Mental activities include beliefs, desires, hopes, fears, pains, tastes, sensations, etc.
Mental events are correlated with brain activity.
Correlation can mean identity, or causation. A pain could be correlated with brain activity because it just is brain activity, or because brain activity causes pain, or because pain causes brain activity.
Let's consider the case that brain activity and mental activity are identical. Two different labels for one event. In the same way that Mark Twain and Sam Clemens are two different labels for one person.
So that means that pain is the firing of C fibers and the firing of C fibers is pain. They are two different labels for one event, as with Mark and Sam.
But this cannot be so.
If pain is the firing of C fibers, then anyone who lacks C fibers cannot feel pain. So what about aliens? They may have followed a different evolutionary track and lack C fibers. Or future Artificial Intelligence. Or non-human animals who lack C fibers. None of these beings would be able to feel pain, were this true. This is clearly absurd.
So the second option is better: brain activity causes mental events, but is not identical to it. Different brains can cause pain: C fibers in humans, silicon circuits in A.I., and crystal fibers in aliens. Different cells can cause the same mental event: beliefs, pains, etc.
But this won't work either.
Consider locking your door because you FEAR burglars. The fear is a mental event that causes your hand to flip the lock. For your hand to flip the lock, the brain must be sending signals down the arm into the hand. But the brain also causes the mental event "fear of burglars." So the brain causes the fear, and the brain causes the hand. Now note: the fear does not cause the hand to flip the lock. But clearly, your fear of burglars does cause your hand to flip the lock.
So the correlation of brain activity to mental activity is neither brain-to-mental causation, nor identity.
So the only option left is that brain activity is correlated with mental activity because mental activity causes brain activity.
1. Mental events are correlated with brain activity because they are either A) identical to brain activity, B) caused by brain activity, or C) cause brain activity
2. Not A
3. Not B
4. Therefore, C
5. Therefore, mental events are separate from brain activity