Suppose we transplant the left hemisphere of one person, Alexandra, into the skull of another person, Alex, from whom both cerebral hemispheres have been removed; and transplant Alexandra’s right hemisphere into the skull of another person, Sandra, both of whose cerebral hemispheres have been removed. Both of the resulting persons will then have some of Alexandra’s brain and probably almost all of her memories and character. But since at most only one of them can be Alexandra, being Alexandra must, by (...) the “principle of the identity of composites,” involve having another essential non-physical part—her soul. It is our soul and only our soul which makes us who we are. (shrink)

Cartesian or substance dualism is the view that concrete substances come in two basic kinds. There are material things, such as biological organisms. These may be either simple or composed of parts. And there are immaterial things--minds or souls--which are always simple. No material thing depends for its existence on any soul, or vice versa. And only souls can think.