David Lewis presented a celebrated argument for the identity theory of mind. His argument has provided the model for the program of analytic functionalism. He argues from two premises, that mental states are analytically tied to their causal roles and that, contingently, there is never a need to explain any physical change by going outside the realm of the physical, to the conclusion that mental states are physical. I show that his argument is mistaken and that it trades on a crucial ambiguity in the second premise. He argues for a weaker version of that premise and then uses a stronger version in the argument. The weaker version of that premise will not allow the inference and the stronger version is contested in the dialectical context. In general then this strategy for providing analytic reductions will not be guaranteed to succeed.