Use of 'but' in 'Not a star but might not shoot down ...'

Question

The young moon lies on her back tonight as is her habit in the tropics, and as, I think, is suitable if not seemly for a virgin. Not a star but might not shoot down and accept the invitation to become her lover.” (No Signposts in the Sea by V. Sackville-West)

My question here lies in how to understand the second sentence:

• Not a star but might not shoot down and accept the invitation to become her lover.

One thing I don't quite understand is the use of “not” and “but might not”. Does that conform to any grammatical rule? And if it does, please tell me how it works. According to my lecturer the sentence should be paraphrased as “every single star might come down quickly and accept the invitation to become her lover." Do you think it is right?

Answer 1

Not a star but might not shoot down means there isn’t a star that might not shoot down; they might all shoot down.

Here’s the but you’re looking for. It’s archaic; not a person but could be faulted for not understanding it.

but, prep., adv., conj., and n.²
C. conj.
II. In a complex sentence, introducing a subordinate clause.
10. After negative and questioning constructions.
e. Introducing a clause indicating some restriction on the statement about the subject or object in the main clause.
(b) With the pronominal subject or object of the subordinate clause unexpressed, so that but acts as a negative relative: that..not, who..not (e.g. Not a man but felt this terror, i.e. there was not a man who did not feel this terror, they all felt this terror). Now archaic and rare.
_{Source: Oxford English Dictionary (login required)}

Note the example given: Not a man but felt this terror means there was not a man who did not feel this terror; they all felt this terror.

Here’s your whole sentence:

There isn’t a star that might not shoot down and accept the invitation to become her lover.

You can see that you have a double negative, which makes for a positive meaning:

Every star might shoot down and accept the invitation to become her lover.

Your lecturer’s interpretation is correct.

Answer 2

It's certainly not standard syntax. The grammar makes sense, though, if we assume that the author has omitted some words:

[[There is]] not a star but [[those that]] might not shoot down and accept the invitation to become her lover.

Note that "but" is a preposition meaning "except" here.

This still doesn't really make sense. I think that the second "not" should be omitted:

[[There is]] not a star but [[those that]] might shoot down and accept the invitation to become her lover.

Now the sentence does, indeed, mean what your lecturer suggested.