Blogging Alex Rosenberg's The Atheist's Guide to Reality, Chapter 10

If, as a materialist might reasonably believe, a brain is a mind in virtue of the structure of its neuronal interconnections, and a mind is the mind of a particular person for the same reason, then one need not suppose the Freaky Friday scenario presupposes that the mind is an immaterial substance. We leave the two bodies and their brains in place, but we re-organize the neural interconnections in the brains, so each realizes the computational state the other initially realized. It’s possible that the truth is more complex than a straightforward computationalism, and that whether a brain is the brain of a particular person is not settled at so abstract a level, but depends also on features that some other brain might be incapable if instantiating. In that case, persons are tied to particular brains in ways that makes the body-switching scenario impossible. And of course one might contend-implausibly, I think-that sameness of mind does not suffice for personal identity and what we have here is not a body swap, but two persons becoming very confused and losing their memories.

The fact that a human person, a self, persists through all the changes in our body over the course of our lives hardly implies that it is an immaterial thing. If it did, the implication is either that the car I have today is not the one I bought in 1988 or that it has an immaterial component. But no: it’s the same car even though quite a few parts have come and gone. This does not mean that a person survives all possible changes to a body over time. Whether a person at one time is the same person at another time depends on what kinds of changes the body has undergone: a person survives some changes and not others.