 Any person who is not Cretan can state that all Cretans always lie. For a Cretan this is not possible because of the universal negative self-referential nature of the statement. If the statement is true, he is not lying which makes the statement untrue: a real paradox based on self contradiction. Along the same lines Russel coined the concept of the set of all sets that are not member of themselves, for which membership cannot be determined. Apparently the set of all sets is an inadmissible object within set theory. In general there is in philosophy and mathematics a limit to the extent in which a system can verify statements about itself within the system. (For further discussion, see the entry on  Russell’s paradox.) 