Unexpected hanging paradox

Episode #10 of the course “Brain-twisting paradoxes”

The unexpected hanging paradox is told through the story of a prisoner, a judge, and an executioner. At dawn on a Sunday, the judge sentences a prisoner to be hanged but doesn’t tell him exactly when. All he says is that, “At dawn, in one of the next five days, you shall be surprised, dragged out of your cell, and hanged. You will not know what day you will be hanged.”

The prisoner then goes back to his cell and thinks about what the judge had said. His hanging can’t be on Friday, he concludes, because that would be the last possible day of the hanging and therefore he would expect it to be that day. So if Friday is out, then it has to be either Monday-Thursday. But then he reaches the same conclusion, that, since he can’t be hung on Friday, that would also make Thursday expected and thus not possible. Using this logic, every other day of the week is ruled out since, one by one, they all become predictable. The prisoner knows his hanging will come as a surprise and will not be predictable. Because of this contradiction in logic, the prisoner concludes that if the judge is to be taken at his word, he will not be hanged.

However, that Wednesday at dawn, he is dragged out of his cell and hanged. Some have suggested this to be a significant problem in philosophical thinking, since there is no way to reconcile the man’s hanging if what the judge said is true. Two main explanations exist—one suggests that the problem arises because of the self-contradictory, self-referencing statement at the heart of the judge’s sentence. Another approach suggests the unexpected hanging paradox is an example of our concept of knowledge turning us to confusion.

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