What Is so Bad about Permanent Coincidence without Identity?

'What is so bad about permanent coincidence without identity?' (Mackie 2008: 163). This is the very question at the heart of the debate between pluralists and monists about constitution (Baker 1997, Fine 2003, Gibbard 1975, Johnston 1992, Lewis 1986, Thomson 1983). My answer to Mackie's question is that it contradicts a supervenience principle we all believe we know to be true. I approach this by considering three possibilities and the supervenience principles with which they conflict. One is somewhat politically controversial; the others are described by Wittgenstein (1967) and Dummett (1979). I focus on the possibility described by Dummett and the supervenience principle with which it conflicts. Our reaction to that possibility shows that we believe that supervenience principle to be true. But I argue that (as is obvious), it is inconsistent with permanent coincidence without identity. That is what is so bad about permanent coincidence without identity.