Is there any consensus yet on how double negations should be treated?
I don't need no doctor. (coll.)
Does the speaker need a doctor or not? Some authorities emphasise that logic prevails, in which case the speaker would need a doctor (no and no means yes). However, there are plenty of others who say this is not true.
When one starts from the meaning of what a speaker wants to express, he would easily come to tell that double negations do NOT make a positive sentence. The aforementioned logic-thinker, however, would just call that rum ram ruf and continue by saying that the world needs to learn their language again.
So: intention of speaker > logical structure of language, or not?
Also, as a side note, my mother dialect (a Dutch (Flemish) dialect) does have double negations as its default way of making a sentence negative.
Da'k 'et nie-j-en wee = That I not-en know