That's a philosophical one... 

There are, of course, some people on this planet who claim for having supernatural powers, and they do show some extraordinary phenomenons.

Science and formal logic, can't explain rules, or principals which it doesn't consists. Therefore if it's supernatural e.g. beyond nature as we know it, science can't explain whether it's exists or not. 

If science can explain it, then it wouldn't be supernatural.

It all comes to believing. Some proved as charlatans, some not. For those who weren't you have the right to choose- believe or not.