  In recent years, different types of adversarial examples from different
fields have emerged endlessly, including purely natural ones without
perturbations. A variety of defenses are proposed and then broken quickly. Two
fundamental questions need to be asked: What's the reason for the existence of
adversarial examples and are adversarial examples unsolvable? In this paper, we
will show the reason for the existence of adversarial examples is there are
non-isomorphic natural explanations that can all explain data set.
Specifically, for two natural explanations of being true and provable,
G\"odel's sentence is an adversarial example but ineliminable. It can't be
solved by the re-accumulation of data set or the re-improvement of learning
algorithm. Finally, from the perspective of computability, we will prove the
incomputability for adversarial examples, which are unrecognizable.
