Fernandodelucia

Incompleteness theorem

Please see the section here. Another editor and I have both been unable to locate the paper that you recently added as a reference to the incompleteness theorem article. — Carl (CBM · talk) 11:50, 20 July 2012 (UTC)

A third editor succeeded in finding an online copy of the paper. However, your input at the discussion here would still be appreciated. — Carl (CBM · talk) 17:38, 20 July 2012 (UTC)

Edit warring at Gödel's incompleteness theorems

Dear Ed/Trovotore et al

Your objections are not of substance.

Please address the content.

The publication is not ephemeral. What is a 'marginal' publication except a selective piece of abuse on your part.

Your self appointed role as intellectual censor is very odd in this context.

If you have a substantial intellectual objection to the article lets hear it. That might be worthwhile.

Fernando

Dear Ed

It seems that you and a group of associates are doing the edit warring here.

Please say what your objection is to these articles is.

They have been around for a long time. No attempt is made to suggest that they have been authoritatively made out.

Take the Godel one.

1) Is the article of relevance if its claims turned out to be accepted. Yes/No

2) Is it absurd to think that provability predicates could be confined to closed sentences. Yes/ No

3) Does the proof of limitative theorems depend on the validity of the diagonal lemma? Yes /No

4) Does the proof of the diagonal lemma depend on provability predicates being applicable to open sentences? Yes/No

Connect the dots yourself if you are capbale of understanding the problem.

Your thoughts thanks.

Fernando

Hello Fernandodelucia, and welcome to Wikipedia. Please be aware that trying to force your material into this article by reverting is unlikely to work, and is against Wikipedia policy. See the page at Wikipedia:Edit warring. You are insisting that Neil Thompson's 2012 paper be included. In many articles, editors have decided that only recognized work (i.e. recognized by other scholars who are seen as experts in the field) ought to be included. See WP:SECONDARY which explains the Wikipedia concept of secondary sources. If Neil Thomson's paper isn't yet referred to by secondary sources, or included in summaries of the field by people who write review articles, it should perhaps wait until it is more generally noticed. If you still believe the article should be included, please join the discussion at Talk:Gödel's incompleteness theorems and try to persuade the other editors there. Thank you, EdJohnston (talk) 15:36, 20 July 2012 (UTC)

Dear Ed

I think you are a little confused about the role of refereed journals. Articles in them are not 'reviewed'. Books are, but a journal article is quite different.

I have given an account of the article on my reading of it. Please respond to that after having read the article.

None of the other editors who deleted it repeatedly have attempted to give a critique of just a lot of 'throw away' lines. What they should do is seek to respond to the article in an informed fashion by showing that it is nonsense (say) or publishing a response to it themselves in a journal.

The entry dew attention to the article andgave a basic idea of what it says. I think the entry offers the necessary caveats if you think it should go further suggest something.

Why wouldn't a Wikipedia site refer to new articles on the subject in peer reviewed Literature?

Peer reviewed journal articles are not like claimed facts which justify the use of secondary sources.

This just looks like muddled censorship by people who haven't put their mind to the article itself.

Fernando Fernandodelucia (talk) 07:44, 23 July 2012 (UTC)

Fernando

Please note the warning which I left you above. You are once again edit warring to add a specific paper. The articles involved are Gödel's incompleteness theorems and Naive set theory. The most recent edit is here. If you won't listen to anyone else, the next step is for an administrator to block you from editing. Thank you, EdJohnston (talk) 02:25, 1 May 2013 (UTC)

Please follow the conventions of threaded discussion. Use the colon (':') to indent your response under the one above. The place for you to make content arguments is at Talk:Gödel's incompleteness theorems. As an admin, I am not in the business of evaluating your content, I merely observe that you are not following the protocol here. You are trying to force your changes in against others' objections. If you can persuade the other editors on the talk page, your content can go in. Thank you, EdJohnston (talk) 03:29, 1 May 2013 (UTC)

May 2013

You currently appear to be engaged in an edit war. Users are expected to collaborate with others, to avoid editing disruptively, and to try to reach a consensus rather than repeatedly undoing other users' edits once it is known that there is a disagreement.

Please be particularly aware, Wikipedia's policy on edit warring states:

1. Edit warring is disruptive regardless of how many reverts you have made; that is to say, editors are not automatically "entitled" to three reverts.
2. Do not edit war even if you believe you are right.

If you find yourself in an editing dispute, use the article's talk page to discuss controversial changes; work towards a version that represents consensus among editors. You can post a request for help at an appropriate noticeboard or seek dispute resolution. In some cases it may be appropriate to request temporary page protection. If you engage in an edit war, you may be blocked from editing. DMacks (talk) 05:44, 1 May 2013 (UTC)

Please see Talk:Gödel's_incompleteness_theorems#Thompson. Tkuvho (talk) 09:00, 1 May 2013 (UTC)

DMacks and Tkuvho seem to more Edit Warriors than anything else. I have seen no intelligent reason offered for the cutting out of my contribution. It simply appears to be their diktat or say-so.

Please respond to the following: (posted elsewhere)

Godel's Theorems are not the pure stuff of mathematicians and it would not be surprising that a critique would be found in a philosophy journal. I wouldn't think its critical that you couldn't find in the MIT library.Its a new journal. Its paywalled but you can find it (unpaywalled) at http://www.davidpublishing.com/davidpublishing/Upfile/2/29/2012/2012022981760545.pdf . The first step is to try and read before taking down things without any acquaintance with them A year or more ago a couple of editors tried to include something similar and it was suggested that it was too early to do so. Apart from Russell and Wittgenstein who were unhappy with the Theorems and who didn't seem to be be able to put a finger on what was wrong this is the first real challenge to the Theorems. Whilst the Theorems mights sound OK their counterpart Lob's Theorem is certainly hard to accept. As Boolos says it offerss a way of proving that Santa Claus exists. I'm not trying to give an authoritative account of what Thompson says but the paper is very short and not hard for anyone competent in logic to understand. Its certainly easier than Godel's! A rough outline: In this context, a proof is a sequence of sentences using the standard rules of inferences and resulting in the conclusion which is also a sentence. Godel introduces the idea of arithematisation which translates a symbolic system into a system of numbers which serve an indexical function. His arithmetisation is intended to be isomorphic to the original system. He then introduces an arithmetic idea of proof which allows that any godel number of any formula is capable of proof including a single bracket. This is most odd and almost certainly wrong but doesn't matter that much. Boolos' text talks about sentences being proved. Boolos' text does not draw a distinction between open sentences which contain a free variable and closed sentences where all the variables are bound. This doesn't seem surprising to mathematicians who tend to be focussed on formulas rather than sentences but in normal English its like using a sentence contain a pronoun where the person who is talked about is never identified. Quine, America's greatest logician point out that open sentences are true of things but not true or false in themselves. Sentences, properly so called must be true or false and open sentences are neither. If you look at Godel's informal proof it quickly emerges that the sentence he talks about is an open sentence. As far as his formal proof is concerned arithmetic proof because it is intended to be isomorphic to ordinary proof can only be concerned with the proof of the godel numbers of closed sentences. His famous sentence starts with 'x is arithmetically unprovable' ; that formula has its own godel number; that godel number (which is the godel number of an open sentence) is then used to to create a new 'sentence' saying the godel number of the original open sentence is arithmetically unprovable. But its not a valid sentence if both proof (including arithmetic proof) is restricted to closed sentences. In theory, we could stick to Godel's idea of proof or something similar and allow open sentences into proof. But there's no good reason I can see for doing so. If Thompson is right a lot of people will find it shocking but is that so important? I am certainly sure there is nothing crazy about what he is saying and that a lot of logicians think that there is a problem here. Lets ask all the snipping editors to get together and show (within say 7 days: Thompson's thesis rests on some untenable assumption or mode of reasoning or say Godel's approach to proof of open sentences is right. This shouldn't be too hard given their convictions about these things. Fernandodelucia (talk)FernandoFernandodelucia (talk)

Hi Fernando (if I may), Your interest in Thompson's paper is perfectly legitimate. I also think it would be appropriate for a suitable discussion forum (of which there are several). But wiki is specifically not such a discussion forum. Information provided here ideally stems from secondary sources and is based on well-established material that Thompson's paper is not yet, though may become in the future. If you do take this to a discussion forum, please provide the link since I am personally interested in following this up. But not at wiki! Tkuvho (talk) 07:34, 2 May 2013 (UTC)

Dear Tkuvho

It is essential you read the article before discussing it further.

Your criteria for excluding such material is confusing and vague -- and unworkable. How long does a journal article have to be out there for your to think it worthy of discussion?Indefinitely apparently. Is it just a convenient way on the part of editors of avoiding dealing with new developments.

I get the impression that none of the snippers has made any attempt to grapple with it and indeed peruse it. In spite of their pretensions I shall be very agreeably surprised if anyone responds to my challenge.

Anyone interested in logic should offer more than a bad appeal to authority.

The posting never suggested Thompson's thesis has been authoritatively accepted merely recorded the fact of its having been made and after a year unchallenged. It is in the philosophical databases.

I suggest you make an attempt to understand it and suggest (indeed challenge you to say) why it is not worthy of notice.

This would be a start to making sense of the people who merely want to things down on a whim --say because it is in the wrong category of journals or is not in their local library.

Otherwise users of Wikipedia will be denied material indefinitely about new developments in the field until some self elected group decides its worthy in their view.

Fernandodelucia (talk)Fernando

The criteria for inclusion at wiki are not "confusing and vague". For example, Google Scholar does not list any cites for this article yet. This is a significant indication of lack of notability at this time. If in a year's time the article generates, say, 10 cites, this may be an argument for inclusion, though of course its merits would have to be evaluated on the talkpage. Tkuvho (talk) 08:28, 2 May 2013 (UTC)

Dear Tkuvho

The criteria for Wikipedia may not be unworkable but your interpretation of them may be. Please tell me what you rely on

I note you have not said whether you are going to respond to the rest of my post or not.

It must be very significant that you have not said whether you have perused the article referred to or intend to

It would of course be very relevant if you had or decided to do so.

It seems to me that your assumed right to editing allows you or others to keep material out on a whim forever.

Where is it laid down that references in Google Scholar are a determining criterion or is this just something you think is appropriate?

Regards

Fernandodelucia (talk)Fernando

Thanks for a calmer response. I wouldn't say that Google Scholar hits is a "determining criterion". Rather, it is a significant factor. Another significant factor is citations as listed in MathSciNet (Math Reviews). The latter of course take much longer to materialize. I don't recall now where these are mentioned in wiki guidelines; perhaps other editors can help. Tkuvho (talk) 09:02, 2 May 2013 (UTC)

Dear Tkuvho I don't regard the approach of the gang of deleters as being calm but maybe you weren't part of that. If they had offered calm justifications for their actions it may have strengthened their case

As its stands at the moment:

There is a category in the section on Godel's Theorems called criticisms.

The Thompson article is a criticism.

It is in a peer reviewed journal which is relatively new and may not be in everyone's library. Its been published for well over a year.

Discussions of Godel's theorems may be not just in mathematical journals but in philosophical journals.

It is nevertheless freely available for the deleting editors to read and develop a coherent justification for deletion. Not one of them attempted this.

I'll give it another week or so but none of deleters seem to have read it or claim that its claims are clearly untenable.

You have not come up with any Wikipedia rules which require or strongly support its deletion.

Most of all the Godel's Theorems are probably the most important in all of the Foundations of Mathematics and Philosophical Logic. So any criticisms which may have some validity are important even if to orthodoxy they must seem to be very unlikely to be right.

After a year it is appropriate that it be noticed but of course they must remain extremely controversial and it should not be suggested that they are otherwise and it has not been.

There is nothing amiss with Wikipedia readers being made aware of some claims which can only be seen as controversial in a criticisms section.

And the strong arguments for the deleters are ....?

Fernandodelucia (talk)Fernando

An argument in favor of postponing the inclusion of this material is the absence (as yet) of secondary sources. Again, wiki is not a discussion forum. Tkuvho (talk) 09:47, 2 May 2013 (UTC)

Dear Tkuvho

The absence of secondary sources is the only substantial argument so far. But the absence of any critical response is equally as important.

You have pointed out that Wikipedia is not a discussion forum. Fine. All the deleted entry did was noted in the briefest possible way the existence of a possibly important criticism in a criticisms section. Where's the discussion you apparently criticise it for?

Fernandodelucia (talk)Fernando

The absence of any critical response is uninteresting; there's no evidence that anybody has heard of it! A glance at the article doesn't impress me; someone with a Masters of Law citing undergraduate textbooks to overthrow a theorem many of the greatest minds in mathematics had attacked doesn't really get the time of day.--Prosfilaes (talk) 10:59, 2 May 2013 (UTC)

@Fernando: Thanks for acknowledging that the absence of secondary sources is a substantial argument. Note that even if somebody comes along and proves the inconsistency of Peano Arithmetic, this will not make it into wiki until there are secondary sources. Tkuvho (talk) 11:55, 2 May 2013 (UTC)

[I don't normally do this, but I've posted this both here and at the article Talk. The debris from this particular intellectual train wreck should be quite cool by now and we should all get back to more worthwhile pursuits.] Part of the reason journal reputation matters is that it helps busy people avoid wasting their time reading borderline self-published nonsense. This post, and the extensive responses by the many people solicited to publish in Philosophy Studies, tells the story more than adequately. EEng (talk) 21:19, 2 May 2013 (UTC)

Dear EEng and Prosfilaes

I don't know whether you have any interest in mathematical logic but it doesn't appear so from your comments.

It would seem that the rules of Wikipedia require people to act collaboratively and not tear down edits without consultation or reasons. The 'train wreck' if one exists is caused entirely by those people.

Apart from Tkuvho who has attempted to give a rationalisation for it, the tearers down don't appear to want to argue that there is nothing worthwhile to be found in the Thompson argument. If they did this we might get some where.

Prosfilaes claims to have read it but dismiss it because he's not impressed. So? What does that mean? Does he do all his intellectual shopping by following 'brands"?

He obviously has misunderstood the Thompson reference to the Boolos textbook; it would have not been enough to find a flaw in the 1931 Godel paper if modern accounts did not contain that flaw. Thompson himself points out he has not shown that the Theorem cannot be proved by other methods. He simply says that standard contemporary accounts by Boolos and Smullyan share with Godel's original the same problems about the concept of proof.

EEng seems to suffer a similar intellectual lethargy. If he's 'busy' and can't afford the time to read such 'self-published' nonsense (his claims about this are really unjustified prejudiced abuse) then why does he inject himself into the argument?

I propose to take this matter to dispute resolution. I will be saying that none of the tearer downers are able to point to anything in the article which shows that that the arguments in the Thompson article are simply untenable.

Its not that difficult to understand and nor should it be difficult if the complaining critics to pen a brief critique that shows that Thompson's points have no basis. Ad hominem arguments have to be out of place in a section on mathematical logic.

I certainly wish to make the point during the mediation process that none has attempted to produce even a brief critique and presumably is not capable of doing so.

Fernandodelucia (talk)Fernando

Ho, hum. Look, you gotta stop it with the intellectual lethargy and stuff -- you're being a first-class jerk. When I was studying mathematics there was a clipboard near the department office thick with letters from people who had squared the circle, conquered trisection, proven the parallel postulate, and (yes) found where Goedel had gone wrong. This field tends to attract crackpots, as you no doubt have heard. And as seen via the link in my earlier post, it's no "unjustified prejudiced abuse" to say that publishing in Philosophy Studies is just like posting to your own website, only way more expensive.

For all your powers of logic you continue to misunderstand how Wikipedia works. As must be abundantly obvious by now, it's unproductive for editors to attempt to determine the significance of a paper like this through their own discussion of the subject matter itself; we await, and will rely upon, the commentary of experts in the field. If you are such an expert, Mathematical Reviews would love to publish your thoughts on Thompson's paper. Get back to us when that happens.

In the meantime I'll get back to work on the biography of my lifelong friend Andrew Gleason. Spent many lunches discussing the philosophy of mathematics with someone like that? No? Sorry to name-drop but you need to know the caliber of people you're dealing with here. I'd say you're riding for a fall, except you've already taken the fall but don't seem to realize it. Smarten up.

EEng (talk) 03:13, 3 May 2013 (UTC)

Dear EEng

I think the tone and gratuitous insults in your post makes your point well for me (if unintentionally).

It is also very clear that you at least don't have the inclination to show that there's simply nothing worthwhile in the Thompson paper. If you managed that your contributions might be worthwhile.

That no-one has offered to pen a few words about the content of the Thompson paper makes my point very well

If you know anything about the history of mathematics and I guess you say you do there are plenty of cases where established positions were overthrown. Cantor was tormented by Kronecker who consistently denigrated his ideas.

So throw away dismissals like yours don't necessarily work.

203.32.220.31 (talk)Fernando —Preceding undated comment added 03:31, 3 May 2013 (UTC)

Well, I think my post expresses pointedly what others have said diplomatically.

As with Cantor's, many attacked Goedel's ideas at first, but eventually accepted them; that's why we have confidence in them. That no one here has analyzed Thompson's ideas reflects nothing more than that no one in the field seems to care about them, so we don't either. Here at Wikipedia that dismissal not only works, it's an imperative. (If the self-styled "Mr. Logic" were an established authority, that would be a different story.)

Once again, cut it out with the WP:IDIDNTHEARTHAT. Whether you like it or not, understand it or not, consensus rules.

An editor who arrives here solely to promote a specific idea or viewpoint, even a meritorious one, almost always fails to make any permanent contribution at all, because by limiting himself to a single topic -- one over which by definition he is likely to come into conflict with other editors -- he becomes frustrated and quits before learning all the little things about how Wikipedia works. Despite the mean things I've said (deserved as they were) I would like you to join the ranks of happy contributors. My advice to you, therefore, is that you start browsing articles on topics you don't have strong feelings about -- outside mathematics, or at least outside mathematical logic. Pretty soon you'll find some noncontroversial article which needs work; jump in there and build a sense of achievement for yourself. In time Thompson's paper will seem less important to you; if not, then Wikipedia isn't a good place for you to volunteer. Good luck.

And please, learn to WP:INDENT and sign your posts. By not doing so you reinforce the impression you don't care about getting along, only about Thompson. EEng (talk) 13:03, 3 May 2013 (UTC)

Dear EEng

Lets get down to the point about the Thompson paper. I am asking you to exercise your mind rather than close it.

Please throttle back on the vitriol. It really doesn't get us anywhere and is a distraction from what should be an intellectual exercise. And one concerned with logic rather than attacking other editors.

It is to be placed in a section called "Criticisms'. My entry used the words 'claims'. It obviously does not amount to an endorsement of the Thompson paper. Merely the existence of a criticism in very brief terms. The other criticisms are not endorsed either even though Wittgenstein was one of the greatest minds in logic ever.

Your efforts would be useful if they critiqued Thompson's claims. You say you have the (logico-)mathematical skills to do so. If not you another editor who criticises should.

For example if the paper offered ridiculous reasons for rejected the Incompleteness Theorems then it could be totally ignored. Obviously if Thompson said that Godel was an extra terrestial alien or Peno's axioms were false then you would not take any notice of it.

But there are some things about G's proof which are odd and which should give the thoughtful concern. Firstly the Incompleteness Theorems' corollary, Lob's Theorem. As Boolos' standard text makes clear, there's something very odd here. It seems to allow us to prove anything as long as we accept that there is a sentence involved.

You see propositional logic proceeds on the basis that there are only two forms of sentences ones which are true and ones which are false. If you add a third category, 'open' sentences then you get trivalence and some sentences which are neither true or false and ultimately according to Godel sentences that are neither provable or unprovable.

Godel simply assumes that the provability of 'open' sentences can be treated in this way.

The idea of a proof is bound up in all this. Thompson, challenges this and I think he is justified in so doing. It counts as a worthwhile criticism but that doesn't make it right

There may be very complex answers to all this. So far I 'm not seeing them or even very simple ones either from people who want to tear it down. Its just chatter that's besides the point.

Publication in a peer reviewed journal doesn't prove that much even in the most prestigious journals. Editors and reviewers can have their own agendas. It does provide a necessary filter but doesn't make it right but for someone studying the area it does provide a reference point for consideration.

What I am saying is relevant here is that an arguable criticism exists not that it is made out. Even if its found to be wrong it may allow at the very least for the basis of the Theorem to be refined.

Its over to you and your friends to show that it can't be taken seriously intellectually.

Fernandodelucia (talk)Fernando

You're not listening. Goodbye. EEng (talk) 02:59, 6 May 2013 (UTC)

I take it as a conclusive 'no' that anyone is going to argue that the Thompson article can't be taken seriously.

Fernandodelucia (talk)Fernando

See above, and since you're the last one out, turn the lights and airconditioning off when you're done, will you? Thanks. EEng (talk) 21:00, 6 May 2013 (UTC)

Fernando: you are correct that Thompson has found a defect that should be mentioned in the article. However, the defect is a rather simple one that is easily repaired. Using the lambda calculus, Hewitt showed how to fix the problem in [1]. But the fix exposed even larger problems with Godel's work.63.249.97.145 (talk) 04:33, 7 May 2013 (UTC)

Re The contribution about the lamda calculus. As i understand Thompson's criticism he claims that if you adopt a different view of provable to Godel ( ie one that is restricted to closed sentences) the standard proofs of the incompleteness theorems don't work. That doesn't prove that any standard system that can be used for Maths is complete and consistent. It still open that Godel's theses can be proved by a different route. I am not familiar with the lamda calculus idea but Thompson's claims are really quite narrow. There may be other possible ideas of proof but I think that Thompson's ideas of proof and the lamda calculus idea don't intersect that much.

The lamda calculus really should be journal published in some form to be noted.

Fernandodelucia (talk)

Hewitt used the fixed point construction of the lambda calculus to construct Godel's self-referential sentence and thus repair the defect mentioned by Thompson. The result is published in his article in the prestigious Turing Memorial Volume "A Computable Universe: Understanding Computation & Exploring Nature as Computation" Edited by Hector Zenil with a preface by Roger Penrose published by World Scientific Publishing Company in 2012.64.134.227.39 (talk) 21:00, 7 May 2013 (UTC)

There is an online PDF copy of the above published paper at the following URL: [2]. 171.66.96.74 (talk) 23:46, 7 May 2013 (UTC)

It may well be that Hewitt's paper as published in a book ought tobe referenced in this area. It may indeed ultimately reflect on what Thompson says although a don't see a reference in it to Thompson or the points being made. Neither should be seen as authoritatively upsetting Godel's theorems at this stage. But Thompson's point should be noted (without approval) in a brief way. The same thing might apply to Hewitt's article but it would help if it could be explained in a paragraph or two.

Its different if the criticism didn't make sense or was (say) exclusively 'metaphysical'. Fernandodelucia (talk)

It looks like Hewitt's work preceded Thompson's and consequently did not reference Thompson. Hewitt needed to fix the flaw in Gödel's proof in order to make the following broader point: Allowing self-referential propositions of the kind used by Gödel and Löb leads to contradictions in mathematics.171.66.90.162 (talk) 02:53, 8 May 2013 (UTC)

Thompson's other 2012 paper which suggests that naive set theory can be revised by excluding certain set descriptions isomorphic to Russell's set is relevant to the previous post. Other self referencing descriptions are allowed by his proposals. It is very hard to operate if you exclude all self reference as being illegitimate. But its best to allow reference to these ideas than try and surpress them as somehow 'not respectable'. Ideas that stretch the boundaries are the ones that allow development and progress of ideas.Fernandodelucia (talk)

The solution in set theory is to form sets using {x∈D | P[x]} where D is a set and P is an arbitrary (non-selfreferential) predicate. Self-referential sentences are not useful in mathematics.171.66.167.3 (talk) 19:57, 8 May 2013 (UTC)

I am not all sure about that. As Quine concluded it is useful to have a universal set. And overarching principles are useful; the more the better. The problem is if you have overarching predicates why can't you talk in general, collective terms (sets) about those things to which those predicates relate? You start to impoverish your ontology and your tools of analysis. Its like Russell's Type Theory's Axiom Of Reducibility --- How can such a principle be even expressed in Type Theory? Not all self reference is problematic. And how do justify your restrictions philosophically? Or are they only pragmatic or ad hoc? The ideal way would be to have a theory of set comprehension based purely on logic which is what Thompson proposes is his second 2012 paper.

Having a universal set is rather dubious. For example, is the alleged universal set a member of itself?64.134.236.122 (talk) 02:14, 12 May 2013 (UTC)

Under Quine's systems you find Universal Sets. These do not themselves leave to contradiction or unpleasing results. Some set descriptions on the other hand do. Like the set descrpition of Russell's set they lead to contradiction. By reductio it is shown they are false.c So any filter fo set comprehension ought to perhaps limit itself to those that lead to contradiction. Otherwise we weaken our tools of analysis. Fernandodelucia (talk)

I've attempted to get everyone to make their considered objections to my proposed edit. So far I have had much in the way of takers. At first I got a storm of takers (possibly co-ordinated) down who did not offer any clear objection. I was accused of edit warring but it seems to be the rule if you take something down you should offer some explanation Few offered any kind of objection. Some may have been hampered by thinking they could not fin it free on the net. I'm quite happy to enter into some sort of dispute resolution about it but given the lack of any response I propose to renstate an edit in the Criticisms Section as follows:

Thompson ('Arithmetic Proof and Open Sentences' Philosophy Study 2 (1) 43-50 (2012)) claims that only closed and not 'open' sentences containing free variables are capable of proof. Similarly, only gödel numbers of open sentences are capable of arithmetic proof. Gödel's key sentence stating that the gödel number of a certain open sentence is unprovable becomes unsyntactical. On this approach to proof standard proofs of not only Gödel's incompleteness theorems, but of the Diagonal Lemma, Tarski's and Löb's Theorems are all claimed to be blocked. Thompson's critique does not preclude proof of these theorems by other means.

This is as brief as I can make and does not amount to an endorsement of it. Fernandodelucia (talk)

You've been told very clearly why nothing on Thompson's ideas, and certainly not your interpretation of them and their implications or non-implications, is appropriate unless multiple secondary sources (or a single, extremely authoritative one) comment on it. In any event this is not the talkpage for the article; I suggest you repost there (just your last post -- please, not the whole wall of text above) and see what others think. If you proceed straight to editing the article, you will be very close to another block, I assure you. EEng (talk) 10:27, 10 May 2013 (UTC)

Professor Hewitt (one of the world's acknowledged foremost experts) has published articles on the above. But I have heard that he has been banned by Wikipedia and his published work is not allowed to be mentioned. 50.131.244.2 (talk) 20:37, 11 May 2013 (UTC)

I would find your opposition if that is what is rather saying 'no' to everything would be more impressive if you anybody else who you might represent show some understanding of what Thompson was saying. Intellectual curiosity is useful in editors I should think. This is a criticisms section we're dealing with after all not an 'authoritative refutations' section. A completely timorous approach in these circumstances is misguided. I will post there; It has been posted before and no good reason was offered for not including it. Even if Thompson' s stuff is ultimately wrong it may be useful. But please come up with something substantial in the circumstances for saying its not an useful criticism. Fernandodelucia (talk)

The field has been in crises since Professor Hewitt published his papers, e.g., [3]. The high priests at Edinburgh, Melbourne, etc. are busy sorting it out. Presumably, Wikipedia will eventually publish something about it. 50.131.244.2 (talk) 20:31, 11 May 2013 (UTC)

Censorship of the Wikipedia article on incompleteness (including the talk page) is very strong. So it may be a long time before the article catches up with the published science.64.134.236.122 (talk) 02:10, 12 May 2013 (UTC)

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Thank you. --SineBot (talk) 01:43, 15 May 2013 (UTC)

Userpage vs user talk

Hi, I noticed that you recently left a message for another user on their user page. I just wanted to make sure you know, for future reference, that messages should always be left on the talk page. CarrieVS (talk) 10:52, 4 June 2013 (UTC)