Scientific study of the paranormal
It is not mentioned much but science often involves such a leap of faith. A scientist will know instinctively that their idea is right even though they don't have the solid evidence to demonstrate it. Often it means waiting until suitable technology is developed to test the idea.
So what's the difference between a scientist's hunch and someone believing that minds can communicate with ESP, for instance? It is that the scientist must build up a body of good evidence to test their theory. They will also face criticism from fellow scientists. This is not aimed at them personally but at their ideas. If an idea is to be accepted, it must be tested by logic as well as evidence. Further experiments then take place taking the criticism into account. Also, the experiments should be replicated by other scientists. This is in case there is some unknown systematic error in the original experiments. If the theory survives this process then it will be accepted as new science, despite the fact that it started out as no more than a hunch.
So there is no scientific problem with someone believing that minds can communicate with ESP provided they can demonstrate it and are happy to have their work examined, criticised and replicated by others. This is the scientific process.
Many scientific theories have started as unprovable thoughts in direct contradiction to the science of the day. The paranormal always stands in that position. If you have a weird idea, don't be afraid to share it but be prepared to test it.