|Mind-body dualist Rene Descartes|
Here's a wonderful 5-minute video of Alvin Plantinga explaining his modal argument against the view that persons are identical to their physical bodies.
Call myself A, and call my body B. I can imagine that I can exist apart from my body. Plantinga says, "It seems to me that I could exist when B doesn't."
Plantinga makes an analogy with Franz Kafka's Metamorphosis. In this story Gregor Samsa wakes up one morning to find he has the body of a beetle. In other words, from Samsa's point of view, there is an 'I', "Gregor Samsa," that now has a different body; viz., the body of a beetle. We can imagine this happening. That is, it is not logically inconceivable. Therefore it is possible.
If it is possible that A can exist when B doesn't exist, then A (i.e., 'I') is not identical with B. This is becaue "there would be something true of me that is not true of B; viz., possibly exists when B doesn't." So, Plantinga reasons, "it seems to me perfectly conceivable that I should exist when my body doesn't."
Plantinga's claim is: "It's possible that I should exist when B doesn't." Plantinga's reason for thinking this is possible is that he can easily imagine it to be the case. Because of this (to repeat), "there is something that is true of me that is not true of B." My body therefore, is not identical with "me."
If two things are identical, call them A and B, then whatever is true of A is true of B. They are the same thing. So if I am the same thing as my body (which is the philosophical naturalist's claim) then everything that is true of me is true of my body, and vice versa. Now note this: if it is possible that I exist when B doesn't, then there is at least one thing that is true of me that isn't true of B; viz., "possibly exists when B doesn't." Therefore B and I are not the very same thing; i.e., we are not identical. The self is not just one's physical body. Plantinga says: "If there are possibilities that are true for A that are not true for B, then A and B are not the same thing."
This is called "Leibniz's Law," which is: If A is identical with B, then whatever is true of A is also true of B. Every property A has is also a property B has, and conversely. And among the properties are modal properties, like "being possibly such-and-such." So if it is true of A that it is possibly "such-and-such," but it's not true of B that it's possibly "such-and-such," then A and B are not the same thing. Therefore the self is not identical with the physical body. "I" am not simply my physical body.