Reasoning about situations we take to be impossible is useful for a variety
of theoretical purposes. Furthermore, using a device of impossible worlds
when reasoning about the impossible is useful in the same sorts of ways
that the device of possible worlds is useful when reasoning about the
possible. This paper discusses some of the uses of impossible worlds and
argues that commitment to them can and should be had without great
metaphysical or logical cost. The paper then provides an account of
reasoning with impossible worlds, by treating such reasoning as reasoning
employing counterpossible conditionals, and provides a semantics for the
proposed treatment.