I would like to ask about the syntactic analysis of adverbs as what is called "peripheral noun modifiers" in The Cambridge Grammar of the English Language, p436, which is illustrated in the following example:
Possibly the best actress in the world will take the role of Emma.
According to the authors, the adverb "possibly" in the above sentence in one of the interpretations is to be understood as having scope over the noun phrase "best actress" - The person who is possibly the best actress in the world will take the role of Emma.
I'm having trouble understanding this, as semantically the adverb "possibly" clearly serves to hedge the qualification of the actress as the best in the world, not the entire phrase "best actress" - The actress is possibly the best in the world.
A few random examples I picked from Google Books would receive the same interpretation - the modal and temporal adverbs in these examples would be interpreted as modifying the following adjective within the noun phrase rather than the entire meaning of the phrase:
It's a nice neighbourhood. Nice homes, nice gardens, probably nice people who would give you the time of day if you asked.
Freud can be a very annoying person, with his ideas about women, and his sometimes rigid symbol interpretation of dreams.
He has made his Pop elements into a subtle, profound, delicate and at moments very touching and very funny instrument for analysis of a national trauma.