 David Kaplan argued that there could be no cardinality of the worlds. Kaplan did not publish this argument, so Lewis replies to the version presented by Martin Davies (1981: 262). On Lewis’s theory, every set of worlds is a proposition. For any proposition, says Kaplan, that proposition might be the only proposition being thought by a person at location l at time t. So for each proposition, there is a world where it (alone) is thought by a person at location l at time t. That means there is a one-one correspondence between the sets of worlds and a subset of the worlds. Contradiction. Lewis’s reply is to deny that every proposition can be thought. He claims that functionalism about belief, plus the requirement that beliefs latch onto relatively natural properties, mean that most propositions cannot be thought, and this blocks the paradox.