Close and near can be used as adjectives, and in many cases they are the same when talking about physical distances.
The train station is close.
The train station is near.
They are not the same when talking about more abstract concepts, like relationships.
My mother is close [she is 3 feet away].
My mother and I are very close [we have a strong family bond].
My mother is near [she is 3 feet away].
My mother and I are very near [we are 3 feet apart].
Only near can be used as a preposition without the word to.
*We are close the train station.
We are close to the train station [correct: close to is the proposition].
We are near the train station [correct: near is the preposition].
When you convert to adverb form, they are not interchangeable at all. In this case, closely implies "at a small distance", while nearly implies "almost but not quite"
*We are nearly following the news.
We are closely following the news.
*I closely hurt myself.
I nearly hurt myself.
* incorrect usage
I take Barrie's point that plausibility is primarily concerned with appearance rather than actuality. But I think there's a limit to how far one can take such strictly literal interpretations.
In most contexts, probable/possible mean likely/unlikely, but whereas the corresponding negated form improbable means not likely, impossible doesn't mean not unlikely - it means definitely not.
By the same token, convincing/plausible usually mean very believable/just about believable. I'm aware some people use plausible to mean convincing, but I think most people need something very/totally plausible to actually be convinced.
As John Lawler often reminds us, negatives [are] probably the most complex portion of English semantics and the weirdest part of its syntax.
And as Cerberus points out here, [probability] is a complicated issue [in the context of linguistics].
In my version of English, if something is implausible, it's unlikely, but at least feasible. But if it's totally implausible, it has no element of plausibility/feasibility whatsoever, and I personally do not distinguish that from impossible.
Best Answer
By itself, good means (in this usage)
The phrase any good means:
ODO definitions
So good generally implies a higher level of quality than any good. E.g. if a food is good, you look forward to eating it; if it's just any good, you won't spit it out, but you may not relish it.