In this sentence only one "non" is causing the negation. In some circumstances " non" doesn't negate things. This is a particularly tricky sentence because it has both types!! The clue is the word "finché" so approach with great caution!!
There are two ways to use "finché and you need to decide which is being used. Either "until the moment that" (until) or "for all the time that" (while) In the former case the use of " non" can be optional and does not change the meaning as in the above case. In the latter use the meaning is changed.
The apparently additional use of "non" is called pleonastic so you may wish to try googling that word or there is more info here: http://onlineitalianclub.com/free-italian-exercises-and-resources/italian-grammar/finche-finche-non/ Hope this helps :)
I'm not sure if you have modified this, maybe the edit didn't go through. It still says "In the former case the use of "non" can be optional..." Or maybe it did and I'm just not thinking about it right :P Writing here because I can't reply to your last post, for some reason. Thanks for the great explanation, by the way :)
In my own attempts to understand this I had read that when used to express "until" the use of non after finché was optional but, as you suggest, this may lead to misinterpretation if that option is exercised in a way that is not clear.
It may be better to just think of "finché non" as meaning "until" and "finché" as meaning "while" and to hold an appreciation that this can be a bit of a grey area at times. I've modified my original post to reflect this and I sincerely hope I havn't confused more than helped!
yes, what you say is correct
here Lo/La are direct object pronouns (as already pointed by other people above), which must agree in gender and number with the object
-not until you open it
non finché non Lo (book/ tap/masc.sing.nouns) apri
non finché non La (bottle/ door/fem.sing.nouns) apri
-not until you open them
non finché non Li (books/ taps/masc.pl.nouns) apri
non finché non Le (bottles/ doors/fem.pl.nouns) apri http://italian.about.com/library/fare/blfare116a.htm
yeah definitely break it down: lo apri = you open it non lo apri = you dont open it no, non finche = no, not while
the literal translation as such no, non finche non lo apri = no not while you dont open it.
edit jan215: literal translation vs natural translation. natural: No, not until you open it
Finché == as long as. "Until you open it" == "Finché non lo apri" (as long as you don't open it). "Not until you open it" == "Non finché non lo apri" (not as long as you don't open it). "No, not until you open it" == "No, non finché non lo apri (no, not as long as you don't open it). "You are mine until I die" == "Sei mio finché non muoio" (you are mine as long as I don't die. Would this be an accurate breakdown of how these sentences are constructed?
I have similar interpretation though I prefer to use the word "while" rather than "as long as". "No, non finché non lo apri" becomes "No, not while not (you open it)" = "No, not while you don't open it" is correct answer btw = "No, not while it isn't opened by you", which means the same as "Not until you open it", but the perspective is different.
I'm no expert, but the way I had to straighten this out in my head was to translate it as: "No, not while you have not opened it". DL equates this to "not until you have opened it", with "Not While" = "Until". But to keep the meaning the same it has to go from "not while it is NOT opened" to "Until it IS opened". Both forms then indicate the object isn't yet opened in the present.