Bertrand's Paradox

This paradox was discovered by Bertrand Russell in 1901.

Some classes are members of themselves; some are not. For example, the class of all classes that have more than five members clearly has more than five classes as members; therefore the class is a member of itself. On the other hand, the class of all men is not a member of itself, not being a man. What of the class of all classes that are not members of themselves? Since its members are the non-self-members, it qualifies as a member of itself if and only if it is not.