Talk:Controversy over Cantor's theory/Archive 1

message: __TOC__
The never-ending debate about Cantor's Theory in Usenet is very real,
as can be verified using Google Groups. This article is an attempt to give 
an overview of  the more sensible views on this  topic from a neutral point
of view, and also to give some historical background. I (the original
author) have to admit that I've never seen any published research on
the Usenet debate, and hence, possibly this article is "original research",
which does not belong in the encyclopedia. On the other hand, it's likely
that many people, after seeing the debate in sci.math and sci.logic, will
want to look in the Wikipedia for a level-headed analysis of the debate,
and so I think the article is somewhat important.
Also, if anyone out there wants to edit this article, please be sure that
you understand both sides of the debate so that you can give a neutral point
of view.   -Dave
----
Hi Dave. Dave Petry, I think, am I right? I'm Mike Oliver (as it says on my user page; not trying to hide anything).
So certainly there is room in Wikipedia for a discussion of the views of people "opposed" in whatever sense to modern set theory. If it's to be this article, it will need some serious revision, though; right now it does seem to be largely your personal observations. The fact that I don't agree with your characterization of the arguments is beside the point at the moment, unless I want to actually enter into the discussion, which I kind of do, but there are other things I ought to be doing. I'll post a note at Wikipedia talk:WikiProject Mathematics and we'll see what shakes out. --Trovatore 03:59, 3 October 2005 (UTC)
replies: text: Actually, no. You can find out such things by clicking on the "history" tab. (While viewing the article, not the talk page. If you click on history while viewing the talk page, you'll se the history of the talk page.) --Trovatore 01:25, 6 October 2005 (UTC)

text: PS I would encourage you to register an account, and then to sign your remarks on talk pages by appending four tildes: ~~~~ --Trovatore 01:32, 6 October 2005 (UTC)

message: A very, very short and basic test suggests, that even the concept of "anti-cantorian" doesn't exist in scholarly discourse, see:
* http://scholar.google.com/scholar?q=anti-cantorian
Of course, some USENET phenomena may become notable, that they may get their own article without any real life background.
Pjacobi 14:54, 6 October 2005 (UTC)
replies: text: Thanks for providing that reference.  David Petry 00:05, 14 November 2005 (UTC)

text: Constructive mathematics is quite popular among theoretical computer scientists (or at least the constructivists like to say that is so). It's easy to find lots of references mentioning this, but I'm not sure what reference I need to include in the Wikipedia article David Petry 00:05, 14 November 2005 (UTC)

text: The quotes in the article are mostly from expository writings and speeches from prominent mathematicians, and not from peer reviewed journals. I don't see anything wrong with that in an article on this topic. Would you say it would be wrong to quote from Mayberry's book (not peer reviewed), for example? David Petry 00:05, 14 November 2005 (UTC)
replies: text: A further comment: after stating that references need to be from peer-reviewed journals, you have included a quote from the interlingua mailing list (on the internet) in your rewrite of the article (Sowa's quote). Nevertheless, I like the quote, and wish I could find an equivalent quote from a more respectable source. It definitely is the kind of thing the anti-Cantorians like to say David Petry 23:52, 14 November 2005 (UTC)

text: I've always had the impression that Wittgenstein didn't really understand the issues, which is why I didn't mention him. I might be mistaken, and of course, you are free to edit this article. Do you know any concise quotes from him on this topic? David Petry 00:05, 14 November 2005 (UTC)

text: As your rewrite seems to show, including too much Wittgenstein just mucks up the issue. David Petry 23:52, 14 November 2005 (UTC)
thread_title:  Scholarly work on this topic? 

message: I have cut the length down, without, I hope, removing any essential arguments. Charles Matthews 21:23, 6 October 2005 (UTC)
thread_title: Article shortening

message: Recall that Brouwer and Hilbert - two very reputable mathematicians - had a heated debate on this topic. Now imagine what would happen if they both wrote articles on their points of view, and then each of them edited the other's article. That's similar to what is happening here. The purpose of this article is to present the views of those who (like Brouwer, Poincare, Kronecker, Weyl, Bishop etc) think that Cantor created a fantasy world. Granted, that view is now definitely not mainstream. But some of you guys are editing an article about things you don't really understand, and don't like. In doing so, you are injecting you own point of view (which undeniably is the mainstream point of view). But there is nothing wrong with having an article which describes an alternate view taken by respected academics. When you guys insert rebuttals to points being made, right in the middle of a paragraph, the result is paragraph with a garbled message. I'd like to ask you to move your rebuttals to a separate paragraph, with a disclaimer such as "in contrast, the standard view is that ..."  David Petry 21:26, 26 October 2005 (UTC)
replies: text: A further comment: in the original article, I proposed that the reason for the controversy may be that applied mathematicians tend to view mathematics as a science, and the pure mathematicians tend to view mathematics as an art. Certainly mathematicians have told me that in person, and I've read comments similar to that in the informal literature. So I thought the idea should be presented. But Charles Matthews edited the whole paragraph out. I'd like to hear some discussion on this.  David Petry 00:21, 14 November 2005 (UTC)
replies: text: I am a pure mathematician, and view mathematics as a science; I'm far from alone in this among realist-leaning set theorists. You should look up some of Maddy's work where she discusses this view. Basically I agree with you about the applicability of empirical methods; I just disagree when you claim that set theory fails the test. I think that you're confounding empiricism with materialism, assuming beforehand that there can never be empirical evidence of non-physical objects. --Trovatore 00:47, 14 November 2005 (UTC)
thread_title: Comments on purpose of article

message: I intend to remove the "Original Research" tag soon. I'd also like to point out that if you put that tag on an article, you are expected to make comments in the discussion page about why you have placed that tag. The guy who put it there didn't leave any comments, and hence it's questionable whether it really should be there at all. I'll wait for comments before I remove the tag. David Petry 00:43, 14 November 2005 (UTC)
thread_title: Removal of OR tag

message: A very, very short and basic test suggests, that even the concept of "anti-cantorian" doesn't exist in scholarly discourse, see:
* http://scholar.google.com/scholar?q=anti-cantorian
Of course, some USENET phenomena may become notable, that they may get their own article without any real life background.
Pjacobi 14:54, 6 October 2005 (UTC)
replies: text: Thanks for providing that reference.  David Petry 00:05, 14 November 2005 (UTC)

text: Constructive mathematics is quite popular among theoretical computer scientists (or at least the constructivists like to say that is so). It's easy to find lots of references mentioning this, but I'm not sure what reference I need to include in the Wikipedia article David Petry 00:05, 14 November 2005 (UTC)

text: The quotes in the article are mostly from expository writings and speeches from prominent mathematicians, and not from peer reviewed journals. I don't see anything wrong with that in an article on this topic. Would you say it would be wrong to quote from Mayberry's book (not peer reviewed), for example? David Petry 00:05, 14 November 2005 (UTC)
replies: text: A further comment: after stating that references need to be from peer-reviewed journals, you have included a quote from the interlingua mailing list (on the internet) in your rewrite of the article (Sowa's quote). Nevertheless, I like the quote, and wish I could find an equivalent quote from a more respectable source. It definitely is the kind of thing the anti-Cantorians like to say David Petry 23:52, 14 November 2005 (UTC)

text: I've always had the impression that Wittgenstein didn't really understand the issues, which is why I didn't mention him. I might be mistaken, and of course, you are free to edit this article. Do you know any concise quotes from him on this topic? David Petry 00:05, 14 November 2005 (UTC)

text: As your rewrite seems to show, including too much Wittgenstein just mucks up the issue. David Petry 23:52, 14 November 2005 (UTC)
thread_title:  Scholarly work on this topic? 

message: I have cut the length down, without, I hope, removing any essential arguments. Charles Matthews 21:23, 6 October 2005 (UTC)
thread_title: Article shortening

message: Recall that Brouwer and Hilbert - two very reputable mathematicians - had a heated debate on this topic. Now imagine what would happen if they both wrote articles on their points of view, and then each of them edited the other's article. That's similar to what is happening here. The purpose of this article is to present the views of those who (like Brouwer, Poincare, Kronecker, Weyl, Bishop etc) think that Cantor created a fantasy world. Granted, that view is now definitely not mainstream. But some of you guys are editing an article about things you don't really understand, and don't like. In doing so, you are injecting you own point of view (which undeniably is the mainstream point of view). But there is nothing wrong with having an article which describes an alternate view taken by respected academics. When you guys insert rebuttals to points being made, right in the middle of a paragraph, the result is paragraph with a garbled message. I'd like to ask you to move your rebuttals to a separate paragraph, with a disclaimer such as "in contrast, the standard view is that ..."  David Petry 21:26, 26 October 2005 (UTC)
replies: text: A further comment: in the original article, I proposed that the reason for the controversy may be that applied mathematicians tend to view mathematics as a science, and the pure mathematicians tend to view mathematics as an art. Certainly mathematicians have told me that in person, and I've read comments similar to that in the informal literature. So I thought the idea should be presented. But Charles Matthews edited the whole paragraph out. I'd like to hear some discussion on this.  David Petry 00:21, 14 November 2005 (UTC)
replies: text: I am a pure mathematician, and view mathematics as a science; I'm far from alone in this among realist-leaning set theorists. You should look up some of Maddy's work where she discusses this view. Basically I agree with you about the applicability of empirical methods; I just disagree when you claim that set theory fails the test. I think that you're confounding empiricism with materialism, assuming beforehand that there can never be empirical evidence of non-physical objects. --Trovatore 00:47, 14 November 2005 (UTC)
thread_title: Comments on purpose of article

message: I intend to remove the "Original Research" tag soon. I'd also like to point out that if you put that tag on an article, you are expected to make comments in the discussion page about why you have placed that tag. The guy who put it there didn't leave any comments, and hence it's questionable whether it really should be there at all. I'll wait for comments before I remove the tag. David Petry 00:43, 14 November 2005 (UTC)
thread_title: Removal of OR tag

message: Oh dear.  I don't think it would be a good idea to separate out the "philosophical" as against the "mathematical" objections.
The purpose of the rewritten article was 
* to explain in simple terms what Cantor's argument actually is.  You can't really have an article about an objection unless you say what the objection is to
* to divide the argument in a way that makes the main steps clear 
* Thus I divide the argument into the 4 steps: Cantor's Theorem, Hume's Principle, Axiom of Infinity, Power Set
The reason it doesn't make sense to split the article into "philosophical" versus "mathematical" objections is that anyone who accepts the four steps above accepts the whole argument, end of story.  Anyone who has an objection, objects to one or more of the steps, or they object to the logic of the argument.  Thus I split the rest of the article into 5, namely, those objections which question the logic nature of the argument (such as those who deny proof by contradiction), and those who object to other 4.  End of story.
So I don't understand the split between "philosophical" and "mathematical".
You are very welcome to add "mathematical" objections to the article, but you need to supply references.  Either peer-reviewed article, or a book (which by virtue of being a book as usually gone through a detailed review process, at least if an academic imprint such as Clarendon or Routledge &c).  
You say e.g. that "Contemporary anti-Cantorians today are typically lay mathematicians (that is, not pure mathematicians), who professionally apply mathematics. Younger researchers in the field of artificial - intelligence seem to be especially attracted to the anti-Cantorian point - of view."
I deleted this because, while it is an interesting claim, it has not been verified.  Who are these lay mathematicians?  Who are the researchers in the field of artificial intelligence?  You need to cite one.
Dbuckner 20:19, 15 November 2005 (UTC)
replies: text: I'm convinced that although you obviously know a great deal about Wittgenstein's opinions about Cantor's Theory, you really have little understanding of the issues from the point of view of the constructivists and applied mathematicians who adopt the anti-Cantorian view. Thus, I've taken the liberty of moving your version of this article to Philosophical objections to Cantor's Theory.
I want to emphasize that Dean Buckner is writing about a different topic from the original topic of this article. I have therefore, move his article to a new topic name. Please respect that, or at least explain why you don't.   David Petry 20:29, 16 November 2005 (UTC)
thread_title:  Mathematical vs philosophical objections? 

message: I've have reverted to the article before Buckner's revisions. If you want his views to be in the article, please start a new section on philosphical objections to Cantor's Theory. Certainly his explanation of Cantor's proof has no business being in this article David Petry 21:28, 17 November 2005 (UTC)
thread_title: Reverting

message: Earlier I wrote:
:I think the material here divides into three sets of concerns: concern about the consistency of ZFC; concern about whether the axioms of ZFC, even if consistent, should be taken at "face value", and concern about the role of set theory in mathematical education and exposition. "Cantorianism" doesn't cover the issues well; better might be an article formulated as a question, such as "Is set theory the right foundation for mathematics?". I'm guessing tha with the right name, the problem of how to deal with the content will become easier.
which I repeat here, since I think it gets to the crux of the matter here.   Most ways of combining these three concerns make sense, and one might have a number of reasons for any of these concerns.  I say this to highlight the multiplicity of possible critical views.  Dave's original article had what I understood to be exemplars of all three concerns: Poincare was concerned about consistency, Thurston about the Platonist interpretation of the system, and Kline about the ill effects of set theory.
This is the heart of my objection to the original article: it paints a unity where there is diversity.  If Dave believes there is a unity, after all, fine.  But the NPOV requirement means that this article cannot be an essay on what follows given Dave is right.
I'd like Dave to stay around and comment on changes.  I don't think he is so far from being a good editor, and there is no shame in not grasping what WP policy demands from articles stright off.  And I'm personally sorry if I have been discouraging in the tone of my comments: it is certainly not because I found the material to be dull.  --- Charles Stewart 00:20, 18 November 2005 (UTC)
replies: text: Just want to add my voice to Charles' here (although Dave's been contributing, so maybe it's not necessary). There is absolutely a place for these arguments in the Wikipedia. They just have to be presented in an encyclopedic and NPOV way, not as a personal essay, and with serious counterarguments given (an early version offered as a counterargument "For the Cantorians, the bottom line is that they have won", which is quite beside the point). --Trovatore 02:20, 19 November 2005 (UTC)
thread_title: Doubts about set theory