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Proof theory is a branch of mathematical logic which treats proofs just like other mathematical objects, like numbers and sets. It's an extremely technical field, involving Gödel-numberings, derivability conditions, reflection principles, and transfinite ordinals (oh my!). Contrary to what seems to be a common belief on Math.SE, it's NOT about what makes a good and rigorous proof, how to write proofs, and the general subject of the role proofs play in pure mathematics.

Yet that seems to be the meaning people are assuming when they select the tag. It seems like almost all the questions with this tag are mislabeled. I'm aware that if you hover over a tag, descriptions pop up, but a lot of people, especially first-time users, may not notice them. So would it be possible to do some kind of cleanup of the questions associated with this tag?

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  • $\begingroup$ I wonder if there is a good alternative name for that tag, without the danger of being misused so often. $\endgroup$ – azimut Oct 8 '13 at 8:24
  • $\begingroup$ Well, there are tags that more closely match what people seem to think proof theory means: the [proof-writing] tag and especially the [proof-strategy] tag. As far as alternative names for proof theory, it may be good to have an ordinal analysis tag; at least the proof theory questions I've personally been asking fall largely in the subfield of ordinal analysis. $\endgroup$ – Keshav Srinivasan Oct 8 '13 at 13:27
  • $\begingroup$ @KeshavSrinivasan, I think the proof-strategy tag is misused as well, and the proof-verification one is actually defined wrong. Really, very few questions should have any tags relating to proof. $\endgroup$ – dfeuer Oct 13 '13 at 21:53
  • $\begingroup$ Might the problem be alleviated by renaming "proof-theory" as "theory-of-proofs"? More emphasis on "theory" might deter some of the misuse. $\endgroup$ – Andreas Blass Oct 19 '13 at 0:18
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It is possible to do. It would be a good thing to do. And you can help by suggesting edits that change the tags of incorrectly tagged questions.

Some advice:

  • Don't edit too many questions at once. Whenever I have done batches of edits in the past I have tried to ensure that only one or two of my edited questions appears on the front page at any time. (This is somewhat more strict than Martin Sleziak's answer here.)
  • In the "Edit Summary" write something to the effect of "removing incorrect proof-theory tag". Since your edits will need to be reviewed by other users, this will help explain why, for instance, a retagging edit on a two-year-old question should be accepted.
  • If you notice any other problems with these posts (e.g., non-$\LaTeX$ed mathematics, improper grammar, un-umlauted "o"s in Gödel), you can suggest these changes as well.
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  • $\begingroup$ Is there any way to change tags without bumping up the question? $\endgroup$ – Keshav Srinivasan Oct 8 '13 at 6:58
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    $\begingroup$ @Keshav: No, there is not. $\endgroup$ – Asaf Karagila Oct 8 '13 at 7:05
  • $\begingroup$ @KeshavSrinivasan: (Un)fortunately not. I tend to agree with this MSO answer which essentially states that invisible edits would be open for abuse, and bumping the questions makes "quality control" of edits easier. $\endgroup$ – user642796 Oct 8 '13 at 7:05
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    $\begingroup$ (There is one exception: If tags are deemed to be equivalent, they can be merged, which does invisibly transform all questions tagged, say, settheory to be tagged set-theory. Of course, the proof-theory situation does not fall into this category.) $\endgroup$ – user642796 Oct 8 '13 at 7:09
  • $\begingroup$ Why would they be open for abuse? Don't low-reputation users need to get their edits approved, and aren't high-rep users trusted not to engage in abuse? Maybe there should be a higher reputation threshold for retagging that doesn't result in a bump. $\endgroup$ – Keshav Srinivasan Oct 8 '13 at 13:25
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    $\begingroup$ @Keshav: Don't you think that CEO of financial companies are trusted enough not to commit Ponzi schemes? Oh wait... nevermind. $\endgroup$ – Asaf Karagila Oct 8 '13 at 22:48
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    $\begingroup$ @KeshavSrinivasan: I witnessed a top-30 user on one of the beta SE sites "rage-quit" and edit all of their posts to include nothing but nonsense. For some reason the self-edit rate limit was removed for "sufficiently high-rep" users, and instead of 4 or 5 edits going through, closer to 70 were made (again, a beta site). Unfortunately, high-rep users cannot be trusted to always act in a responsible manner. $\endgroup$ – user642796 Oct 9 '13 at 4:11
  • $\begingroup$ @ArthurFischer But aren't high-rep users trusted with all sorts of privileges? What makes this one so different? If not high-rep users, what about giving moderators the ability to do it? $\endgroup$ – Keshav Srinivasan Oct 9 '13 at 4:54
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    $\begingroup$ @KeshavSrinivasan: What makes this different is that the people who designed the site have decided against it. And except for certain extra tools, I am more than happy to be treated as a normal user. $\endgroup$ – user642796 Oct 12 '13 at 4:22

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