What was princess Elizabeth's argument against Cartesian dualism?

Well, I've never heard of this disagreement, so I found you some resources.

http://oregonstate.edu/instruct/phl302/philosopher...

http://www2.fiu.edu/~hauptli/DescartesandPrincessE...

http://en.wikipedia.org/wiki/Elisabeth_of_Bohemia,...

Causation & Physical closure

(PC) Two things x and y can causally interact with one another only if x and y are physical things.

Argument 1: The Argument from Top-down Causation

(1) The mind is a non-extended—hence, non-physical—thing. [Assumption for RAA]

Therefore,

(2) The mind is causally impotent with respect to the body. [From 1,(PC)]

(3) Top-down causation requires the mind to cause the body to φ. [Premise]

Therefore,

(4) There is no top-down causation. [From 2,3]

(5) There is top-down causation. [Premise]

Therefore,

(6) It’s not the case that the mind is a non-extended—hence, non-physical—thing. [From 4,5]

Argument 2: The Argument from Bottom-up Causation

(1) The mind is a non-extended—hence, non-physical—thing. [Assumption for RAA]

Therefore,

(2) The body is causally impotent with respect to the mind. [From 1,(PC)]

(3) Bottom-up causation requires the body to cause the mind to φ. [Premise]

Therefore,

(4) There is no bottom-up causation. [From 2,3]

(5) There is bottom-up causation. [Premise]

Therefore,

(6) It’s not the case that the mind is a non-extended—hence, non-physical—thing. [From 4,5]