The existance of a paradox disprooves whatever notion it was formed for.

For instance, time travel. Say someone invented a time machine to fix some catastrophic event that happened in the past. He or she goes back in time and corrects the problem... but that would then mean the problem never existed in the "future", therefore the time machine wouldn't have been created to fix it, therefore it would've never been fixed; therefore time travel to the past is IMPOSSIBLE.

"Can God create a rock he cannot move?" ~Yet another paradox.....