The problem of metaphysical omniscience
There's a striking tension in Lewis's philosophy. His epistemology and philosophy of mind, on the one hand, leave no room for (non-trivial) a priori knowledge or a priori inquiry. Yet for most of his career, Lewis was engaged in just this kind of inquiry, wondering about the nature of causation, the ontology of sets, the extent of logical space, the existence of universals, and other non-contingent matters. My paper "The problem of metaphysical omniscience" explores some options for resolving the tension. The paper has just come out in a volume, Perspectives on the Philosophy of David K. Lewis, edited by Helen Beebee and A.R.J. Fisher.
I'm interested in the question not just (and not even mainly) as an exegetical question about Lewis. I like the basic ideas in Lewis's epistemology and philosophy of mind. I like that there's no room for a priori knowledge and inquiry. The idea that there are special aspects of reality to which we gain access through a priori reasoning looks highly implausible to me.
In the paper, I end up proposing a somewhat deflationary interpretation of metaphysics (and, I guess, by implication, maths), on which metaphysical questions are rather unlike ordinary, empirical questions. I doubt that this would have been Lewis's answer to the tension. But it's the best I can find. It's also very sketchy. I'd like to understand it better.