1. The laws of physics at the time scales, space scales, and energies of the human brain are "known" and we have deep reasons to believe that more will not be discovered. He spends a great deal of space explaining and arguing that the credence that physics is "complete" in this regime should be very, very high.
2. Given the current laws of physics, there is no place or room for non-physicalist explanations of consciousness (or, I suppose, for other dualist ideas like a soul) because there is no mechanism for them to effect change in the physical world.
3. Anyone who wants a non-physicalist approach to consciousness must either claim they can violate the laws of physics in our brains, or cannot affect the physical world.