 Lewis’s way of handling this problem was exceedingly simple. His original version of interpretationism had it that belief-states were ultimately probability distributions over possible worlds, and desire-states were ultimately utility functions, again defined over possible worlds. In “Attitude De Dicto and De Se” (1979b), he argued that this isn’t correct. Beliefs and desires are, at the end of the day, probability and utility functions. (Or at least they are approximations to those functions.) But they are not defined over possible worlds. Rather, they are defined over possible individuals.