We haven't done this in a while, haven't we?
I am aware that this is a double negative, and technically it should be "have we?" at the end of the sentence.
However, is the question grammatically incorrect or not just advisable not to use?
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Is it grammatical? I don't think so. As @KarlG mention in a comment, there are a few informal exceptions to the rule, but double negatives aren't just frowned upon as a rule, they are actively confusing to the listener.
Would anybody misunderstand your sentence? Probably not, but it would still give enough pause for thought that the listener would stumble over the interpretation.
It tends to be triple negatives when things get completely incomprehensible
Didn't we not go to the shops, didn't we?
But there's just no good reason to use double negatives in a way that doesn't risk mistunderstanding, unless you dealing with slang where people are familiar and understand what's going on.
I ain't never going to do that, no way, no how.
I ain't got none.
That above, as an example of London dialect, is completely acceptable (in the right context), and everybody would immediately understand that all the negatives simply intensify the degree of negativity. The subject of the sentence is really not going to do that, and definitely doesn't have any.
Philip said to Charles, that he was not never going to do that, no way, no how.
Sylvia and Gerard asked me if I don't have none.
...would immediately leave people questioning whether you meant Philip is going to do that, or whether you do have some. My use of names associated with upper or middle class people is partly in fun, but, in all seriousness, will make the double negatives more confusing for the listener. By making it clear we are not dealing with an informal and working class dialect context, the double negatives simply 'stop working' to the ear of the listener. Or my ear at least. Saying 'ain't' immediately marks a sentence as 'informal' and 'working class' and the native English ear makes a completely smooth adjustment to accepting double negatives.
"Is [the question] not just advisable not to use?"
Very clever. But you prove your point ... I'm questioning whether you meant to put in the two negatives, implying a positive sense, or whether you just meant the negative form: "it's advisable not to use". I don't know, so part of the meaning of your sentence has been lost.
Clearly the English rule about double negatives is largely artificial - which is why social background alone can lead to people interpreting the meaning differently. At one point in the past, multiple negatives were completely acceptable, as they are in other languages, and as they still are in dialects. But the fact is that today double negatives aren't just a signifier of 'informal' speech avoided by pedants, they can actually actively confuse people.