In a certain small town, there is a barber named Bill. Since Bill is the only barber in the town, he decides that he will shave all the town's residents who do not shave themselves, but (obviously) not the ones who do.

If Bill follows this rule, will he shave himself or not?

For any person P,this holds.
If Bill shaves P,then P does not shave P.
If Bill does not shave P,then P shaves P.
If P is Bill,then we get the following contradiction.
If Bill shaves Bill,then Bill does not shave Bill.
If Bill does not shave Bill,then Bill shaves Bill.
His rule is a paradox.

Posted by Tim Axoy on 2003-03-22 13:20:24