 The three lambda abstracts in (1a)–(3a) represent, respectively, the meanings of the three noun phrases in (1)–(3). These lambda-abstracts occur in predicate position, as predicates of predicates, so that (1a)–(3a) can be read, respectively, as: every Greek is instantiated by being mortal; the president of Greece is instantiated by being Greek; the president of Greece is instantiated by being mortal. Given lambda-conversion plus quantifier and propositional logic, the argument is valid, as desired. It should be noted that lambda abstracts such as these can be taken to stand for peculiar properties of properties, classifiable as denoting concepts (after Russell 1903; see Cocchiarella 1989). One may then say then this approach to semantics makes a case for the postulation of denoting concepts, in addition to the more obvious and general fact that it grants properties as meanings of natural language predicates (represented by symbols of the formal language).