(a) (Russell paradox) A logical difficulty arises from the idea, which at first appe...

(a) (Russell paradox) A logical difficulty arises from the idea, which at first appears natural, of calling any collection of objects a set. Let’s say that set B is ordinary if For example, if B is the set of all chairs, then because B is not a chair. It is only in the case of very unusual collections that we are tempted to say that a set is a member of itself. (The collection of all abstract ideas certainly is an abstract idea.) Let X = {x: x is an ordinary set}. Is What should we say about the collection of all ordinary sets?

(b) In the town of Seville, the (male) barber shaves all the men, and only the men, who do not shave themselves. Let A be the set of all men in the town who do not shave themselves. Who shaves the barber? (That is, is the barber an element of A? Is he not an element of A?)