David Lewis’s central work in epistemology is his article “Elusive Knowledge,” defending a version of contextualism constructed out of a relevant alternatives theory of knowledge. If your a fan of RA theories of knowledge, the view might have more plausibility than it will for those of us not so enamored, and in any case, it is a depressingly deflationary approach to the subject, informing us that knowledge may flourish when we pay it no mind, but the slightest bit of reflection destroys it entirely.
There is a different Lewisian approach, however, one that he instances in a number of other areas, that it is somewhat surprising to find missing here.
Think of what he has to say about chance, for example. What he looks for is not exactly a theory of chance, but a theory of whatever it is that plays the role of chance in our ordinary thinking. Whatever does the best job theoretically of accounting for this role is judged to be the best theory, and whatever is left over in the ordinary notion of chance or, for the more metaphysically inclined, the property of chanciness, is ignored: spoils to the victor, as Lewis likes to say. The initial theory, then, is driven by the Principle Principal, since Lewis initially thought that it is the best guide there is to the role chance plays in our thinking.
So why not do epistemology this way? Why not try to figure out what role knowledge plays in our thinking and try to identify some guiding principle or principles about it? That would be a Lewisian theory of knowledge. It would be interesting to see what the guiding principles for the knowledge role might be, though I know what a number of epistemologists will say: it’s just justification itself! So then a Lewisian theory of knowledge would be one that identifies knowledge and justification. Quite stunning, and disappointing. But maybe there are other ideas?