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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The result was Speedy keep Snowball, withdrawn. NAC. Ten Pound Hammer and his otters • (Broken clamshells • Otter chirps • HELP) 17:21, 16 September 2008 (UTC)[reply]

Abstract nonsense

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Abstract nonsense (edit | talk | history | protect | delete | links | watch | logs | views) (delete) – (View log)

The following is why this article should be deleted:

  • This article is unencyclopedic since it is not giving any specific useful information
  • This article does not seem to have any particular purpose. It is well cited but this does not give any reasons as to why this article is useful
  • Just because 2-3 people have used the term 'abstract nonsense' does not mean that an article on the topic should be created
  • This article may give the wrong impression of category theory
  • This article is not important enough to serve as an article in an encyclopedia (despite the references) per WP:N
  • This article is therefore unencyclopedic; it does not provide any useful information nor does it give sufficient evidence that this article should be in an encyclopedia
  • It is not possible to add any further input to this article; citing a couple of people who have used the term is useless

Topology Expert (talk) 11:22, 16 September 2008 (UTC)[reply]

  • keep. The expression proving things by abstract nonsense" is well-established and frequently used. Moreover, its use is not limited to category theory. The article itself is well-written. It would be far-fetched to say that it is derogatory toward category theory. The article can definitely be helpful to a novice not yet familiar with the expression. I find the last two sentences particularly helpful. Perhaps the examples section should be expanded. I would like to make a more specific point given the nature of the expertise of the deletion nominator: specifically in topology, "general nonsense" arguments using classifying spaces and diagram-chasing are common, though perhaps more so in homotopy theory than in low-dimensional topology. Katzmik (talk) 12:13, 16 September 2008 (UTC)[reply]
I understand your point. However, do you have any specific references indicating that this term is 'well-established and frequently used'. I don't have much experience in WP; is it common for articles to be about a single quote, joke etc...?
I agree that diagram chasing is somewhat a 'nonsense' argument but is nevertheless as formal as any other argument. The same goes with results in homotopy theory. Because of this I am compelled to ask whether there is any specific classification of arguments; i.e when it is 'nonsense' or 'sense'. Or, does one just use his intuition to determine whether an argument is 'nonsense'? In any case, this article does not describe which arguments are 'nonsense' and only lists a couple of 'nonsense' arguments. In my opinion, this is pointless; the whole purpose of the article is to describe why diagram chasing is 'nonsense' (or other such arguments).
Topology Expert (talk) 12:37, 16 September 2008 (UTC)[reply]
  • The title abstract nonsense should link somewhere, as it is a well established phrase and a likely search phrase. http://stats.grok.se shows that "Abstract nonsense" and its redirect "General abstract nonsense" receive a steady stream of page views, which we want to continue to support.
       Overall, I think the deletion nomination speaks to the need to improve the article - which I agree with. However, established practice is that articles are not deleted only because they require improvement.
       I do think there is a valid question of whether this topic should be covered independently, or in a section of the category theory article. But I don't find the deletion rationale compelling to delete the content altogether. — Carl (CBM · talk) 12:43, 16 September 2008 (UTC)[reply]
    • Thankyou for your response. However, I must emphasise that I am not saying that the article needs to be improved. For a start, it can't be improved (how many more quotes can you give from people who use the term 'abstract nonsense'). Second of all (as I mentioned earlier), it is not notable enough per WP:N. Basically, the content does not deserve to be in an encyclopedia. Topology Expert (talk) 12:48, 16 September 2008 (UTC)[reply]
      • I'm quite confident the material could be improved. As I said, the question of merging this into category theory is very valid. I tend to lean towards merging. By the way, please use bullets to indent replies to bulleted posts, to make conversation easier to follow. — Carl (CBM · talk) 12:51, 16 September 2008 (UTC)[reply]
I would define an argument by "abstract nonsense" as an argument characterized by the following:
  • it uses very general principles rather than specific techniques; the advantage of this is in general both that (1) one can avoid being clever (which is difficult) and merely rely on erudition, and (2) frequently such an argument is more convincing to a more sophisticated crowd.
  • it is typically formal, non-constructive, or "by contradiction".
Hope this helps. At any rate, even if one does not have a formal definition, the term is well-established in the mathematical community, and therefore a legitimate subject for a page in my opinion. Katzmik (talk) 12:45, 16 September 2008 (UTC)[reply]
That's interesting. I tend to view "abstract nonsense" mainly as a synonym for "category theory". Mathworld has a different definition. — Carl (CBM · talk) 12:48, 16 September 2008 (UTC)[reply]
In my opinion, category theory is a generalization of different notions in mathematics (along with other concepts, of course). For instance, a morphism in category theory is a generalization of homomorphisms, continuous maps, k-times continuously diffentiable maps (between smooth manifolds) or even morphisms (in the case of fibre bundles)! This article critizises category theory and instead of stating its use, states why its 'nonsense'. In any case, category theory is definitely not 'abstract nonsense'. Topology Expert (talk) 13:00, 16 September 2008 (UTC)[reply]
Yes, category theory is not nonsense. But the term "abstract nonsense" has long been used to refer to it. As Salix Alba points out, this is not much different than calling i imaginary, when it certainly is not. — Carl (CBM · talk) 13:02, 16 September 2008 (UTC)[reply]
I agree but is this term so important that it should be kept in an encyclopedia? The other criterion for determining the importance of the article is to see how it relates to other concepts in its field. From what I have seen, the only purpose of this article is to give a 'synonym' for category theory. Despite the fact that it is well accepted, it does not seem so have any particular purpose other than 'teaching a new term'. Topology Expert (talk) 13:00, 16 September 2008 (UTC)[reply]


  • Keep article is well sourced, well written and encyclopedic; term is sufficiently notable to have a MathWorld entry; "does not seem to have any particular purpose" is a subjective view and is not grounds for deletion. Gandalf61 (talk) 12:49, 16 September 2008 (UTC)[reply]
  • Keep. I would not say this article is well written, but that has nothing to do with whether it should be deleted or not. "Abstract nonsense" is a widely used term in mathematics, and its usage is very well attested. As Katzmik points out, it doesn't just refer to category theory, and these days it is hardly derogatory - it is even used with some affection, and not just by category theorists. I've no idea what "useful" is supposed to mean in the context of deciding whether an article is encyclopedic, or how it pertains to any criterion for deletion from, say, WP:NOT. Please remember that Wikipedia's coverage of mathematics is not limited to mathematical coverage of mathematics. Just because it is not a mathematical term with a precise definition does not mean it is unencyclopedic. The term is an important part of the sociology of mathematics if nothing else. Geometry guy 12:52, 16 September 2008 (UTC)[reply]
  • Thankyou for your opinion. You said that 'abstract nonsense' is a widely used term in mathematics but from what I know it is only used in category theory. Second of all (now that I have established that it is not widely used), why create an article describing why diagram chasing is nonsense (which is basically what the purpose of the article is at this point in time)? It does not seem to be a useful thing to do. However, I could be wrong about saying that this term is only used in category theory. If you have any references contradicting what I said, could you please give them? Topology Expert (talk) 13:09, 16 September 2008 (UTC)[reply]
  • Could you define for me what you mean by "only used in category theory"? In a sense, everything is category theory, in which case you are surely right, but that doesn't contradict my assertion that the term is widely used. Was Grothendieck doing category theory when he proved his version of Riemann-Roch? Are schemes category theory or algebraic geometry? Can you define for me what you mean by "useful"? You obviously seem to think that the term "abstract nonsense" can only be read literally as saying "abstract mathematics is nonsense". This completely ignores the history and sociology of the term, which the references in the article already document. Geometry guy 13:30, 16 September 2008 (UTC)[reply]
I would move it to Proof by abstract nonsense. Any buyers? Katzmik (talk) 12:53, 16 September 2008 (UTC)[reply]
I think abstract nonsense is a more likely search term and a more likely phrase to be linked (would you prefer to see "this is a proof by abstract nonsense" in an article?). — Carl (CBM · talk) 12:58, 16 September 2008 (UTC)[reply]
That's not a problem necessarily. One could leave abstract nonsense as a page with a redirect. Katzmik (talk) 13:02, 16 September 2008 (UTC)[reply]
Sure, but the title we use should reflect the way that most people would expect the page to be named. The main role of the title is to make the article easy to find. — Carl (CBM · talk) 13:04, 16 September 2008 (UTC)[reply]
  • Keep An important part of the history of mathematics. There are many example of degority terms used to express resistance to change for new mathematical concepts, irrational numbers, imaginary numbers, normally marking the start of important developments in the subject. Abstract nonsense is a fine example of this tradition. --Salix alba (talk) 12:56, 16 September 2008 (UTC)[reply]

I definitely agree. The question in this case: Is the article useful enough to serve as encyclopedic content. This is a term describing category theory and is not a 'definition' unlike your examples. —Preceding unsigned comment added by Topology Expert (talk • contribs) 2008-09-16T13:02:31

  • Keep (or maybe merge into category theory.)
    • It is a commonly used phrase in the mathematics community, used to refer to diagram chasing arguments which tend to straight forward but lengthy and usually not very illuminating.
    • The article provides useful information in the sense that when first encountered by students it might be confusing.
    • There might be a case for renaming the article to something like proof by abstract nonsense.
    • Alternatively, it could be merged into category theory as a subsection, but I see little reason for deletion —Preceding unsigned comment added by TimothyRias (talk • contribs) 2008-09-16T13:07:44
      • I was not refering to the possible confusement of students of category theory, but to the confusement of students (or other people unfamiliar with the phrase) first encountering the phrase "abstract nonsense" in certain proofs. For them it could be quite useful to google the term and find the wikipage that explains what is meant by it. Note that there are also wikipages for proof by inpection, trivial (mathematics) and other mathematical jargon. (TimothyRias (talk) 13:25, 16 September 2008 (UTC))[reply]
      • The fact that students find epsilon-delta confusing has served as a basis for endless amounts of verbiage at at least half a dozen distinct pages. I am not sure if this page describes a sociological phenomenon or a I need an aspirin phenomenon, but it is certainly a phenomenon :) Katzmik (talk) 13:17, 16 September 2008 (UTC)[reply]
  • That is true but I do not think that the same should apply to category theory (most students who do category theory would have a sufficient mathematical maturity to be able to understand it after some thought). Topology Expert (talk) 13:22, 16 September 2008 (UTC)[reply]
    • The fact that many mathematicians have heard the term does not give any specific reason as to why the article should be created. Many mathematicians know what the fundamental group is for instance and therefore there is an article on it. However, the fundamental group is an important concept in mathematics. On the other hand, 'abstract nonsense' is not a concept in mathematics and means nothing. Topology Expert (talk) 13:22, 16 September 2008 (UTC)[reply]
  • Speedy keep The term [general] abstract nonsense is in widespread use, especially in topology. Google Scholar search shows that, contrary to what the nominator claims, it is far from having been used only by a 2-3 people such as Saunders Mac Lane and Norman Steenrod (actually two of the founders of category theory). I imagine it should be enough to attend a single conference on algebraic topology to see this. (I haven't, but then I don't claim to be an expert in topology. It's merely an area in which I attended a handful of lecture courses and a couple of seminars.)
It may make sense to merge this article into category theory. It may make sense to optimise the text in order to make it absolutely plain even to the humour-impaired that the term "abstract nonsense" does not imply that category theory is nonsense any more than use of the term "field" implies that algebraists are peasants. But an absurd deletion discussion that should never have been started is not the right place for this. --Hans Adler (talk) 13:29, 16 September 2008 (UTC)[reply]

The term abstract nonsense is used to describe proofs and arguments which use more abstract methods then (apparently) necessary to prove the desired result, often used to refer to category theory or topos theory.(unsourced, and probably unsourcable). The following have used it[1][2][3][4].

  1. Re It gives no useful information Possibly. Though I am not opposed to such a criterion, let's suppose that every article needed an auxiliary "usefulness" statement to be filled out by the article creator. How would one fill this out say for an article on Wings of Desire? I think if we decide "utility" is a criterion, we need to carefully think through what this would imply for article generally.
  2. Re Just because 2-3 people have used the term 'abstract nonsense' . The phrase "abstract nonsense" is widely used, certainly by far more than 2-3 people. The suggestion "just because 2-3 people use it" is misleading.
  3. Re This article "may" give the wrong impression of category theory Any article "may" give the wrong impression about its subject. That seems to me like a very strange use of a modal argument for deletion.
  4. Re It is not possible to add any further input to this article; citing a couple of people who have used the term is useless Since when is the possibility of adding anything a requirement for an encyclopedia article? For example Hilbert's fifth problem is solved completely, and the solution pretty much killed an area of mathematics. There is Montgomery-Zippin's book which is the definitive statement.. Since it's not possible to usefully add input to the article on Hilbert's fifth problem, should we delete that also. Maybe the proposer means something else by this comment, but I think more clarification is needed.
  5. Re: Arthur Rubin's objection. I think it's true that the usage does not refer to a specific technique or result such as diagram chasing or the five lemma. But the term is often used and does have a meaning in terms of mathematical activity.
--CSTAR (talk) 17:13, 16 September 2008 (UTC)[reply]

Hi, Please take a few minutes to use the material discussed here to improve the page abstract nonsense. Katzmik (talk) 13:42, 16 September 2008 (UTC)[reply]

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.
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