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.)
This also applies to my piano analogy. Remove the middle C string, and you'll hear silence wherever there's supposed to be a middle C. Remove the dampers, and the piano will sound like the sustain pedal is constantly held down. Tune each G# string a semitone higher, and you'll hear an A wherever a G# is supposed to be.
That doesn't seem at all similar. The brain is, in this analogy, more like an instrument where if you remove one string it still works for most things but will no longer let you play anything by Mozart, and if you remove another everything comes out syncopated, and if you remove another then you can still play everything but all rubato disappears so that rhythms become metronomic. See also my reply to billswift.