A standard line in "personal identity" goes like this: Suppose your mind were put into another person's body, and vice-versa? Which person would now be "you"? It's pretty reliable to assume that if one puts the issue that way to a philosophy class, most people will have the intuition that they follow their mind: that "they" will now be "in" the other person's body, and thus the person embodied by that body will now be "them." Thus theories of psychological continuity have been more popular than theories of physical continuity since the time of John Locke.
I suspect that this is all wrong or, like the man said, "not even wrong." That is, in order for supporters of a psychological continuity of personal identity to be wrong it would have to be possible (conceivable) for them to be right. But it's not. The whole discussion is question-begging. An argument is question-begging when there is a premise in the argument that could be questioned, but isn't. In this case, that premise is, "There is something that is 'mind' that can be distinguished from 'body.'"
If there was something that was "my mind" that could be distinguished from my body, then it would be possible to imagine my mind existing independently of my body. That is what I'm doing when I imagine my mind in another body (or in heaven, or just out of my body, or whatever). Now, it seems as if we can imagine such a circumstance: we have a rich tradition of fiction, for example, that imagines minds switched between bodies, or the souls of dead people haunting the present world, etc. So the tricky part of my claim is the argument that, while you may think that you can (obviously, unequivocally) imagine your mind existing without your body, that is an illusion: in fact you cannot do that. For that is my position.
Today I'm thinking that maybe some arguments about skepticism can be deployed here. Someone says that there is a real issue as to the existence of the external world, say. It might exist, or it might not. I don't think that this is a coherent question. My view is that I neither "know" nor do "not know" that the external world exists: it is a spurious application of the verb "to know" in either case. The "external world" is not something separable from my experience.
The argument that persuades me here is one common to Zen Buddhism and to Wittgenstein, although I think that it is also the view that emerges from a correct interpretation of David Hume. The key is to see that "the world" does not collapse into "the self" any more or less than the self collapses into the world (the common German, Kantian interpretation of this material - Buddhism, Wittgenstein - tends to miss this crucial point). My world is the world as it is constituted by my body. In the absence of my body, this world also is absent. To say that my mind might be in another body is equivalent to saying that my world might be experienced by another.
Well that's vaguer than I'd like, but on the right track. Notice that there's another route to go here: one might make arguments to the effect that there is no such thing as "mind" at all. I think that that is also a valid way to go, and brings the question-begging nature of the traditional personal identity literature into clear focus. If there is no such thing as mind then there is no question of an alternative between psychological and physical continuity. Physical continuity, in that case, is the only coherent option.