Wikipedia:Articles for deletion/Bishop–Keisler controversy


 * The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review).  No further edits should be made to this page.

The result was   Complete trainwreck. However, there was no consensus to delete the article, and that results in a keep outcome by default. I would expect this article to be back here within a few months if it isn't significantly improved in the meantime, and if/when it is, I heartily recommend long comments and discussions are placed on the AFD talk page. Stifle (talk) 11:12, 19 December 2008 (UTC)

Bishop–Keisler controversy
Current title: Criticism of nonstandard analysis

Proposed title: Impact of nonstandard analysis or Impact of nonstandard mathematics
 * ( [ delete] ) – (View AfD) (View log)

Article seems to be a freely written essay about one adverse review of an out-of-print textbook. It does not treat the general topic of teaching of Non-standard analysis to undergraduates, which is a subject that has been discussed at length by reputable educationalists in the academic literature. The Non-standard analysis article should have a section on the teaching of NSA, including a merge of the material from here related to Bishop's book review (part of the content has already been merged). Mathsci (talk) 05:20, 14 December 2008 (UTC)
 * Update. The AfD debate seems to be converging on the proposal to broaden the scope of the article according to one or other of the proposed titles above. (Impact of nonstandard analysis or Impact of nonstandard mathematics). The article would discuss the impact of nonstandard analysis on mathematics, theoretical physics, economics and teaching and include a summary of criticisms. Please add your comments (or further comments) below. Thanks, Mathsci (talk) 02:22, 19 December 2008 (UTC)
 * The Update seems to be a fantasy of the nominating editor as nobody else seems to support what he describes as "convergence". Katzmik (talk) 09:36, 19 December 2008 (UTC)
 * Please refactor this personal attack and read the discussion below more carefully. Mathsci (talk) 09:55, 19 December 2008 (UTC)
 * Note: Somewhere in this discussion someone says the deletion policy mentions merge and delete as a possible outcome. I quote: "Note that an outcome of "merge and delete" may potentially cause GFDL problems if attribution for contributed content is lost in the process. The essay Merge and delete discusses this." Seeing how this can cause possible problems, I don't recommend doing it. Beter would be to move to talk space and merge and redirect from there if the title is really a problem. - Mgm|(talk) 15:49, 14 December 2008 (UTC)
 * Merge and delete redirect with a more apt title. Mathsci (talk) 06:49, 14 December 2008 (UTC)
 * Comment: AfD should primarily address the suitability of the topic for inclusion in the encyclopedia. The current state of the article only matters when it is argued that there is some problem in principle with ungrading to article to meet inclusion standards. If it is being argued here that the scope of the topic is too narrow, as defined by the chosen title, a request to move may be more appropriate. Charles Matthews (talk) 07:48, 14 December 2008 (UTC)
 * Keep, based on Michael Hardy's research on sources below. This seems to be a typical case where there are "reliable sources" that can establish notability of the required kind, and the rest of the discussion is largely irrelevant once that is shown. The sources can be used to place the "controversy" (not an inept choice of title) in context. Charles Matthews (talk) 08:13, 16 December 2008 (UTC)s
 * Remark. Michael Hardy has provided single-sentence references to this "vitriolic" book review, but that does not warrant a separate article on the negative review nor can it be used to justify the title. That is WP:SYNTH. This case is not "typical", even if the dismissive bluster is. Mathsci (talk) 08:40, 16 December 2008 (UTC)
 * Remark2 I don't see that you can talk about "advancing" a proposition based on those sources, until they have been added and properly integrated. In other words, please don't over-intepret WP:SYNTH. If the article is properly expanded, and a suitable scope and title found, it seems to me that there is every chance that the material involved has a home here on Wikipedia. But the work should be done, so that the position can be assessed. Any novel and tendentious synthesis can be zapped, but you are prematurely assuming that there must be such a proposition. Often it is a plain writing issue, to get round that type of problem. Charles Matthews (talk) 13:44, 16 December 2008 (UTC)


 * Move, Merge and delete Redirect (aka merge & redirect with more apt title) I also support a move, merge and delete . The way the article is written, including its title, imply there was a serious controversy over this book review.  After reading the sources provided and attempting to find more, I feel this article is solely about the negative book review.  The one response listed in the article is a 10-page practical guide written by Keisler (the author of the book that was reviewed).  But it is no way clear that this guide is a response to Bishop's review.   Giving this review the status of controversy has cased it to be listed in the articles Mathematics, Foundations of Mathematics, giving it the illusion of being a major foundational controversy.  Thenub314 (talk) 06:26, 16 December 2008 (UTC)
 * Comment It was pretty famous, for a book review. The article doesn't seem to mention the role of Halmos, who intentionally assigned the review to the constructivist Bishop, basically to provoke controversy. (He had a habit of doing such things - more power to him. :-)  ).  A merge somewhere might be best, but there might be enough to support an article out there, e.g. in Halmos' autobio.John Z (talk) 09:34, 14 December 2008 (UTC)
 * Strong Keep Non-standard analysis is an important topic of research in mathematics and an article on a discussion as to whether it should be included in the teaching of mathematics is definitely a necessity. This is a very famous controversy with a lot of books on it. Topology Expert (talk) 10:09, 14 December 2008 (UTC)
 * Don't Merge (or keep) (on behalf of Katzmik) I don't agree with the merge as I think such a discussion is premature. If you consult the talk page of the article, you may notice that it is an article in progress. Once the text stabilizes, it may be possible to have a meaningful discussion of the desirability of a merge. — Preceding unsigned comment added by Topology Expert (talk • contribs)
 * "Keep" is apparently what was meant here, if we judge by Katzmik's comments below. "Don't merge (or keep)" could be taken to mean "don't do either", so the bolded opinion was written quite ambiguously. Michael Hardy (talk) 02:43, 16 December 2008 (UTC)


 * Comment. I put the tag asking for inline citations on the article. I doubt that in the restricted time for an AfD we will get a reasonable result. Personally I tend towards keeping, although merging might make sense as well. It really depends on how well this dispute is covered in the sources, and I don't have the time to read them all. (Formally, "merge and delete" is not a possible result, and forcing a merge with a deletion discussion is a bit unorthodox and should be restricted to really problematic cases, e.g. related to nationalism.) --Hans Adler (talk) 10:21, 14 December 2008 (UTC)
 * Comment. The "dispute", if there was anything beyond a negative book review, does not seem to be covered in any recognized sources. Certainly none of the articles by Tall et al refer to a dispute. They refer to a debate and an "experiment" that was conducted in some universities in the US and at one university in England and describe the subsequent impact on undergraduate teaching in mathematics. However, this does not seem to be what the article is about. At the moment it seems to be an essay on NSA vs constructivism. Mathsci (talk) 12:06, 14 December 2008 (UTC)
 * Comment Indeed. In addition I don't think there was ever a direct conflict between NSA and constructivism.  Bishop made clear in his '75 article that his comments were not about NSA because he did not study it.  He was strongly criticizing the way NSA was being taught in calculus courses for encouraging students to perform formal manipulations (in his opinion). Thenub314 (talk) 13:03, 14 December 2008 (UTC)
 * Comment Please stop being obnoxious (applies to User:Thenub314 and User:Mathsci). First of all, ‘merge’ and ‘delete’ are different things. You can’t do both (I learned this the hard way). If you want to delete, then keep a redirect to the article into which it is merged. Don’t delete just for the fun of it (which seems to be what these two editors are doing). This article will expand and it is notable (I have read about this controversy in many places). Stop being obnoxious and refocus on the project. Topology Expert (talk) 10:59, 14 December 2008 (UTC)
 * Request I request an administrator to close this discussion because:

a) This article should not be deleted. Originally these two editors wanted to merge it (and keep a redirect) and now they want to delete. In any case, this article is important enough for at least a redirect to the article into which it is merged.

b) You can’t ‘merge’ and ‘delete’. A merge implies that a redirect must be added but if you delete, this cannot be so.

The discussion should now be restricted to whether this article should be merged or not. Deletion is ridiculous. Topology Expert (talk) 11:06, 14 December 2008 (UTC)


 * Comment I do not intend to be obnoxious. Merge and delete is one of the possibilites mentioned at Deletion policy as something that can occasionally happen. I feel dubbing this as a controversy leads to confusion and undue weight, which is why I would like the redirect deleted.  Other titles might be more appropriate, but I feel the current title is harmful for the reasons stated above.  Thenub314 (talk) 11:21, 14 December 2008 (UTC)


 * Request Let's keep the discussion civil. Being called obnoxious comes across as a personal attack.  I promise I am not here for fun, nor am I enjoying this, but I feel it should be done. Thenub314 (talk) 11:21, 14 December 2008 (UTC)


 * Comment I am not really convinced that you are 'obnoxious' but from previous experience, User:Mathsci is generally obnoxious about such things (he once put references to his own work on many articles and there was a discussion about this). Anyhow, it is highly unlikely that this article will be deleted as you two are the only ones in support of it. Topology Expert (talk) 11:38, 14 December 2008 (UTC)
 * Comment. Even with a short summary of the teaching of Non-standard anaylsis (it is described in the references I added as having had a weak impact educationally after a small number of experiments), there does not appear to be sufficient material for one article. There will be no loss of knowledge if the content appears in the parent article, which is where most people would look anyway. As other people have written, it is very hard to write about NSA outside the context of the original article, which is another good reason for a merge.Mathsci (talk) 11:56, 14 December 2008 (UTC) No personal attacks please: I have never added references to my own work in any wikipedia article that I have edited - TE might possibly be confusing me with Katzmik. Other mathematics editors, with unquestionable credentials in RL, have added references to my work before I started editing wikipedia.
 * Comment Personally attacks anyone are inappropriate. It's not constructive.  Let's focus on the issue at hand.  I do not feel this particular book review is notable, but I certainly will look at Halmos's autobiography as soon as the library's open. Thenub314 (talk) 12:05, 14 December 2008 (UTC)
 * Comment I did not wish to make personal attacks but the circumstances left me no choice. I remember that there was a dispute between User:Mathsci and User:Arcfrk where User:Arcfrk accused the other user of adding references to his/her page. I would advise User:Mathsci not to deny this when I can provide evidence easily (by asking User:Arcfrk for example). Anyway, it is unlikely that this article will be deleted and currently, the odds are against User:Mathsci and User:Thenub314 because ‘non-deletion’ is more favored (except for them, no one is voting for deletion). Topology Expert (talk) 12:30, 14 December 2008 (UTC)
 * If you are referring to this thread, then please read it, and then remove your absurd accusations and this response. An apology to Mathsci (and one to Katzmik, who perhaps didn't want to be reminded of this once more in a place where it just doesn't belong) might also be a good idea. --Hans Adler (talk) 13:09, 14 December 2008 (UTC)
 * If I remember correctly, Katzmik had nothing to do with the issue. It was only User:Arcfrk and User:Mathsci. I am not bothered enough to actually go and find this thread but User:Arcfrk accused User:Mathsci of referencing his own work (which I believe is against several policies) and several users agreed with these accusations. I think this will 'ring a bell' for User:Arcfrk at least but I can't (and won't) trust User:Mathsci's word.
 * And my 'accusations' are not absurd: you should calm down, take a deep breath, and perhaps start refocusing on the project as I will do know. I too don't want to remind anybody of that incident (and I regret that I had) but I won't apologize because the incident with User:Mathsci (and again I note that User:Katzmik had nothing to do with it) was real. I won't say anymore about it but if people want to challenge it (which of course they have every right to do), I can personally ask User:Arcfrk and waste my time searching for that thread. Topology Expert (talk) 15:23, 14 December 2008 (UTC)


 * Comment The other problem with ‘merging and deleting’ is that the history will be lost. So you won’t know who actually created the content which is a problem. Why are you so keen (and excited) to delete this article anyway? The only thing absurd here is this ‘deletion’ and I request an admin to close it before people start losing their heads (figurative language). Topology Expert (talk) 15:59, 14 December 2008 (UTC)
 * Strong keep per WP:SNOW and WP:SK Topology Expert (talk) 15:59, 14 December 2008 (UTC)
 * Note: This debate has been included in the list of Education-related deletion discussions.   -- • Gene93k (talk) 16:15, 14 December 2008 (UTC)
 * Merge and delete: Keep the history in a comment on the talk page. Do you really want to know who fixed the typos? You just want to get the gist of who wrote the main stuff. It's just one or two contributers, so say: Bishop-Keisler controversy used to be free standing, and the content is based on contributions of User blah blah and User blah blah who did such and so.Likebox (talk) 16:52, 14 December 2008 (UTC)
 * There's a much better solution: replace the contents of the page with a redirect, don't delete the page, and leave the talk page and history intact. Going to the redirect page and looking at the history will allow anyone to reconstruct what happened.Likebox (talk) 18:03, 14 December 2008 (UTC)
 * Comment User Topology Expert keeps attempting to dissuade us from discussing this further because there is (in his opinion) little chance the article will be deleted. But we should at least focus on actually discussing the merits of the article.  I have stated the case for why I think a merge and delete is appropriate in this case.  The argument that this is very famous and in lots of books is not particularly persuasive without mentioning which books.  I care for the only reason anyone cares,  like Topology Expert,  I would like to improve Wikipedia.  Can we simply discuss this rationally instead of trying to get administrators to close the discussion out of hand? Thenub314 (talk) 16:54, 14 December 2008 (UTC)
 * Comment TE, aside from Mathsci and Thenub314, you are the only one voting (EC: now Likebox also votes to delete), which you have done twice, although Katzmik has given tentative support in absentia. Fully a quarter of the discussion now has been about your rash comments towards other participants, followed by hasty attempts at closure.  Other than the personal attacks, you have expressed your strong opinion largely by unsupported assertion and casual dismissal of the opposition.  I do not apprehend what events impelled you towards insult, but it doesn't look like anything someone else said.  A newcomer to this discussion could be excused for thinking that your comment and request for speedy keep are a desperate attempt to obscure the self-embarrassment you've accomplished, since it is clear that the discussion is not, otherwiwse, done.  Maybe you are the one who should calm down. Ryan Reich (talk) 17:01, 14 December 2008 (UTC)
 * Merge with Non-standard calculus I have already given three arguments in support of a merge on the article talk page, to which no one -- especially, no one against the merge -- has yet responded. Accordingly, it is hard for me to understand why someone would be passionately against grouping the material of this article with other cognate material, in an article that seems more stable and less likely to be deleted in the future.  Plclark (talk) 17:37, 14 December 2008 (UTC)
 * Comment: I think that "deletion" is not the right word to describe this process. The article should of course be left as a redirect, as geometryexpert says, in case someone searches for "Bishop Keisler". Perhaps nonstandard calculus could have a "pedagogical debate" section, and if the interesting history of this debate grows so long that it distracts from the topic, then it can be forked off again. But I think a more inclusive title for the fork might be "Pedagogy of non-standard calculus", and then the rest of the people involved can be included. I don't like going through the deletion process, because nobody is arguing that the content should be included in the encyclopedia.Likebox (talk) 18:00, 14 December 2008 (UTC)
 * No one is disputing it, you mean. Ryan Reich (talk) 18:12, 14 December 2008 (UTC)


 * Comment As I said above I think leaving a redirect from Bishop-Keisler Controversy is not a great idea, as I said above it seems to lead to the idea that this is one of the major controversies in mathematics, (for example it is linked from the Mathematics page). There is no clear evidence to me there was controversy, which was the reason I suggested to delete. Thenub314 (talk) 18:23, 14 December 2008 (UTC)


 * Comment. I want to add 2 further comments about the article. (1) It was originally entitled "Bishop vs Keisler". This was not an encyclopedic title (it sounds more like "rumble in the jungle"), so was changed to the "Bishop-Keisler controversy" by Charles Matthews, without, however, verifying that this was supported by secondary literature (it appears not to be). (2) The secondary literature is by educationalists, following the experiment to teach calculus through NSA. Here is the article by Michèle Artigue cited in the references of BKC, an example of a good secondary source. (The author is professeur at Paris VII.)  In this article on the teaching of analysis, Artigue devotes one page to "NSA and its weak impact on education", page 172. Here is a slightly shortened version of what she writes:


 * Mathsci (talk) 18:50, 14 December 2008 (UTC)
 * Comment Please. I said that we would drop the matter about Mathsci, but since people do not wish to, I am going to fish through the archives and hopefully people will calm down once I find my fish (just the people who are obnoxious but I am not going to mention who, this maybe an empty set). Anyway, I have already suggested (also what User:Likebox said) that we keep a redirect and merge the article into non-standard calculus. I don't understand why User:Mathsci (not User:Thenub314 anymore, I apologize to him for calling him obnoxious) is hell-bent on deleting the article and is not accepting to reasoning. My reasoning is that: why not keep a redirect and merge (what is the apparent enjoyment that this user gains by deleting this article?)? In this case, this AfD should be closed and a discussion as to whether this article should be merged, should begin. Of course,User:Mathsci is an important contributor to Wikipedia, but the fact that he gets involved in these discussion and does not follow policies (I do not claim I do) leads me to believe that he should stick to contributing his knowledge rather than wasting his time here. Topology Expert (talk) 19:07, 14 December 2008 (UTC)
 * Then perhaps we can rename the article to "Bishop vs. Keisler", and make that page a redirect either to nonstandard calculus or to a free standing page on pedagogy of nonstandard calculus. Seeing that this is very notable in the mathematics education community, from the quoted source above, perhaps there should be a free standing article on NSC pedagogy.Likebox (talk) 18:59, 14 December 2008 (UTC)


 * I'd lean toward KEEPing this article. Consider:
 * In the community of mathematicians there seems to be some folklore surrounding this episode. As someone said above, "pretty famous, for a book review".
 * Errett Bishop was a major figure among those taking a certain minority position in philosophical foundations of mathematics. He would be a notable mathematician even if that were not the case, but he wrote a detailed book showing how to rewrite the principles of mathematical analysis from the constructivist point of view.
 * Jerome Keisler may be the only person to bring Abraham Robinson's non-standard analysis down to the freshman level, and his textbook doing that is what this is about. I think it is deplorable that infinitesimals were banished from the freshman calculus curriculum.  I don't necessarily think that means one should follow Robinson's approach with most undergraduates learning calculus for the first time, since I don't think logical rigor fits very well with non-math majors (e.g., I wonder why the mean value theorem should be included at all, since its actual role can only remain quite obscure given the way the first-year calculus course is usually done).
 * I think the main difficulty at this point would be in documenting my "folklore" statement above. Michael Hardy (talk) 19:24, 14 December 2008 (UTC)


 * Comment I have a few things to say about the User:Mathsci issue. For a start, Hans' link was the correct one but I did not think it was so I did not look at it. Sorry for that. Second of all, after re-reading that, I see that it was not User:Mathsci who was referencing his work so again I am sorry for not remembering correctly (and making false accusations). However, the actions of User:Mathsci there were not appropriate (in particular those insults) and were obnoxious (in my opinion). I won't say anymore since that issue is irrelevant to this discussion. Topology Expert (talk) 19:27, 14 December 2008 (UTC)


 * Score so far: 3 Keeps and 2 Deletes. Every other vote is merge and redirect. Since this is an AfD discussion, this AfD should first be closed and then there should be a discussion as to whether this article should be merged or not. I encourage User:Mathsci to read WP:SNOW. Topology Expert (talk) 19:30, 14 December 2008 (UTC)


 * This discussion is not a vote, it's an attempt to get everybody's opinion and come to consensus. If it were a vote, you could lump all the "merges" with either keep or delete, creating a voting paradox. I think this article should be kept only as a redirect, because it prevents a real article on NSC pedagogy to be written. Bishop's book review constitutes a pretty sorry attack on NSC, it is mostly attacking the book itself. The surrounding issues need to be brought out, and that's not going to happen when the article is so narrow in scope.Likebox (talk) 19:39, 14 December 2008 (UTC)
 * I can well believe the folklore statement about Halmos deliberately choosing Bishop as reviewer, but I think it is unlikely to have got into print (I searched for it a little because it would be extremely amusing if he had in fact put it into print). He was also slightly allergic to topological K-theory, at least if it was used to prove results in single operator theory :) Mathsci (talk) 20:16, 14 December 2008 (UTC)
 * In connection with one of Michael Hardy's other points, there is also Henle and Kleinberg, referred to by Artigue (see above). It was reprinted by Dover. On mathscinet the reviewer described it as "charming". Mathsci (talk) 20:27, 14 December 2008 (UTC)


 * Comment (On TE's post) I feel I should point out that many people on both sides have not chimmed in yet. Very notably Katzmik (who is in favor of keeping the article) has not have a chance to contribute, nor has Dominus who (judging form the talk page) had some concerns about the article.  And there may be many others. I don't see any reason to close the discussion early.  As others on both sides may point out to you, this is not case of counting votes.  We should listen to arguments and do what is best, which hopefully will be clear after we have discussed it a bit. In such a situation a better argument should carry more weight.  Thenub314 (talk) 21:37, 14 December 2008 (UTC)


 * Agreed. I have corresponded with TE and have, it seems, gotten him to agree to stop negatively participating in this discussion.  There is no hurry and plenty of people yet to hear from.  In particular I hope that TE's comment "on behalf of Katzmik" will be replaced by an actual comment by Katzmik, who has contributed the most content to this article.  Plclark (talk) 22:29, 14 December 2008 (UTC)


 * Delete Per WP:NOT - this is simply an unnotable and unencyclopedic topic. Eusebeus (talk) 23:15, 14 December 2008 (UTC)


 * Weak delete. I find the evidence of notability unconvincing and largely based on primary sources.  While a brief mention of this may have a place in a survey article on NSA, it is simply not notable enough for an article of its own.  The only independent source listed in the references section of the article, "Advanced Mathematical Thinking", only mentions this purported "controversy" in passing, and in a way that does not seem to establish notability for an encyclopedia article.   siℓℓy rabbit  (  talk  ) 01:48, 15 December 2008 (UTC)


 * Merge, leaving a redirect. I agree entirely with Geometry guy's assessment below, and have changed my vote accordingly.  Let me also comment to the closing admin that it does not establish notability of a controversy that Alice writes a book and Bob writes a critical review of that book.  This material is fine if situated in an article in the appropriate context.  For now, that context appears to be the Nonstandard analysis article, which already has a section into which the material could easily be merged.  In the future, an article on Nonstandard analysis in education could be forked off (there is certainly enough notable material).  But today is not that day.   siℓℓy rabbit  (  talk  ) 19:04, 16 December 2008 (UTC)


 * Comment. I feel that this AfD discussion was started prematurely.  There is simply not enough information available to make a good decision about this article.  For me, the decision hinges on whether there really was a significant controversy in 1977, or whether, as some claim, the article is merely Katzmik's personal essay about a single book review.  This is a question of fact, and right now the facts are unavailable.  More discovery is needed.


 * (continued) If there really was a controversy worthy of the name, then one would expect to be able to find evidence of that, in the form of multiple contemporary and later discussions of the controversy in third-party sources. So far, not one source has been produced to support the argument that this was a notable controversy.  But it is not clear that anyone has tried to produce one.  I think the burden of proof here is on the people who want to keep the article, but I also think they deserve a chance to meet that burden.


 * Michael Hardy mentions that this is part of the mathematical folklore. Fine, but that does not satisfy the WP:V policies. If this affair was truly of historical importance, it ought to be possible for an interested reader to follow it up in the literature.   But the article at present gives one no way to do that.


 * Comment. Michael Hardy has provided some references below.  I had seen some of these before, and I think they illustrate my point: someone trying to follow up the matter would learn little from these sources other than that Bishop wrote a negative review of Keisler's book.  The matter is mentioned briefly and in passing.  If there was more to the matter than that, these sources do not hint at it, and better sources should be found.  If not, then I think the topic fails to meet the notability standard. —Dominus (talk) 19:59, 15 December 2008 (UTC)


 * I suggest that the AfD be closed immediately with no decision and without prejudice, and that the interested parties be given time to establish notability. If they fail to do that, then an AfD is in order.  -- —Dominus 04:47, 15 December 2008 (UTC)
 * Comment. Having scoured the literature for some time now, there seems to have been no evidence of a controversy. Katzmik has had over six weeks to provide secondary sources concerning this, since being asked on November 1st, and that is a reasonable period of time. What does appear to be the case is that the book was part of an experiment to see whether it was possible to use NSA in the teaching of calculus. This was tried elsewhere with different books and was analysed and debated by academics in mathematics education. It is easy to find secondary sources about this, like the one above. The particular teaching experiment with Keisler's book was analysed at the time by Sullivan; there was also an experiment at the University of Essex. The book review was written while these experiments were being conducted. However, the notoriety of this negative book review, which is undisputed, does not merit a separate article. As for mathematical folklore, like many others I know that the science author Gary Taubes and the mathematician Cliff Taubes are brothers, but this does not appear to be recorded officially, so it cannot be added either to their BLPs or on the Taubes disambiguation page. Mathsci (talk) 08:02, 15 December 2008 (UTC)


 * References in the literature:
 * Advanced Mathematical Thinking by David Orme Tall, D. Tall, page 172:
 * The appearance of the second book by Keisler (1976) led to a virulent criticism by Bishop (1977) in the Bulletin of the American Mathematical Society, accusing Keisler of seeking the goal of modern mathematicians: to convince students that mathematics is only "an esoteric and meaningless exercise in technique", detached from any reality. These criticisms were in opposition do the delarations of the partisans of non-standard analysis who affirmed with great passion its simplicity and intuitive character.
 * "A nonstandard proof of a lemma from constructive measure theory", by David A. Ross Mathematical Logic Quarterly, volume 52, number 5, pages 494–497, (2006):
 * To some constructivists nonstandard analysis represents the worst extreme of nonconstructive (i.e. classical) mathematics; see, e.g. Bishop's review [2] of Keisler's calculus text.
 * "Intuitive infinitesimals in the calculus", by David Tall:
 * Meanwhile, Bishop [1] fiercely criticised Keisler’s text for adopting an axiomatic approach when it is not clear to the reader that a system exists which satisfies the given axioms. Although Bishop’s review adopts an extreme viewpoint, the benefits reported by Sullivan have failed to convince the vast majority of mathematicians to switch to infinitesimal techniques.
 * "The Burgess-Rosen critique of nominalistic reconstructions", by Charles Chihara, Philosophia Mathematica 2007 15(1):54–78.
 * ... development of the calculus within the framework of nonstandard analysis. For example, Errett Bishop, in his review of H. Jerome Keisler's Elementary Calculus ...
 * (I haven't been able to get the whole quote on this one yet.)
 * "Natural and Formal Infinities", by David Tall:
 * Criticism of the use of the axiom of choice in the non-standard approach however, draws extreme criticism from those such as Bishop (1977) who insisted on explicit construction of concepts in the intuitionist tradition[.....]Bishop, E., 1977: "Review of ‘Elementary Calculus’ by H. J. Keisler", Bulletin of the American Mathematical Society, 83, 2, 205–208.
 * Michael Hardy (talk) 06:32, 15 December 2008 (UTC)


 * *keep. Wikipedia aught to be allowed to reflect the true stature and influence of Robinson's theory in the real world, as exemplified by the whopping 974 cites of "Non-standard analysis" at Google Scholar (for the sake of comparison, note that Mikhail Gromov's wildly successful "Hyperbolic groups" lags behind at 965 cites). Robinson's theory has certainly had its detractors and sceptics; indeed, it is the purpose of the page under discussion to reflect one such dissent.  The page could be expanded to reflect Halmos' sceptical reception of the proof of his conjecture by Robinson. Katzmik (talk) 10:40, 15 December 2008 (UTC)
 * Comment. This article is about a book review, not about Halmos' views on Robinson's NSA proof that every operator on a Hilbert space with compact square has an invariant subspace. What is the relevance to this article, apart from the circumstantial evidence that Halmos was Bishop's Ph.D. supervisor and was in charge of book reviews at the Bulletin of the American Mathematical Society at the time? Please provide secondary sources that describe a controversy between Bishop and Keisler, rather than continuing to produce WP:SYNTH, WP:OR based on mathematical hearsay. Perhaps you had in mind an article entitled Reactions to non-standard analysis. Mathsci (talk) 11:10, 15 December 2008 (UTC)
 * "Circumstantial evidence that Halmos was Bishop's Ph.D. supervisor"? Geeez, doesn't Halmos say that explicitly in his autobiography?  And doesn't it say so explicitly here?  With the genealogy project, how can anyone speak in such terms?  And how can there be doubts about whether Halmos was or was not in charge of book reviews in that journal at that time?  Can't you just look it up? Michael Hardy (talk) 07:24, 17 December 2008 (UTC)
 * I think what Mathsci meant is: the fact that Halmos was not a supporter of non-standard analysis, and he was Bishop's thesis adviser is weak circumstantial evidence that Halmos is connected to the subject of this article. As you say, it is easy to verify the fact that Halmos was the supervisor of Bishop.  His objection I think might be summed up by the question: Why a page titled "Bishop-Keisler controversy" should talk about "Halmos' sceptical reception of the proof of his conjecture by Robinson"? Thenub314 (talk) 09:55, 17 December 2008 (UTC)


 * Delete - topic is not sufficiently notable to merit its own article. Gandalf61 (talk) 11:21, 15 December 2008 (UTC)
 * Note: This debate has been included in the list of Science-related deletion discussions.   -- the wub  "?!"  12:57, 15 December 2008 (UTC)


 * It seems to me that the main goal of this article is to discuss a certain criticism of nonstandard analysis. So I think this material should be merged into nonstandard analysis. We generally put criticism sections directly into the main article, unless they become so long that they have to be split off. But that would mean an article on criticism of nonstandard analysis, not an article about this particular book review (this seems to agree with what Katzmik and Mathsci say above about expanding the article to include other criticism). Overall, I favor "merge the content, save the edit history, delete the redirect" &mdash; Carl (CBM · talk) 13:14, 15 December 2008 (UTC)
 * Comment Seeing that numerous editors object to the word "controversy" in the title, perhaps the page could be renamed "Bishop-Keisler incident". This would retain the name of the two protagonists and therefore give a good indication of the contents of the page (as noted several times in this space, the incident can be described as "famous").  Additional material can be added here without any serious contradiction; the reader readily recognizes that the page deals with powerful philosophical objections to NSA, even without replacing the title with a bland "criticisms of NSA". Katzmik (talk) 16:00, 15 December 2008 (UTC)
 * I still don't get it. A textbook received a negative peer review. It happens in academia every day. What makes it famous? IMO the Galileo affair is famous, but not this incident. If, indeed, there was something important behind the case, the article fails to present it. NVO (talk) 22:50, 15 December 2008 (UTC)
 * (I agree with name change/keep history but I like redirect to NSC or criticism of NSC) The point of the "criticism of nonstandard calculus" idea is that Bishop's article is not very good as a representative of criticisms of NSA. His book review is just a touchstone for people who want to talk about less well documented clashes over the topic. These clashes came from many sources, with different points of view, and I believe they should be discussed together in one comprehensive article, without singling out Bishop. Bishop's review is most notable in the larger context of criticism of NSA.Likebox (talk) 16:41, 15 December 2008 (UTC)
 * If it is a touchstone and if there are "many such sources", as you mention, why shouldn't there be a separate page on this? Katzmik (talk) 17:08, 15 December 2008 (UTC)
 * Comment One could equally well ask why should there be a separate article on Bishop's book review (I assume that is what Katzmik means by this). This question by itself is not so helpful.  I think the reasons for the merge and delete because of notablility concerns, which would be solved by putting this in a broader context, and we certainly could add a redirect from Bishop-Keisler (review, incident, exchange?, or something more appropriate then controversy).  So people searching for it specifically could find it.  I think Criticisms of NSA (while maybe bland) is neutral, clear, and effective at communicating what the article would be about. Potentially the article could expand to give a much better picture of exactly the difficult reception that NSA has had to deal with. Thenub314 (talk) 18:53, 15 December 2008 (UTC)
 * Merge, leaving a redirect. I don't see sufficient secondary source material for an article, but the issue is notable enough for a redirect to a broader discussion which includes the primary source material cited here. Geometry guy 23:07, 15 December 2008 (UTC)
 * Redirect and merge as per Geometry Guy. Many thanks to Michael Hardy for posting those quotations above. It looks like this incident isn't notable enough for an article of its own, but does deserve a mention in a discussion of non-standard analysis. Ozob (talk) 00:59, 16 December 2008 (UTC)
 * A comment in response to mathsci: Your remarks above allege WP:SYNTH and WP:OR violations on my part. On the contrary, I fully support the guidelines contained in WP:SYNTH, and all the more so WP:OR.  On the other hand, I feel that it is germane to the current discussion that Non-standard analysis is a legitimate viewpoint of a significant minority.  This fact is reflected in what I described poetically as the whopping 974 cites at Google Scholar.  I am aware of the opinion of certain wikieditors who believe NSA to be marginal.  Such a  viewpoint is heard in tearoom conversations in pure math departments with no hyperreal presence.  Wikieditors should be aware of the fact that, with all due respect to Halmos, the "marginality" slur is merely a debatable viewpoint.  As far as secondary sources are concerned, there is no shortage of them as we saw above; at least one secondary source, added to the article by Charles, has been removed (twice) by one of the editors who initiated this AfD.  Katzmik (talk) 13:02, 16 December 2008 (UTC)
 * P.S. One of the two editors involved is continuing his hostile edits at Bishop-Keisler controversy, I would appreciate administative input. Katzmik (talk) 13:10, 16 December 2008 (UTC)
 * Note: I have by now revised the lead paragraph in such a way that it is clear that the Bishop-Keisler episode is the touchstone that sparked an important controversy (rather than the controversy itself), so on the whole I think the title can be left in its current form without change. Katzmik (talk) 14:04, 16 December 2008 (UTC)
 * I disagree. I don't find the current title very encyclopedic, and I don't think it is nearly as good as Criticism of nonstandard analysis if that is actually the topic of the page. However, there is not enough material there to justify a separate criticism article - it could just be merged into the main article on nonstandard analysis. &mdash; Carl (CBM · talk) 14:22, 16 December 2008 (UTC)
 * Comment: On the talk page of the article, the nominating editor is indicting me not just for being completely unencyclopedic, but no fewer than on WP:NPOV, WP:RS, WP:V, WP:OR, WP:SYNTH. Could someone please comment? Katzmik (talk) 14:29, 16 December 2008 (UTC)
 * Remark. What you write above is inaccurate. It concerns one of your latest edits, which was exceptionally poorly written and totally unsourced. The main issue remains that you seem completely unconcerned with providing secondary sources. Have you made any attempt at all to find secondary sources? Mathsci (talk) 21:38, 16 December 2008 (UTC)
 * one adverse review of an out-of-print textbook? The original AfD submission describes the page in an unflattering fashion.  I feel the page deals with an important meta-mathematical issue that transcends the boldfaced description. The term "meta-mathematical" has been recently defined on the talk page as applying mathematical methods to understanding of mathematics itself.  Now Robinson brought tools of modern logic to bear on the foundations of analysis.  Bishop objects to NSA, certainly on constructivist grounds (there have been claims on the talk page that my claim is unsubstantiated, I would like to get some input from fellow editors).  In this sense this controversy can be viewed as meta-mathematical as per the above definition.  Now it is possible that professional philosophers of mathematics would object to using the term "metamathematics" in reference to this debate, but I think we should defend our right to use the term in its lay meaning.  I would like to get some input from fellow editors on this point, as well. Katzmik (talk) 05:44, 17 December 2008 (UTC)
 * Additional secondary source. An editor recently requested an additional secondary source on this controversy.  P. R. Halmos writes in "Invariant subspaces", Amer Math Monthly 85 ('78) 182-183 as follows:
 * the extension to polynomially compact operators was obtained by Bernstein and Robinson (1966). They presented their result in the metamathematical [emphasis added--MK] language called non-standard analysis, but, as it wasa realized very soon, that was a matter of personal preference, not necessity. Katzmik (talk) 05:56, 17 December 2008 (UTC)


 * Comment How is this an additional source? It mentions neither Bishop nor Keisler, nor is it about the teaching of non-standard calculus. Thenub314 (talk) 09:40, 17 December 2008 (UTC)
 * Comment By some mistake I don't understand, I accidentally deleted a comment of Micheal Hardy in this edit. I would like to call attention to it, and apologize.  He is an excellent editor whose opinion I value and I will do my best to be more careful in the future. Thenub314 (talk) 07:53, 17 December 2008 (UTC)

Section break
Remark. The new form of the article is no better and perhaps even more problematic, even though the new material was lifted from the NSA article. Connes has expressed himself at length about NSA on his blog (I believe I'm some kind of superuser there). He makes it clear there that it's not a polemic and that he is not interested in controversy. The last time I saw him he was a living person, so we should be careful not to misrepresent him. He used McDuff's ultraproduct construction in his classification of injective factors, for which he was awarded his Fields medal. He developed the Dixmier trace as a uniform method for explaining the residue of Guillemin and Wodjicki for pseudodifferential operators. As far as I remember it can be constructed using invariant means on an ax+b group. It applies to operators which just fail to be trace class usually because of a log term in the partial sum of eigenvalues; for specific classes of operators it can be constructed effectively. It's not clear that it has anything at all to do with NSA. Mathsci (talk) 11:22, 17 December 2008 (UTC)
 * Criticism of nonstandard analysis One of the key administrators above has committed himself to a position that such an alternative title is much better than the current one. I don't see much explicit support at this page for retaining the current title.  The new title does have the advantage of being broader, so that one can include Connes' criticism as well as Halmos' scepticism (documented above).  At any rate, even if the original title is ultimately reinstated, it is worth retaining the "criticism" title as a re-direct as it is certainly a valid possibility.  I hereby modify my position in support of the new title.  Katzmik (talk) 09:44, 17 December 2008 (UTC)
 * Now my opinion is Keep and Delete. I like the place of the new article much better, the history has been preserved, so everything works with GFDL, but I am still in favor of deleting the redirect from Bishop–Keisler controversy for my initially stated reasons. Thenub314 (talk) 09:59, 17 December 2008 (UTC)
 * epsilon, delta The current version of the article contains a direct quote from Bishop concerning the epsilon, delta definition of limit. I would like to add the following material to elaborate on this comment on Bishop's (note that my proposal here differs significantly from earlier versions that were criticized on the talkpage).  I would like to present two definitions for the benefit of a reader not familiar with technical aspects of infinitesimal calculus: the standard one that Bishop refers to, as well as the infinitesimal one contained in Keisler's book.  Then I would like to point out that according to the secondary source Davis, Bishop's opposition to infinitesimals stems from his constructivism.  Furthermore, I would like to add that Keisler claims in his book that the two definitions are equivalent.  The boldfaced material is my attempt to avoid issues of OR and POV that seem to have bothered editors earlier.  Please comment.  Katzmik (talk) 09:58, 17 December 2008 (UTC)
 * Comment I think this is a discussion better suited to the talk page, but here goes. I difficulty I had with presenting two definitions and stating their equivalent is that it seems to try to make a point Bishop is incorrect or he misunderstood.  The quote which you want to relate this to is one where he says mathematics (including the delta epsilon definition of limit) are common sense.  I don't think "Kiesler claims" is a necessary clause, it is just not clear what equivalence has to do with anything.  Bishop (and this is synthesis on my part) presumably felt that one definition was common sense, while the other definition was not.  He never mentions equivalence.  It seems out of place to bring it up. Thenub314 (talk) 10:15, 17 December 2008 (UTC)
 * Comment 2Davis doesn't say that Bishop's opposition to infinitesimals stems from his constructivism. I believe your referring to the quote "[Bishop] objects to Keisler's description of the real numbers as a convenient fiction (without informing his readers of the constructivist context in which this objection is presumably to be understood)."  He is speaking about a specific objection in Bishop's review. Thenub314 (talk) 10:27, 17 December 2008 (UTC)
 * Controversy Contrary to the title, I do see support on this page for a sentence that has now been deleted in the current version: "A review by Errett Bishop of a textbook on nonstandard calculus by H. Jerome Keisler served as the touchstone for a debate among mathematicians in the 20th century concerning the role of nonstandard analysis in mathematics." I would like to reinstate the sentence if there is support for such a move in this space. Katzmik (talk) 10:05, 17 December 2008 (UTC)
 * As per Thenub's comment: I am neither claiming that the two definitions are equivalent, as I was careful to point out, nor that Bishop is incorrect. In fact, I think Bishop is correct.  From the constructivist viewpoint, not only are the two definitions not equivalent, but in fact the infinitesimal one does not make any sense (AC, etc).  I hasten to add that I do think think the last sentence should go into the article, merely that Bishop is correct but from Keisler's foundational viewpoint (as well as the standard foundational viewpoint), the two definitions are equivalent.  Katzmik (talk) 10:23, 17 December 2008 (UTC)
 * I am still unclear why we are bringing it up? Thenub314 (talk) 10:38, 17 December 2008 (UTC)
 * Misleading I believe mathsci's comment above is misleading. Connes expressed himself on the subject of NSA not just on his blogpage, but in print, and repeatedly.  I understand he did so in the Bourbaki from 96, though I have not seen this yet.  Saying that Connes criticized NSA is not the same as saying that he is interested in a polemic. Katzmik (talk) 14:10, 17 December 2008 (UTC)
 * Axiom of Choice: The point of mentioning the ultraproduct stuff is that it also involves choice. Connes NSA criticisms are about overreliance on choice, and here is Connes using choice. It seems that both NSA and this operator business you're talking about can both be given a reasonably effective description, so the parallel is not inappropriate.Likebox (talk) 14:41, 17 December 2008 (UTC)
 * mathsci's contribution I find your contributing to the article by developing the reference section, very helpful. It is all the more puzzling that you have chosen to devote so much energy to this unwise AfD attempt.  When an editor resorts to slurs of lifting from other articles, it is a sure sign that he has run out of good arguments.  I see a reasonable consensus on this page in favor of keeping the article under the new name.  I would greatly appreciate it if an administrator could close this discussion with a "keep under new name", as this somewhat unnecessary controversy about a controversy has taken a toll on everyone's time.  Katzmik (talk) 15:59, 17 December 2008 (UTC)
 * Comment As per my original comments, I think we should delete the redirect. Was mathsci accusing of lifting? I interperated his comments to mean "I have a problem with this, even though it came from some other article."  I think we all agree that we may borrow material form other articles as necessary.  Having now gone and read some of the posts on Connes blogs he doesn't come across as a critic of NSA.  He has comments like "I don't want controversy" and "I fell in love with NSA." Could we be taking his quote out of context?  Do we have a secondary source that talks about his critique? Thenub314 (talk) 16:14, 17 December 2008 (UTC)
 * Keep. Although not under the name Keisler-Bishop controversy.  Nonstandard analysis is the subject of enough criticism that a separate article is justified.--CSTAR (talk) 17:19, 17 December 2008 (UTC)
 * autobiography: John Z made the following comment above: "there might be enough to support an article out there, e.g. in Halmos' autobio". The current version of the article contains a section on Halmos' scepticism.  If you are aware of relevant material related to NSA, please expand the section. Katzmik (talk) 18:27, 17 December 2008 (UTC)
 * To belatedly answer, and with the title change somewhat irrelevantly, I am quite sure that Halmos did somewhere write that he deliberately chose Bishop in order to create a tempest in a teacup, but thousands of miles from my books and files, I can't be of much help tracking it down. IIRC he wrote he had been criticized for making this selection but said it was intentional and he did it in other cases, that philosophically opposed reviewers would be likely to produce thought-provoking reviews, essentially, that there is no light without heat.John Z (talk) 05:30, 19 December 2008 (UTC)


 * Comment. With the page move and the generally shifting sand, this AfD is rapidly turning into a waste of editors' time and should probably be closed. However, I stand by my view that a separate article should not exist without reliable secondary sources. Who discusses the significance of Bishop's review? Who says Halmos is sceptical of NSA? Who says Connes is a noted critic? Without attributing these assertions to secondary sources, the article engages in original research by synthesis. The only source that comes close to being secondary is Davis, but the article deploys it as a primary source instead. Geometry guy 18:38, 17 December 2008 (UTC)
 * Comment. I think you are being too demanding of an article under construction by demanding perfection.  Who discusses it?  Michael provided a series of secondary references.  Who says Halmos is sceptical?  Halmos himself, when he describes Robinson's NSA proof of the famous conjecture as "a matter of personal taste" (not that I think there will not be an abundance of additional sources).  Who says Connes is a noted critic?  You must be kidding.  If you get a chance please respond to my query about the two definitions, but be lenient if you can :) Katzmik (talk) 18:53, 17 December 2008 (UTC)
 * These references all consist of one sentence. They support the assertion that the review generated controversy and little more. They provide no analysis of the review. Halmos is not a secondary source for his own scepticism: we cannot assert that "a matter of personal taste" amounts to scepticism unless we can attribute that statement. I regard the use of nonstandard analysis as a matter of personal taste, but I'm not sceptical of it, despite generally agreeing with Connes position on the axiom of choice and non-measurable sets. If Connes is a noted critic, then someone must have noted he is a critic. That someone should be cited. Suppose we cut all of the analysis in this article for which reliable secondary sources are not provided. There would, essentially, be nothing left. I'm not asking for you to cite every statement right now. I'm simply asking for evidence that secondary sources actually exist to support an article on this topic. Geometry guy 19:36, 17 December 2008 (UTC)
 * References in the academic literature do not have to be long to be significant. They are coded calls for attention--- they say "I belong to this side" or at least "here's a notable reference for this side". Each one provides great evidence of notability, academics don't cite frivolously--- they cite when they feel they must acknowledge another's contribution.Likebox (talk) 20:11, 17 December 2008 (UTC)
 * "Coded", according to whom?
 * I feel somewhat misunderstood, and I think Katzmik does too! Of course those references are significant, but they support a one line article: "Bishop's review of Keisler's book was critical and contributed to a controversy about nonstandard analysis and the teaching of it". I want to see a case that there are sources which allow us, at Wikipedia, to say more. We don't engage in analysis here. We can't interpret or speculate. Where are the sources we can cite to write an article on this topic? Geometry guy 21:24, 17 December 2008 (UTC)
 * I'm sorry for misinterpreting. What I meant to say is--- it's bad form to repeat arguments--- if you want to acknowledge something, you cite it. When there's enough cites, you can use the original as sole reference for the argument contained in it, and also as a basis for notability for what people use it for. The word "coded" was a bad choice on my part, it should be "by universal unspoken agreement". There's nothing secret about it.Likebox (talk) 21:59, 17 December 2008 (UTC)


 * Keep as Criticism of nonstandard analysis (edit: or Impact of nonstandard mathematics) per CSTAR. CRGreathouse (t | c) 19:39, 17 December 2008 (UTC)
 * Suggestion. I think that a better title might be Impact of non-standard analysis. It is more positive - certainly a lot of physicists have tried to use it - also it would make the discussion of the teaching experiments fit in better. I think Katzmik could have done a better job of cutting and pasting my typed out version (yes, that's what I did!) of Artigue's article. Mathsci (talk) 21:15, 17 December 2008 (UTC)
 * Excellent suggestion. In addition to physicists, economists have used it to model markets with large numbers of consumers. --CSTAR (talk) 04:43, 18 December 2008 (UTC)


 * Impact: The idea of an article on the impact of NSA is an excellent one. It certainly goes in the direction of my remark above concerning the 974 Google Scholar cites.  However, I think we are talking about a different article here.  As far as impact is concerned, I would be very interested to read such an article if anyone has a patience to go through the 974 and write some sort of a synthesis.  Katzmik (talk) 07:48, 18 December 2008 (UTC)
 * Primary versus secondary as per Geometry G's comment: there is a bit of a problem with infinite regression here, to the extent that every secondary source becomes a primary one once a third source comes in and comments on it. The main primary material here is NSA.  I would argue that Connes himself can be viewed as a secondary source, particularly since Abraham Robinson was no longer around when Connes came in.  Katzmik (talk) 07:53, 18 December 2008 (UTC)
 * Oh my, you seem to have no understanding of what a secondary source is. Sources can be both primary and secondary, depending on how they are used. Bishop's review can be used as a secondary source for facts about Keisler's book and NSA. Connes can be used as a secondary source for Bishop's opinions. However, neither Bishop nor Connes are secondary sources for their own opinions. If you can't get that straight, there is no hope for this article. Geometry guy 12:13, 18 December 2008 (UTC)

User mathsci who nominated this page for deletion has now unilaterally moved the page to a title that has not been agreed upon. I ask for administrative assistance in restoring order. Katzmik (talk) 07:59, 18 December 2008 (UTC)


 * It is noted that "Moving the article while it is being discussed can produce confusion", at Guide to deletion. It goes on to say that "If you do this, please note it on the AfD page, preferably both at the top of the discussion (for new participants) and as a new comment at the bottom (for the benefit of the closing admin)." I believe that the title may be an improvement; but it would of course have been better to discuss the scope and title before bringing a deletion proposal, and much better if Mathsci had followed the indicated guideline. Confusion certainly has resulted. Further, the creation of a POV fork under a "criticism of" title is a retrograde step here, from a "controversy" title. Therefore an "impact" title would be better.


 * The solution here is surely for the nominator to withdraw the nomination in the light of discussion, and debate to adjourn to the talk page of the article. Charles Matthews (talk) 08:06, 18 December 2008 (UTC)

Comment. Ahem, Katzmik has already changed the title himself during this AfD, without consensus, so these remarks are best addressed to Katzmik. Katzmik might indeed be exercising WP:OWN. His copy-pasting of my hand-typed transcript of Artigue's article (including my abbreviations and possible errors) seems like lazy editing. Returning to the quote from Connes, perhaps people should look at the original article. The remark prefaces an explanation of how the classical integral can be quantized using Connes' own version of "infinitesimal", part of his theory of noncommutative geometry. He makes a passing reference to nonstandard analysis. Connes made it quite clear in his subsequent blog that his remarks on NSA were not polemic or designed to be controversial. The original content was written in 2004 before the blog came into existence. Given Connes' own subsequent clarifiaction, continuing to use these remarks out of context in an article on controversy/criticism seems to be a violation of BLP. Mathsci (talk) 09:21, 18 December 2008 (UTC)

Proposal I am very happy that Charles likes the suggestion for a broad article on Impact of non-standard analysis, including its impact in mathematics, theoretical physics, economics and teaching. Criticisms should be included, provided they are not plucked out of context. If Katzmik could agree to such an article, which would need carefully written and properly sourced encyclopedic sections on education and applications in mathematical physics - rather than editorialising commentaries on logic and analysis - then it would be quite appropriate to bring this AfD to a close, as this seems to be the consensus of all these discussions. If Katzmik (and others of course) can agree to the new title and proposed enlarged encyclopedic content, then this AfD will have served its purpose. If we can have a useful encyclopedia article instead of an irritating OpEd, that would be great. Mathsci (talk) 09:52, 18 December 2008 (UTC)
 * Unfortunately Katzmik does appear to be exercising WP:OWN, by only allowing his own edits. He has restored all of the irrelevant content on noncommutative geometry and the BLP violations. I hope that he will reverse these edits and please respond positively to my proposal; otherwise we'll be back to square one. Mathsci (talk) 10:25, 18 December 2008 (UTC)


 * Impact of nonstandard mathematics seems like a fine title to me. I would be happy to help edit such an article. Thenub314 (talk) 10:26, 18 December 2008 (UTC)
 * Since I have never visited or edited Noncommutative geometry, I consider the above allegation by user:mathsci as yet another violation of the guidelines at WP:SLUR. As far as the current title Criticism of nonstandard analysis is concerned, there was wide support on this page for the change and no objections were voiced after the change was made.  Katzmik (talk) 13:35, 18 December 2008 (UTC)
 * I think mathsci is not suggesting you edited Noncommutative geometry, but rather you put the information from Connes (which was about Noncommutative geometry back into the articles on Nonstandard analysis and the article we are currently discussing, what ever its current title, I have lost track. Even if I didn't object (I saw it as an improvement over what we had) doesn't mean I don't like the new suggestion much better.  And there seems to be a bit of a consensus supporting the Impact of nonstandard mathematics.  I made no specific commentary on an exact title before Katzmik moved it the first time.  Thenub314 (talk) 14:40, 18 December 2008 (UTC)
 * What happened was that User:Mathsci carried out radical deletions at an established page non-standard analysis. This material has been worked on by numerous editors over the years, including myself.  Radical deletions here were inappropriate.  I therefore reverted the deletions, explaining my reasons in the edit summary.  As the superuser at Connes' page, it may be inappropriate and a conflict of interests for user:mathsci to carry out deletions of material related to Connes.  Katzmik (talk) 16:10, 18 December 2008 (UTC)


 * Delete? Sigh It seems that a page title Impact of nonstandard mathematics treads painfully close to the newly created page Influence_of_non-standard_analysis.  So shall we delete the old one and keep the new one? Thenub314 (talk) 14:32, 18 December 2008 (UTC)
 * I would oppose an AfD attack against Influence_of_non-standard_analysis as I opposed the current unwise AfD. Katzmik (talk) 16:12, 18 December 2008 (UTC)
 * Katzmik, please stop gaming the system in this way. It is a very ill-advised thing to do. At present you are being uncooperative by creating new articles to prove a point. This seems highly disruptive. I won't bother asking why you have duplicated sections in the new article that you also recently introduced into the article of this AfD. You have not been taking any notice of what other editors have been writing, including Charles Matthews. Please calm down. As for being a superuser on Connes' blog, I have never used the account: the creation of the account was suggested by Alain at his 60th birthday conference where I was one of the invited speakers. I suggest that it might be an idea to drop your current line of argument as I can't see it leading anywhere. I know quite a lot of Feilds medallists in RL, which is probably true for lots of mathematicians. Thanks, Mathsci (talk) 16:59, 18 December 2008 (UTC)
 * Contrary to the WP:SLUR above, I did not duplicated sections in the new article. Rather, your colleague user:thenub duplicated it.  You're welcome.  Katzmik (talk) 18:39, 18 December 2008 (UTC)
 * Sorry, I hadn't realised the duplicated material was added by someone else. The stub you created was unencyclopedic with no relevant inline citations for the main text (Nelson, economists). The suggestion of Charles Matthews for an expanded article with a new title was excellent. Perhaps you could explain why you have apparently rejected it? I took it to be a very insightful and sage way of ending this AfD. Why did you disregard it? Mathsci (talk) 22:03, 18 December 2008 (UTC)

New sweeping deletions by user:thenub
A section of criticism of nonstandard analysis was just deleted by user:thenub. I find these continued antics by both user:mathsci and user:thenub increasingly tedious, and hereby request administrative help. Katzmik (talk) 16:16, 18 December 2008 (UTC)
 * Could you be more specific about what you think an administrator should do? As an admin, the only thing I would suggest is that participants tone down the occasional personal characterization (for instance a "you don't understand" upstairs somewhere). Aside from that the discussion seems to be in good faith in my opinion.  As far as shutting down this AfD, I don't see a clear consensus as to what should be done.  Am I missing something? Anyway a non-participating admin should do this.--CSTAR (talk) 16:39, 18 December 2008 (UTC)


 * Comment Just like to point out that this is all way off-topic for an AfD page. Content issues should be discussed (civilly, of course) at the article's talk page; requests for admin intervention should be taken to WP:AN/EW, WP:ANI or similar noticeboard if appropriate. FWIW, this AfD now seems to be FUBAR, and should probably be closed. Gandalf61 (talk) 16:37, 18 December 2008 (UTC)


 * Could people please comment on the change of title suggested by Charles Matthews (Impact of non-standard analysis)? That seems the best way forward. Mathsci (talk) 17:02, 18 December 2008 (UTC) I see that Katzmik has already created the unhyphenated title as a redirect.


 * It seems slightly less general than impact of non-standard mathematics you suggested above, but maybe more useful. I suppose non-standard mathematics could be (potentially) construed as mathematics which deviates from normal practice. But I really am indifferent to one or the other.--CSTAR (talk) 17:57, 18 December 2008 (UTC)
 * In my haste I made a slip, but it's quite unimportant. Either one is fine by me :)Mathsci (talk) 22:28, 18 December 2008 (UTC)


 * As I said I like the title and support the change. Thenub314 (talk) 18:15, 18 December 2008 (UTC)
 * There is already an article Influence of non-standard analysis which is more precise than "impact" (we are not talking about car crashes here, nor about K-T boundary).  As far as the deletions at Criticism of nonstandard analysis, these should be discussed on the talkpage.  A case can be made that education-related material belongs at "Influence", but a case can also be made that education-related material belongs at "Criticism" if it contains an element of criticism.  I was hoping an administrator would remind editors that drastic deletions should be discussed at the talkpage first.  Katzmik (talk) 18:34, 18 December 2008 (UTC)
 * "Non-standard mathematics" is too vague and may cause confusion. There is a wiki page on non-standard decimals which has nothing to do with NSA. Katzmik (talk) 18:36, 18 December 2008 (UTC)

Deletion of Connes' critique
The nominating users have deleted Connes' critique from the article under discussion. I don't see how an article entitled "Criticism of nonstandard analysis" can fail to mention Connes. mathsci and thenub, what is going on? Katzmik (talk) 18:51, 18 December 2008 (UTC)
 * I did not delete the quote from Connes from the article. Please provide the diff. In answer to your questions:
 * (1) Connes is not a critic of NSA, as he has publicly stated since the original content was added to WP in 2004. In the light of these intervening public statements, it is a BLP violation to suggest otherwise.
 * (2) Connes' use of the Dixmier trace in noncommutative geometry has nothing to do with nonstandard analysis.
 * (3) The quote from Connes' paper was taken out of its original context, where it was a parenthetic side remark, prefacing a description of Connes' own work.


 * If you need fuller technical explanations of any of these points, I will be happy to provide them by email. Mathsci (talk) 22:17, 18 December 2008 (UTC)
 * Please do, but this should be discussed before you try to impose your viewpoint on the article. Katzmik (talk) 08:37, 19 December 2008 (UTC)


 * Comment: Criticism of nonstandard calculus is different than criticism of nonstandard analysis. This article is about pedagogy, not about mathematics. Connes critique is mathematics. The Bishop-Keisler debate is pedagogy. This is reflected in their sources and cites.Likebox (talk) 00:40, 19 December 2008 (UTC)
 * Well, such finetuning can be ironed out on the talk page of the article itself. I feel that a strong case can be made that both Connes' and Bishop's criticisms are appropriate at this page.  It is true that Bishop's criticism has a component in pedagogy.  However, secondary sources noted by Hardy clearly point out that the source of Bishop's opposition is his rejection of the axiom of choice due to his constructivist foundational outlook.  This is principled opposition to NSA and not just NSC.  Now Thenub disagrees with the contention that Bishop rejects AC.  This may or may not be true, but his personal opinion is irrelevant until he brings secondary sources.  Once such sources are found, they can be cited in the section on Bishop's criticism, as well.  I don't see how we can choose which secondary sources to follow and which to ignore.  Katzmik (talk) 08:35, 19 December 2008 (UTC)
 * I reproduce the following interesting comment by John Z, made above in a place where it is virtually impossible to find unless you know it's there. His comment shows that there is secondary literature corroborating the fact that we are dealing with a philosophical challenge to NSA, rather than just a pedagogical debate:  "To belatedly answer, and with the title change somewhat irrelevantly, I am quite sure that Halmos did somewhere write that he deliberately chose Bishop in order to create a tempest in a teacup, but thousands of miles from my books and files, I can't be of much help tracking it down.  IIRC he wrote he had been criticized for making this selection but said it was intentional and he did it in other cases, that philosophically opposed reviewers would be likely to produce thought-provoking reviews, essentially, that there is no light without heat.John Z (talk) 05:30, 19 December 2008 (UTC)"
 * I wonder if Katzmik could respect the subdivisions he created? (Halmos and Bishop have nothing to do with "Connes' critique".) Secondly CSTAR, who wrote the original material on Connes in 2004 that Katzmik copied-and-pasted from another wikipedia article without checking things for himself, has agreed that he does not wish to misrepresent Connes' views or work on wikipedia and that this material can be updated as appopriate (see his talk page). In the intervening four years, Connes has given far more detail on why he should have mentioned NSA. Mathsci (talk) 09:03, 19 December 2008 (UTC)

Consensus?
Consensus now seems to have been reached - the new broader title and scope mentioned at the top of the AfD Impact of non standard analysis (or some minor variant). So far nobody seems to have raised an objection and almost everybody seems to have agreed that this is the way forward. It is true that yesterday, deliberately or not, Katzmik chose to create a redirect page with almost the same name. However, that technical detail is irrelevant to this discussion; any confusion that this might have created can easily be ironed out by an administrator. Mathsci (talk) 09:03, 19 December 2008 (UTC)
 * It so happens that I wrote most of the material at the page Influence of non-standard analysis, to which both Impacts are now a redirect. The consensus is reached that a separate article is needed for the influence of non-standard analysis.  However, this is irrevant as far as the current AfD is concerned.  If you would like to change influence to impact please discuss it at the talk page of Influence of non-standard analysis.  Katzmik (talk) 09:09, 19 December 2008 (UTC)
 * Correction: I wrote most of the material, which you was copied and pasted from the Artigue quote here. Mathsci (talk) 09:25, 19 December 2008 (UTC)
 * Correction to correction I already mentioned above that the material from Artigue was copied by thenub, not by me. All the other material at Influence of non-standard analysis was written by me.  I consider this a further WP:SLUR on your part.  Katzmik (talk) 09:30, 19 December 2008 (UTC)
 * Sorry, you're quite correct. MY BAD. It's quite hard to keep track of the new articles and redirects being created during this AfD. Regards, Mathsci (talk) 10:17, 19 December 2008 (UTC)
 * As far as Criticism of nonstandard analysis is concerned, I see only one serious criticism of it on this page, namely Geometry Guy's objection to my broad definition of what constitutes a secondary source. I am not sure how he feels about the article itself with its current title and scope, but I see broad support for retaining it and closing this page with a "keep under new title Criticism of nonstandard analysis".  Perhaps it would be better to add a dash in line with Non-standard analysis but this can be ironed out later.  Katzmik (talk) 09:13, 19 December 2008 (UTC)

(noindent) I have read what CSTAR, Charles Matthews, Thenub and others have written and am waiting for comments. Katzmik's creation of yet another redirect just now seems to indicate that he is actually disrupting the normal functioning of wikipedia. I wonder whether he could please calm down and let other editors comment. I think by now we are all aware of his views, his methods of checking material and for creating articles. Please could he allow other editors to make their comments, rather than trying to crowd out this final request for comment. This is exactly the proposal of Charles Matthews. Please could Katzmik stop disrupting this AfD. Mathsci (talk) 09:22, 19 December 2008 (UTC)
 * You must be reading a different talk page. Here is what I read at this page: "The solution here is surely for the nominator to withdraw the nomination in the light of discussion, and debate to adjourn to the talk page of the article. Charles Matthews (talk) 08:06, 18 December 2008 (UTC)" Katzmik (talk) 09:27, 19 December 2008 (UTC)

(unindent) Charles Matthews wrote:

After you have taken this in, and read what CSTAR, Greathouse, etc, have written, please refactor the comment you have added at the top of the page, which is some kind of personal attack on me. Please stop making personal attacks like this, where rather than commenting on my edits you are calling into question my "sanity". Read other people's comments more carefully before speaking in their place. Thanks, Mathsci (talk) 09:53, 19 December 2008 (UTC)


 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.