The problem with supernatural occurrences is that they are almost entirely anecdotal. There are tons of stories about strange and unexplainable phenomenon, but very few people actually put forth the time and energy to do a proper scientific study. Without proper examination, it is impossible to tell what is real and what is false.
Take ghosts for instance. A television show with grainy footage and muffled audio makes for a poor scientific study. If someone wanted to do a proper study of ghosts, they would need to set up a vast array of equipment at an alleged haunted location. Lots of sensors monitoring all objects. Temperature sensors. Video and audio recording 24/7 for all locations. A constant log of all interfering activities (people, cars, lights, weather). And the study would have to go on for weeks if not months. And this is just one location. You need to study multiple haunted sites to collect as much data as possible. And then you need a control group studying multiple sites that are not haunted to have a set of baseline data to compare it to. All of this could costs tens of millions of dollars and a ton of manpower. But this is the minimum needed to try to find out if ghost are real or not.
Psychics. You'd need to collect a bunch of people who claim to be psychics and collect data on them over the course of probably months/years and then compare their predictions/information to a group of people who are not psychic. Is there a meaningful statistical difference?
The afterlife. This would probably be impossible to prove. I'm not going to volunteer to die over and over to try to get 1-2 minutes of afterlife data each attempt. We'll all find out eventually. One way or another.
Out of Body projection. I've read about people claiming to be able to leave their physical bodies and observe other locations while doing so. This one would be easy to prove. Put them alone in a room. Go to a separate room and write something on a piece of paper. Then ask the projector to leave their body and look at the piece of paper and report their findings. Enough positive responses and it would pretty much prove the existence of a soul. But...why has nobody done it?
I'm definitely in favor of science putting to rest these questions one way or another. There are things that have been debunked already such as Astrology. But science isn't easy and it isn't cheap. Someone needs to have the vision (and money) to see these things through. And each thing could take years.
