My thought is:
We have disproven many psychics.
We have proven no psychics.
In a world this big, if there is any sort of psychic powers, it's so negligibly weak as to be unimportant. If people could predict anything with certainty, we'd know about it, because some yutz would have tried selling his services, and would have actually made people millionaires.
You cannot prove psychics don't exist, just like you cannot prove you're not in the Matrix experiencing reality as a digital illusion. But you can look at the whopping lack of proof of the existence of psychics, and infer that there ain't any.
Sea monsters, though, that's another story. I heard one wrecked this little old ship that was just out on a three hour tour.