Well, not with the horns and pitchfork and flames and all that.
Ivan's Satan appears in the manner of a mild-mannered, impoverished, elderly gentleman sitting amiably on his sofa.
Ivan sternly tells the nice old man that he's just a figment of everything that's base and, above all, stupid in his imagination, but the devil insists on his reality.
The devil reminds him that he had gone to see Smerdyakov to find out what he had told Katerina, which he still doesn't know. But Ivan tells the devil that this is no proof of the devil's existence: the devil only remembers this point because Ivan was about to.
Ivan then decides to wet a towel and place it on his head. Of course – wouldn't you if you were sitting across from the devil?
The devil then reminds Ivan that he had once accused Alyosha of spying on their conversations (of which they seem to have had several). Ivan admits that this was a momentary lapse, but insists that the devil is still a hallucination.
The devil goes on to tell some silly stories about himself and his adventures incarnated on earth. He wants nothing more than to be a simple "fat, 250-pound merchant's wife" and light candles to God, but instead he ends up with rheumatism.
Ivan decides the wet towel is useless and throws it away.
The devil complains about catching a cold while flying through the freezing heavens. But he was fortunately cured by Hoff's extract of malt.
Ivan rejects all of these anecdotes as stupid. The devil justifies his existence by claiming he exists only to "negate," to create doubt, because if everything was meaningful, there would be no more events.
He tells the story of a philosopher who all his life denied the existence of an afterlife. Upon his death, he discovered there was an afterlife, but he refused to go to heaven because it went against his convictions. He was then sentenced to walk a quadrillion kilometers as punishment, but since this also went against his convictions, he refused to walk. After a thousand years, he decided, oh heck, I'll walk. Once he got to heaven he sang its praises enthusiastically.
Ivan again rejects the devil – the anecdote wasn't his, it was a story Ivan made up when he was 17.
The devil tells another couple of stories: the first is about a man who lost his nose to some dreadful disease. The man complained to his priest that he wanted his nose back, but the priest told him that, hey, at least without your nose you won't have to worry about your nose being "out of joint" (i.e., bothered) about its being out of joint (as in, literally broken) ever again.
The second story is about a young floozy who confesses to her priest that she has slept with a man. After her confession, the priest and the floozy set up a booty call.
Ivan just becomes more and more infuriated by the devil's stupid stories (as are you, no doubt). The devil continues to mock his philosophy and his writings to his face, including the one about the Grand Inquisitor.
At his wit's end, Ivan throws an inkstand at the devil.
Their conversation is interrupted by a knock at the window. Suddenly Ivan feels as if he's been tied to his chair. He breaks free from what seem to be imaginary bonds and opens the window.
It's Alyosha, and Ivan lets him in. Alyosha announces that Smerdyakov has hanged himself.