Negation of a Negative Statement

Question

My understanding that negating a negation is proof.

like:

They are not uncooperative = They are cooperative.

I understand that the use of the negative statement could slightly change the meaning or give more info, but in the end, they have the same major meaning.

Now, sometimes I see this is not the case.

for example:

I don't know nothing

which I guess from the context it means:

I don't know anything

or

I know nothing

So, what am I missing here?

Answer 1

In Standard English, multiple negatives cancel each other out, but there are many dialects where they are used as intensifiers. This answer explains how to interpret multiple negatives in colloquial use.

Attention to context and emphasis will usually make it pretty clear what is intended.

The other answers in that thread are also useful.

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Practical English Usage by Michael Swan:

(220.3) double and multiple negatives and their meaning

Two or more negative words can be used in one clause, but then both words normally have their full meaning. Compare:

Say nothing. (= Be silent.)
Don't just say nothing. Tell us what the problem is. (= Don’t be silent...)

Multiple negatives are sometimes used instead of simple positive structures for special stylistic effects. This is rather literary; in spoken English it can seem unnatural or old-fashioned.

Not a day passes when I don't regret not having studied music in my youth.
(More natural: Every day I regret not having studied music when I was younger, OR I wish I had studied music when I was younger.)

(220.4) dialects

In many British, American and other dialects, two or more negatives can be used with a single negative meaning.

I ain't seen nobody. (Standard English: I haven't seen anybody.)
I ain't never done nothing to nobody, and I ain't never got nothing from nobody no time. (American song by Bert Williams)

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The Cambridge Grammar of the English Language by Huddleston and Pullum:

(Chapter 9, 6.2)

i [He didn’t say nothing:] he said it didn’t matter.
ii Not all of them made no mistakes.
iii Not many / Few people found nothing to criticise.
iv [We not only made no progress:] we actually moved backwards.

CGEL uses a lot of linguistic terminology here, but in short, the first three sentences are all interpreted as positive: He said something; Some of them made some mistakes; Most people found something to criticise. The last example is different from the others in that we can drop the not only without changing the no: We made no progress: we actually moved backwards.

(Chapter 9, 6.3)

In many dialects, ranging from Cockney (spoken in the East End of London, England) to African American Vernacular English (AAVE, formerly known as Black English Vernacular, spoken in segregated African American communities in the USA), the absolute negators no, no one, nothing, etc., are used in negative clauses where the standard dialect has the NPIs any, anyone, anything, etc.:

[6]         NON-STANDARD                            STANDARD
i   a. !He didn’t say nothin’.               b. He didn’t say anything.
ii  a. !You gonna spend your whole life      b. Are you going to spend your whole life
       [not trustin’ nobody]?                   [not trusting anybody]?
iii a. !Nobody here didn’t point no gun at   b. Nobody here pointed any gun at
       nobody.                                  anybody.

Non-standard clauses with negative concord are characteristically homonymous with standard dialect clauses containing multiple semantic negation. Standard He didn’t say nothing means “He did say something (it’s not true that he said nothing”). The bracketed clause of [6iia] could likewise be used in the standard dialect with the meaning “not being in a state of refusing to trust anyone”. In principle [6iiia] could be used in Standard English to express a meaning containing four semantic negations, though in practice of course it would be far too complex to process. There are, however, some constructions – such as imperative Don’t nobody move! – that cannot be used in the standard dialect to express multiple semantic negation.