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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.

  • @Gordon Cantor's proof is a very common source of people who want to 'fight the established view' in mathematics/philosophy/whatever else, and it is something that is very often attacked in what I think is fair to call outlandish ways. I know I've seen questions doing that on this site before, but personally nothing that this person did made me think of any other specific questions. I guess it's possible, but I don't think there's enough information to tell, at least from my perspective. However, there definitely have been cases of what you're describing happening. But I couldn't judge here. – Not_Here Oct 20 '18 at 20:50
  • I mean, I know that there is a specific professor at a German university who has some very incoherent theories about why uncountable sets don't exist and Cantor was wrong and he likes to make multiple accounts here and on quora to promote his ideas. If that's who you're referring to, I didn't see any similarities between this post and that person, he is usually much more indignant about using sources openly and receiving feedback. I remember him telling me one time that only God can see the well ordering of the reals. – Not_Here Oct 20 '18 at 23:05
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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.

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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.

  • I guess that my question is still why you would want to leave the question open and not have closed it until the unecessary parts are removed. Maybe I should be using the phrase "on hold" as opposed to closed, because I guess that's actually what I mean. When you yourself admit that 1) the answer you're giving (pointing out a fallacy) isn't even what the person is asking for and 2) you are admitting that there were formatting and extra question issues, which are both against the rules, why would you want to keep it open? Because you want to clarify something for them? – Not_Here Oct 20 '18 at 20:55
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    @Not_Here It didn't matter to me. The OP edited the question. This triggered it going to the "Reopen Votes" review queue. I saw it there. Since I like the question and earlier voted when it was in the "Close Vote" review queue to leave it open, I voted to reopen the question not expecting it would actually be reopened, but I am glad it did. It allowed the OP to clarify the position. Regarding whether I answered his question, I think I actually did. The OP specifically asked: "is this logic incorrect, if so, how?" I view questions as opportunities for answers, not opportunities to close them. – Frank Hubeny Oct 20 '18 at 21:19
  • I agree that we both fundamentally disagree on how we view questions here. I don't view questions as opportunities to press a button that says 'close' though, I view questions as things that should conform to the rules for this question & answer site. – Not_Here Oct 20 '18 at 21:24
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    Three points I deem relevant here: First, not every case of "wrong thinking" is philosophy and should be treated as such. This is the essence of point three of my answer and I think a crucial one to keep in mind. Secondly, questions that do only ask "am I right (and if not, why)" are exactly the reason why there is the "push of personal philosophy" close reason. Thus, they should be closed. Thirdly, the status "put on hold" gives seven days to amend the question. There should not be any reopen votes before it is a good fit for the site, regardless of the number of (bad!) edits. – Philip Klöcking Oct 21 '18 at 9:12
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    To make point one more explicit: Yes, questions about fallacies are on topic here if they are explicitly asking to identify/clarify the fallacy. This does not mean that every question/deduction that involves a fallacy becomes on topic. – Philip Klöcking Oct 21 '18 at 9:15
  • I have sympathy for the view that grasping the substance of a question takes collaborative input from people answering it. I also have sympathy for the view that this position works more effectively in a more populated forum, and the practicalities of a SE board with irregular freelance contributions means it's not a sustainable practice. Perhaps what this suggests is we could be clearer around the appropriate use of comments in questions like this where there is a case for relating to a substantial body of work, but where workshopping the question is necessary to draw out a quality answer. – Paul Ross Oct 21 '18 at 19:14
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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))

  • I guess my response to your first point is that I think there is more nuance involved. Yes in principle that is what moderators do, I agree and I think in principle there isn't an issue. What I tried to say in my post and what I believe is that in this specific example it is a little bit different because of the specific people involved. There are only a handful of people who use this site regularly, a lot of them have been around for a very long time, and some of those people were the ones who were voting to close the question, and I think that's relevant. – Not_Here Oct 20 '18 at 21:02
  • And let me be explicit, I am not saying that in this type of situation the community should outvote the moderator. I am saying that in this situation, I believe it would be best to open it up on meta, which is what I did. I might agree to a raw number being a limit for when the community could outvote, probably something in the 100s at least, which is infeasible in the first place, but at any rate that isn’t what I am advocating for here. I think the situation warranted a discussion and to be fair the question has since been closed. – Not_Here Oct 20 '18 at 21:02
  • To your second point, I guess maybe I should have used "put on hold" because that's really what I meant. I feel like I've done that in the past as well, used "closed" for "put on hold until they can fix the issues". I do think that those criteria you mentioned warrant putting on hold, but agree with you that it probably doesn't warrant fully closing, especially if it can be salvaged. And I agree with your third point and your parenthetical. I think math.SE would react very negatively to the question, to be honest. – Not_Here Oct 20 '18 at 21:04
  • @Not_Here: I elaborated the points a bit to make more clear where we are perfectly in line, as I admit that due to brevity, the answer might have appeared a bit hostile/oppositional where it really wasn't meant that way. I also suspect that Math.SE would not have been welcoming, that is why I usually ping the mods of the receiving site and ask them before migrating. Of course, it is not a good fit for SE in general, so this does in no way mean it should be allowed here because of this. But that is not what you wanted to imply anyway I guess, just a clarification for third parties reading this. – Philip Klöcking Oct 21 '18 at 8:55
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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.

  • When you go to a question you can see under the main body a link that says "x edited the question at y time" and you can click that link and it will show you the history of edits to the question. When I posted this question, I believe this was where the question was. – Not_Here Oct 21 '18 at 18:54
  • @Not_Here, despite your linking it, I have no inclination to read through that huge wall of text, so I remain somewhat uninformed! That said, I think my point of criticism still stands - the integrity of the question as it currently sits given its genealogy is not entirely clear, and I think the questioner should be prompted to step back, reflect, and perhaps try again with a different, more focused question. – Paul Ross Oct 21 '18 at 18:58
  • I don't disagree with your criticism nor was I compelling you to read a giant wall of text; I was informing you that you are able to see the history of edits made to a question and giving the specific state of the question when my post was made. – Not_Here Oct 21 '18 at 19:16

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