It sounds like Jiro was saying that the Jester really does not assume that "The content of the boxes can be deduced from the the inscriptions." He just assumes "The inscriptions are either true or false," and it logically follows from what the inscriptions say that he can deduce the contents. So the problem wasn't making an assumption about how the contents could be discovered, but making an assumption that the inscriptions had to be either true or false.
Ok, thank you for that clarification.
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.)