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I am a big fan of applying paraconsistency to logic, geometry, and all around mathematics. Such few people know about it, but to me it is an important concept and should be part of this stack exchange playground. I think that it should be called "paraconsistency" rather than "inconsistency". The difference to me is in connotation because inconsistency is usually considered unwanted and used to prove that something is impossible. Paraconsistency is often times used on purpose to deal with imperfect information or discuss logic systems that might have a truth that cannot be proved in ZFC, but leads to statements like the square root of 2 is rational.

EDIT: Here is my thought for a tag description,

Questions dealing with logical inconsistencies without admitting the principle of explosion that are somehow considered useful, such as for a real life application or proving something.

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    $\begingroup$ Is there a need for it? Do you have examples of enough questions already in the site that would benefit from it? $\endgroup$ – Andrés E. Caicedo Jan 23 '18 at 23:13
  • $\begingroup$ I doubt there are a lot of questions, but it makes it hard to find them without a tag. The philosophy stack has several questions on paraconsistency. My last question dealt with it, and I will likely have many more. Paraconsistency is a difficult concept for people to put into words and searchbwithout knowing the word. With a tag more people can be exposed. $\endgroup$ – Teg Louis Jan 23 '18 at 23:59
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    $\begingroup$ If people don't know the word, how is the tag going to help? $\endgroup$ – Andrés E. Caicedo Jan 24 '18 at 0:03
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    $\begingroup$ When someone asks a question and uses it, people who read through questions will accidently see it. And some of those people will look it up. Then some of those people will think about. And some will ask a question about it. And then it becomes a positive feedback loop. $\endgroup$ – Teg Louis Jan 24 '18 at 0:06
  • $\begingroup$ Currently there are no tags close enough for it. $\endgroup$ – Teg Louis Jan 24 '18 at 0:10
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    $\begingroup$ Ok, I am fine with that. Do you have a suggested description for the tag? Why don't you edit the question here to include the description, so people can weigh in with suggestions for changes, if there are any? $\endgroup$ – Andrés E. Caicedo Jan 24 '18 at 0:11
  • $\begingroup$ Will do tonight. $\endgroup$ – Teg Louis Jan 24 '18 at 0:12
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    $\begingroup$ And after waiting a day or so for feedback, if people seem fine with it, then later you can create the tag and we can proceed to add it to the relevant existing questions. $\endgroup$ – Andrés E. Caicedo Jan 24 '18 at 0:15
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    $\begingroup$ (I found what seemed like enough relevant questions without searching too hard, so I expect the tag will survive.) $\endgroup$ – Andrés E. Caicedo Jan 24 '18 at 0:17
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    $\begingroup$ To the list at the end of the tag description, I would add "knowledge bases in artificial intelligence" or some such. Also, rather than "logical inconsistencies" perhaps it would be better to say "logics admiting inconsistencies but". $\endgroup$ – Andrés E. Caicedo Jan 24 '18 at 2:53
  • $\begingroup$ I agree. If we give examples like AI, it might be good to add "or necker cubes". I just don't want people to conceptually pigeonhole. $\endgroup$ – Teg Louis Jan 24 '18 at 3:14
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    $\begingroup$ I am still not convinced of the necessity of this tag. $\endgroup$ – Asaf Karagila♦ Jan 24 '18 at 4:42
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    $\begingroup$ @AndrésE.Caicedo Regarding your suggestion that (if some consensus is reached) the OP should create the tag, I will point out that only users with reputation at least 1k can create tags. (And I will add that I agree with you that there is no need to rush this - waiting for ten days or two weeks to see how much feedback on the new tag we get here seems reasonable timespan for me.) $\endgroup$ – Martin Sleziak Jan 24 '18 at 8:17
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    $\begingroup$ I agree with @AsafKaragila tag not necessary at this time $\endgroup$ – GEdgar Jan 26 '18 at 11:49
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    $\begingroup$ I'm where @AsafKaragila and GEdgar are at. Ditto. Don't rush this tag. Provide more of an argument to try to convince me we need the tag. (And MSE is not Philosophy.SE, so whether the tag is used there, or not, has no bearing on whether MSE should have the tag, or not.) $\endgroup$ – amWhy Jan 26 '18 at 21:23
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There are currently two questions with answers mentioning paraconsistency, https://math.stackexchange.com/search?q=paraconsistency, which would suggest that there is really no need for the tag. This figure, however, seems a bit misleading since, on the other hand, there are 63 results mentioning "paraconsistent". https://math.stackexchange.com/search?q=paraconsistent. After a brief glance, most of these questions deal with technical issues, some of them within logic, some within computer science (which, in the context of artificial intelligence, is one of the main areas where paraconsistency is investigated). This suggests there is a demand, although admittedly small, for the tag.

It seems to me that the kind of already existing questions that could use the tag suggests that there is a market, albeit small, for it. Combining this with the mere number of questions mentioning the keywords above which, although not terribly large, is not insignificant, I can see some of the benefits of having the tag around. By way of contrast, there are 37 questions with the tag , 16 with the tag , 13 with the tag , and only 3 with the tag . I confess the latter I found quite surprising, I would have expected a significantly larger number.

None of the current logic-related tags suggest or hint at the specific topics one may want to discuss in the context of paraconsistency, so I don't feel the tag would be redundant. I also don't feel it would be useless, as I expect that there are questions that could use the tag and are simply "invisible" at the moment to their intended aaudience. Let me give a closely related example to illustrate this last claim. There are several questions on the site pertaining to knowledge bases, and they are tagged , sometimes combined with something else, because we do not have a tag for knowledge bases or many of the other topics that appear in the setting of logic in computer science. Even some experts in logic may be unaware of what knowledge bases are, so the current tags are not terribly useful here. A more specific tag would very likely help. I believe paraconsistency would benefit in a similar way.

An objection to having this tag seems to be that people who are not aware of the meaning of the word would not benefit from it. That said, as mentioned in the comments beneath the question, people who use the site may actually learn about it by reading questions carrying the tag. In that sense, I do not find the tag useless or superfluous. (I admit I do not know statistics indicating that this has been a side benefit of introducing other tags.)

I would be happy to create the tag if it comes to that, so that Teg or other users who may be interested in having it around do not have to wait until they reach the 1K reputation requirement to create it themselves.

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  • $\begingroup$ Sorry to bother you, but it might clear up some of our tagging rules if you could weigh in here. From the current tag wikis it is not clear to some of us whether ordinals/cardinals and transfinite induction fall under elementary-set-theory, set-theory or neither. I have been very happy with your (and Asaf's) work in keeping the site organized in this matter. To avoid mistagging in the future it would help to have these points clarified. $\endgroup$ – Jyrki Lahtonen Aug 14 '19 at 6:35

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