Does double negation confirm or annihilate the original negation

Question

I am trying to understand whether adding a second negation word to a sentence confirms the negation to cancels it out.

Take the sentence: Il n'y a qu'un livre dans le sac (1). This can be translated as "There is only one book in the bag".

When we add the word plus to the negation as in: Il n'y a plus qu'un livre dans le sac (2), the meaning doesn't essentially change, at least it is not flipped: "There is only one book left in the bag". Exclusivity of the one book still holds.

Now when we use pas instead of plus, as in: Il n'y a pas qu'un livre dans le sac (3), the meaning changes completely: "There is not only one book in the bag". The exclusivity is actually negated.

Second and third sentence use two negation words, in addition to ne. However, while the second sentence doesn't negate the first, the third does.

Are all form of negation I used valid grammatically (namely sentence 2 and 3)?

Answer 1

All of your sentences are valid and usual French.

The third sentence indeed negates the first one :

(1) Il n'y a qu'un livre: there is just one book (i.e. there are no more books than that one)

(3) Il n'y a pas qu'un livre: there is not just one book (i.e. there are more books than that one)

In the second sentence, plus isn't there no negate anything but to add a piece of information:

(3) Il n'y a plus qu'un livre: there is just one book (and before, there was more)