Mojo
Mostly harmless
1. We’ve been talking about two different kinds of “self.” There is 1) the self that is all the person’s characteristics -- and then, there is 2) the SELF that is the person’s self-awareness.
That looks suspiciously like another attempt to force your desired conclusion into the argument by means of an unsupported assertion. The "SELF that is the person’s self-awareness" is just something that results from the functioning of the brain. Brains in identical states will therefore produce identical "selves", identical "SELVES", identical "selves", identical "selves", identical "selves" and even identical "SELVES".
Changes to the typography won't make any difference. You need to provide some evidence that the soul (for this is undeniably what you mean here, and since we are now in R+P you have no further need to deny it) exists.
2. We accept that could we perfectly replicate a person’s brain, we could replicate the person’s self – but, not the person’s SELF.
You claim this; I can see no indication that anyone other than you accepts it.
3. IOW, there is no bio-chemical recipe exclusive to a particular SELF.
You haven't established this. There is no reason to suppose that consciousness is not the result of brain function, and that identical brains will not produce identical consciousnesses.
4. And, while we can safely say that a self is defined by its brain, we cannot safely say the same about a SELF.
You have provided no reason that we cannot say the same about a SELF, and no evidence that there is some special sort of "SELF" that is not the result of the functioning of the brain.
5. Bio-chemically speaking, a SELF comes out of nowhere…
Biochemically speaking, the self is the result of the chemistry of the brain at a particular moment. You haven't established that the "SELF", as you call it, exists.
6. And, if bio-chemistry is all we can call on to define a SELF, there is no pre-existing, exclusive recipe for a particular SELF.
If you cannot establish that the SELF exists, it's not really worth worrying about whether there is a "pre-existing, exclusive recipe for a particular SELF", is it?
7. And, even if time and space are finite, a new SELF is brand new, and does not come from a pre-existing pool (limited by the number of possible recipes) of potential SELVES.
Evidence that there is some sort of "SELF" that does not result from brain chemistry, please. If you can't provide it, none of your points in this iteration of your argument is supported.
8. And, while the number of actual SELVES possible in a finite universe would be finite, the number of potential SELVES would be infinite.
Nope, because you have failed to establish that the "SELF" exists, or that there is any component of the self that is not the result of brain function. In a finite universe, or even for brains of a finite size in an infinite universe, there will only be a finite number of possible states in which a brain can be. Your "proof of immortality" therefore requires brains to be of infinite size. They are demonstrably not (and it would probably be rather impractical if they were. Even Marvin only had a brain the size of a planet, not an infinite one).
In any case, since you failed to support the assertion you made in point 1, none of the points you made following from it have any validity.
Incidentally, you keep saying "we", for example:
We accept that could we perfectly replicate a person’s brain, we could replicate the person’s self – but, not the person’s SELF.
You and who else?