If we decide to treat objects as semantic interpretant of our names, sets of possible worlds as the semantic interpretant of our sentences, then:
- one-place predicates correspond to functions from objects to sets of possible worlds.
- ‘walks’ is a function from objects to the worlds in which that object is walking.
- adverbs, like ‘slowly’, is a function from one-place predicates to one-place predicates.
This apparatus gives us a way to talk precisely about certain distinctions that come up in philosophy language. E.g. adverbs come in two flavors: - Attributive: ‘walked slowly’ which implies one walked at all - Non-attributive: ‘walked in one’s imagination’
We can now say what this distinction is, set-theoretically.