Conceivability and Personal Identity

I was pondering the role of conceivability in metaphysical investigations recently and I produced the following:

I ask myself, “What am I?  Am I my body?”  And I think that to answer this it is perfectly reasonable to imagine that my body undergoes various changes up to and including a complete, molecule-for-molecule replacement and then ask myself certain questions about these imagined scenarios.  What if part of my body, my arm, were removed and attached to another body; Who would be me?  What if my brain were removed and placed in another person’s skull; Where would I be?

But why let my imagination be a guide here?  Isn’t it possible, for all I know, that if my brain were removed, and a new one were placed in my skull, that I would still exist here, in this body, with this new brain?

But surely there are some things that, by merely imagining, we can rule out.  Suppose someone became convinced that he was a rock on Mt. McKinley.  Not just any rock, but a specific one, one that he had held himself just last summer on a hiking trip through Denali National Park.  Is it conceivable that Bob might really be the rock?  Well, we might examine him as follows,
“You say that you are this rock?”
“Yes”
“But you admit that the rock does not have eyes or ears or any other sense organ?”
“No, that I do not admit.  Identity is transitive. Since I have ears and eyes, and I am a rock, it follows that the rock has ears and eyes.”
“But if I kick this rock, you will not feel pain.”
“True.”
“And tomorrow you will leave Alaska and travel back to your home in California.”
“Yes, that’s the plan.”
“And yet the rock will stay here?”
“Clearly, since I am the rock, the rock will also travel.”
“But you will not carry this rock in your suitcase?”
“No.”
“And if I stay here and come back to this spot, next week, I will see this rock.”
“Yes”
“Even though you are thousands of miles away?”
“No.  I am the rock and thus I will be here, but my body will be in California.  And since my sense organs are attached to this body, I can see, hear, and feel, where this body goes. And so, if you come here next week, you will see me, but, since my eyes will be in California, I will not see you.”
“You are some kind of composite organism, then. A rockperson, so to speak?”
“The same is true with respect to what you believe yourself to be:  You claim to be a complex organism made up of parts; a head, and a torso, and arms, and legs, and a heart, etc.  And you believe that some of these things are not essential to your identity.  If you remove your heart, and replace it with an artificial one, you would still exist.  That is what you believe, is it not? You do not take yourself to be identical to your own heart and you do not believe that your arms are essential to your own existence.  You are a composite being, albeit one that your language has a convenient name for.”
“But all of my parts are attached, all are present in one spatial location.”
“If you wish to limit your own conception of yourself, that is none of my concern.  I exist as a rock who has a body which, because of its sensory and motor functions, can explore the world, while I remain here, safe.”
“And what happens to you when your body dies?”
“Then I cease to have a body, and I cannot see or hear or move anything of my own volition.  But I still exist. And I can hope that someday I will get a new body.”
“And what would happen to you if I were to destroy this rock; if I pulverize it into dust?”
“If you destroy the rock, you destroy the person.  Pulverize the rock, and I cease to exist.”

We can appeal to Bob’s sense of imagination and ask him to imagine that the rock is destroyed and that, nonetheless he still exists; but this will not convince him.

I am at least as convinced that I am my brain as Bob is that he is the rock.  I am convinced that if my brain is destroyed, then I am gone, just as Bob is convinced that if the rock is pulverized, he is gone.  At least one of us is wrong.  But what role does conceivability play here?  Sure, I can conceive that I am not a brain, but that no more makes it so than does the fact that I can conceive that I am a rock make it the case that I am a rock.: