If you object to the term "mind", just leave it out and read "brain and mind" as just "brain". I'm a physicalist so I don't think the mind is something separate from the brain anyway, so it's all the same to me.
It's also famously unprovable that there is not an invisible dragon in my garage that cannot be detected by any means whatever, to use Carl Sagan's example. That doesn't mean such an idea is worth discussing or including in your thought processes.