It's easy to start confusing things here. I'm absolutely convinced some people have 'psychic' abilities, but that doesn't mean they are predictive. We've been discussing both here as if they were the same thing. But the word 'psychic' usually connotes something paranormal. I'm also not convinced someone who is 'psychic' is actually having experiences which are somehow magical. It's just that we don't understand the physical mechanisms involved. In other words, they aren't paranormal.
My mother was psychic to a certain extent, but never, as far as I know, predictive in the events that happened to her. The ones she told me were all 'after the fact' kinds of events that had a lot of emotion attached to them. For example, her father, an MD, was on some sort of medication. He practiced in Gunnison, Colorado. My mother lived at the YWCA in Denver. He somehow ran out of medicine and was unable to get any. He asked my mother to help him get it. His voice was heard by everyone in the room. Of course, he was several dozens of miles away on the other side of the Rocky Mountains. No one understood the message save for my mother, who recognized his voice and the fact that he used a family pet name for her. She was able to get the medicine to him in time.
Now, she was strongly attached to my grandfather and loved him deeply while deeply resenting her step-mother. My real grandmother died at age 42 of TB in 1916. So they had a strong emotional connection and there was strong need for immediate action. The event happened and was corraborated by other women in the room. There were several other events like that one that happened to her. I won't bore you with details.
Now, was she 'psychic'? Well, if we define the term to include instances such as I have related, yes. Does that mean it was 'paranormal'? Once again, we can change our definition to be more or less inclusive at will. But my feeling is that these instances weren't 'magical' in that they violated any physical laws; it's just that we have incomplete understanding of what is really going on. I have an inherent faith that science will be able to 'catch up' to these events and be able to explain them the same way science caught up with electricity and now presents a solid foundation for harnessing it. It's slow going because science does not change paradigms easily, but it can happen, as it did from a Newtonian view of reality to that of quantum mechanics. Evidence for this sort of self is inherently anecdotal, which is one of the reasons science has such a hard time dealing with it.