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.
I found this a wonderful read. I had the feeling of seeing Lewis's system manipulated dexterously, being turned inside out and then back again.
I think I'm broadly with imaginary-Lewis in preferring to make make room for substantial hyperintensional facts. But, I suspect the whole idea of doing this via an 'account' might be obscuring a need to get clearer about the things that make such an account seem necessary in the first place, i.e. the fact that the idea of such facts and us gaining access to them by thinking seems *mysterious*. I suppose I see more room for a therapeutic approach there, or an approach which shows clearly how the feeling of mystery comes about and thereby perhaps debunks it.
I feel like a lot turns on the briefly-canvassed issue of the merits of extending the worlds model of contingent knowledge to necessary knowledge using impossible worlds. I'd want to get clearer about the ways in which the worlds model of contingent knowledge is actually useful in the first place (rather than just compelling or bewitching), and how much that depends on thinking in terms of 'worlds' as opposed to something like sets of statements. I suspect there are ways it might be useful w.r.t contingent knowledge where it's just not useful w.r.t. necessary knowledge and that we should be able to get an understanding of why that is, but also that there are use cases where the approach will carry over well. (This may depend on assuming that modal realism is the wrong way to think about possible worlds, though. If I were with Lewis there, I don't know what I'd think!)