Should this question have been reopened?

Question

The question is Logic related to Cantor's Argument and I am wondering if in it's current state it should be open because I feel like it still has many of the problems it was closed for.

I do not remember all of the people who voted to close it, I know that it was Conifold, Maruo, EliranH, and myself and my apologies to the other person whom I cannot remember. However, I also think it's telling that the only comment on the question that has been upvoted is one of my comments explaining that the question should be rewritten. However, it was voted to be reopened by Frank Hubeny and then Geoffrey Thomas used his moderating power to reopen it. The reason why I am bringing up the specific people is because, although it was five people voting against it and only two people voting to reopen it, all of the people involved are people who take an active part in the community and improving question, so I believe that instead of "hey it's not fair that a moderator outvoted a group of users", we should instead have a discussion about the question.

My opinion as of right now is that the question still fails to live up to both the official guidelines as well as the implicit guidelines the community itself enforces on questions. Right now the question has two down votes and two up votes, which isn't as bad as a lot of questions here get but I think that is still pretty contentious.

I saw this question after there had already been about 12 or so comments made and it was a perfect example of a question that becomes longer and less organized as the original poster responds to comments by adding more text instead of rewriting things. I skimmed the question looking for all instances of '?' and could not find a single thesis-statement-like question that clearly related to the title of the question itself. However, even after this was pointed out and the user deleted some 3000 characters from the question, it still fails to be concise, have a clearly stated question, and or be structured in a way that pushes all irrelevant background information out of the main thrust of the question.

As of right now, it has four paragraphs in the beginning that do not mention Cantor or his diagonal argument. It's last paragraph is a block paragraph that reads like a run on sentence even though it has some punctuation and still it is not entirely clear just from looking at that paragraph what the penultimate question is. This is especially bad, since it is in the guidelines that questions should only contain one question. I think that is a rule that is broken sometimes, but as a community we usually agree that if there are some distinct minor questions that ultimately contribute to understanding the larger question, that's fine. But I do not believe that is the case here.

Actually on that point, Frank's answer to the question even admits as much:

This answer only addresses the part of the question about Cantor's diagonal method, not Haim Gaifman's discussion of Richard's solution. Hopefully it provides a usable partial answer.

This is an admission that the question does not contain one concise question as per meta (one question per post). The question has been edited so that the additional question about Gaifman's discussion is no longer there, but I think it still shows that Frank's opinion on what questions do and do not conform to site rules is different than mine, at least in this specific case, so I think the discussion is still warranted (especially since the question, even after edits, still has multiple questions).

In summation, I do not believe that this question should have been reopened, I think it still has major content and formatting problems, but since there seems to be a disagreement between active contributing members of the community on this, I would like to hear from everyone and see if we can get to an agreement on it. I would especially appreciate it if Geoffrey and Frank could explain their views on why they wanted to reopen it in its current state, specifically if they would address the content and formatting issues I have outlined.

Answer 1

Here's another reason for closing. Questions that are mostly "Here's my argument. Am I right?" are generally not a good fit here. They invite discussion and don't admit of clear and focused answers. There may be exceptions, perhaps if the argument in question is short and precise, but this isn't one of those cases.

Answer 2

Although this question might be one that could be answered on Math SE it also illustrates a fallacious use of logic which makes it relevant here. This is why I attempted an answer and why I think the question should remain open.

The fallacy involved is similar to a straw man. Rather than using Cantor's premises, the OP replaces them with something else and then argues against those new premises as if they were Cantor's. At least that is how I see the OP's argument.

The original, now removed, reference to "Haim Gaifman's discussion of Richard's solution", as I described it, was irrelevant once one understood that the particular example did not fit the premises Cantor was using when setting up his diagonal argument.

People who ask questions often do not understand what they are asking. Clarifying this for them should be part of the answer. Leaving such questions open provide a value to readers later on who might have similar questions of their own.

Answer 3

I will just give my 2 cents on that issue:

First, it is no problem in principle that a moderator outvoted 4 other users (5 close vs. 1 open + mod vote). That is actually the only possible mechanics allowing for mods doing what they are supposed to do: Doing the right thing where the community cannot or does not do it.

Close votes are usually only cast by quite active and prolific users, in all StackExchange communities. Therefore, mod votes that disagree with a successful community vote (i.e. five votes) always stand against such users and their views. That being said, I welcome opening a discussion about that as it seems to be rather about policies regarding a certain type of question, and that is not only what Meta is for, but something warranted as necessary in this case, given the history of comments and answers unfolding right now.

Second, the question is definitely bloated and ill-stated, both in content and form. This is in principle not a reason to close, as long as there is a more or less determinable and answerable question. It is - certainly - a reason for a downvote.

This is something that should probably be discussed in another Meta question, as there also seem to be different stances. There is "unclear what you are asking" as a close reason, and if one feels puzzled by the body of the question and left with the impression that there is a question in there one cannot get hold of, I'd say it is perfectly fine to cast the corresponding vote. The thing I want to point out here beyond the particular case at hand is that there is a line to be drawn between "ill-stated/bloated, but with a determinable/identifiable and answerable question" - here, it is probably better to help with an edit - and "confused thoughts put together", where the former does not necessarily justify a close vote.

The difference "put on hold" and "closed" is only technical in nature here, put on hold means nothing but temporarily closed and is the outcome of a close vote. Thus, I'd argue it should be left aside when discussing policies, even though it is important when communicating with newbies.

Third, this is a question purely on set theory, not on any philosophical implication of it, but its inherent logic and functioning. Other than most questions about formal logic, it is not related or transferable to propositional statements. And other than most questions on set theory, there is no link to a philosophical problem. This makes it a bad fit regardless its form! And other than the points mentioned before, this does constitute a principal reason to close it on Philosophy.SE as off-topic.

Not every mistake in a line of thought is philosophical. Sometimes, it is a simple contradiction and calling it a paradox is nothing more than euphemistic. Furthermore, not every error in proofs or deductions - especially when the contents and not only the notations are purely formal - is "fallacious" or "paradoxical". This is in no way philosophy, it's simply maths done/understood wrong.

What I'd like to emphasise here is that not every deduction or proof is an "argument". Arguments are about states of affairs in the world. The reason why I put up a difference here that is not in line with the meta-linguistic views of every philosopher is that if we do not draw a line here, all maths become philosophy and on topic. And that is certainly not what we want as a community. Using mathematical relations, deductions, and proofs as part of an argument or asking about philosophical implications is perfectly fine, but they themselves, possible mistakes within them, etc. are not and should not be on topic here.

Forth, I completely agree with the answer of @EliranH that, in addition to the problem mentioned under point three, there is also no genuine question, it is rather a problem that is presented with a solution sketched, asking whether the deductions are correct. As such, it should also be closed as "pushing a personal philosophy", even if one does not agree with point three.

I would have asked Math.SE whether they would take it for migration (and chatted with Geoffrey on that), but as it is now in public per this question, I will just leave this here to see how the community thinks about these points.

((I know there are many users here able to answer this type of question perfectly well on an expert level but that's really not the point))

Answer 4

I am unfamiliar with the question as it was originally. As it currently sits, I believe it is an awkwardly formed set theory question. My intuition is that it's primarily there as a reformulation in order to be a question that survives scrutiny, rather than in order to have a problem solved.

Keeping it closed seems appropriate, but I believe this much should be clearly communicated. The original questioner is welcome to reflect on the discussion and to create new questions that arise from that reflection to support their learning, if they like.