The paradigm concept of vagueness is one of the most dominant approaches to the problem of vagueness. According to it, the vagueness of a term consists in its having indeterminate borderline cases. In this paper, we will show the incompatibility thesis, that the paradigm concept of vagueness entails incompatible sentences. To prove this thesis, we shall show, if we accept the paradigm concept of vagueness, that there is a term that is indeterminate about whether it has borderline cases, and, based on the existence of such a term, two incompatible sentences are implied. One sentence implies the rejection of the exhaustiveness of true and false, and the other implies the indeterminacy of the exhaustiveness. Therefore, what we show is that the problem of vagueness cannot be solved by means of indeterminacy without inconsistency.
