A better way of looking at it is that what one person knows to be true, another does not. Well, you get the picture. Joe and Bill leave us scrabbling to figure out who the liar really is. And so mathematicians write books about paradoxes. For a computer engineer, logical paradoxes promise serious mischief in a machine's operation.
Paradoxes do more than make nice games.
They're profoundly important just because they expose skeletons in the closets of reason. They warn us what a minefield language is. The most minor failing of words opens the door to logical conflict. But if I am, then you have to negate the sentence. I am in fact a truth teller.