Wikipedia:Articles for deletion/Foundational status of arithmetic

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 of the debate was delete. I count five deletes, two keeps, and lot of hand-wringing, but the consensus seems to be that people don't like the title, they don't like any of the writing, and all of the material is covered elsewhere. Chick Bowen 16:28, 19 February 2006 (UTC)

Foundational status of arithmetic

A convoluted content fork of Arithmetic pushed forth last 2003 by Jonhays0, inventor of the term Generatics and Generating arithmetic.-- Perfecto 21:54, 12 February 2006 (UTC)

• Delete per nom. Nothing links here, nothing to merge to anywhere. --Perfecto 21:54, 12 February 2006 (UTC)
• Comment. I've created a few links to this page, and asked User:R.e.b. if he'd like to comment here or contribute to the article. He is a somewhat regular contributor to some of the articles on foundational issues in mathematics and a well-respected professor of mathematics. Michael Hardy 01:16, 13 February 2006 (UTC)
• Keep a topic extensively covered in Gödel, Escher, Bach and apparently not described on any other page I could find. May need a name change. —Wahoofive (talk) 17:18, 13 February 2006 (UTC)
• Weak delete. There's some stuff here that's sort of interesting, but it's highly POV and could be OR. If kept it needs serious cleanup, and I'm not sure just what the path to that cleanup would be. BTW the article arithmetization of analysis, on which this article relies, has similar problems. --Trovatore 21:39, 13 February 2006 (UTC)
• Weak delete, per Trovatore . It clearly requires cleanup, but I don't think there is anyone who is capable (with with the knowledge and ability) of it. Needs, at least, a name change and total rewrite. Arthur Rubin | (talk) 22:38, 13 February 2006 (UTC)
• Delete, per Arthur Rubin (the last three votes, mine including, resemble a successor function :) Oleg Alexandrov (talk) 00:17, 14 February 2006 (UTC)
• Keep: It's a poor article for being excessively chatty, insufficiently detailed or focused, and poorly styled as well, but the subject is historically interesting and the article is not inherently worthless. Put an expert attention notice (and hey, why not a sources-needed notice too?) at the top and let it fix itself; this article is merely bad, not perniciously bad.

I also disagree with Arthur Rubin that there is no one with both the knowledge and ability to fix the article: I think there are plenty of mathematics history buffs out there. The first one to read the article will surely improve it. Meanwhile, the cleanup notices will warn other people not to take it too seriously, or encourage them to look up some facts to improve it themselves.

I also disagree with Trovatore: it is very unlikely to be original research, as it basically makes note of some famous quotations, a few prominent historical trends, and some very basic mathematics. It is also not "highly POV": it is weakly so at worst, and mostly just in the writing style and lack of details. The "arithmetization" of mathematics, which is the point of the article, is well-known to mathematicians. Ryan Reich 02:55, 14 February 2006 (UTC)

• I think the agenda of the article is clear; the author thinks that all of mathematics can be reduced to the arithmetic of the natural numbers. He's quite wrong about that; the reals are fundamentally richer than the naturals. (Of course the reals can be thought of in terms of the naturals in second-order logic, but I seriously don't think that's what the author has in mind.) To get a clearer picture of his agenda, check out this link from his user page: http://members.fortunecity.com/jonhays/fable.htm .

Now I didn't say the article was worthless; I said there was some interesting material there. But it is extremely POV, not just a little bit, and I still think it's kind of OR, which is not to say there aren't citations, just that I think his synthesis of them may not be what the original authors had in mind. --Trovatore 04:05, 14 February 2006 (UTC)

• • You know, reading it again, I'm still pretty sure the author has an agenda, but I'm less sure what it is (and I'm also less sure what the point of the "fable" is). Maybe that's what you meant about being "POV in the writing style". Ordinarily a good test for NPOV is if you can't figure out the author's opinion, but I think that doesn't apply if the reason you can't figure it out is that it isn't written clearly. --Trovatore 05:38, 14 February 2006 (UTC)

Remember, you don't need full second order logic here; the only sets you need are Weierstrass cuts; I think that is what he has in mind. Septentrionalis 06:04, 15 February 2006 (UTC)

An arbitrary set of naturals can be coded by a real, so yeah, I think you pretty much do need full second-order to get the reals from the naturals. And of course "mathematics" doesn't stop with the reals.... --Trovatore 06:13, 15 February 2006 (UTC)

Delete basically seems to be the flawed program of Principia Mathematica and Axiomatic set theory, I would class this as original research. --Salix alba (talk) 11:45, 15 February 2006 (UTC)

• Comment With two days left in the AfD, I'm not convinced any two of us agree on what the article is actually about. That's certainly not an indication of a good article, but it also makes me nervous about deleting it, because there might be something there that could be cleaned up. Should someone invite Jon Hays to comment? Probably, on general fairness grounds, though having browsed some of his comments, I'm not sure he's really going to clear things up for us. --Trovatore 18:26, 15 February 2006 (UTC)

• Comment. After several tries, I have no idea what the article is supposed to be about. Dmharvey 17:43, 16 February 2006 (UTC)
• Delete. Trovatore and Arthur Rubin cannot make sense of it, nor can lesser beings like I. Therefore, this article is not useful to the reader, who can better turn to Peano axioms. It is also not useful to editors, as it needs to be completely rewritten. Better to delete it and, if somebody feels like it, they can start afresh. -- Jitse Niesen (talk) 18:56, 16 February 2006 (UTC)
• Comment, not really sure whats its about, but there is some stuff here which should be covered, but I think its best to start afresh. (Some material may be covered elsewhere, I've not really found my way around the relavant articles yet). Heres my take on some of the points in the article:

1. 1. Gerneral thesis: much of mathematics can be generated from simpler elements.
   2. Sucessors: how to get the natural numbers from set theory, I think this is how Russle did it in Principica Mathematica, covered at length in Godel Escher Bach. Covered in successor operation
   3. Reals from Integers: use cantor sets
      • The effort to have a Cauchy sequence of pairs is odd. Septentrionalis 21:07, 16 February 2006 (UTC)
   4. Complex numbers from reals: this seems dodgy, while we can go easily go from pairs of reals to complex numbers, we do not get the additional multiplication structure. Personally I don't like this approach. In a lot of situations (analalytic, poles) complex numbers behave more like the reals than pairs of reals. My understanding of complex numbers improved a lot when I gave up thinking of complex numbers as pairs of reals and started thinking of them as an algebraic extension, sort of the number line with a bit more.
   5. Random philosophical notes. Contrast between geometry and arthmetic, there is scope for a good treatment of this. I saw Atiyah give a great keynote speach on the link between the two along the lines that they are two side of the same coin and much of the best mathematics has happend when one has been transfered into the other.
   6. (Off topic) Are numbers a real thing? There is a good history of people questioning various extensions, negative numbers, zero, irrationals (named because Descarte/Kroneker? though they were not a rational concept to hold), imaginary numbers (likewise name as a put down). Theres was a recient edit somewhere which addressed this but it was quickly deleted.
   7. minuend, subtrahend two terms new to me, don't know if are common, not given any proper treatment.
      • Standard nineteenth century usage. Septentrionalis 21:07, 16 February 2006 (UTC)
   8. Pedagogy (teaching). There is definatly a school of thought that one way to teach maths is a purely genarative, start with the most basic concepts (sets) and work up. Well it took Russle several thousand pages to get as far as the natural numbers using this aproach, and then we find that maths is axomatic after all Godel/ZFC.
   9. Links. Mostly to authors own pages so OR.

• So there is the germ of some good articles here, much is probably already covered elsewhere. Unconviced it is a coherent whole, or this article is a good starting point. --Salix alba (talk) 19:30, 16 February 2006 (UTC)
• What everyone agrees on is that the writing is, as per nom, convoluted. It is a POV fork (see Wikipedia:Content fork). The concept's principal author is also the article's principal author, Jonhays0 (see Wikipedia:No original research). Because I find absolutely everything in the article is somewhere else, I deny merge. Until I see reliable sources independent of Jonhays0, I say delete. I'm disappointed we've been serving as free web hosting to jonhay0's ideas since 2003. End this. --Perfecto 20:51, 16 February 2006 (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.