Double negatives
 

I thought this was cute...

A linguistics professor was lecturing to his English class one day.
"In English," he said, "A double negative forms a positive. In some languages, though, such as Spanish, a double negative is still a negative. However, there is no language wherein a double positive can form a negative."

A voice from the back of the room piped up, "Yeah, right." :showoff:

That's really funny. I never thought of it that way.
There are a few exceptions to the double negative law that are not unsaully shown learn in textbooks--at least the ones I've seen. They include the words anymore and yet. These two words are almost always negative, but must accompany another negative word.
(I don't do that anymore. I haven't done that yet). Yet can sometimes but rarely be used without another accompanying negative, but I think the meaning is slightly different (She has been ill, yet she is able to continue to work.)

It sure is very cute, and very funny.:D

I love it.:applause:
You ain't the boss of us for no reason.
:warning: Caution:Your English might suffer after reading the sentence above.

Any more is not an exception, Poli.
Both some and any are positive words in themselves, but we associate any and its compounds with the negative because they appear in negative (and interrogative sentences).
Have a look at this:
He isn't here any more.
He is no more. (sorry I chose such a depressing example).:sad:

In my opinion yet has neither negative nor positive connotations in the sense explained in David's joke (as far as I know it should not be included in the single/double negative 'scenario'.)
You can use yet in interrogative sentences: Have you finished yet? and as you see there is no other negative word in the example question.
In my example and in the negative sentences you mentioned, yet is an adverb . But in your second sentence: 'She's ill, yet... it is a conjunction.

There must be something in this forum that makes me go into teacher mode.:confused: I promise you I hardly ever explain grammar...:o

I try to analyze the word anymore. It appears to be the opposite of lately.
Example: I've been going there lately
I'm not going there anymore....You still don't think this is a double negative? You certainly dont say, "I go there anymore" unless you're from southern Illinois. I'm no grammarian but sometimes it can be puzzling and challenging and not dull.

Sorry to seem stubborn. I'm no grammarian either, but what I wanted to say is that words starting with any (all of them) are positive in themselves.
1. I have some milk AFFIRMATIVE
2. I haven't got any milk NEGATIVE. Only one negative (n't)
3. I have no milk NEGATIVE. Only one negative (no)
4. I ain't got no milk DOUBLE NEGATIVE AND THUS INCORRECT (n't, no)

In the same way:
I'm not going there any more would be an example of number 2.
No more, never more would be examples like the ones in 3.
I am not going there no more is a double negative (4) and grammatically incorrect, though widely used by some.

OK
Perhaps it confuses me that the word anymore always accompanies the negative. It sounds wrong when it accompanies a positive

One interesting note is that double negation in English was acceptable and used commonly until prescriptive grammarians wrote against it in the 18th century. For example Chaucer makes extensive use of double (and even triple) negatives in his writing. Today, double negatives are not considered "correct", especially for written English, but are somewhat accepted in spoken English, especially in humorous and informal usage. Double negatives are more extensively used in some dialects of English than in others.

According to what I have found, these are considered the negative words in English:

barely, hardly, neither, no, no one, nobody, none, not, nothing, nowhere, scarcely.

In England if you use a double negative, you might be told you sound 'like an Essex man'.
And one more thing, children often use double negatives when learning to speak, which as somebody mentioned in another thread, is indicative of 'illogical aspects' within our linguistic systems.
I know lots of bilingual children (like many of you, I imagine) and I find each and everyone of them, fascinating.
An anecdote: When my eldest son was around two, he would call his Dad after going to the toilet and say: Papá, límpiame el botón.I'll leave the guessing to you guys, but I thought it was hysterical.;)