ABSTRACT
This chapter discusses multiple denotation as a primitive semantical relation and considers three alternatives. The three alternatives are satisfaction, determination and designation alternatives. The chapter discusses the semantical meta-language based on satisfaction, semantical meta-language based upon designation and a semantical meta-language based on determination. It considers the circumstances under which the semantical relations taken heretofore as primitive become definable. The chapter reviews some of the general features of the semantical meta-languages based on special primitives, and compare and contrast these with meta-languages such as based on the method of definition, before going on to non-translational semantics. A semantics based on a special primitive is in some respects analogous to a direct axiomatization of arithmetic, in which natural numbers are taken as values for variables. The chapter talks about four general methods for constructing semantical meta-languages: the method of definition, the truth-as-primitive method, the method of special primitives and non-translational method.
