I've long wondered just how to define the term "supernatural" as it seems to be very often without much clarity. Richard Carrier has made an effort here: richardcarrier.blogspot.com/2007/01/defining-supernatural.html. I felt it was good. Does anyone else on here like his view? If you have a better definition, I'd love to here that too.
It's a long, long post and I got sick of it after a while, but it's an interesting idea, and has some merit. But I don't think it is correct.
1. Take his Harry Potter example. A wand and a word produce an effect and there's no physical connection, so he regards that as supernatural. But I would call it magic, and in the Potter world, magic is natural - people discover and invent spells and potions just like in our world we discover and invent things. So I think he's wrong there.
2. But suppose he's right. Then a physical thing (wand) is partially responsible for the effect, but because there's no physical connection, it's supernatural. Then a parallel is the human brain and mind, which he discusses. The brain produces an effect (thoughts) which we assess as supernatural if there's no physical connection. Now the physical mind is controlled by physical laws. So if there is a physical connection between brain and thought then it's not supernatural, and its all determined. But if we exercise genuine libertarian choice, then there's a break in the physical connection and by his definition it's supernatural. So libertine freewill is supernatural to Carrier. I think that would be news to philosophers like David Chalmers and Thomas Nagel, who (if I understand them correctly) think there is something mental that isn't physical but is natural, and thus we do have freewill.
Carrier's test is to mean what ordinary people mean. I don't think ordinary people would thing freewill was supernatural.
I don't have a better definition, but I suspect instead of linking supernatural to mental, I would link supernatural to not natural (yes!!!!) - i.e. produced by a being that isn't a physical part of this universe. But I'm sure we could shoot holes in that obvious statement, but that is still the direction I think I'd head.
1. He defines supernatural as an irreducibly mental cause or effect. Thus magic can be supernatural if there's no reducible natural physical cause or effect behind it, going by this. I don't think it's ubiquity would have determine it.
2. What he discusses are possible minds which have no reducible physical properties behind them (like brains). So if our brains are merely housing, that seems like a fair example. Your overview seems to exclude compatibilist views, but that is another discussion. I think you're right that ordinary people don't view free will as supernatural, but then I'm not sure if they have an explicit definition either. Most would probably feel free will isn't reducibly physical, and thus by his definition it's supernatural.
His definition has some merit, but like you it seems best when applied to a being that is above or beyond nature (i.e. the "super" in "supernatural), so probably a god or something close enough. Still, it was the first essay I'd seen dealing with the matter and provided great food for thought.