All of these comments on the jester wrongly assuming the box inscriptions related to the world seem overwrought to me. I created this account just to make this point (and because this site looks amazing!):
The jester's only mistake was discounting the possibility of both inscriptions being false.
That's it...the inscriptions (both) 'being false'. Not 'pertaining to the real world', not 'having truth values'...just 'being false'.
He figured out that it could not be the case that both inscriptions were true---so far so good. He then assumed that it must be the case that one must be true and the other false, which was only allowing for 1 out of the 2 remaining possibilities (1 true and 1 false, or 2 false). He was modelling his solution after the earlier problem he had constructed (with the frog and the gold), or he was essentially trying to maximize the number of true inscriptions, or both. Neither was warranted.
(I mostly agree with the poster above (Chrysophylax), or at least the first two paragraphs of that long post, in that the inscriptions certainly did have truth values pertaining to the world and specifically to the contents of the boxes. That is mostly the point I wanted to make. I disagree with her or him about this part, though: "The statement "Both inscriptions are false" is meaningless because it is inconsistent - we cannot assign a truth-value to it." I see that statement as false, not meaningless. So I actually take slightly more possible statements as pertaining the world and having actual truth values than does Chrysophylax (which in turn is far more than most other commenters here seem to be reporting). ...basically anything that does not match Chrysophylax's other examples of meaningless statements. I could even go so far as saying that the statement "The invisible unicorn is happy." is false though maybe also being 'meaningless' (maybe because it demands the acceptance of the false statement "An invisible unicorn exists." and could be translated as "There exists an invisible unicorn, and it is happy."). I'd love to hear opinions on that, though!)
That's it...the inscriptions (both) 'being false'. Not 'pertaining to the real world', not 'having truth values'...just 'being false'.
If they were both false, that would make the first inscription true.
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:
On the second box was inscribed:
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:
And the second box was inscribed:
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.)