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.”
Suppose the second inscription is false. In that case, the first inscription must also be false, in which case the king can put whatever he damn well pleases in the boxes.
The first inscription says that the inscriptions have the same truth value. If the second one is false then the first one implies that it is false which, in turn, implies that the first one is true. Contradiction. So the premise that “the second inscription is false” is false. So the second inscription is true.
The Jester’s logical inference is right. The point isn’t that the Jester’s logic was wrong—it wasn’t. It’s that the Jester assumed that the locations of the key and the dagger would follow the logic when there really was no good reason to assume so. This is meant to illustrate that making unwarranted assumptions about reality isn’t a good idea.
Suppose the second inscription is false. In that case, the first inscription must also be false, in which case the king can put whatever he damn well pleases in the boxes.
The first inscription says that the inscriptions have the same truth value. If the second one is false then the first one implies that it is false which, in turn, implies that the first one is true. Contradiction. So the premise that “the second inscription is false” is false. So the second inscription is true.
The Jester’s logical inference is right. The point isn’t that the Jester’s logic was wrong—it wasn’t. It’s that the Jester assumed that the locations of the key and the dagger would follow the logic when there really was no good reason to assume so. This is meant to illustrate that making unwarranted assumptions about reality isn’t a good idea.
That would make the first inscription true. (And therefore false, and therefore paradoxical, etc)