Often the most difficult part of responding to a Question is helping the OP to clarify it, particularly when the problem amounts to some kind of misunderstanding.
Notwithstanding the difficulty and frustration of these situations (both for the OP and the Reader), these are certainly opportunities for learning (aka teaching moments). I think labeling these as "wrong questions" is not the best approach, but I appreciate the reasoning behind that.
Here's an example I've been wrestling with:
The OP did respond to my original request for clarification, though not in a fully satisfactory way. So I'm trying again. Eventually I will tire, of course, if things continue to go in circles.
At that point I would probably vote to close as unclear what you're asking rather than for lack of context. My thinking about this distinction is that the OP has responded to requests for clarification, showing the minimal investment in the Question that counts (for me) as context. It just will not have resulted (assuming the worst) in a Question that makes much sense.
Potentially one or more Readers will post answers that patiently explain why the Question makes no sense (i.e. nothing can be said about incompleteness or about recursive enumerabilty unless more is known about "system $E$" than that it concerns "some standard arithmetic"). My comments will have laid some groundwork for that sort of answer (although I'll probably lack the enthusiasm to post one myself).