Hi, my very first post! 
I’m just at this moment reading this web page. About 20% of the way down, under “4. Minimal Physicalism and Philosophy of Mind”, it states:
But I’m confused by this. Let’s take identity theory. If a pain literally is the very same thing as a neuron firing, then surely this is not the same as the pain supervening on the neural event? Or is it? 
Hello there Ian. Glad you joined!
I don’t exactly understand what you are specifically trying to ask, but I do know this:
Pain is usually the name assigned to the chemical reaction that occurs in our body when we experience pain-full sensations. The nerve-system of the body sends signals back and forth to the brain to process the sensations that we describe in words as being painfull.
However, psychogenic-pain (I think that that is what it is called, but I could be mistaken) is a rare condition that affects certain people. People have reported feeling severe chronic pain in their body for most of their life, yet doctors are never once able to find any forms of biological causes. The pain is simply caused by pure psychological happenings. The person truly does feel the pain just like if it had a normal biological cause, but in reality, it is purely psychological. And thus, is often times untreatable. 
Actually, I’ve read some more of that article, and I think I understand. Basically I wasn’t paying attention. One has to at a minimum subscribe to supervenience if one is a materialist. Obviously identity theory is over that minimum
Psychogenic-pain? It must have a biological correlate if materialism is correct. Otherwise all forms of materialism are false!
Interesting though. I’ll have to look it up