What is the significance of imagined fears?

Imagined fears distort reasoning. It factors in something into the conclusion that does not belong. It only exist in the imagination.

If you ever meet someone you cannot reason with, someone who will deny all evidence, what can you do?

You try reasoning but he will blank out the evidence, he will selectively read, listen etc. In short there is no way of reaching that person until he decides he wants to see the evidence, want to examine his own irrational fears. And that is something only he can decide. A wise man once said, "you cannot teach anyone anything, they can only learn".

Note: Since the fears come from faulty thinking, the first step must be to learn to reason. Learn to examine the facts without preconceived notions or the fears cannot go. He will just imagine more and more. There is no end to imagined fears.

When I find someone is beyond reasoning, I've learned to walk away. Trying to explain is a waste of time and energy. It doesnt work.

But chess is an amazing training tool that the person can use. But only if he apply the lessons beyond the 64 squares. In chess if you ignore the evidence, you lose. That is self evident.