What is the mind-brain question? This phrase is not official, it's just how I think of the question of whether the mind, or the personality, who someone is, is entirely a function of the physical brain, or partly a function of a non-physical soul. Is there a part of me that exists separately from my body, that can continue to exist after my body dies? Many people believe that there is a non-material component, commonly called a soul or spirit, that makes up the personality and can exist without a material body.
In considering this question, when I look at what the body of evidence tells me, I would tend to say that there is no aspect of the mind/personality that is not entirely a function of the brain. That is, when the brain dies, the mind dies with it. Not a comforting notion for many of us, perhaps. Yet this is what the evidence suggests to me. What do I mean by "evidence"? In defense of the existence of the soul, we have a great deal of anecdotal reporting, whether of the "near-death-experience" and other "out-of-body-travel" variety on the one hand or ghostly sightings on the other. Frankly, anecdotal evidence exists to buttress all manner of fantastical creatures, from Bigfoot to the Chupracabra. As evidence is does not stand up. On the other side, there is a great deal of scientific evidence, repeatable evidence. There is, for example, the evidence of the effects of damage to the brain, where every conceivable aspect of who a person is, is verifiably dependent on the proper functioning of the brain.
Consider the tragic case of Alzheimer's disease. I have been witness to two grandparents dying of this disease, but not before the disease, bit by bit, erased their essences, everything that made them who they were. (I recommend this interactive tour of the brain that demonstrates and explains the effects of Alzheimer's on the brain.) Consider also the bizarre cases of brain damage that result in a man being convinced that the woman who claims to be his mother (and really is his mother) is an impostor; another man comes to believe he is on the verge of understanding the meaing of everything, from a grain of sand to his car; and a woman who, when asked to draw a picture of a flower, draws beautifully only the right half, not even being aware that she has left out the other half. (I believe this was a PBS documentary; I wish I had a recording of it!)
All of these things tell me that the human personality is completely brain-dependent. I welcome thoughtful discussion on this subject, especially if you disagree with me.