Do we need a tag? I removed one from a question yesterday, and it appeared on another sometimes later.

I'm not sure whether or not they are actually useful, but since some people do think they might be, I figured a meta thread is in order.


Okay, it seems that the general notion is learning towards indifference and favouring keeping the tag. That's fine. But I think we should decide what should be in it.

Someone had asked a question about proving the existence and uniqueness of remainders in division of natural numbers. Clearly not a foundational issue as most mathematician would think of it.

I propose that we rename the tag to or some other $\leq25$-letters variation that will tell newcomers that this is tag for foundational issues, and not "elementary" issues from the first steps in mathematics.

The second thing, I think, is that we need to get some general notion of what fits under this tag. Borderline philosophical questions? "How to develop X within Y"? What is the best beer for set theoretical work? And so on.

  • $\begingroup$ FWIW, I added the tag to the new question because I didn't notice that you removed the other one. I don't have an opinion on whether we need a foundations tag; I figured that "assuming foundations is a good tag, this question would be a perfect fit for that tag". $\endgroup$ – Willie Wong Feb 27 '13 at 23:09
  • $\begingroup$ @Willie: Some comments on that edit maybe? :-) $\endgroup$ – Asaf Karagila Mar 8 '13 at 9:04
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    $\begingroup$ I don't see how (foundations-of-math) is suppose to be better at explaining what it is compared to (foundations). For those who don't know about foundations, the two tags are likely to mean the same (wrong) thing. For those who do know, the two tags are likely also to mean the same (right) thing. A good tag wiki is a must, though I am not convinced that changing the tag name will help much. $\endgroup$ – Willie Wong Mar 8 '13 at 9:54
  • $\begingroup$ It also doesn't help that the Wikipedia article does not quite capture what we think of as foundational issues. Do you have a good two sentence summary of what a foundational issue is that can be understood by a layperson? $\endgroup$ – Willie Wong Mar 8 '13 at 9:56
  • $\begingroup$ @Willie: That's a tough cookie. How about "Mathematical foundations is the development of mathematics within mathematics itself." or something like that? $\endgroup$ – Asaf Karagila Mar 8 '13 at 10:16

My attitude towards tags is generally "why not?" Foundations is definitely an area which is on topic here, so why not tag it so that people who are interested in those questions can find them?

I scanned through the top 200 voted set-theory questions, and found the following questions where I think a foundations tag would be on topic.

1: When we say, "ZFC can found most of mathematics," what do we really mean?

2: What would happen if ZFC were found to be inconsistent?

3: Advantage of ZF over other set theories such as New Foundation

4: Are there areas of mathematics (current or future) that cannot be formalized in set theory?

5: Why use ZF over NFU?

6: How can there be alternatives for the foundations of mathematics?

7: Why was set theory inadequate as a foundation to the emerging new fields and why category theory isn't?

8: Are there any areas of mathematics that are known to be impossible to formalise in terms of set theory?

9: If all sets were finite, how could the real numbers be defined?

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    $\begingroup$ A general answer to "why not" is that having a too deep hierarchy of tags with overlapping scopes will increase the chance that some relevant tags will be missed by questions (there's a 5-tag limit), and therefore make the question less visible to users following the missed tags. Keeping up with all subtags of the areas one is interested will be more difficult the easier it is to create new tags. $\endgroup$ – hmakholm left over Monica Feb 28 '13 at 4:33
  • $\begingroup$ Would you consider the sort of "How to prove $1+1=2$?" questions as [foundations]? They do bother with the foundations of mathematics, but... differently. $\endgroup$ – Asaf Karagila Mar 8 '13 at 23:42
  • $\begingroup$ I've accepted this answer because it seems the tag is here to stay... $\endgroup$ – Asaf Karagila May 6 '13 at 11:27

No, we don't need it. There is already a tag whose tag-wiki explicitly mentions "foundations". The two questions Asaf alludes to in the OP (this one and this one) are both easily within the scope of the philosophy tag, and I highly doubt we will see many questions on foundational issues that for which this tag is ill-suited.

  • $\begingroup$ I can easily make foundations a synonym of philosophy. FWIW we should probably edit the philosophy tag wiki excerpt to have a bit more than just one sentence. $\endgroup$ – Willie Wong Feb 27 '13 at 23:04
  • $\begingroup$ Many people are averse to tagging their question philosophy. To many people, "philosophy" is a pejorative whereas "foundations" is not. Maybe we need a hierarchy of tags so people don't have to worry about something being under the tag they aren't searching under. $\endgroup$ – Jacob Wakem Jan 13 '14 at 21:10

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