Do native speakers use double negatives in order to mean positive situations REALLY

Question

I stumbled upon VOA (Voice Of America)'s video about the use of the combination of either/or and neither/nor.

Well, the guy in the video says, the double negatives, as he says, the sentence such as

Neither Adam nor his friend cannot swim.

But I rarely or never met a person this kind of double negatives spoke in order to mean the positive situations.

I know for sure that double negatives should mean positive, but how rare in the real word is is? Or am I dead wrong?

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Thank you for your answer, JavaLatle,

However, will you kindly "break into parts" of your example according to which such double negatives turned positives can be used particularly in formal situation so that I can understand the English 1819's parliament quote? The part, especially after had they ~ is making difficult for me to grasp what this decree or statement is trying to say.

The executive government assuredly would not not have done its duty, had they not made use of all lawful means to thwart the designs of such confederacies... The parliamentary history of England, 1819

Answer 1

It is not uncommon to use not with the negative form of an adjective, as I have just demonstrated. This can be used as a way of phrasing a diplomatic answer: the intended meaning is that you don't want to commit to a full positive, but you are denying a negative.

Using two nots in a row can happen when an adjective does not have a negative.

Father: You're not ready, are you?
Son: I am not "not ready"!

In this case, "I am ready". would probably be much more widely used, but the double negative is much more emphatic.

In this Ngram for not not, most of the instances are gobbledygook and can be ignored, but there are a few real usages of not not. Here is an example:

The executive government assuredly would not not have done its duty, had they not made use of all lawful means to thwart the designs of such confederacies... The parliamentary history of England, 1819

This sentence is meaningful, but it is not easy to interpret. That's why we use double negatives rarely, if at all. The sentence could easily have been written as "...not have failed in its duty..., but the author chose not to: looking at the NGram, there was a big blip in occurrences about 1800, and I wonder whether it was some temporary fashion. More modern usages tend to be either literary or philosophical.