Yes. The judge's statement is only valid because of the prisoner's short-sightedness (i.e., it is a prediction, not a logical statement). If the prisoner knows

Yes. The judge's statement is only valid because of the prisoner's short-sightedness (i.e., it is a prediction, not a logical statement). If the prisoner knows the punch line of the joke, the judge's pronouncement becomes undecidable and therefore meaningless. It's no different than if the judge said, "you will be hung, and this statement is false", and the prisoner was surprised that they got hung. Heck, even if the prisoner doesn't know the punch line, the judge's statement is invalid if they incorrectly judge the depth of the prisoner's thought. The prisoner could stop their logical reasoning after 2 days instead of 5, and be sure that they're being hanged Wednesday, making the judge's prediction false. In summary: the judge made (intentionally or not) a prediction; the prisoner interpreted the prediction as a logical statement; the prisoner failed to see that the statement is undecidable, and drew a logical conclusion from it; the conclusion the prisoner drew happened to make the prediction true.