Inconsistency without Contradiction

1. Genuine worlds, ersatz worlds David Lewis has argued that impossible worlds are nonsense. 1 If there were such worlds, one would have to distinguish between the truths about their contradictory goings-on and contradictory falsehoods about them. One would have to distinguish between, say, the alleged truth (1a) In so-and-so world pigs can fly; and in that world pigs also cannot fly, and the contradictory falsehood (1b) In so-and-so world pigs can fly; and it is not the case that, in that world, pigs can fly. But this—Lewis argues—is preposterous: there is no such distinction to be drawn. (1a) and (1b) are equivalent. Of course, Lewis does distinguish between the following: 2 (2a) In the world of Sherlock Holmes, Watson limps; and in that world Watson also does not limp. (2b) In the world of Sherlock Holmes, Watson limps; and it is not the case that, in that world, Watson limps. (2b) is contradictory. But (2a) is, in a sense, true: there is a discrepancy in Conan Doyle's writings. In one of the Holmes stories, Watson limps because