   Russell dubbed the notion of truth applicable to elementary propositions “first truth”. This notion of truth serves as the ground for a hierarchy of different notions of truth applicable to different types of propositions depending on their complexity. A proposition such as “(x)(x has quality q)” which involves a first-order quantifier, has (or lacks) “second truth” depending on whether its instances have “first truth”. In this case, “(x)(x has quality q)” would be true if every proposition got by replacing the “x” in “x has quality q” with the proper name of an individual has “first truth” (PM, 42). A proposition involving the simplest kind of second-order quantifier, i.e., a quantifier using a variable for “predicative” propositional functions of the lowest type, would have or lack “third truth” depending on whether its allowable substitution instances have second (or lower) truth.  Because any statement apparently about a class of individuals involves this sort of higher-order quantification, the truth or falsity of such a proposition will ultimately depend on the truth or falsity of various elementary propositions about its members. 