The last chapter raised the problem of deciding which interpretation is the correct one. I want now to raise a particular case of what is in fact the same problem. To do this I will take ℒ and pretend that its intended interpretation is extremely small. I shall assume that W contains only two worlds w1 and w2 and that D contains only two individuals, say Adriane and Bruce, whom I shall refer to as a and b. I will assume that, for the interpretation of possibly, w1Rw1 and w1Rw2. That is, each world is possible relative to itself and w2 is possible relative to w1. Assume that a runs in w1 and b runs in w2 while a sees b in w1 and b sees a in w2. I shall ignore whistling. It is convenient to refer to running and seeing as w1 and w2 where

What this means is that the set of worlds in which a runs is just {w1}, i.e. the set whose only member is w1, while the set of worlds in which b runs is {w2}. To state w2 we need the symbol ø, which stands for the empty set, the set which has no members.