Origin of the adverbial phrase “all but” meaning “very nearly”?

The definition of “all but” means “very nearly,” but this makes no sense logically. For instance, if someone says “That word is all but forgotten” it means that whatever word the speaker is referring to is almost forgotten. But if you take apart the phrasing you’ll see that it means almost the exact opposite. By saying that something is all but forgotten, one is really saying that the thing is everything but forgotten i.e. it may be other things, but it is very much remembered. How is it that “all but” came to mean “very nearly” when really all should be negated by but, and that which comes after but should be in the affirmative?

(I understand that this may be worded in a slightly...abstruse manner. I apologize if this is the case. Perhaps someone can word it better?)

Solution 1:

In the expression all but X, all but expresses the degree of X, not X as distinct from everything else. Think of it as "all but completely X": everything up to X but not quite including X.

Solution 2:

If you could have ten (10) things, and you have all but one of them (9), then you very nearly have ten (10). If you think of 99 out of 100 it's even closer to all.

Another possibly helpful thing to do is transliterate it as everything except, which is also precisely its meaning, which in every case implies there is but one remaining obstacle. A man running a race may have all but finished, if he has just a step remaining to cross the line, say. Someone who's passed all their exams but not received their certificate has all but graduated.

Idiomatically, that may be slightly less literal, the man may have a handful of steps to go, but that's language for you.