I think supernatural things don't exist by definition. If ghosts would exist, they would be just natural.

The real question is whether there is a two way link between consciousness and the physical world. Obviously the physical world is observed by consciousness, so that direction checks out. What about the other direction? Is the physical world at all influenced by consciousness? The mindfulness folks seem to argue: no. They argue that consciousness is like a person watching a movie, where the movie is experience. The person is so immersed that it thinks, it controls the movie, but in reality it's a fully passive observer. But this can't be true! Otherwise, the discussion of consciousness could never have come up in human history. A population of "philosophical zombies" could never initiate this discussion. So somehow consciousness must cause physical neurons to activate. The movie knows about the person watching!