If I say " This statement is a lie", it is a paradox. But nothing happens. The universe doesn't explode. Therefore, it is possible for paradoxes to exist. But a paradox by it's very definition defies the laws that govern our universe. Something that defies a universal law cannot exist. Therefore, a paradox existing is a paradox in itself. Sorry if I did something wrong, this is my first paradox I've thought of by myself.