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As simple as that: Are questions objectively having no valid answers, valid by themselves?

I'm not considering workarounds that are popular on the main SO site. In other scientific disciplines "no answer" is common and well may be the only answer. Still, it may require a proof that there's no answer.
Should I mark such questions non-constructive, say on Linguistics.SE?

UPD: The reason why the Q might be non-valid: Since there may be various proofs for unsolvability, all answers containing such will be equally valid.

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Related: Is "Don't do it" a valid answer? – Time Traveling Bobby Oct 5 '12 at 9:10
Wait, are you asking about questions which can be answered with "It's not possible (right now/not anymore)" or questions which are "uhhhh...nobody knows that"? – Time Traveling Bobby Oct 5 '12 at 9:13
@UnicornifiedBobby I'm talking about the problems like Halting problem, when someone is asking for a solution that is proven (provable) to be none. – bytebuster Oct 5 '12 at 9:19
up vote 10 down vote accepted

Of course is "There is no answer" an answer, and of course there can be questions which can not be answered but are still valid. One such question might be "Is there life out there in the Universe (except us)?". While it scratches hard at the "not a real question" mark, it can be reasonable answered with "We don't know...and some mumblings about theories, calculations and statistics".

There are also questions which can be definitely answered with "No". Such question is the example you've given, the Halting Problem. It can be definitely answered with "there is no solution because of...". Another, more technical question, would be "Can I install and run Linux from a FAT32 partition?", it can be clearly answered with "No, that's not possible because FAT32 misses the necessary POSIX file-permissions." or the famous "What's the solution to the NP/P problem".

Such questions can qualify as valid (as long as they're of quality, of course), but do not have a definite answer "we don't know" or have a 'negative' answer "that's not possible".

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