My first impression is that Dawkins is equating genetic code with personal identity. His first statement:
"The potential people who could have been here in my place but who will in fact never see the light of day outnumber the sand grains of Arabia. Certainly those unborn ghosts include greater poets than Keats, scientists greater than Newton."
seems correct. But in the next part, he appears to equate personal identity with a specific genetic combination:
We know this because the set of possible people allowed by our DNA so massively exceeds the set of actual people. In the teeth of these stupefying odds it is you and I, in our ordinariness, that are here.
To me, this seems wrong (as you point out as well). I can think of a couple more examples:
- Suppose there was another human out there with DNA identical to mine, I would hardly want to say that that person was me.
- Suppose my DNA were to change due to a virus (or radiation or simple copying error—something that has most likely already happened), surely that would not change who I was.
Dawkins, I'm sure, is making this connection through his reductive materialistic worldview: I.e. he assumes the truth of reductive materialism, which implies that personal identity must supervene on the physical—i.e. the body—which is an expression of your genetic code: similar to positing that a copy of a computer program is the same program. This is not my view, just what I imagine Dawkins would say if challenged.
In general, however, I think the problem of personal identity is much harder than Dawkins assumes in the above passages. Consider the following questions:
- Where does my personal identity from?
- Why should there be such a thing as personal identity in the universe at all? If we consider the continuum of matter, why should some clumps within the continuum have specific personal identities?
- Why am I me and not someone else?
This last question was considered by Thomas Nagel, in his book 'The View from Nowhere,'
One acute problem of subjectivity remains even after all points of
view and subjective experiences are admitted to the real world—after the world is conceded to be full of people with minds, having
thoughts, feelings, and perceptions that cannot be completely
subdued by the physical conception of objectivity. This general
admission still leaves us with an unsolved problem of particular
subjectivity. The world so conceived, though extremely various
in the types of things and perspectives it contains, is still centerless.
It contains us all, and none of us occupies a metaphysically
privileged position. Yet each of us, reflecting on this centerless
world, must admit that one very large fact seems to have been
omitted from its description: the fact that a particular person in
it is himself. What kind of fact is that? What kind of fact is it—if it is a fact—that I am Thomas Nagel? How can I be a particular person?
Nagel does not offer an answer; he only points out how difficult and profound the question is. And it doesn't seem like simply connecting DNA to self will suffice.