On Firmly Inedecipherable Prepositions of Mathematics and Related Systems

For those who like logic paradoxes, this one is a beaut, Bruce. It is called

THE PARADOX OF THE UNEXPECTED HANGING.

It concerns a condemned prisoner and his Judge. The man, already sentenced to death by hanging, is told two things by the Judge.

1) “You will be hanged at noon on one day of next week, Monday through Friday.”
2) “The execution will be a surprise to you: You won’t know the day of the hanging until the executioner knocks on your cell door at 1155 on the day of the hanging.”

In his cell, the prisoner reflects thus:

“I can’t be hanged on Friday, since by Thursday night I will know that I will be hanged Friday, so it won’t be a surprise. “

He smiles.

“So if the hanging is not on Friday, it cannot be on Thursday either, since by Wednesday night I will also know that my execution will be on Thursday. “

His smile broadens.

It broadens further when he realises he can extend this logic right up to Monday, coming to the fabulous conclusion that he cannot possibly be hanged at all, because the Judge apparently has made an erroneous statement.

He is really smiling now.

However, he actually has to go beyond surprise into astonishment when, on Tuesday at 1155, the executioner turns up and he is hanged at noon, expiring with the most comical look of surprise on his face you have ever seen.

So what was wrong with the prisoner’s argument? Did the Judge make an erroneous statement? The sentence was carried out to the letter, all in accordance with the Judge’s two statements, yet the prisoner’s logic seems ironclad.

Much has been written about this paradox, and I have my own take on it.

However, surprisingly enough, I will await the comments of those in the know before divulgence.