  A one-one transformation of a class onto itself, also called a permutation, induces permutations of all the types in the hierarchy of types of “notions” determined by the class. Thus, a permutation P of a domain of individuals D induces a permutation of the class of n-ary relations of elements of D, a permutation of the class of functions with n arguments with domain Dn and range included in D, a permutation of the class of n-ary relations among relations of elements of D, etc. A notion or object O of a certain type t is invariant under all permutations of the universe of discourse if, for every permutation P of this universe, the permutation P̃ induced by P in the class of notions of type t is such that P̃(O)=O.