A logician in hell June 14, 2011Posted by Ezra Resnick in Logic.
The following is true.
I was arrested for breaking the laws of logic, and sentenced to be hanged unexpectedly within the week.
As I sat in my cell trying to reason my way out of my predicament, I saw the local executioner passing by. He looked like a logical fellow (and rather familiar), so I attempted to strike up a conversation: I asked whether he hanged all the condemned outlaws around these parts. “All those who don’t hang themselves,” he answered grimly. (I decided not to ask what would happen if he himself were sentenced to be hanged…)
I tried to bribe my way to freedom by offering the executioner a heap of gold coins; but he was not persuaded by my argument that zero coins constitute a heap.
Instead, he offered to set me free if I could guess the natural number he was thinking of. After an uncountable number of incorrect guesses, I gave up. (It turned out that he was thinking of the smallest natural number not definable in under eleven words.)
When the guards came (unexpectedly!) to take me to the gallows, I protested that I was insane and therefore unfit to be executed; but the executioner pointed out that insanity defenses are never accepted because anyone pleading for his own life must be sane.
As the rope was placed around my neck, I broke down and told the executioner that due to time travel gone wrong, I was actually his grandfather — so by killing me he would be undoing his own birth.
“I sure hope it works this time,” he said, and pulled the lever.
By the way, the first sentence of this post is false.