The Language of D. Lewis’ Counterpart Theory: A Critical and Logical Investigation

[The philosopher and logician D. Lewis (1941-2001) created a language which he called ‘counterpart theory’. He created this language in order to translating into it the standard language of modal predicate language. The latter contains in its vocabulary (in addition to the basics of the first) the box and diamond which represent necessity and possibility respectively. The main aim of Lewis’ creation of that language and its rules of translation was 1) reducing necessity and possibility into the two quantifiers, i.e. the universal and the existential ones, 2) providing an extensional logic for modal predicate logic versus the standard intentional one, 3) and grasping the meaning of modalities. Although Lewis’ counterpart theory has metaphysical implications, i.e. realism concerning the nature of possible worlds, but these metaphysical implications has no impact upon scrutinizing the adequacy of counterpart theory. Therefore, this paper tries to check the syntactical and semantical adequacy of counterpart theory in respect to it its: 1) expressional adequacy, 2) ability to saving the truth or falsity of the formulae we know that they are true or false at the standard modal logic language, 3) as well as ability to saving the validity of the inferences of the standard language of modal predicate logic. I shall confirm the adequacy of Counterpart theory by insisting on critical translation approach of G. Hunter and W. Seager.]