A user flagged a comment of another user, with the specific request to delete the other user's comment because it is "factually incorrect".

Now, I'm inclined to just ignore flags like this, as I've thought that the job of the moderator is to look after the community's interests and to catch/prevent/clean-up-after abuse; you know, little odd jobs here, little lubrication there. I'm pretty sure the community didn't elect little-o-me to be the ultimate authority on what's right and what's wrong (mathematically)!

To play the devil's advocate against myself, I realize that perhaps Mathematics.SE is the only StackExchange site in which "correctness" can be largely decided (please don't quibble with model-theoretic issues, or things about AC/ADC etc here). So if I were to have been a properly educated Mathematician, I may have in fact been able to decide whether the comment was factually correct or not. So it may be feasible to honour such requests (very slim chance of me being the actual perfect mathematician though).

Anyway, this post is part call for discussion, and part call for sanity:

People! Please think before you flag!

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Oh snap, I have a deja vu. Didn't you post this sort of thread on the meta several months ago? –  Asaf Karagila Jun 29 '11 at 18:23
    
Related: meta.math.stackexchange.com/questions/1156/… –  Aryabhata Jun 29 '11 at 19:04
    
@Asaf: maybe? I do like to crowd-source checks of my own sanity. –  Willie Wong Jun 29 '11 at 20:14
    
Quis custodiet ipsos custodes? en.wikipedia.org/wiki/Quis_custodiet_ipsos_custodes%3F –  Georges Elencwajg Jul 3 '11 at 22:48
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5 Answers

If the flagger believes that a comment is (mathematically) incorrect then I think that the appropriate course of action is to reply with a logical argument - not to request that the comment be censored.

Consider an analogous historical example. If such censorship powers were granted to journal editors then many of the seminal papers on orders of infinity and nonstandard analysis probably would have been censored by Cantor - who mistakenly thought that he had proved the inconsistency of infinitesimals. As J.L. Bell wrote, Cantor's "abhorrence of infinitesimals went so deep as to move him to outright vilification, branding them as `Cholera-bacilli' of mathematics".

History is a great teacher on such matters. Let's not repeat such mistakes here.

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It wasn't a mathematical statement that was in dispute, if the comment in question is what I think it is. –  Qiaochu Yuan Jun 29 '11 at 19:52
    
Actually, I am asking about this in general with regards to mathematical statements being in dispute. (@Qiaochu: I'm pretty sure it is not what you think it is.) –  Willie Wong Jun 29 '11 at 20:11
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I don't think so.

If X sees a post which appears incorrect, then X should really leave a comment indicating this and explaining why. If a comment is not enough, then X should probably consider leaving an answer of her own.

If I see a post flagged on those grounds and if I happen so see that the post is incorrect, then I might leave a comment indicating so, but deletion is really something I would not consider at all.

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the only time we do such things on Stack Overflow is when the answer is not just incorrect but wildly incorrect; eg when the question asks "how do I increment a number in python" and someone answers "switch the electrical input from AC to DC". If it is just a mistake, unless it is the type of mistake that may result in the death of hypothetical children, it should be commented as such, downvoted, etc. –  Jeff Atwood Jul 1 '11 at 5:22
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Incorrect posts can still be helpful (or more commonly posts that give the right idea but have a mistake in them somewhere or don't cover a degenerate case or something) -- the easiest way to make sure the reader is aware of these issues is to add comments. –  Alice Aug 15 '11 at 13:58
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To answer the question in the title: No, it's not in the moderator's job description to patrol for correctness. The correct action for a user who disagrees with the correctness of a comment would be for that user to post a follow-up comment.

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I don't think it is the responsibility of the moderators to enforce correctness either.

But on a different note, I think that it can be useful for mistaken comments to remain posted in the sense that others will correct them. In this way, the comment chain might address misconceptions or vagaries in the answer, or provide a more complete answer. This is useful.

On a side note:

On Qiaochu's old question on the same topic, mentioned in the comments above, he mentioned the potential problem that on posts with many comments, only the most voted get shown. This means that incorrect comments might be shown while the corrections are not. I don't see a way around that within the scope of this site as long as we cannot downvote comments and as long as we allow answers or significant information within the body of comments. But I think it's more reasonable to expect people to expand all comments than to demand perhaps unreasonable changes to the SE architecture.

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+1 especially for the side note. –  Isaac Jun 29 '11 at 19:42
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I don't think that a moderator should "patrol" for correctness.

But I think that a moderator should delete a flagged comment if

  1. there is no doubt that the comment is factually wrong
  2. the commenter does not react.

Mathematical content in comments should generally be discouraged, precisely because it can be neither down-voted nor edited, it should be reserved for interactive content, hints, suggestions for clarification, etc. Therefore, mathematical content of comments should not have any protected status at all (that is, deletion of content that has deliberately be sheltered from downvotes is not censorship).

It would be better to move the comment to an answer but I doubt that this is as easy as deletion.

I would not expect a moderator to do anything about a flagged comment if the mod cannot immediately decide its correctness, but this is because of the undue burden on the mod, not because of the rights of the comment writer.

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I disagree with this opinion in general. I try to maintain a certain (admittedly subjective) standard in my answers and would not want a trivial or only tangentially related comment of mine be moved to an answer signed by me. Also, it is unclear to me what it means for a commenter not to react. What is the time threshold? Finally, I sometimes leave factually wrong comments, provided they are not all-too-silly goofs, in order not to isolate the reactions from their context. This is a matter of honesty, I believe. –  t.b. Jul 1 '11 at 11:25
    
Also, see Jeff's comment to Mariano's answer. –  t.b. Jul 1 '11 at 11:28
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