 Russell’s own response to the paradox came with his aptly named  theory of types.  Believing that self-application lay at the heart of the paradox, Russell’s basic idea was that we can avoid commitment to \(R\) (the set of all sets that are not members of themselves) by arranging all sentences (or, more precisely, all  propositional functions,  functions which give propositions as their values) into a hierarchy. It is then possible to refer to all objects for which a given condition (or predicate) holds only if they are all at the same level or of the same “type.” 