TITLE: Plantinga's logical argument for mind-body dualism
QUESTION [6 upvotes]: Some may feel this is not appropriate for the mathematics stack exchange, but it is a question in logic, and I feel it is entirely a good fit. The following argument has been put forth by the philosopher Alvin Plantinga in favor of mind-body dualism. I cannot see any logical error, but also have a hard time believing dualism has been demonstrated by a purely logical argument. If someone could please point out what is logically wrong with this, I would be appreciative. 
The argument: 

If A and B are identical then any statement of A is true of B and vice versa. 
I can imagine existing without my body, for example in the body of a bird. I cannot imagine my body existing without my body. 
By (2) we showed the existence of a statement that is true of (me) but not true of my (body). 
By (1) my body and me are not identical. 

End argument. 

is true by definition. The first part of 2. is true by my experience -- I can imagine waking up in a bird's body, can you? The second part of 2. is true by my experience, and if I'm not mistaken it must be true of everybody's experience since one cannot imagine something logically invalid -- my body is my body by definition and cannot exist and not exist at the same time (P and $\not$ P cannot both be true). 3. and 4. are simply logical conclusions. 

Has Plantinga rigorously proven an age old philosophical position defended by Descartes hundreds of years ago? 
Update: Maybe this is better suited for the philosophy stack exchange? Could I please have it moved? Thank-you.

REPLY [10 votes]: If A and B are identical then any statement of A is true of B and vice versa.
I think the unidentified serial killer is a horrible person. I do not think my son is a horrible person.
Therefore, my son is innocent.

Further reading: masked man fallacy.

Also, even if one accepts the argument as stated, the kind of mind-body dualism it supports is in any case an extremely mild one, of the same sort as the President/Obama dualism. (Replacing "me" and "my body" with "the President" and "Obama" in the posted argument is a fun exercise.) That doesn't mean that Obama is not the President, nor does it confer upon the office of the President some mysterious metaphysical status.
Are you sure what you've written is exactly Plantinga's argument? Perhaps there is some subtlety lost in your paraphrasing?