logical type

"This statement is a lie." true or false? 
Bertrand Russell' s theory of logical types arose in the early part of the twentieth century as a result of contradictions and paradoxes in the mathematical theory of infinite sets. For example, "the class of all those classes that are not members of themselves" was self-contradictory. One such contradictory entity within mathematics endangered the self-consistency of all mathematics, so that Russell came to the conclusion that all such paradoxical statements had to be ruled out. He devised a hierarchical "theory of types" in which the legitimate members of a set at one level all belong to the level just below. 

A parallel consideration of language leads to a corresponding hierarchy of simple statements, statements about statements (metastatements), statements about metastatements and so on. To avoid paradox, each statement may only be about elements at the next lower level. Thus the paradoxical "this statement is a lie" is illegitimate, because it is a statement about itself rather than about elements at a lower level. 

In the years following the Macy conferences, Gregory Bateson increasingly used the Russell theory as a heuristic device and metaphor for describing human communication. He employed it for a general theory of play and fantasy as well as for the double-bind hypothesis in schizophrenia.