The term "supernatural" is frequently used in discussions related to skepticism. I am trying to establish the category that people refer to with this term.
All uses of this term appear to imply a separation of concepts and events into two disjoint categories: "natural" and "supernatural". Some examples of things typically classified into "supernatural": God, ghosts, telepathy, telekinesis, aura. Things typically classified as "natural": animals, rocks, talking, earthquake, body temperature.
I will try to follow the advice given in Similarity Clusters and try to establish some verbal hints as to what causes a concept to be classified into either similarity cluster.
One idea I had is the following: anything we expect to be able to experience, if the necessary prerequisites are met, is "natural"; anything we expect to fail to experience even if we try hard is "supernatural". This seems to work quite well on the concepts mentioned above. This works for unlikely events too: a plane crash is not "supernatural" because if I'm at the right place and the right time then I expect to be able to experience it.
It's still a bit weak for exceedingly unlikely events. For example, proton decay has never been witnessed, and we don't know if it can even occur. But "proton decay" is not classified as "supernatural"; rather as a "hypothesis". Telepathy, however, might for all we know be as rare as proton decay (thus being exceedingly hard to confirm experimentally), and yet it's classified into "supernatural". Something is missing from this verbal hint.
But what?
Approaching this from a different perspective, it appears that one can classify "supernatural" as having the property of being "outside of the universe". On further thought, however, this isn't helpful at all: the latter is not so much a verbal hint as a label in itself.
If taken literally, one might argue that all supernatural things therefore don't exist. They are said to be outside the universe, but we can only experience things within the universe, because anything we can experience must be part of the universe, and thus "inside" it. This is quite useless, however, in my opinion: as used by actual people, the category "supernatural" isn't intended to preclude existence. So this doesn't work.
Could it be that the category "supernatural" is actually completely useless, by offering so little information about the things that belong to it that knowing that something is classified as "supernatural" doesn't tell us very much at all?
Thinking about this led me to the idea that perhaps "supernatural" simply means "something that science has shown false or doesn't accept as a valid theory". That is certainly a property I infer about P when told that P belongs to "supernatural".
This is still quite unsatisfactory. It can't be the only property. People explain away God's undetectability by being "supernatural", intending it as a convincing argument - but even those who do things like this wouldn't claim that "not a valid theory" is an argument in favour of God. They must mean something else.
But what?
Your reply and anonym's are fundamentally right, I believe. To spell it out more, we need to extend the concept of Similarity Clusters to laws. I mean laws as in "natural laws" and perhaps "supernatural laws", not as in rules passed by legislatures. To take the supernaturalists seriously, we have to hypothesize that there are exceptions, perhaps even regular exceptions, to natural laws. Where natural laws conflict with supernatural ones, the hypothesis goes, the supernatural ones triumph. That's what makes them super. By the way, supernatural "laws" might just be descriptions of alleged supernatural properties. E.g., telekinesis is the power to move stuff just by wishing.
Doesn't this just push the puzzle back a step? How do we distinguish natural laws from supernatural ones? By clustering. Natural laws form a tightly knit explanatory framework. For example we can explain lots of chemistry via QM. Natural laws use terms like mass, charge, acceleration. Etc. Supernatural items are claimed not to fit into the same tightly knit explanatory framework. They are described using terms with no apparent relation to mass, charge, acceleration. Etc.
But, let me say where the "ontologically basic mental things" account is onto something. The paradigm examples of supernatural objects and qualities are usually mental. Or if not the paradigm examples, then at least a large and important category. Since it is indeed hard to see how painfulness or the sensation of sweetness relates to mass, charge, acceleration, etc. - especially if one glosses over the difference between epistemic puzzles and metaphysical ones - the mental has long been an attractive zone for claiming that a different constellation of laws are in play.
ETA: I see Manfred beat me to it. I'll leave mine here because my version is a little further out on a limb.