The difficulty for using a “conceptually prior” class of possible worlds — more about what is meant by the phrase in scare quotes in a moment — to the purpose of giving an account of the intension of predicate terms (at least one which is epistemically responsible) is more apparent. Say we assume, as Lewis does, that for the purposes of explaining the truth of modal claims, there are possible worlds as he understands them and there is a class of all such worlds. If this account of modality is to be a reductive one, then to avoid circularity in it, we must assume that the worlds exist independently of our conceiving of them, else we would be attempting to reduce the modal to a class that was delimited with the aid of some sort of modal ability (our conceiving of the these worlds — this is why I say that the worlds must be “conceptually prior”). But, if we have a mind-independent class of possible worlds to explain the truth of modal claims, then we’re unable to use this class of worlds to explicate the intension of predicate terms given that we understand those intensions.
Why? Well, say for example, we want to use possible worlds to understand the intension of the predicate ‘is a mountain’. What do we do? Simple: the intension of ‘is a mountain’ is the set of all individuals picked out by ‘is a mountain’ in each possible world, or, rather, the set of mountains in all possible worlds. The trouble is that we do, prephilosophically, understand the intension of ‘is a mountain’ and so can use the predicate appropriately in conversations about counterfactual situations, but on the possible world account of the intension of ‘is a mountain’, it remains mysterious how we can have knowledge of the intension of ‘is a mountain’ given that the class of possible world exists mind-independently. Any claim that we have some sort of special access to possible worlds runs counter to the idea that a class of possible worlds serves as the reductive ground for modality (and so counter to the claim that the worlds are “conceptually prior”).
From part II, we’ve seen that Ray’s adaptation of Menzel serves only to place the formal machinery for providing the semantics of a language with modal operator atop notions which are fundamentally modal (meaning notions), and so can’t shed light on more fundamental modal notions. If I’m right about the foregoing in this post, then any method which uses Lewisian possible worlds to account for the intensions of predicate like ‘is a mountain’ by identifying those intensions with the set of all individuals in the extension of ‘is a mountain’ in each possible world can’t also be part of the theory which is reductive account of alethic modality.
One might say that the use of Lewisian possible worlds to explicate modal semantics could be part of a non-reductive account, but this leaves one with the question of why use complete, non-temporally related, physical universes as the basis for explaining something like fundamental modal properties or dispositions. Perhaps objects this “large” are the sort of thing to explain these sorts of properties or dispositions, but I suggest in the final post that we need something different (yet very similar) to explain de dicto modal claims and simultaneously explain intensions of predicate terms.