Ivan is the brainiac of the three Karamazov brothers. Intellectual and bookish, he can argue circles around everyone in town. No one, it seems, can outwit him in an argument, whether the topic be literature or religion, society or politics, or even affairs of the heart. He always seems to have an opinion, and yet, just when you think you have a handle on him, he seems to argue something else entirely.
Ironically, it may be that Ivan, not the fiery Dmitri, is the real rebel of the novel. In his simple and direct manner, Alyosha points out that Ivan's theoretical musings constitute "rebellion" (5.4.22). While Dmitri still clings to the idea of a higher order, Ivan rejects all higher orders and instead sets up the individual man as the sole judge of what is right and wrong, independent of any system of religious belief or morality. In Ivan's view, "everything is permitted," even cannibalism, if the individual feels like it.
Tellingly, Ivan, despite his intellectualism, is the brother most inclined toward fiction and fantasy. It is "rational" Ivan, not Dmitri or Alyosha, who imagines the two fantastic fictional characters in the novel: the Grand Inquisitor and the devil. These two figures seem to be grandiose productions, but they undermine Ivan's pretensions to greatness, to original and independent thought. The Grand Inquisitor, after all, is a frail old man, the devil a harmless "sponger," an impoverished middle-aged guy.
When Ivan's Grand Inquisitor says that man is essentially a weak and servile creature, easily manipulated by "myth, miracle, and mystery," he is essentially describing Ivan. Ivan is so caught up in his intellectual pride that he ultimately becomes a slave to it. He is so tormented by his own desire to appear superior to everyone else that he cannot be truly happy.
There is, after all, a limit to Ivan's powers of reasoning. He may try to explain away his own complicity in his father's murder, but in the end he has to admit that the only reason he didn't do anything was his cowardice. He may try to explain away his love for Katerina and pretend indifference to her, but he can't help his attraction to her. He may try to justify how he didn't rush to the police station right after he heard Smerdyakov's confession (which would have exonerated his brother Dmitri), but he simply can't. If the devil appears to Ivan at this key juncture, it's to remind him that his intellectual fictions are just that – pure fiction and fantasy.
In a sense, Ivan's fate bears out his theory that when everything is permitted, yes, even cannibalism is permitted. Ivan is eaten up by his own doubt and pride, and he catches a terrible brain fever at the end of the novel.