rigid designation of general terms and trivialization problem

Kripke in his famous book, Naming and Necessity, introduces the concept of “rigidity” for designation of singular terms; and by using it, he refutes the Descriptive Theory of Meaning. If a term is rigid it means that it designates the same thing in all possible worlds in which it exists. Kripke, in third lecture, extends the concept of “rigidity” to all natural kind terms. This extension has had several interpretations which can be put into two categories: the sameness in designation, and the essentialist approaches. The sameness in designation approach, however, confronts “the trivialization problem”,i.e. not only natural kind terms, but also all general terms are rigid designators since each of them designates a property which remains the same across all possible worlds. An argumentative way has been proposed to refute trivialization problem. This approach is based on considering abundant objects as the designatum of singular terms and parallelism between these words and general terms. In this paper we will criticize this approach and show that it conflicts with some semantic roles of general terms and also our intuition concerning the truth value of sentences containing them.