An argument for the existence of 'the soul'

By "soul", I mean something beyond the body that is nevertheless an essential part of "me".

I will use the method Reductio ad absurdum (Latin: "reduction to the absurd"), where I assume the opposite of what I am trying to prove, hoping to derive an absurd outcome, and then conclude that the original assumption must have been false.

1. Assumption: I am merely an organised collection of material "stuff" (atoms, molecules, cells, ...).
2. Therefore, what I call "my thoughts" must be merely sequences of electrochemical changes in my brain.
3. All beliefs are thoughts.
4. Therefore, a belief is a sequence of electrochemical changes in the brain.
5. These electrochemical changes are caused by external events in the past (plus a certain amount of quantum randomness).
6. Therefore, my beliefs (including my original assumption) are no more connected to the actual truth about the universe than the fizzing of an antacid tablet in a glass of water!
7. This is absurd. [As CS Lewis wrote: 'You cannot have a proof that no proofs matter.' (Meditations in a toolshed)]
8. Therefore, there is something more to "me" than my physical body, which we may identify as "the soul".