Massimo Pigliucci reviews a collection of essays, Doctor Who and Philosophy: Bigger On The Inside. He tackles one essay on the Doctor's regeneration:
If physical continuity, personality, and not even memory are necessary to speak of someone being a particular person, what on earth grounds the very idea of personhood? One possibility, not explored in Hand’s essay (but discussed in several of the others in the same collection) is that personal identity requires spatiotemporal continuity. In this sense, we all are four dimensional “worms” extending in space-time, accounting for the fact that I am the same person I was as a child, even though all the atoms in my body are different, my personality has somewhat changed, and I don’t recall much of that time of my life. That being the case, the Doctor is now in trouble: because he can jump from one space-time coordinate to another, he is not a continuous “worm,” but rather a set of unconnected fragments scattered around space-time. Does that mean that it is not regeneration, but rather time travel, that is logically incoherent?
The Dish 