No plot spoilers here, just wanted to flag a bit of poor reasoning that shows up in Chapter 39:
I shouldn't have believed it even for all of thirty seconds! Because if people had souls there wouldn't be any such thing as brain damage, if your soul could go on speaking after your whole brain was gone, how could damage to the left cerebral hemisphere take away your ability to talk?
This is a surprisingly common fallacy. Just because X depends on Y, it doesn't follow that X depends on nothing but Y. A phenomenon may involve more than just its most obvious failure point.
To illustrate: Suppose I'm trapped in a box, and my only way to communicate with the outside world is via radio communication. Someone on the other end argues that I don't really exist -- "There's no person beyond the radio receiver, for if there was then there wouldn't be any such thing as damaged radios!" Pretty silly, huh? But people say this kind of thing in defense of physicalism all the time.
(N.B. This is not to defend the existence of souls. It's just to point out that this particular argument against them is invalid.)
I endorse this refinement. What brain damage demonstrates is not dependency of talking on the brain, but that the complex computations of thought can be damaged in internal detail by damaging a specific brain part, whereupon its outputs to other parts of thought are damaged. This is strong evidence that the brain is doing the internal computations of thought; it is part of the inner process producing thoughts. The radio hypothesis, in which the output is produced elsewhere and received, decisively fails at that point.
We could suppose that you had a hundred soul-parts, all of which can only communicate with each other through brain-area radio transceivers which receive a call from one soul-part, and then retransmit it to another. But leaving out the epicycleness of this idea, the degree to which it contradicts the intuitive notion of a soul, and its, if you'll pardon the phrase, sheer stupidity, the end result would still be that destroying the brain leaves the soul incapable of thought. You're not likely to find a remotely reasonable hypothesis, even in the Methodsverse where magic abounds, by which the internal parts of a thinking computation can be damaged by damaging the brain, and yet removing the whole brain leaves the soul capable of internal thinking.
I kind of liked one of the HPMOR recursive fanfics which played with this since in the Methodsverse wizards continued to be able to think even when their brain was replaced with that of a cat.
If I remember right in that fic the blood-purists maintained that only wizards had souls and that the thing they used to prove it was by feeding polyjuice to a non-wizard who would lose their own personality in favor of the body they were copying for the duration of the potions effects. (not having a magical soul with which to maintain their thought patterns when their physical brain was changed)