MAubrey wrote:David Lim wrote:But as I said it depends on which formal system we think underlies natural language
No formal system doesn't underlie natural language.
Intrinsically it does, and we build it up when we learn a language, which is why we are able to tell whether something is grammatical or not, because we essentially check it against a formal system, consciously or not. There are three main alternatives concerning prepositional phrases:
(1) Prepositional phrases are intrinsically adverbial, and adverbs can be "put in an adjectival box" when wanted to function adjectivally. This is my view, which explains why a lot of adverbs can be "made like" nouns by the article as I said above, whereas on the other hand there is no generic way to "make" adjectives function as adverbs without using conjunctions or adverbs. Since prepositional phrases modify verbs directly in the same manner as normal adverbs, it is not a far stretch to suppose that they are equivalent to adverbs. Then it follows that, when preceded by the article, a copulative verb is implicit. Whether the prepositional phrase is inside an "adjective-box" that is the predicate nominative of the copulative verb is not a crucial matter. Another possibility with the same external observable structure is that the prepositional phrase adverbially modifies the implied copulative verb.
(2) Prepositional phrases are intrinsically neither adverbial nor adjectival. They are definitely adjectival when preceded by the article, but could be either when anarthous. I presume this is what Stephen is suggesting. However so far we have not seen evidence of any anarthous prepositional phrase that is unambiguously adjectival. And for Rom 5:15 in particular the context together with the parallel structures imply that the prepositional phrase is indeed adverbial.
(3) Prepositional phrases have no intrinsic grammatical function but only function correctly within the correct context. I would say that this is true only for idiomatic expressions, which are not restricted to prepositional phrases anyway.