the issue i see here is it is only a paradox if it requires the judge tells the truth and is always correct. but if that is the case then the prisoner is concluding that the judge is lying or made a mistake when he concludes he will not be hanged. so since the conclusion he won’t be hanged is a contradiction itself how can he conclude it is definitely true? if he can’t conclude his conclusion is definitely true then he will be uncertain each day
the issue i see here is it is only a paradox if it requires the judge tells the truth and is always correct. but if that is the case then the prisoner is concluding that the judge is lying or made a mistake when he concludes he will not be hanged. so since the conclusion he won’t be hanged is a contradiction itself how can he conclude it is definitely true? if he can’t conclude his conclusion is definitely true then he will be uncertain each day