Is it an adjective? Or something else? What does willen mean? I know the translation of the whole expression, but I want to make sure that understand what all of its parts mean.
I’ve noticed too that people sometimes capitalize Willen. Why is that?
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Technically, um … willen is a circumposition. A circumposition is, in essence, the same thing as a preposition; but a preposition comes before its so-called complement whereas a circumposition surrounds it. Finally, there are postpositions, following after their complement. Because postpositions and circumpositions are quite rare in German (and in English), preposition is sometimes used as an umbrella term for all three kinds.
Regarding the etymology, um is the well-known preposition and willen is originally the noun Wille in accusative. Both words used to have a much wider scope than today, so um jemandes Willen could mean ‘in someone’s interest’, ‘because of someone’ etc. When the scope of the individual words narrowed, um … Willen was already a collocation that retained its original meaning and, by a process known as grammaticalization, turned into a circumposition. The original meaning of Willen, which only a person or perhaps an animal could have, has bleakened, making um … willen also applicable to things.
Regarding the spelling, the two parts of the construction are still recognizable today, even though they no longer make sense when interpreted separately (‘around someone’s will’?). Therefore, a writer may feel that Willen continues to be a noun and capitalize it.
The Duden states it's a preposition. It's used with a genitive. And it derived from Wille (will) as its accusative singular.
I don't know how to translate erstarrt (solidified) correctly. But I would apprechiate its correct translation very much!
Herkunft: eigentlich erstarrter Akkusativ Singular von Wille
Grammatik: Präposition mit Genitiv
um Himmels Willen -> um des Himmels Willen -> um den Willen des Himmels
um den Willen -> prepositional complement
des Himmels -> posessive complement to the prepositional complement
Remains of a complete sentence that sometime in the past must have been something like (and I am making up this part)
e.g. Ich bitte dich -> [um den Willen des Himmels] -> ( das nicht zu tun! )
Ich -> Subject
bitte dich -> predicate
bitte -> verb
dich -> direct object
das nicht zu tun! - infinitive-construction (as alternative to a sub-clause)
Ich bitte dich -> [um den Willen des Himmels] -> dass du das nicht tust!
Or it could originally have been a final-sub-clause like this infinitive construction:
-> Um den Willen des Himmels zu erfüllen bitte ich dich, dass nicht zu tun!
Um -> final conjunction
zu erfüllen -> infinit verb
um zu erfüllen -> final infinitive construction
den Willen -> direct object to the infinitive
des Himmels -> possesive complement to the direct object
German grammarian tend to make prepositions and conjunctions out of former clauses and are covering up their original former structure. Multi-word prepositions and conjunctions are a relatively new phenomena in the history of language in general.
And the Duden editors do actually have a strong tendency to interpret a lot of structures as prepositions - even preposition that govern a Nominative ;-)
And 'erstarrt' would rather be 'archaic' when talking about language phenomena.