 Another question that arises is whether the global supervenience thesis should be a weak global supervenience thesis, an intermediate global supervenience thesis, or a strong global supervenience thesis (see Section 4.3.2).  But notice that an intermediate global supervenience thesis would allow a world physically indiscernible from this one, in which precisely the same mental properties are instantiated as are instantiated here, but in which the physically indiscernible individuals (if any) swap mental lives. And that seems to be something that physicalism should not allow. A weak global supervenience characterization of physicalism would allow much more mental property swapping. It would allow a world physically indiscernible from this one, in which precisely the same mental properties are instantiated as are instantiated here, but in which they are differently distributed among the inhabitants—a world in which Paris Hilton, Colin Powell, and the Pope all exchange mental lives, for example (see Section 4.3.5).