# Tag pairs such as elementary-set-theory and set-theory are hard to decide upon and may appear to be condescending. (With proposed solution.)

### Proposed solution:

Rename:

• elementary-set-theoryset-theory
• set-theoryadvanced-set-theory

### Motivation:

Set theory is a hugely popular field of study, even indispensable — a chapter introducing it is seen very often in course books that do not directly deal with the theory. So it is important to make the corresponding set of tags accessible. I observe that the current situation, where we have elementary-set-theory and set-theory, has drawbacks:

1. The majority of questions in any discipline are of the simpler, more shallow variety — which is not to downplay their value, as without strong basics there can be no progress. So it stands to reason that the tag for basic questions should be more discoverable. My claim is that elementary-set-theory is less discoverable than set-theory. I base it on my own experience but I hope the reader finds it plausible too, if only because «elementary» is an added qualifier and therefore has to be thought of explicitly.

2. My introspection is that attaching either «set theory» or «elementary set theory» is disheartening. So because there is an hierarchy attached, an hierarchy that has reputational, socioeconomic consequences. It is evident even by the description of the tags: words like «graduate» versus «under-graduate». Compare with «orthogonal» tags, such as set-theory and logic, which are not immediately comparable is either sociological or administrative sense. To be explicit:

• Attaching «set theory» opens one to having the tag removed by a protective wielder of a gold tag badge — with effect ranging from a mild annoyance to a humiliating experience. To justify my use of the adjective «protective»: I suspect that the tag gets «downgraded» to elementary-set-theory more often than the other way around — of course I am open to be shown wrong.
• Attaching «elementary set theory» when there is doubt in one's heart is an admission of inferiority upfront, by the same logic as above, and with equally disastrous consequences to one's psyche.
3. The dividing line is arbitrary and vague. For example, the words «undergraduate» and «graduate» have very little meaning to me since I am not a part of the academic structure of the U. S. A. and hence have only indirect experience with what they mean. In some other countries, the academic life is structured differently. Furthermore, Mathematics is studied and used in many technical disciplines that will each have a different progression of mathematical expertise. It follows that the moral dilemma of assigning one tag or another is going to come into play fairly often despite tag descriptions. See also this discussion as regards tag high-school that goes by the same argument.

Confusion is also evidenced by questions here on meta such as this one — but even the descriptions of tags show that the distinction is not clear-cut from the point of view of Mathematics (or else why invoke administrative trivia).

In Mathematics, we go to great lengths to postulate the merit of the mind over worldly hierarchy and to grant every field equal, or rather incomparable, importance. This convention seems to be vital to the mental health of the Mathematics society. But if hierarchy is natural, as in the case here, we can as well make it «extra-gratifying» rather than «extra-disparaging» simply by attaching a positive qualifier instead. Then questions would go to the simpler category by default and be sometimes promoted.

Of course the proud set theorists will have to give some way by admitting that elementary set theory is also set theory. It could be good for them, since it is those elementary applications that endow the field with the significance that it enjoys, so swiping them under the carpet as «elementary» seems to be taking a saw to the branch they sit on.

On a final note, and to the immediate objection that there are too many repetitive trivial questions: the right way to deal with such is to institute a perfect community answer and close each new question as a duplicate. Eventually we shall have an artificial intelligence suggest the perfect answer to the prospective questioner as if by magic, and everyone will be happy.

### P. S.

To address an objection brought up in a comment by @rschwieb that I am sure comes to the mind of many a reader.

"Elementary" is a perfectly sensible modifier to apply to some questions. If it can be easily explained by basic principles from the field, then it is reasonable to call it "elementary." If it were really pejorative then I doubt people would try to sell books like these. Set-theory is a broad tag, and captures a lot of things. It is useful to have a sub-tag that narrows down to elementary questions, for someone who is learning the subject.

Two presuppositions can be extracted from this argument:

• A word must be pejorative by itself in order for its use to be harmful. («Argument to word value».)

• The tags x and elementary-x are not pairwise exclusive. («Argument to non-exclusivity».)

That the first is not always true should be clear from an example kindly provided by Najib Idrissi in a comment:

This kind of creative writing exercise belongs on your blog, not here.

It is easy to see how such a comment may be characterized as condescending and dismissive, thus harmful, even though all of the words are neutral.

To the second, I take it that the tags are intended to be (or, rather, «usually thought of as») pairwise exclusive, based on another quote from Najib: (And also on my own informal observation.)

It's always been my impression that these sort of tags are mutually exclusive: set-theory vs elementary-set-theory, abstract-algebra vs algebra-precalculus, probability vs probability-theory, etc.

A further objection: («Argument to insignificance».)

I think you are suggesting a calibration of caution to prevent ego-harm that is far too sensitive. We cannot put everyone on eggshells because some people are very good at finding ways to be offended. Now, sometimes in culture such things need to happen, but in this case I do not believe it is necessary. Having asked elementary questions myself, I do not feel anyone should feel ashamed or demeaned if their question only relies on basic principles in a field.

This one seems to arise from the lack of understanding of the mechanism by which the ego-harm is inflicted. It is not necessary for the asking about basic principles to be shameful or demeaning in order for the harm to occur. It is enough that a negative comparison to others is made. Particularly, I propose that a comparison is going to arise when an «overly pretentious» tag is forcibly stripped from a question.

Furthermore, it is not the case that «ways to be offended» need to be intently looked for. It is not a consciously initiated action, but an automatic reaction. I welcome the reader learned in psychology to correct me here.

Finally, even if the likelihood and magnitude of harm is small, there are thousands of questions already asked on the site, and hopefully many more to come. The scale suggests that it is worth paying a thought. On the other side of the cost-benefit analysis, I do not see anyone at all harmed by the change I propose — both the novice and the advanced set theorist will be flattered.

• "Elementary" is a perfectly sensible modifier to apply to some questions. If it can be easily explained by basic principles from the field, then it is reasonable to call it "elementary." If it were really pejorative then I doubt people would try to sell books like these. Set-theory is a broad tag, and captures a lot of things. It is useful to have a sub-tag that narrows down to elementary questions, for someone who is learning the subject. – rschwieb May 22 at 12:31
• @rschwieb  I understand your objection. Indeed the word has its use. But that does not negate my argument. See: a word does not need to be pejorative in order to inflict harm if used in certain contexts. See for example the comment by Najib Idrissi above, which, as I hope you can imagine, brings me pain, while using only neutral words. Further, if it were a sub-tag, surely no one would insist on one being removed when the other is added? In the case here, set-theory explicitly excludes elementary-set-theory by its description, so you cannot say that the one is a sub-tag of the other. – Ignat Insarov May 22 at 12:46
• Indeed see Najib's question nearby, particularly «It's always been my impression that these sort of tags are mutually exclusive: set-theory vs elementary-set-theory, abstract-algebra vs algebra-precalculus, probability vs probability-theory, etc.» – Ignat Insarov May 22 at 12:49
• @IgnatInsarov I think you are suggesting a calibration of caution to prevent ego-harm that is far too sensitive. We cannot put everyone on eggshells because some people are very good at finding ways to be offended. Now, sometimes in culture such things need to happen, but in this case I do not believe it is necessary. Having asked elementary questions myself, I do not feel anyone should feel ashamed or demeaned if their question only relies on basic principles in a field. – rschwieb May 22 at 12:55
• @rschwieb  I cannot agree more. Ego-harm (while being very real and even lethal in many cases) should not justify arbitrary eggshells. It is a call to personal judgement as to when eggshells are needed. However, there is also a benefit of structure. The arrangement I propose is simpler and more natural with respect to the behaviour of the users. Note for example that there are some threefold more questions in elementary-set-theory than in set-theory. Further, it is not clear who would be harmed by eggshells in this case, so it seems that cost-benefit analysis is on my side. – Ignat Insarov May 22 at 13:02
• @IgnatInsarov I disagree with your claims. I think there is a significant harm that could be inflicted by instituting your claims, as it would make it far more difficult for professional mathematicians to understand the structure of the site, due to it not following the normal taxonomy of mathematics. More than anything, we have an issue of retaining top talent. So, we don't get anything by coddling amateurs, and we potentially could turn off professionals from using the site. – Don Thousand May 22 at 16:07
• @IgnatInsarov At the end of the day, if these minor issues are deal breakers for anyone, I don't think mathematics is for them. – Don Thousand May 22 at 16:08
• @DonThousand  This is a very good, practical and revealing argument. I would appreciate if you could expand it to an answer. – Ignat Insarov May 22 at 16:35
• set-theory vs elementary-set-theory, abstract-algebra vs algebra-precalculus, probability vs probability-theory, ?? The comparisons are not equivalent. Please get better acquainted with tag descriptions. – amWhy May 22 at 18:08
• @amWhy  You have a point. I was not very attentive and did not do as much of my homework as I could have. But it seems to me that my argument applies even better to algebra-precalculus — does it not? It does strike me as an artificial distinction. – Ignat Insarov May 22 at 18:19
• @DonThousand At the end of the day, if these minor issues are deal breakers for anyone, I don't think mathematics is for them. Perhaps not even the internet is the place for them :/ – rschwieb May 22 at 21:04