The supervisor remained obdurate in refusing to accept excuses.
My M-W Collegiate Dictionary has 5 meanings for 'in' as a preposition:
1) used as a function word to indicate inclusion, location, or position within limits <in the lake> <wounded in the leg> <in the summer> b : INTO 1 <went in the house>
2) used as a function word to indicate means, medium, or instrumentality <written in pencil> <bound in leather>
3) used as a function word to indicate limitation, qualification, or circumstance <alike in some respects> <left in a hurry> b : INTO 2a <broke in pieces>
4) used as a function word to indicate purpose <said in reply>
5) used as a function word to indicate the larger member of a ratio <one in six is eligible>
I just can't figure out which of them really define the 'in' used in the sentence above. Isn't it a preposition? And the logical link between 'remain obdurate' and 'refusing to accept accuses' remains subtle to me. Is there any cause-and-effect? Um..
Cambridge Advanced Learner's Dictionary have this definiton
IN cause In refusing (= Because she refused) to work abroad, she missed an excellent job opportunity.
The government banned tobacco advertising and, in doing so (= because of this), contributed greatly to the nation's health.
And Macmillan English Dictionary have this:
in doing something
used for saying that as a result of doing one thing, you also do something else: In trying to solve one problem, I created another.
Is it true that the supervisor remained obdurate is because he refuse to accept the accuses? It seems to me the reverse is more reasonable -perhaps he's a person who is always obdurate , and the refusal is just a manifestation of his obdurateness...
M-W #3 seems the closest in describing the relationship. However, prepositional use after verbs, adjectives, etc, is often random and hard to categorise by dictionary definition. Here, the 'circumstance' works, doesn't it? The circumstance of his remaining obdurate was his refusal.
Look at 'plague'. We say 'A plague on your house', not 'in. I think the main function of English prepositions is to keep teachers in employment.