Two-Sorted and Intensional M-Logic

Abstract

In the previous chapter, we distinguished the second level of predication for intentional objects. The predication on this level, the external predication, has the same formal structure as we used to associate with the predication for ordinary individuals. Thus, M-objects as subjects of external predication, like individuals, are insensitive to the complexity of properties predicated of them: possessing a complex property by M-object is tantamount to its possessing simple properties in an appropriate propositional form. In particular, M-objects as subjects of external predication must be consistent and complete from the point of view of classical logic. Because of that insensitivity there is even no need to introduce complex properties to classical logic. And since M-logic comprises the classical syntax, we will utilise this fact for expressing external predication, simply by allowing constants to occupy argument positions in a (relaxed) M-language.