Critical Section

In praise of Epiminedes

Sunday,  05/08/05  11:24 AM

Epiminedes is one of my favorite Greek heroes.  Only he wasn't Greek, he was from Crete.  And as a Cretan, he is known for saying, publicly, "all Cretans are liars".  (So, was he lying?)

The short version of Epiminedes' Paradox is: This sentence is false.

We had a great discussion about this yesterday.  My daughter Megan thinks it is so cool that something can be true and not true at the same time.  It relates directly to Godel's Theorem and [the limit of] the power of logic.

We visited the island of the Knights and Knaves ("I am a knave!"), and the famous Monty Hall Problem.  ("Should you switch?  Yes, you Cretan!")

Here's a sample problem, courtesy of my friend Yogi:

"You come to the gates of heaven, and there are two doors.  St. Peter explaines that one door leads to Heaven, and one to Hell.  There are twin brothers guarding the doors, one of whom never lies ("a knight") and the other never tells truth ("a knave").  You may ask one brother one question, and then must select a door.  What question do you ask?

Stay tuned for an answer...

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