The prisoner's anticipated response seems entirely irrational here. There are a range of possible outcomes the prisoner faces: - Will not be hung this week -

The prisoner's anticipated response seems entirely irrational here. There are a range of possible outcomes the prisoner faces: - Will not be hung this week - Will be hung on Monday - Will be hung on Tuesday - Will be hung on Wednesday - Will be hung on Thursday - Will be hung on Friday You can use logic in order to determine that each of the above outcome is logically impossible. But once you've ruled out all possible outcomes as being "impossible", why would the prisoner stubbornly believe the very first outcome to be true. It too contradicts what the Judge had explicitly said. In such a situation, the prisoner should consider that all 6 possibilities have some significant likelihood of being true, since they all deviate from the Judge's promise in some way. And when dealing with such a rational prisoner, the Judge's promise is impossible to uphold. Perhaps that is the true resolution to the paradox. The judge was able to make and deliver on his promise, only because he correctly anticipated the prisoner's irrational response. When dealing with a rational prisoner, it would be impossible to uphold such a promise.