I am not convinced that everyone who uses the term means the same thing -- or even compatible things -- by it, actually.
Some people seem to mean a combination of subtle, unexplained, and sacred... that is, E is a supernatural event if it's hard to notice, they don't know why it happens, and they approach it with awe (rather than, say, with curiosity).
Other people seem to mean inconsistent with natural law. Most of the people who believe the supernatural doesn't exist seem to adopt this meaning, although many people adopt this meaning and believe it has a real referent.
On this site, the idea that the supernatural involves the irreducably mental ("ontologically basic mental entities") is popular; I'm not sold on it myself. For example, if someone told me that they believed in a Law of Karma that caused events to occur in a way that reflects Cosmic Justice, I would understand that to be a belief about the supernatural, but it would not be clear to me that they consider the entities being described either mental or ontologically basic, nor that it matters in either case. (Of course, nothing prevents either of those things from being true.)
The Law of Karma would need to determine which events are concordant with Cosmic Justice and which are not. I suppose your hypothetical friend would agree that the Law of Karma behaves as if there were a god with a sense of Cosmic Justice. So their cosmology is a theist's cosmology except with the "exists" tag removed from all gods.
I'm not sure what Richard Carrier's definition makes of this.
ETA: Looking a second time at this post, it seems clear that Richard Carrier would regard a Law of Karma as a mental property of the universe, even if there ...
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?