I know it’s a post by Eliezer when I find myself nodding in agreement through the whole article. Here he relates an occasion where somebody is not convinced by a probabilistic argument. I have had similar discussions, and they usually leave me exasperated 
Overcoming Bias: But There’s Still A Chance, Right?
The last sentence raises an important issue on the nature of rationality:
“Consider his example if you ever you find yourself thinking, ‘But you can’t prove me wrong.’ If you’re going to ignore a probabilistic counterargument, why not ignore a proof, too?”
In the end, we must decide to be rational or not. Nobody can force us to be rational, and many people unfortunately choose not to be rational (in full awareness of the fact; this is often combined with feeling proud about not being rational. Strange, but true).
As Sir Karl Popper said:
“There are many difficulties impeding the rapid spread of reasonableness. One of the main difficulties is that it always takes two to make a discussion reasonable. Each of the parties must be ready to learn from the other. You cannot have a rational discussion with a man who prefers shooting you to being convinced by you.” (from Wikiquote)
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