There are good reasons to think of it as being a word. For example, much like the particle 's, it applies to a phrase without being at all concerned with what word it modifies. (Think "a week and a half ago"; which word would you argue "ago" is being suffixed to?)
Does this make it different in any meaningful way from an agglutinative morpheme? No, obviously not. Whether to call a language "agglutinative" is already more a question of cosmetics than facts. It reminds me of the feature tagging guidance on Universal Dependencies, which notes that no language can ever simultaneously have "gender" and "noun class" features, because they are the same thing. If there are three or fewer, the feature is called "gender"; if more, "noun class".
It applies to a phrase in all cases. If you don't like "a week and a half", you should rethink your approach to the problem, but you can still consider examples like "five years and fifteen days ago".
It's more like a preposition that exceptionally comes after the noun phrase instead of before it. (Is there another thing like that in English? I can't think of one, though there's one in German: entlang)
Etymologically it's a past participle: three days agone (gone) => three days ago
> It's more like a preposition that exceptionally comes after the noun phrase instead of before it. (Is there another thing like that in English? I can't think of one, though there's one in German: entlang)
There are some similar constructions:
- Three days hence. (archaic)
- Three days later.
- Three days beforehand.
- Three days afterwards.
I failed to think of one that didn't have to do with time.
You could think of "three days later" as being supposed to have a complement supplied to later, as in "three days later [than that]", but interestingly enough this isn't possible for "beforehand" or "afterwards".
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postscript: I think this can be conflated with a general syntactic possibility in English. I can describe an establishment as being "one floor up" from some other contextually-determined establishment, or, as with later, I can make that relationship explicit by saying "one floor up from [wherever]". This is also similar to the bog-standard measurement construction that gets you phrases like "three feet tall".
The nonjudgmental term of art appears to be "adposition". It isn't clear to me why this was coined as "adposition" and not "apposition".
"Preposition" is already something of an unnatural word class. They have two main functions in English: to describe some kind of location ("Sam? He's with Natasha"), and to mark certain arguments to verbs ("The tools? Sam's playing with them").
It's just a coincidence that prepositions serve both of these purposes in English; in Mandarin, the same two purposes are served by completely separate word classes. Verb argument markers are preposed; location markers are postposed.
> It's just a coincidence that prepositions serve both of these purposes in English
Not really… these categories fall together in a lot of languages. It doesn’t even require prepositions: a lot of languages have case markers which can be used for both location and verbal arguments.
The specific examples you’ve given are, respectively, called the ‘comitative’ and ‘instrumental’ uses of with. These two categories are particularly prone to falling together, mostly because the boundaries between them aren’t particularly clear: for instance, if you say, I made the coffee with milk, you could say that the coffee is accompanied by the milk (comitative), but you could also say that you’re using the milk (instrumental).