An Improvement on Holmesian Logic

When you have eliminated all which is impossible, then whatever remains, however improbable, must be the truth.

Arthur Conan Doyle, The Case-Book of Sherlock Holmes

   “But I understand nothing—but nothing of all this! The enemy that this Ratchett spoke of, he was then on the train after all? But where is he now? How can he have vanished into thin air? My head, it whirls. Say something, then, my friend, I implore you. Show me how the impossible can be possible!”
   “It is a good phrase that,” said Poirot. “The impossible cannot have happened, therefore the impossible must be possible in spite of appearances.”

Agatha Christie, Murder on the Orient Express (Glasgow: Fontana, 1984; 1934), p. 116.