Meaning of "however" in "possible, however unlikely, ..."

What is the meaning of the word "however" in the phrase "possible, however unlikely"? An example of a sentence containing this phrase (taken from Star Wars: Episode IV - A New Hope) is,

If the Rebels have obtained a complete technical reading of this station, it is possible, however unlikely, they might find a weakness and exploit it.

The word "however" can have two meanings according to google. These are:

1. used to introduce a statement that contrasts with or seems to contradict something that has been said previously,
2. in whatever way; regardless of how.

So the example sentence could be interpreted as:

1. It is possible they might find a weakness and exploit it; however, this is unlikely.

Or it could be interpreted as

2. However unlikey it is, it is (nevertheless) possible that they might find a weakness and exploit it.

Is one or the other of these "the correct way" of interpreting it, or are the two ways so similar that the speaker would not intend for the phrase to be interpreted one way or another, and you are free to choose whichever meaning you want?

Solution 1:

The phrase however unlikely is ambiguous in this sentence. You've already pointed out two ways it can be interpreted.

The first way however is used to modify the complete clause. = It is possible, however [it is] unlikely...

The second way, however modifies only the word unlikely. = No matter the extent of the 'unlikeliness'.

Both readings are possible, although to me the second one seems forced and less apt to be the intended meaning.

So, yes, if the usage is ambiguous and both readings are possible, you can pick the way you want to read it; and this may not be in accord with how the writer meant it. Alternatively, the writer could have been ambiguous on purpose, although in such a mundane text I doubt this is the case.

If the writer had meant the first meaning he could have chosen another word, such as although or but. As it is he's left himself open to misinterpretation.

Solution 2:

The first usage you mention uses the adverb 'however' to modify a clause:
It was raining. However, we went for a walk. (Note the full stop after 'raining' and the comma after 'however'.)
The second usage seems to use it to modify an adjective:
However unlikely, it is possible.
I.e., As unlikely as it is, it is possible.

If this were the first kind of 'however', I would expect "It is possible. However, it is unlikely..." because 'however' is not a conjunction. The first usage of 'however' has the synonym 'still':
Still, we went for a walk. = We still went for a walk.
"...it is possible, still unlikely, they will..." does not work.
And, finally, you cannot just remove the 'however', as you usually can when it refers to a clause:
"...it is possible, unlikely, they will..."

Interestingly, "...it is possible, albeit unlikely, they will..." is a textbook use of 'albeit, which is defined as 100% conjunction. 'Although', 'but', 'yet' and even 'while' could work there, too.

I think the only correct use this could be would mean "in whatever way," and a repeated "it is" is understood:
"...it is possible, however unlikely it is, they will..."
The most likely incorrect use is as a conjunction, since people make this mistake all the time. But what it REALLY means, in the context of the film, is that the rebels definitely WILL find a weakness and exploit it.