Unexpected Hanging Paradox
en.wikipedia.org
en.wikipedia.org
- the premises are correct,
- the individual steps in the prisoner's reasoning appear to be sound,
- but the conclusion is wrong.
So from correct premises and seemingly sound inference steps, an incorrect conclusion can be drawn. A resolution then ought to propose a new set of inference rules that can only derive correct conclusions from correct premises. This is like physics' famous Ultraviolent Catastrophe, but in logic instead of physics.
I have an intuition for how to resolve the paradox:
Most people say that the reasoning is correct as far as it rules out Friday, but is wrong when it rules out Thursday. Notice then that if the premises were posed as
A prisoner is scheduled to be executed next week. He won't know his date of execution before it happens.
The prisoner has **not** been informed that his date of execution must be a surprise to him.
then we can rule out that the prisoner will be executed on Friday, but not rule out that he'll be executed on Thursday. This also eliminates the self-referentiality of the reasoning, because the reasoner is no longer the condemned prisoner.Assume he'll be executed on Thursday. Then it means that by Wednesday, he'll know that he'll be executed the next day. So it won't be a surprise then. But this contradicts the premise that the day of execution will be a surprise. So the assumption that he'll be executed on Thursday leads to a contradiction. Hence he won't be executed on Thursday.
Similarly, Wednesday can be eliminated, and then Tuesday, and then Monday. Which contradicts the premises. But the premises were true anyway.