  Let us turn briefly now to a very general position, a possible  version of reductionism according to which identity nevertheless  still matters. This view is typically defended by advocates of  four-dimensionalism, according to which objects have both  spatial and temporal parts (see, e.g., Lewis 1971, 1976;  Noonan 1989; Sider 2001a). This view allows one to say that, in the  fission case, both post-fission people existed all along, completely  coinciding spatially pre-fission (so that each shared that temporal  stretch of his life with the other). In other words, they might be  like two distinct roads that coincide for a while before separating  off in different directions. Thus, if both post-fission person-stages are stages of the same person as the pre-fission stages (but there  are indeed two distinct persons all along), then one can maintain the thesis that the identity relation is what matters, for now identity  is also preserved through fission (whereas in Parfit's version while  what matters is preserved through fission, identity is not).