“Either both inscriptions are true, or both inscriptions are false.”
If this statement is true then the second box must hold the key by the jester’s reasoning. However if this statement is false then it doesn’t require that the second statement be true. In his testing the jester negated only half of the statement at a time. If this statement is entirely false then it could simply mean that the true-false values of the statements on either box have no relationship to each other. Which did indeed turn out to be the case.
In other words: If the statement on the second box is false, then the statement on the first box claiming that the statements on the two boxes are in any way related is also false and the fact that both being false would cause a paradox if the first statement were true is not relevant.
The jester made the mistake of assuming “at least one of the statements is true” and confused validity and soundness, and therefore deserved to be stabbed.
The jester should have seen this coming.
“Either both inscriptions are true, or both inscriptions are false.”
If this statement is true then the second box must hold the key by the jester’s reasoning. However if this statement is false then it doesn’t require that the second statement be true. In his testing the jester negated only half of the statement at a time. If this statement is entirely false then it could simply mean that the true-false values of the statements on either box have no relationship to each other. Which did indeed turn out to be the case.
In other words: If the statement on the second box is false, then the statement on the first box claiming that the statements on the two boxes are in any way related is also false and the fact that both being false would cause a paradox if the first statement were true is not relevant.
The jester made the mistake of assuming “at least one of the statements is true” and confused validity and soundness, and therefore deserved to be stabbed.