Philosophy | Logic | Thought Experiment
The Hangman’s Paradox
A Significant Problem
When I was in middle school, my math teacher would surprise us with a pop quiz once a week. We always knew the quiz would come at some point during the week, but we never knew which day. A pop quiz in math, being everyone’s favorite subject, was a death sentence.
Is it really a surprise if we know it will happen at some point during the week? One can reason that the quiz will only take place on certain days, otherwise, through process of elimination, one could make an accurate inference on when the quiz will happen. This is a paradox, because no matter what, the pop quiz will be a surprise.
This paradox was first introduced in 1963 by Martin Gardner, a writer who’s published work on math, science, philosophy, literature, and magic. The paradox was originally called the “unexpected hanging paradox,” but I like the hangman’s paradox better. The paradox goes like this:
A prisoner is told by the court that he will be sent to the gallows at noon between Monday and Friday of the coming week, but it will be a surprise. The poor prisoner won’t know what day he will die until the hangman comes to his cell at noon. Little does the court know, this prisoner has an understanding of logic.
