   In the Introduction to Principia Mathematica, as part of his explanation of ramified type-theory, Russell described various notions of truth applicable to different types of propositions of different complexity. The simplest propositions in the language of Principia Mathematica are what Russell there called “elementary propositions”, which take forms such as “a has quality q”, “a has relation [in intension] R to b”, or “a and b and c stand in relation S” (PM, 43–44). Such propositions consist of a simple predicate, representing either a quality or a relation, and a number of proper names. According to Russell, such a proposition is true when there is a corresponding fact or complex, composed of the entities named by the predicate and proper names related to each other in the appropriate way. E.g., the proposition “a has relation R to b” is true if there exists a corresponding complex in which the entity a is related by the relation R to the entity b. If there is no corresponding complex, then the proposition is false.