When we talk about the semantics of prepositional phrases, we are talking about a specific kind of conventionalized pattern. Conventional patterns are arbitrary in the sense that they are not predictable from one language to another. But in another way, they are nevertheless motivated (Sweetser 1990). There is a reason they occur as they do. Basic cognitive processes influence how different prepositions extend from spatial meanings to more abstract ones.

I fully acknowledge there is certainly an appeal for monosemy as a theoretical construct. The ability to schematize all usages or senses within a single abstract sense does indeed simplified and elegant semantic theory. Such a theory is an attractive prospect for all linguists.