Where does the trouble come from? With respect to the semantics,the main problem of the above paradoxes is that they kind of refer to themselves. "So you might want to restrict the use of self references if you want no trouble. With respect to sets,the main problem comes from "Comprehension Principle. COMPREHENSION PRINCIPLE YOU CAN PICK AN ARBITRARY PROPERTY P.AND DEFINE A SET S OF OBJECTS HAVING PROPERTY P,LE., S-XP(X)). To avoid paradoxes,mathematicians call things defined this way classes in stead of sets. Some classes are sets,but others are not. Of course,all sets are classes. For formal definitions,refer to axiomatic set theory books.Where does the trouble come from?  With respect to the semantics, the main problem of the above paradoxes is that they kind of refer to themselves.  So you might want to restrict the use of self references if you want no trouble.  With respect to sets, the main problem comes from “Comprehension Principle.” Comprehension Principle You can pick an arbitrary property p, and define a set S of objects having property p, i.e., S={x|p(x)}. • To avoid paradoxes, mathematicians call things defined this way classes in stead of sets. • Some classes are sets, but others are not. • Of course, all sets are classes. • For formal definitions, refer to axiomatic set theory books