In short, he distinguishes between the brain and the mind (consciousness, memories, etc). While the brain may be required for an embodied creature to use their mind, they are not the same thing.
If a bomb vaporized your brain you would cease to be an embodied creature and you wouldn't have a mind anymore. You can test this theory yourself but only once.
You actually can't test this theory at all, if it's correct.
On destruction of your body, if the mind does not continue, you cannot observe its discontinuance. Thus, you cannot test the theory.
If the theory is false, then you could presumably falsify it by this technique.