How "sōlā fidē" means what it is supposed to mean

Question

The question is whether the phrase (a) denies there being more than one faith or (b) excludes there being any other means of salvation.

BACKGROUND

I am assuming that the phrase is intended to accomplish (b). To express that in English, one might have to say:

only by means of faith

But "sōlā fidē" on the surface looks like:

by means of faith whose number is one

Which would not exclude any other means.

Just for clarity, let me offer this analogy:

(a) The screw can be tightened with a screw driver, of which there is but one instance (but there may be any number of other means to tighten a screw).

(b) The screw can be tightened only with a screw driver (but there may be any number of screw drivers).

The answer I expect might look like one of these.

1. "Sōlus" generally qualifies the noun and sets its number at one, and "sōlā fidē" is no exception. That is, the only thing "sōlā" does in it is to set the number of faith at one, i.e. (a) above. If some Christians use it to exclude other means, i.e. (b), that is done through something other than strict meaning. For example, "sōlā fidē" has become a slogan.

2. "Sōlus" generally qualifies the noun and sets its number at one, but in some rare cases the word (as it were) comes out of the ablative context and qualifies the whole phrase to achieve the exclusion of other means.

3. "Sōlus" generally has two functions, setting the number of the qualified noun at one or (as it were from outside the ablative context) exclude the availability of other means.

ADDENDUM

Or maybe I am totally wrong to be fixated on the number of anything? Perhaps "sōlus" here just means "unaccompanied" and the whole phrase:

by means of faith that is unaccompanied by anything else

If so the phrase in and of itself would allow there being any number of faiths and any number of means of salvation, but simply assert that faith unaccompanied by anything is a means.

On this view, "sōlī Deō glōria" too would just mean:

glory to god as unaccompanied.

That is to say, you can separately give glory to to your own nose. Just don't give it to god and your nose together.

In sum, "sōlus" seems to be doing a job that it cannot do if it is confined to qualifying the noun either as to its number or state of being accompanied or not.

Answer 1

The word solus is a little ambiguous. While it has been discussed before (here and here), the topic is certainly not exhausted.

I can think of several translations of sola fide:

By means of the only faith
Only by means of (a) faith
By means of (a/the) lonely faith

For comparison, observe the effect of articles in the following, all of which could look the same in Latin:

Only faith can save you.
The only faith can save you.
Only the faith can save you.

Only context will tell how to parse sola. This is somewhat similar to how summus mons can mean the highest mountain or the highest peak of a single mountain.

Your option 3 is closest to truth in my opinion. The word just has several meanings. (Of course, in the context of Christianity the meaning is specific. My point is that the language alone does not indicate it as specifically as you might expect. See fdb's comment below for more Christian context.)

Also: You tagged the question as ablativus-absolutus, but I think this is instrumental rather than absolute ablative. Parsing it as absolute sounds convoluted; it would be something like "because/when the faith is alone". The absolute ablative can give a reason or a time, but it is not instrumental. (One could argue that the canonical classification of different ablatives is pointless, but that makes both the question "is it absolute or instrumental" and its answer moot. I made this point for subordinate clauses earlier, and it makes sense for ablatives as well.)