Similar Paradoxes Liar Paradox:This statement is wrong. If it is wrong,then it is right;if it is right,then it is wrong. Barber's Paradox:A barber shaves,and only shaves,all people who do not shave themselves.Does he shave himself? (p|Barber shaves p}={plp does not shave himself} If Barber belongs to the above set,he does not belong there;but if he does not,he does. Unexpected Hanging Paradox:A prisoner is sentenced to death and his execution is scheduled in the next week.The precise date of the execution is such that it should not be known before the day of execution itself. D={d if the execution is on day d,then it is not known before day d} But what days belong to D? Saturday,the last day of the week,clearly does not belong to D. Given that we can exclude Saturday from consideration,Friday becomes the last possible day,and thus it does not belong to D... Keep going this way,we can exclude all days of the week! Does that mean we can always know what day is the execution day in advance?Similar Paradoxes  Liar Paradox: This statement is wrong.  If it is wrong, then it is right; if it is right, then it is wrong.  Barber’s Paradox: A barber shaves, and only shaves, all people who do not shave themselves. Does he shave himself?  {p|Barber shaves p}={p|p does not shave himself}  If Barber belongs to the above set, he does not belong there; but if he does not, he does.  Unexpected Hanging Paradox: A prisoner is sentenced to death and his execution is scheduled in the next week. The precise date of the execution is such that it should not be known before the day of execution itself. D={d| if the execution is on day d, then it is not known before day d} But what days belong to D? • Saturday, the last day of the week, clearly does not belong to D. • Given that we can exclude Saturday from consideration, Friday becomes the last possible day, and thus it does not belong to D… • Keep going this way, we can exclude all days of the week! • Does that mean we can always know what day is the execution day in advance?