Sometimes I hear examples of paradoxes, like The Grandfather Paradox: if you went back in time and killed your grandfather then you wouldn't have been born, so you couldn't go back to kill your grandfather, which means you couldn't have killed your grandfather, so you would have been born so you could go back and kill him, etc.
Whenever I've heard other people interpret paradoxes, they have always seemed to interpret a paradox as a problem that needed to be solved, they seemed to put effort into looking deeper and finding a way that you could, for example, go back to kill your grandfather.
For me, paradoxes seem like a simple counterexample, or a proof against an idea.
When I hear an example like the grandfather paradox, I interpret it as a counterexample to "going back in time", or a proof that "going back in time" is not possible.
So I think that paradoxes are counterexamples, while other people seem to think that paradoxes are problems that need to be solved.
Are these other people irrational? Or am I missing something?