Unexpected hanging paradox (nonfiction)

The unexpected hanging paradox or hangman paradox is a paradox about a person's expectations about the timing of a future event that he or she is told will occur at an unexpected time. The paradox is variously applied to a prisoner's hanging, or a surprise school test.

Despite significant academic interest, there is no consensus on its precise nature and consequently a final correct resolution has not yet been established.

One approach, offered by the logical school of thought, suggests that the problem arises in a self-contradictory self-referencing statement at the heart of the judge's sentence.

Another approach, offered by the epistemological school of thought, suggests the unexpected hanging paradox is an example of an epistemic paradox because it turns on our concept of knowledge.

Even though it is apparently simple, the paradox's underlying complexities have even led to its being called a "significant problem" for philosophy.

The paradox has been described as follows:

A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. He will not know the day of the hanging until the executioner knocks on his cell door at noon that day.

Having reflected on his sentence, the prisoner draws the conclusion that he will escape from the hanging. His reasoning is in several parts. He begins by concluding that the "surprise hanging" can't be on Friday, as if he hasn't been hanged by Thursday, there is only one day left - and so it won't be a surprise if he's hanged on Friday. Since the judge's sentence stipulated that the hanging would be a surprise to him, he concludes it cannot occur on Friday.

He then reasons that the surprise hanging cannot be on Thursday either, because Friday has already been eliminated and if he hasn't been hanged by Wednesday night, the hanging must occur on Thursday, making a Thursday hanging not a surprise either. By similar reasoning he concludes that the hanging can also not occur on Wednesday, Tuesday or Monday. Joyfully he retires to his cell confident that the hanging will not occur at all.

The next week, the executioner knocks on the prisoner's door at noon on Wednesday — which, despite all the above, was an utter surprise to him. Everything the judge said came true.

Other versions of the paradox replace the death sentence with a surprise fire drill, examination, pop quiz, or a lion behind a door.

The informal nature of everyday language allows for multiple interpretations of the paradox.

Fiction cross-reference

• Unexpectedly Hanging Chad - a documentary film (nonfiction).

Nonfiction cross-reference

External links:

• Unexpected hanging paradox @ Wikipedia