Mister Micawber

“How could it be a preposition?  It has no object.

”

Actually, there's a linguistic analysis that allows prepositions to have no complements. The argument runs that "prepositions" exhibit transitivity, like verbs do, so that prepositions without complements are "intranstive prepositions". If you accept this argument, this certainly applies to situations like: "I came here," or "I fell in." (Pdf-article, summarising some arguments - mostly Emonds and Jackendoff.)

The problem is that "up" in "shut up" is a particle. It looks like an independent word, but you need both components to arrive at the meaning through the lexicon. You cannot guess what "shut" + "up" means from just the meanings of "shut" and "up". This is different from collocations such as "Drink up!" where "drink" means "drink" and "up" means something like "completely"; which is again different from "look up", where "up" has a directional meaning. (But that's - of course - semantics...)

It's actually an interesting question.

Personally, I find the adverb-category unwieldly if we add too many disparate words into the category. And I quite like the "intransitive preposition" analysis, but it does have its problems. I do think, though, that placing these words with the prepositions gives us more insight into how language works.