Resolving the Hangman's Paradox (optional material, p. 1)

The Hangman's Paradox A judge, known always to be true to his word, decreed that a certain convict would be hanged on one day of the following week (Monday through Sunday), with the further stipulation that he would not know on the morning of his execution that that day would be his execution day. Contemplating his fate, the convict reasoned as follows: If I am hanged on Sunday, then I will know on that morning that Sunday is the only day left and hence that my execution day has arrived. That, however, would contradict the judge's stipulation. Therefore I will not be hanged on Sunday. If I am hanged on Saturday, then I will know that morning that Saturday is the only remaining day (since Sunday is logically excluded). Again, I will know that my day of execution had arrived, contradicting the judge's order. So I cannot be hanged on Saturday. By similar logic, I know that I cannot be hanged on Friday, on Thursday, on Wednesday, on Tuesday—or even on Monday. In short, I cannot be hanged at all! The convict's conclusion, although supported by impeccable syllogisms, contradicted his original premise: namely, that the judge, whose word was fully credible, had decreed that he would be hanged that week. The contradiction was compounded when he was hanged on Tuesday, protesting the logical impossibility to the end.