The suggestion that the claim that a double negative is logically positive receives support only from math is false. You don't need support from math.
Just consider language.
"Say nothing." means 'don't say anything', 'keep your mouth shut'.
So how can "Don't say nothing" logically also mean 'don't say anything'? You've added a negative and somehow the meaning doesn't change? It's not logical. It's as illogical as claiming that 'I have money.' and 'I don't have money.' have the same meaning. Whether you add a negative to a sentence that already has a negative or add a negative to a sentence without a negative, you can't say that the meaning is logically the same.
Of course nobody can stop people from using "Don't say nothing." when they mean 'Don't say anything.', but it is hardly logical.
What do you think "I can't get no satisfaction" means?
"That young girl," he added unexpectedly, "is one of the least
benightedly unintelligent life forms it has been my profound lack
of pleasure not to be able to avoid meeting."
The next paragraph calls that a "labyrinthine string of negatives", but perhaps it was mazelike rather than labyrinthine. :)
Now I am sure I don't know why I don't know nothing when I don't watch european but american movies.
Do people pay double for the same thing? No
Do people double the negation in the same sentence? Yes
If they paid for the words they use they for sure wouldn't do it.