This chapter shows how to expand the ideas of Chapter 5 for a language involving quantifiers, and offers a more rigorous treatment. Since the contents of states of being for are treated as properties, predicates are treated as semantically contributing functions from objects to properties. Lambda-abstractions are introduced to denote properties, and open lambda-abstractions to denote functions from objects to properties. After improved versions of the main developments in Chapter 5, it is observed that both the treatment of inconsistency and the constructive feature of the semantics turn essentially on the assumption that all sentences in this simple language express the same kind of mental state. From this, it is argued that the only way to incorporate descriptive language is if belief is itself analyzed in terms of being for.
Keywords: predicate logic, lambda-abstractions, descriptive language,