It says that: If the meaning of a pronoun is negative, it must always be used in a negative sentence. Similarly, pronouns with positive meanings must always be used in positive sentences.

Oke, I understand that part. But when I read the examples than i get confused.

I saw nothing. --> Hiçbir şey görmedim

When I translate this myself, I thought it said: I didn't see nothing. So you use two times not. So than you saÿ: I see anyhting. Right? So no I am confused how to use this.

Yes, it is two times negative. There is nothing wrong with this. Your translation is also very good.

Hiçbir şey görmedim : I didn't see nothing.

This is a literal translation. This is the way we speak. There are always differences between languages. You just need to accept them and move on. If you fight with the language you just lose time.

By the way I have heard people saying "Don't shoot nobody" (Eddie Murphy said this in a movie) or "Don't say nothing" so it might be more reasonable than it looks at first glance.

The 2x no in a sentence, like the examples you gave erdinc, is because languages are always changing. If I'm right these 'I didn't do nothin' 'sentences are originated in the outskirts of the USA, but are finding its way into the language nowadays. It's not officially correct, but in especially in speaking its used more and more..

Then this rule not working at all Türkçede ,right ?

negative of the nagative İS affirmative

Like to say,

İ did NOT, see NOTHİNG

Means,i saw something

Then this rule is not exist in any case in Türkçe,right ?

ok,now i'm confused

When does this rule work,and when it doesn't ?

A rule,is a rule,mostly it works in any cases,
Specially rule like this

İ know there would be exceptions,but,maybe with suffix or something like that

But to differentiate between nagative and affirmative ?

Sometimes double nagative means STİLL negative,and other times
Double nagative means affirmative ???

That is very confusing ...

What is the rule then ?
When is which?

No,its ok,i understand what you said,and i understand that triple negative thing too
thx,

but here

Hiçbir şey görmedim : I didn't see nothing

Hiç means Never, so in English we consider it double nagative

But i may understand,so correct me if i am wrong pls,

Here in this sentence,from Türkçe point of view,it is only 1 negative,because hiç doesn't considered a negative sentense ,it is only supportive with the negative sentence,or with a question

But in Türkçe point of view,
Double negative is when we use 2 negative suffix together,like (ma) negative suffix with (değil)
Or double (ma) negative suffix together

İn this case,the double negative mean affirmative

Doğru mu ?

Çok TŞK

Anladım