Last week, I gave a talk in Manchester at a (very nice) workshop on "David Lewis and His Place in the History of Analytic Philosophy". My talk was on "Lewis's empiricism". I've now written it up as a paper, since it got too long for a blog post.
The paper is really about hyperintensional epistemology. The question is how we can make sense of the kind of metaphysical enquiry Lewis was engaged in if we accept his models of knowledge and belief, which leave no room for substantive investigations into non-contingent matters.
The problem is often regarded as a technicality. Standard Bayesian models imply that all necessary truths have probability 1; standard epistemic logic implies that knowledge is closed under logical consequence. The usual response is to treat this as an obviously false idealization that needs to be corrected in a more adequate model. I disagree. I think there's an important sense in which we are logically omniscient, and in which we can't make epistemic progress merely by thinking.
But we certainly don't seem to be logically omniscient. Or mathematically or metaphysically omniscient. So the challenge is to explain what our apparent logical/mathematical/metaphysical ignorance consists in, and to explain what happens when we appear to make epistemic progress in logic or maths or metaphysics, merely by thinking.
One idea is that what appears to be ignorance of non-contingent matters is really ignorance of contingent matters about words and concepts: metaphysical progress is the discovery of contingent facts about our linguistic dispositions. This might be part of an answer, but I don't think it's the full answer. I think we have to accept that there is a kind of quasi-epistemic progress that consists not in acquiring new information, but in converting representations of information into a format suitable for performing a certain task. That's how I would like to account for metaphysical and mathematical enquiry.
The resulting picture has a somewhat anti-realist or relativist flavour, so I'm not sure Lewis would have liked it.