Talk:Cantor's first set theory article
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Title containing "article"
This looks like a fascinating (Wikipedia) article, and I'm looking forward to reading it in detail.
I'm not too convinced by the title, though. I think it's more usual to refer to such contributions as "papers" rather than "articles". To me "article" sounds like something you find in a magazine, not a journal. Also, as I alluded to above, it's a bit problematic that "article" also is used to refer to Wikipedia articles, and there's possible interference from that, for editors discussing the Wikipedia article, but more importantly also for readers.
We could move it to Georg Cantor's first set theory paper, but to be honest I would rather move it to the actual title, On a Property of the Collection of All Real Algebraic Numbers, and put it in italics. I think in general we write articles on notable papers by their titles. See for example On Formally Undecidable Propositions of Principia Mathematica and Related Systems (not sure why it's not in italics; I think it should be). --Trovatore (talk) 03:38, 13 February 2016 (UTC)
- Just an update on the italics issue — I went ahead and added {{italic title}} to the other article. But now I'm having second thoughts; there may be an argument for preserving a distinction between book titles, which are italicized, and titles of papers, which are not. I don't know. I think it looks better with italics; it makes it clearer that it's a title of a published work. --Trovatore (talk) 03:59, 13 February 2016 (UTC)
The article rewrite and thanks to all those who helped me
It's been challenging rewriting the "Cantor's first uncountability proof" article because it's listed in the categories: History of mathematics, Set theory, Real analysis, Georg Cantor. So I had to consider both the math and the math history audiences. I did this by writing the article so all the math in Cantor's article appears in the first two sections, which is followed by a "Development" section that acts as a bridge from the math sections to the math history sections. I changed the title to "Cantor's first set theory article" to reflect its content better; actually, the old article could have used this title. It's a well-known, often-cited, and much-discussed article so I suspect the Wikipedia article will attract a number of readers.
I would like to thank SpinningSpark for his excellent critique of the old article. I really appreciate the time and thought he put into it. The new article owes a lot to SpinningSpark. His detailed section-by-section list of flaws was extremely helpful. I used this list and his suggestions to restructure and rewrite the article. I particularly liked his comment on whether the disagreement about Cantor's proof of the existence of transcendentals "has been a decades long dispute with neither side ever realising that they were not talking about the same proof." The lead now points out this disagreement has been around at least since 1930 and still seems to be unresolved. It was a major flaw of the old article that the longevity of the disagreement was never mentioned. I find it ironic that this disagreement is still around, while most mathematicians now accept transfinite (infinite) sets so the old dispute about the validity of these sets is mostly resolved.
I also thank JohnBlackburn for his comments. His comments that made me realize that I should think of the readers who just want to understand the math in Cantor's proof. This led to the restructuring mentioned above in the first paragraph. His comments also led me to put the long footnotes containing math proofs into the text. I also added some more math to the article.
I thank Jochen Burghardt for his help on the rewrite. He did the case diagrams for the proof of Cantor's second theorem, the subsectioning of "The Proof" section, the calculations in the table "Cantor's enumeration of the real algebraic numbers", and he pointed out places where my writing was unclear. The need for the case diagrams came from reading SpinningSpark's comment on what is now Case 1. I realized that a reader's possible confusion on whether there is point in the finite interval (aN, bN) besides xn could be handled with a diagram. I contacted Jochen with three simple ASCII diagrams. He took my simplistic diagrams and produced diagrams that capture the dynamics of the limiting process.
I thank my daughter Kristen who read a recent draft and made a number of suggestions that improved the writing. Especially important were her suggestions on improving the lead.
I also thank those who edited the old article. I started with a copy of the old article and have kept up with recent edits so that your edits would be preserved (except perhaps in the parts of the article where large changes were made).
Finally, I wish to thank Michael Hardy for his GA nomination for the old article, for giving me the go-ahead for the rewrite, and for his patience with the amount of time it has taken me to do the rewrite. I hope that this rewrite is much closer to GA standards than the old article. --RJGray (talk) 15:26, 13 February 2016 (UTC)
No need to merge article with Cantor's first uncountability proof -- already contains its content
There is no need to merge this article with Cantor's first uncountability proof because this is a rewrite of that article with guidance from the GA Review of that article. What is needed is a redirect from Cantor's first uncountability proof to this new article. Note that Cantor's first uncountability proof appears in boldface in first paragraph so readers will know that this article contains the content of that article. --RJGray (talk) 15:37, 13 February 2016 (UTC)
- Ok, but in that case we needed to merge the histories to make it clearer that much of the content was rewritten from the older version. I have completed a history merge, so now the histories of both articles are in one place, and removed the merge tags. —David Eppstein (talk) 21:41, 13 February 2016 (UTC)
Requested move 13 February 2016
 | It has been proposed in this section that Cantor's first set theory article be renamed and moved to On a Property of the Collection of All Real Algebraic Numbers. A bot will list this discussion on the requested moves current discussions subpage within an hour of this tag being placed. The discussion may be closed 7 days after being opened, if consensus has been reached (see the closing instructions). Please base arguments on article title policy, and keep discussion succinct and civil. Please use {{subst:requested move}}. Do not use {{requested move/dated}} directly. |
Georg Cantor's first set theory article → On a Property of the Collection of All Real Algebraic Numbers – Article is about this paper, so name it after the paper. See more elaborate remarks at the section #Title_containing_.22article.22 above. Trovatore (talk) 20:20, 13 February 2016 (UTC)
A few points to think about:
- The title of Cantor's article "On a Property of the Collection of All Real Algebraic Numbers" does not capture what the article is famous for--namely, the uncountability of the set of real numbers. Gödel's article "On Formally Undecidable Propositions of Principia Mathematica and Related Systems I" does capture what the article is famous for. The reason for Cantor's choice of name is covered in the Wikipedia article.
- If we drop the "Georg" in the Wikipedia article's title, a reader who is interested in Cantor can type "Cantor" into the Search box and see the Wikipedia article along with other articles about Cantor's work. Being a reader who uses this feature of the Search box when I'm curious about a mathematician's or scientist's work, I think "Cantor's first set theory article" would be more reader-friendly than "On a Property of the Collection of All Real Algebraic Numbers."
- As far as "article" vs. "paper". See Difference Between Research Article and Research Paper. Two items of interest: "• There is a trend to refer to term papers and academic papers written by students in colleges as research papers whereas articles submitted by scholars and scientists with their groundbreaking research are termed as research articles. • Research articles are published in renowned scientific journals whereas papers written by students do not go to journals."--RJGray (talk) 21:35, 13 February 2016 (UTC)
- As to your first point: Yes, that's true, but that's an interesting story in itself, which as far as I can see (but I haven't read the article carefully yet), the article does not currently discuss, but should probably be added. As I'm sure you know, Cantor is thought to have chosen this (somewhat inferior) title deliberately, to avoid a confrontation with Kronecker. Dauben goes into some detail on this point, I believe (don't have him to hand unfortunately). In any case I don't see that this should determine what this article should be called. This article is about the paper, and the paper has that name, and I really think that ought to settle it. Update — it looks like you say that the point about the reason for the title of Cantor's paper is covered in the Wikipedia article. I took a quick look, and I still don't see it; can you point me to it? I would expect it to be more prominent.
- As to typing in the search box, it works for redirects too. Try it. There is in any case going to be a redirect from the current title, so I don't really see a problem.
- I still strongly prefer "paper". To me a "paper" is more academic; an "article" is more likely to be for mass consumption. Also a "paper" is more likely to be a primary source, whereas an "article" is probably a secondary or tertiary source. Also the interference issue is real; the word "article" invites confusion with Wikipedia articles, whereas "paper" does not. But in any case we don't need to decide that in this RM as the proposed title does not contain either word. --Trovatore (talk) 21:46, 13 February 2016 (UTC)
I've looked more into "article" vs. "paper" and am I now neutral on the issue. But we can deal with this later. I do think it would be good to consult the readers to see if they think that a general change of "article" to "paper" throughout the entire Wikipedia article is a good idea. If they do, I'd be happy to make the change.
Let's talk about Wikipedia:Article titles and how your title compares to the existing title. Wikipedia says that: A good Wikipedia article title has the five following characteristics:
- Recognizability – The title is a name or description of the subject that someone familiar with, although not necessarily an expert in, the subject area will recognize. Your suggested title On a Property of the Collection of All Real Algebraic Numbers is unfortunately not recognizable even to students taking set theory unless they have read a historical work that discusses the reason for this strange name. Georg Cantor's first set theory article is recognizable because it's talking about Cantor's work and, in particular, his first article on set theory.
- Naturalness – The title is one that readers are likely to look or search for and that editors would naturally use to link to the article from other articles. Such a title usually conveys what the subject is actually called in English. I don't think that readers will look or search for On a Property of the Collection of All Real Algebraic Numbers while they will search for Cantor's first set theory article since they are likely to start typing "Cantor" and unlikely to start typing "On a Property." Also, since Cantor's first set theory article is a natural shortening of the current title, there is no need to boldface Cantor's first set theory article in the text.
- Precision – The title unambiguously identifies the article's subject and distinguishes it from other subjects. On a Property of the Collection of All Real Algebraic Numbers does not even identify the property that is discussed in Cantor's article. It certainly doesn't capture the Wikipedia article's subject.
- Conciseness – The title is no longer than necessary to identify the article's subject and distinguish it from other subjects. Georg Cantor's first set theory article is shorter than On a Property of the Collection of All Real Algebraic Numbers
- Consistency – The title is consistent with the pattern of similar articles' titles. There are other titles with "Cantor's ..." in it, while your title shares consistency with the Wikipedia article on the Gödel paper.
I also decided to see what effect your suggested title and a redirect would have on the lead. Here's the modified lead (I removed the refs):
On a Property of the Collection of All Real Algebraic Numbers is Georg Cantor's first set theory article. It was published in 1874 and contains the first theorems of transfinite set theory, which studies infinite sets and their properties. One of these theorems is "Cantor's revolutionary discovery" that the set of all real numbers is uncountably, rather than countably, infinite. This theorem is proved using Cantor's first uncountability proof, which differs from the more familiar proof using his diagonal argument. The title of the paper, "On a Property of the Collection of All Real Algebraic Numbers," refers to its first theorem: the set of real algebraic numbers is countable.
One problem with your suggested title is that readers who are redirected from Cantor's first uncountability proof may get confused when redirected to a Wikipedia article titled On a Property of the Collection of All Real Algebraic Numbers. The current redirect to Georg Cantor's first set theory article is less confusing because of the "Cantor's first" in the title and because the 2nd sentence in the current article talks about uncountably infinite and the next sentence has Cantor's first uncountability proof in it.
Also, the first sentence in the modified lead is only necessary because of the suggested title change, which also requires the boldfaced Georg Cantor's first set theory article to handle the redirect. I believe quicker leads are better because they entice users to read the article. Also, I wrote the original lead to relegate the obscure title of Cantor's paper to the bottom of the paragraph since the Wikipedia article doesn't devote much space on the countability of the real algebraic numbers. (I deal with the title more in the section "The influence of Weierstrass and Kronecker on Cantor's article.")
I guess my feeling is Cantor got stuck with a poor title for his paper. I don't think we need to get stuck with the same obscure title.--RJGray (talk) 00:43, 15 February 2016 (UTC)
- The article is about a published work, so we go with the title of that work. I don't know any exception to that. If you had made it about the content, then there would be more options, but you made it about the paper itself, so I think there is really only one choice. --Trovatore (talk) 05:37, 15 February 2016 (UTC)
- I am inclined to keep the present title. @Trovatore: Have you attempted to find out which articles on published works exist on Wikipedia and examine them to see whether some Wikipedia article titles differ from the titles of the published works? Michael Hardy (talk) 01:40, 16 February 2016 (UTC)
- I'm not sure how I would really do that except by serially looking through articles on published works. I'm not aware of any exception.
- Can we agree that, as article titles, descriptions are inferior to names, assuming a canonical name exists? I would think that's kind of obvious, actually. Sometimes there is no agreed name, and you have to fall back to a description, but that's an unfortunate necessity. But pretty much every published work has a name, namely its title, so I don't see any justification for titling this article with a description. --Trovatore (talk) 19:17, 16 February 2016 (UTC)
- I am inclined to keep the present title. @Trovatore: Have you attempted to find out which articles on published works exist on Wikipedia and examine them to see whether some Wikipedia article titles differ from the titles of the published works? Michael Hardy (talk) 01:40, 16 February 2016 (UTC)
- The article is about a published work, so we go with the title of that work. I don't know any exception to that. If you had made it about the content, then there would be more options, but you made it about the paper itself, so I think there is really only one choice. --Trovatore (talk) 05:37, 15 February 2016 (UTC)
On suggested move
On Formally Undecidable Propositions of Principia Mathematica and Related Systems
- I'm not sure what you're trying to say here. Are you saying there's a disanalogy because this article is (currently) more about the content than about the paper per se? If so, then the title should refer to the content, and not to the published work; it currently refers to the published work.
- But really I don't think the content of the paper is a very natural topic for an article, given the divergent character of the two results. I think we should have an article about the paper, and I think it should be named after the paper, and it should spend more time on the paper per se than it currently does. (For example, currently, the article doesn't even seem to give the journal in which the paper was published, which I believe was Crelle's Journal.) --Trovatore (talk) 21:59, 16 February 2016 (UTC)