8
$\begingroup$

This question was just asked and quickly closed and downvoted, with 'lack of clarity' given as the reason. However I think the question is about as clear as it can be when it's asking about maths from a pre-rigorous standpoint. They have a particular, quite common, confusion about the empty set, and require an explanation of how the empty set is dealt with rigorously, and how this differs from pre-rigorous intuition about the empty set. I don't think I would have done as good a job of communicating where my confusion was coming from at the same stage of mathematical development. I posted an answer to it, though not one I'm wholly satisfied with.

I think people are viewing the question as unclear because it can be seen as arising from a double-meaning in English (contains nothing vs contains an object called nothing), and from a rigorous perspective, this is obvious, and seems trivial. But I don't think this is obvious from the perspective of someone just starting at set theory, and when the question is about a misunderstanding produced by ambiguity, I don't think it makes sense to close the question for containing ambiguity.

I see this as a question about an ambiguity, rather than an ambiguous question. It's like downvoting someone for misinterpreting the identity axiom of groups in a question about why the empty set isn't a group: if they knew how to avoid that misinterpretation, they wouldn't have the question anymore. So questions about confusions will, I think, necessarily be a bit confused, and the mark of a good question about a confusion is making legible what they are confused about- which I think this question does.

I also think this is a question that a lot of people at this stage of mathematical development would benefit from a good answer to, and which isn't particular to the phrasing chosen. There's a genuine conceptual subtlety here that requires explanation.

You can show that there is no set 'nothing' that the empty set contains very easily, which is largely a matter of pointing out the language confusion, but op's question was why the formalism disagrees with the intuition, which in my opinion is genuinely a question about mathematics, albeit a soft question. And if the question was closed because the community has taken the view that it isn't a question about mathematics, it should have been closed as off topic, rather than as unclear, which I would still disagree with, but which would be more comprehensible to me.

So I think this is actually a good, albeit basic, question, but this apparently puts me starkly at odds with the majority. So I want to ask: should this question have been closed as ambiguous? and if so, how are you determining that it is an ambiguous question rather than a question about an ambiguity?

$\endgroup$
8
  • 6
    $\begingroup$ Agree with you. I think it is a well asked and a useful question.But since I neither down voted, nor was I involved in the closing process, I can't post an answer. $\endgroup$
    – Srini
    Commented Aug 31 at 20:57
  • 11
    $\begingroup$ I did not downvote, but as a general matter I think that questions arising from ambiguities in English usage, as opposed to those arising from mathematical usage, aren't very interesting. In what sense are "right" triangles right? Why aren't there "left" triangles? That sort of thing. Beyond pointing out that the mathematical terms don't mean what they mean in daily English use, what is there to say? $\endgroup$
    – lulu
    Commented Aug 31 at 21:33
  • 2
    $\begingroup$ @lulu I don't think this is analogous to your example, because there is a genuine conceptual confusion underlying it, rather than just using two names for the same thing. It's something that requires an understanding of what precisely $\in$ means (i.e. just knowing it means 'is contained in' isn't good enough), and what is and is not an object in ZFC and why. Pointing to the ambiguity in English is the start of an answer, but in my opinion it doesn't fully address the confusion. $\endgroup$
    – Zoe Allen
    Commented Aug 31 at 21:47
  • 9
    $\begingroup$ In the interests of transparency, Zoe, you ought to have mentioned that you posted an answer to the question. $\endgroup$
    – Gerry Myerson
    Commented Aug 31 at 21:59
  • 4
    $\begingroup$ Given how common confusion about the empty set is, I'd be surprised to find the question isn't a duplicate. $\endgroup$
    – Gerry Myerson
    Commented Aug 31 at 22:00
  • 1
    $\begingroup$ @lulu Agree that the question is uninteresting. However, as I understand MathSE protocol, that does not automatically imply that the question is to be regarded as low quality. $\endgroup$
    – user2661923
    Commented Sep 1 at 22:06
  • 2
    $\begingroup$ @ZoeAllen I have genuinely had a student confused about the meaning of "right triangle". In their high school classroom, their teacher had always drawn right triangles with the angle that had a square in it on the bottom right. $\endgroup$
    – Xander Henderson Mod
    Commented Sep 8 at 0:07
  • $\begingroup$ Puns are fun, but I agree with @Fedja, this question belongs on a linguistics site if anywhere, not on a mathematics site. In my undergraduate algebra class, my professor (Ed Ingraham of Michigan State University) would talk about theorems of algebra proved by "our team". I was very impressed at the unity of purpose and the work of his team, and I wondered if this was what mathematical research life was like, working on such productive teams. My bubble was burst later in my mathematical life when I learned of the great family of mathematicians (including more than one algebraist) named Artin. $\endgroup$
    – Lee Mosher
    Commented Sep 10 at 12:05

1 Answer 1

Reset to default
3
$\begingroup$

It is about the ambiguity of English language and the idea is at least as old as Lewis Carroll's "A Tangled Tale": put 40 pigs into 4 pigsties on the circle so that each next pigsty contains the number of pigs closer to 10 than the previous one, with the answer 16, 14, 10 and 0 ("nothing is closer to 10 than 10"). As long as you write the statement in the formal logic language (which you should do every time when the natural language is ambiguous or fails to express the meaning exactly), you just get $\forall x, x\notin \varnothing$ and the whole game of words, which is exactly what it was before, dissolves. So, yeah, it is not a question about math. but about English and, as such, it was properly closed on MSE. If you want, you can try it on some linguistic website, but even there it would be most likely considered too old and non-interesting to generate a meaningful discussion.

$\endgroup$
1
  • 13
    $\begingroup$ Oh, older. Odysseus defeats Polyphemus by saying his name is Noman. Thus, after being blinded, the Cyclops can only tell his cohorts "Noman did this" which, surprisingly, is enough to keep them from taking action. The story would have ended quite differently had he managed "Some little guy who told me his name was Noman did this", but here we are. $\endgroup$
    – lulu
    Commented Sep 1 at 11:09

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .