Full Idea
If one accepts the supervenience of mental on physical, this logically implies that there can only be one Cartesian soul, because such souls are physically indiscernible, and hence mentally indiscernible.
Gist of Idea
Supervenience says all souls are identical, being physically indiscernible
Source
Jaegwon Kim (Philosophy of Mind [1996], p. 10)
Book Reference
Kim,Jaegwon: 'Philosophy of Mind' [Westview 1998], p.10
A Reaction
Not very persuasive. Brains are certainly discernible, and so are parts of brains. Egos might be mentally discernible. I don't find my notion of personal identity collapsing just because I espouse property dualism.