What does functionalism tell us about personal identity?

Sydney Shoemaker argues that the functionalist theory of mind entails a psychological-continuity view of personal identity, as well as providing a defense of that view against a crucial objection. I show that his view has surprising consequences, e.g. that no organism could have mental properties and that a thing's mental properties fail to supervene even weakly on its microstructure and surroundings. I then argue that the view founders on "fission" cases and rules out our being material things. Functionalism tells us little if anything about personal identity.