The Parable of the Dagger

Once upon a time, there was a court jester who dab­bled in logic.

The jester pre­sented the king with two boxes. Upon the first box was in­scribed:

“Either this box con­tains an an­gry frog, or the box with a false in­scrip­tion con­tains an an­gry frog, but not both.”

On the sec­ond box was in­scribed:

“Either this box con­tains gold and the box with a false in­scrip­tion con­tains an an­gry frog, or this box con­tains an an­gry frog and the box with a true in­scrip­tion con­tains gold.”

And the jester said to the king: “One box con­tains an an­gry frog, the other box gold; and one, and only one, of the in­scrip­tions is true.”

The king opened the wrong box, and was sav­aged by an an­gry frog.

“You see,” the jester said, “let us hy­poth­e­size that the first in­scrip­tion is the true one. Then sup­pose the first box con­tains gold. Then the other box would have an an­gry frog, while the box with a true in­scrip­tion would con­tain gold, which would make the sec­ond state­ment true as well. Now hy­poth­e­size that the first in­scrip­tion is false, and that the first box con­tains gold. Then the sec­ond in­scrip­tion would be—”

The king or­dered the jester thrown in the dun­geons.

A day later, the jester was brought be­fore the king in chains, and shown two boxes.

“One box con­tains a key,” said the king, “to un­lock your chains; and if you find the key you are free. But the other box con­tains a dag­ger for your heart, if you fail.”

And the first box was in­scribed:

“Either both in­scrip­tions are true, or both in­scrip­tions are false.”

And the sec­ond box was in­scribed:

“This box con­tains the key.”

The jester rea­soned thusly: “Sup­pose the first in­scrip­tion is true. Then the sec­ond in­scrip­tion must also be true. Now sup­pose the first in­scrip­tion is false. Then again the sec­ond in­scrip­tion must be true. So the sec­ond box must con­tain the key, if the first in­scrip­tion is true, and also if the first in­scrip­tion is false. There­fore, the sec­ond box must log­i­cally con­tain the key.”

The jester opened the sec­ond box, and found a dag­ger.

“How?!” cried the jester in hor­ror, as he was dragged away. “It’s log­i­cally im­pos­si­ble!”

“It is en­tirely pos­si­ble,” replied the king. “I merely wrote those in­scrip­tions on two boxes, and then I put the dag­ger in the sec­ond one.”

(Adapted from Ray­mond Smul­lyan.)