. Since his family was German-speaking he most likely called his hometown "Brünn", but it doesn't make the Czech name (from which the German version was once derived) less valid or less English. My proposal (4) is therefore "Brno (Brünn)" with the Czech and present-day English name in the first place and the German name with which he is also associated in parentheses. Qertis 10:09, 18 Apr 2005 (UTC)

I think it should remain in the current form (X in A, now Y in B). This is standard all over the English Wikipedia. We have to include A (here Austro-Hungary) to give information on his nationality at birth. If X (Brünn) was the then-official name of the place, we should give that too, as a matter of record. Charles Matthews 18:37, 18 Apr 2005 (UTC)

I am sure that it was an official name, but perhaps not the (i.e., the only) official one. According to Meyer's 1886 encyclopedia, the city had in 1880 "82660 inhabitants, among them 60% Germans, 40% Czechs, and 5498 Jews". (I see, so Gödel was really German after all, just like Mozart... :-)

But I am sure (again without being able to prove it) that Gödel's certificate said Brünn, not Brno. -- Aleph4 23:41, 18 Apr 2005 (UTC)

[edit] greatest logicians of all time?

As it stands, the article states in its introduction, "...Kurt Gödel was perhaps the greatest logician of the 20th century and one of the three greatest logicians of all time with Aristotle and Frege..."

I find this statement astounding. I am not aware that his work, or even his analysis of mathematically incomplete systems, raised him to the ranks of one of the "three greatest logicians of all time", or even the greatest in the last century (List_of_logicians). Can we have some credible citation for this, or discussion? FT2 18:33, August 28, 2005 (UTC)

• It's definitely POV, but I at least agree with "perhaps the greatest logician of the 20th century." His work was one of the most important turning points in all of mathematical history. — brighterorange (talk) 15:30, 13 October 2005 (UTC)

I'm not sure that having a major impact makes someone "the greatest" in their field. Maybe "one of the most significant". Greatness, to me, implies more than just making a discovery that is a turning point, especially when taken as a whole others have had many more also-significant discoveries. I'm just thinking that "greatest" is POV. Will edit to something more suitable. FT2 09:46, 14 October 2005 (UTC)

I suppose people talk about mathematical logic. Mathematical logic is a well established area of Mathematics. Gödel was probably the greatest mathematical logician of all times. And he did not just stumble about one important discovery. He produced most fundamental work in all areas of mathematical logic. (Even more fundamental than the popular incompleteness thm is the completeness thm, he showed fundamental results about recursion theory, intuitionism and set theory as well.) Another question is his relevance or "greatness" in philosophy (in particular philosophical logic or philosophy of Mathematics). I cannot comment on this. 131.130.190.55 22:02, 24 January 2006 (UTC)

I have to agree: it's not just Hofstader hype: the rumor is true. Gödel really can be called the most important logician of all time, and even one of the most influential thinkers of all time. It does not seem inappropriate to link his name with Aristotle and Plato, although the canon of his most important work is slender by comparision. I think everyone who has encountered his incompleteness theorem must agree that this represents one of the most profound insights yet accomplished in the realm of logic, even one of the most profound insights in the realm of mathematics and philosophy in general. Incidently, although this might sound like a silly joke, no kidding, in logic his [Godel's Completeness Theorem completeness theorem] is equally fundamental.

However, overall, I wouldn't disagree with the proposed change, greatest -> most significant, since IMO any attempt to well order the panooply human achievement quickly becomes silly.---CH 02:18, 27 March 2006 (UTC)

The statement that Gödel was "the greatest logician since Aristotle" is by John von Neumann, as reported by Herman Goldstine in The computer from Pascal to von Neumann. Eubulide 18:36, 23 June 2006 (UTC)

Just because FT2 doesn't agree with something, doesn't mean it isn't true. However, the real point is not FT2's apparent ignorance of Gödel's significance but the purely technical one that it's not for wikipedia editors to declare Gödel the greatest anything; just to report what a significant body of credible opinion thinks of Gödel's achievement. If John von Neumann called him the greatest logician since Aristotle, I'm not going to argue that von Neumann was overrating him, because von Neumann was a giant among mathematicians and I am not a mathematician at all. However, von Neumann is only a start. It could also be pointed out that the economist Oskar Morgenstern, the physicist Albert Einstein and the logician Stephen Kleene had the very highest opinions of Gödel's work. Lexo (talk) 01:01, 4 July 2008 (UTC)

[edit] On psychological disorder

In the section on psychological disorder it is claimed that Gödel "received an anxiety neurosis" three or four years before suffering from rheumatic fever. Since the latter happend when he was six or seven, he would have been three when he had neurosis. This sounds very unlikely: can we have a reference for that information? Similarly, reference is needed for the assertion that he may have had paranoid schizophrenia. Eubulide 19:10, 21 June 2006 (UTC)

I've never come across any references to paranoid schizophrenia in his context. He was definitely a hypochondriac and suffered from several nervous breakdowns over the course of his life, but schizophrenia is a new one on me. —Preceding unsigned comment added by 71.191.118.228 (talk) 11:32, 20 July 2008 (UTC)

[edit] NPOV violation removed

I'm removing the following from the main page as POV:

However, Godel's most revolutionary revision of everyday views of our world, though never substantially popularized--and still predominately rebuffed by the scientific community--was his mathematical proof that the past retains an accessible location in the physical world [to which a space ship can travel at the speed of light.] While the physics community largely acknowledged Godel's proof as valid, it still engages in attempts to invalidate Godel's shocking conclusion. One example is, for instance, in Stephen Hawking's "chronology projection conjecture," which is specifically designed to set aside Godel's revision of our world view--a postulate which nevertheless acknowledges the seriousness of Godel's challenge. In the words of author Palle Yourgrau, while Albert Einstein turned time into space, Godel "made time disappear." [Source-- A World Without Time: The Forgotten Legacy of Godel and Einstein, Palle Yourgrau, Basic Books, 2005.] Godel's mathematical time proof seems, in fact, somewhat consistent with recent affirmation of dark matter in the universe and the resulting implication that our universe is merely a surface fragment of a larger universe many billions and trillions of times the size of our own. To this day, the man on the street has barely any awareness of Godel's revolutionary proof of the perfect physical endurance of "past" events, even while nearly all educated persons are quite aware of the time-warping relativity theories of Godel's constant Princeton walking companion (Einstein)--from which Godel's time proof emanated. His time proof has therefore achieved that distinctive status accorded only to the most surperlative and disturbing of scientific achievements: to be resolutely ignored.

Apart from being biased it also gives disproportionate attention to a subject that seems very minor. If there needs to be anything on this subject in the article I suggest something like:

"Gödel also found a solution to Einstein's field equations, the Gödel metric." --Tengfred 14:07, 2 August 2006 (UTC)

This para violates not only NPOV but also looks suspiciously like original research. I have read the papers in question and am not qualified to say whether or not they really prove what the author of this para (and Gödel himself) says they prove. I have noticed, however, that the editors of Gödel's Collected Works are cautious rather than wholeheartedly enthusiastic about a lot of his later work. If Gödel had really provided a universally satisfactory proof of 'the perfect physical endurance of "past" events', I think it would have been better publicised by now. In short, I agree with the removal of this para. Lexo (talk) 01:06, 4 July 2008 (UTC)

[edit] The constitutional loophole

Does anyone know what Gödel meant could constitute the framework for a "legal dictatorship" in the US? Marxmax 11:23, 2 October 2006 (UTC)

No. Researchers who examined Gödel's voluminous papers after his death looked specifically for this because of repeated enqueries they'd gotten, and they didn't find anything except some straightforward notes from studying for the citizenship exam. See Dawson & Dawson, "Future tasks for Gödel scholars" [1] p. 155. Maybe this could be mentioned in the article. —Preceding unsigned comment added by 207.241.238.233 (talk) 04:20, 6 October 2007 (UTC)

I know that I've read somewhere a description of what was almost certainly the loophole Gödel discovered in the Constitution, but of course I can't remember where. It was a highly technical and rather unlikely situation which, I seem to remember, necessitated the Vice-President becoming President on the incapacitation or resignation of the incumbent President...I will rack my brain and hunt my shelves to see if I can remember what it was. The description of the loophole came not from looking through G's papers but from studying the Constitution in order to work out what it might have been, so it wasn't necessarily the exact loophole G is said to have discovered. Lexo (talk) 23:27, 19 July 2008 (UTC)

I was probably wrong. I have, however, found stabs at the possible loopholes here, here and here. Hope this was helpful. Lexo (talk) 23:33, 19 July 2008 (UTC)

[edit] What Religion was Godel?

What religion was Godel? He clearly spent some time and effort on proving God's existence (well, beyond reasonable doubt according to the related wiki : ), but what religion was he? --MrASingh 21:33, 14 Feb 2006 (UTC)

I have just added an discussion of Gödel's religion as it's relevant to Gödel's ontological proof to that article, with sources. Perhaps some of it belongs in this article, but I'm not sure where to put it. This is a basically well-written article on an important topic, and I'd like to have a better idea on the right length, focus and position for material on Gödel's religion before editing anything in.

There is an interesting problem in the evidence about the motive behind Gödel's Ontological Proof. Morgenstern's contemporaneous diary entry has Gödel telling Morgenstern that he was an atheist, and that the Ontological Proof was purely an exercise in logic. Ordinarily, that would settle the question -- Morgenstern was perhaps Gödel's best friend at that point and his diary is usually reliable.

The problem is that all the other evidence strongly indicates that Gödel did believe in God. Dawson, Gödel's definitive biographer, states directly that Gödel was a "believer" (p. 6), in fact seems to regard the matter as a settled. Other sources show that Gödel was firmly anti-materialist and believed in an extremely wide range of supernatural phenomena. A fourteen point outline of his philosophy which Gödel left in his papers includes statements of belief in higher beings who live in other worlds and reincarnation. Apparently for Gödel these beliefs were fundamental.

For more see the introduction to Gödel's ontological proof, which gives sources. See the discussion page for that article for my rules of evidence, my reasons for including what I did, and more details on my handling of the evidence problem presented by the Morgenstern diary. --Jeffreykegler (talk) 16:01, 25 February 2008 (UTC)

Godel was definitely religious; there are further details on this point in Hao Wang's book "A Logical Journey: From Godel to Philosophy". He wrote a pair of letters to his mother defending his belief in the afterlife, which (if I recall correctly) can be read in their entirety in Chapter 3 of Wang's book. A highly illuminating excerpt (from page 88) is as follows:

"I went home with Einstein almost every day and talked about philosophy, politics, and the conditions of America. Einstein was democratically inclined. His religion is much more abstract, like that of Spinoza and Indian philosophy. Mine is more similar to church religion. Spinoza's God is less than a person. Mine is more than a person, because God can't be less than a person. He can play the role of a person.

"There may exist spirits which have no body but can communicate with us and influence the world. They stay in the background and are not known [to us]. It was different in antiquity and the Middle Ages when there were miracles. We do not understand the phenomena of deja vu and thought transference. The nuclear processes, unlike the chemical ones, are irrelevant to the brain."

I included the last two sentences because Godel included them in this context; I don't understand them completely, but I can make conjectures. In any event, based on this and other evidence throughout Wang's book, I'm convinced that Godel was strongly religious after his own fashion. That said, I don't think he was of a specific religion of the sort we would recognize -- my opinion on the matter is that we should take him at his word when he says he's "a sort of Platonist" and look for connections with Plato if we have a care to seek such connections. —Preceding unsigned comment added by 71.191.118.228 (talk) 22:57, 19 July 2008 (UTC)

Most sources indicate that he was some sort of unchurched Christian. I know that his wife said that although he didn't attend church, he was still religious and read the Bible in bed every Sunday morning.76.64.9.151 (talk) 07:37, 7 April 2009 (UTC)

I changed things in the article to indicate he is a theist but removed information suggesting he was a Christian. The currently cited sources in this and related articles only appear to support him as a theist. Being baptized as a Christian does not mean you should be classified as one. Lonjers (talk) 07:32, 7 July 2009 (UTC)

It's an interesting point -- clearly he was a theist, and clearly his spiritual tradition was Christian, and he does not seem to have ever renounced that tradition. I agree it doesn't really follow that his beliefs were Christian, and a lot of his remarks on the subject suggest that his beliefs may not have been that specific. So it's a bit ambiguous. But I think lots of bios probably report their subjects' religious traditions rather than necessarily their beliefs. --Trovatore (talk) 09:56, 7 July 2009 (UTC)

[edit] Asperger's Syndrome

That comment about Godel having Asperger's syndrome in uncited and almost certainly wrong... Asperger's syndrome does not cause paranoid delusions. I don't know that Godel was ever diagnosed with anything, but paranoid schizophrenia seems more likely a culprit than Aspergers 71.229.63.50 20:27, 22 September 2007 (UTC)

[edit] I plan to add citations to the biographical information

I have started adding citations for the biographical information. I've just finished a novel centering on a part of Gödel's work, which I carefully researched (the novel took me 5 years to write, 3 of them full-time). So I'm freshly familiar with the sources.

This article is fairly accurate and that, while it is unsourced, I believe most of the facts in it can be sourced, many others can be sourced with slight changes, and very few are likely to prove unsourceable.

Adding sources to a text you've written is almost as hard as writing it. Adding sources to text that others have written may be harder. In particular, there's the question of how to deal with material you can't source. Editors are supposed to be bold, but assuming something is unsourced just because I don't know of a source for it is bolder than I care to be. I will follow this procedure:

I'll mark text I can't source like this^{[citation needed]}. In a separate section on this talk page, I'll explain the nature of my problem. For example, I might not believe the "fact" has a source. Or I might suspect that it does, but be unable to find it. If I get no feedback, I'll use my best judgment.

My guidelines for sources: I'll be fussy about sources, but I think properly so. In researching Gödel time and again I'd read the 36th slightly different version of the same "fact" about Gödel. When I was in Grad School, Gödel was still alive and much talked about. None of what I was told can be sourced and I suspect all of it was untrue. Therefore:

1. I use secondary sources only where they were carefully edited from a biographical standpoint. This excludes even otherwise carefully edited textbooks as evidence. It also excludes most biographical treatments of Gödel. Among the secondary sources, I have learned to trust only Dawson 1997 (Gödel's definitive biography) and the apparatus in Gödel's Collected Works .

2. Mathematicians may be lousy biographers, but they tend to be good witnesses. I regard any primary source as good evidence for what the author witnessed. So, for example, Hao Wang's books are extremely important sources because he knew Gödel well. But Hao Wang also included a lot of other material. I treat as evidence what Wang personally witnessed, and what he has a source for. I discount everything else. --Jeffreykegler (talk) 15:56, 27 February 2008 (UTC)

So far I've gotten very little done on this. Other projects (professional & family) took up the time. I'm traveling to California soon, so over the next weeks I won't be able to do much either. Sorry. --Jeffreykegler (talk) 11:40, 22 June 2008 (UTC)

[edit] Editing needed

As I translated the article (and compared it to other good articles) I noticed there is some "confusion" in it´s structure. Almost all of the information about his work is included in the section of his life. The article may benefit from being splitted in one section for his life, and one separate section about his works, wich is the pattern followed in most other entries.--Loyan (talk) 06:28, 26 March 2008 (UTC)

Of the 4 math featured articles, 3 do seem to separate out life history from contributions. What are the good articles you're using as models? Anyway, I certainly do agree this article could and should be written better, and could benefit from reorganization. --Jeffreykegler (talk) 22:48, 26 March 2008 (UTC)

Well there are several: The one on Hilary Putnam is quite good, Foucault, Pascal and not only philosophers, it seems to be the favoured structure, but I know it might sometimes be difficult to separate life from work. By being separate in allows for a more in depth treatment of the work and also allows for a strictly biographical reading for persons who are not concerned with the complexities of the work.--Loyan (talk) 23:24, 26 March 2008 (UTC)

US CITIZENSHIP INTERVIEW, FREE THINKER, BEGINNERS GUIDE After a search on ENIAC I came to Neumann then Godel on Wikipedia.

During the immigration interview Godel must have been attempting to answer as truthfully as possible. He was indicating what we know to be true today. A president could create a dictatorship akin to NAZI Germany (akin to Mugabe in the former Rhodesia).

Key was his openness, which is what free thinkers do. Clearly Godel was not concerned with any form of "Restraint". I would like to see Godel for beginners type links as I am fascinated now. The Chain here is excellent (thank you all) Many people when subjected to official process never question it, clearly Godel Did, with the comment that potentially elections and presidential control would be possible, after all look at elections in Zimbabwe, the US was nearly the same when Dubbyah was elected. Kurt was not wrong! I hope his spirit is reading over my shoulder as I type this wiki

 I dont know if his mother was jewish, but Muzel Tov / God Bless anyway 

Kind Regards dsm@kesgrave.net

[edit] Timeline 1938 to 1940 and the consistency results for AC and CH

According to the article, after moving to Princeton in March 1940,

Gödel very quickly resumed his mathematical work. In 1940, he published his work Consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory which is a classic of modern mathematics.

An article by Gödel with the title "The consistency of the axiom of choice and of the generalized continuum-hypothesis with the axioms of set theory" was published in Proceedings of the National Academy of Sciences of the United States of America already in December 1938 (Volume 24, issue 12, pp. 556–557). Lecture notes with the title "The Consistency of the Continuum Hypothesis" were published in September 1940 in the Princeton series Annals of Mathematical Studies. Is there some confusion here?  --Lambiam 12:04, 4 May 2008 (UTC)

Looks to me like the NAS article was a 2-page notice of the result, while the much longer Annals paper was the formal proof. Both are reprinted in vol 2 of Gödel's collected works. 75.62.4.102 (talk) 03:58, 25 August 2008 (UTC)

[edit] Gödel citizenship hearing -- explaining my edit

I've edited this rather heavily, and re-sourced it. I did considerable research on this story for my novel, and read many different versions of it. It's clearly turned into a legend.

The only solid basis for this story is Morgenstern's diary entry, which is cryptic and unsatisfying. Every reteller fleshes the story out considerably, usually with dialogue and narrative of their own invention. The only careful account is in Gödel's scholarly biography, by Dawson. Dawson interviewed Morgenstern's widow to flesh out the story. She wasn't there, so what she says is hearsay and Dawson normally doesn't use that kind of source. Dawson was not willing to simply let this story disappear as unsourceable.

Dawson is the most careful source for this story. All other versions are based on Morgenstern, Dawson and things people heard in the 30th retelling in the faculty lounge. For Wikipedia's purposes, I think it best to stick to what's in Dawson and I have edited accordingly.

In my novel, I retell this story with some dialogue and incident of my own invention. I can do that there, because it's fiction.

--Jeffreykegler (talk) 06:29, 24 November 2008 (UTC)

[edit] Interesting work

See http://www.jstor.org/pss/2251910 See "The Godel Formula: Some Reservations", by Richard Butrick, 1965, Oxford University Press. —Preceding unsigned comment added by 86.137.170.8 (talk) 09:38, 22 July 2009 (UTC)

The errors in Butrick's argument were pointed out in the same journal, in 1968, by Lacey and Joseph, "What the Godel Formula Says" [2]. They point out that Butrick fails to properly distinguish between mathematics and metamathematics.

One has to take arguments in philosophy journals such as Mind with a grain of salt, because these journals are sometimes willing to publish novel arguments even if nobody apart from the author accepts them, merely for the sake of promoting discussion. Mathematics journals tend to stick more closely to widely-held opinions, but there are still occasionally some idiosyncratic views presented. The only way to properly evaluate individual papers is in the context of the broader literature. — Carl (CBM · talk) 23:50, 22 July 2009 (UTC)

[edit] Inconsistency

In the article on David Hilbert, in note 16, Godel gives the Goldbach and Fermat problems as undecidables. Since then, Wiles has been said to have decided and proved the Fermat problem. —Preceding unsigned comment added by 86.137.170.8 (talk) 09:33, 12 August 2009 (UTC)

No. Gödel says that his undecidable statements are "of the type of Goldbach or Fermat". Technically speaking, he meant (I assume) Π⁰₁-statements, that is, statements of the form

there are no numbers x,...,z such that P(x,...,z),

where P is either a bounded formula, or a quantifier-free formula, or primitive recursive predicate.

"Fermat's last theorem" says that there are no solutions to a certain equation. Gödel's undecidable sentence says that there is no formal proof of a contradiction from the axioms of Principia Mathematica. The two formulas are formally similar, just like the two universal sentences "Everybody likes math" and "Everybody knows math" are formally similar, but formally very different from sentences like "Everybody knows somebody who..."

--Aleph4 (talk) 10:13, 12 August 2009 (UTC)

[edit] Structural cleanup

I went through the article and did some structural cleanup and I think it flows much better now. I relocated the discussions about Einstein and US citizenship into the main "Life" section. I'm not that happy with the section heading "The mid 1930's: further work and visits to the USA" but it's the best I could come up with. Please improve if you can. Manning (talk) 03:41, 25 September 2009 (UTC)

[edit] "Dangerous knowledge" show

The link in the reference about this show has gone bad. Here is another link that still works: [3]. — Carl (CBM · talk) 00:43, 6 October 2009 (UTC)

[edit] Pronunciation of Kurt

I'm native German speaker and to me the pronunciation of Kurt [kʊɐ̯t] seems to be inaccurate. In my option the correct standard German pronunciation is [kʊʁt], whereas [kʊɐ̯t] is more Northern German dialect. Because I'm not that familiar with the IPA I would like to read a second opinion. -- PyroPi (talk) 06:57, 14 November 2009 (UTC)

I think that [kɜrt] and [gɶd'l] are the appropriate IPA transcriptions for "Kurt" and "Gödel", respectively. --PST 14:08, 14 November 2009 (UTC)

I'm German native and I think PyroPi's version is right. Jakob.scholbach (talk) 17:14, 14 November 2009 (UTC)

You must be right then. I am certainly not a professional German speaker. --PST 03:36, 15 November 2009 (UTC)

I don't really know the difference between ʁ and ɐ̯, but I might gently suggest that getting the pronunciation of his first name right is not all that critical. The name Kurt exists in English, after all, and the pronunciation isn't that different after allowing for the systematic differences in letter values between English and German. The key thing is to stop people from saying "Godle" or "Goddle"; even "Girdle" is an improvement over those, and perhaps marginally acceptable in English-language discourse. --Trovatore (talk) 03:46, 15 November 2009 (UTC)

Many people in England particularly in the south have difficulty hearing an r sound. If a person from Ireland says 'thirty' in England it is quite possible it will be taken as 'twenty', the English distinguish between the t and th and the Irish between the r and w. Dmcq (talk) 10:37, 15 November 2009 (UTC)

I don't understand IPA but regardless of the German pronunciation (which I think would be close to "Koort"), Gödel was Austrian and I wonder if his native dialect's pronunciation might be a bit different. 69.228.171.150 (talk) 23:30, 16 November 2009 (UTC)

I'd just like to add that I listened to Jakob's sound file, and I hear no r sound in Kurt, but I do hear one very clearly in Gödel. Jakob actually pronounces Gödel with much more of an r sound than I do myself; I had allowed myself to be told that there was no r sound there, and had tried to get the vowel as close as I could without the r.

It may be that speakers with other accents do not hear an r in Jakob's Gödel. For reference I am a native rhotic speaker of American English. --Trovatore (talk) 23:43, 16 November 2009 (UTC)

I am quite positive that in Jakob's recording there is some kind of r sound in Kurt, but none in Gödel. The letter r has a wide range of normal realisations in German, depending on the speaker and to a lesser extent on position. Jakob's pronunciation sounds to me like the most common one (the one that German adopted from French in the 17th/18th century according to de). It would be equally common to replace r in this position with a short vowel (ɐ̯, similar to German a), but I don't think Jakob has done that. I can't make myself hear anything remotely like an r in Jakob's pronunciation of the ö of Gödel. However, the vowel sound seems to be changing its quality at the end, towards an e-like sound. At first I didn't notice it at all; I guess that it's caused by the following consonant. I believe for a native German speaker it's impossible to identify this with an r or the kind of vowel that could replace one. Hans Adler 07:33, 17 November 2009 (UTC)

Well, of course I'm not talking about a German r sound. I'm talking about an American one. There is absolutely one of those. --Trovatore (talk) 08:42, 17 November 2009 (UTC)

I guess what you hear is the e-like sound, a vowel that is in the range of possible pronunciations of American r. But as I tried to explain, it's hard to switch from ö to de without anticipating the e before the d starts, at the end of the ö. I agree that this short vowel represents an r in English; my point was that it doesn't in German.

To get back to the article, I would say that girdle is an excellent way of explaining to English speakers how Gödel is pronounced. The only real difference between the correct pronunciations of girdle and Gödel is in the quality of the ö sound. Gödel has a long ö; the vowel in girdle has the correct length but has the quality of a short ö. But that's more a matter of accent than of correctness. Hans Adler 10:59, 17 November 2009 (UTC)

It's not something happening just at the end of the ö. The entire vowel is r-colored. Well, maybe except for the first twenty percent of it or something. --Trovatore (talk) 18:30, 17 November 2009 (UTC)

Then my next guess is that you hear it that way because this particular vowel doesn't exist in English other than in syllables that have an r (i.e. in some of the words containing ur or ir). In German it's a regular vowel unrelated to r. The first twenty percent or so seem to be influenced by the preceding g. Hans Adler 19:30, 17 November 2009 (UTC)

Well, so you understand that in rhotic accents, there is no actual consonantal r-sound following a vowel in such words, right? What we perceive as a consonant is actually a coloring of the vowel. A lowering of the third formant, according to a WP article I read recently, though I have no independent way of checking that. Anyway, the ö in Jakob's sound file has that coloring. --Trovatore (talk) 19:49, 17 November 2009 (UTC)