A ‘complex’ theory of personal identity analyses a person P2 being the same as an earlier person P1 in terms of some particular degree of physical or mental continuity between them. All such theories are open to an objection that the postulated degree of continuity is an arbitrary one, and many of them are open to the objection that more than one subsequent person could satisfy them. Necessarily, any subsequent person is either totally the same person as P1 or not at all the same as P1. P2 is identical with P1 if and only if P2 has the same (non-physical and indivisible) soul as P1.