In this paper I argue for the Atlas-Kempson Thesis that sentences of the form The A is not B are not ambiguous but rather semantically general (Quine), non-specific (Zwicky and Sadock), or vague (G. Lakoff). This observation refutes the 1970 Davidson-Harman hypothesis that underlying structures, as full semantic representations, are logical forms. It undermines the conception of semantical presupposition, removes a support for the existence of truth-value gaps for presuppositional sentences (the remaining arguments for which are viciously circular), and lifts (...) the Russell-Strawson dispute of 1950–1964 from stalemate to a formulation in which a resolution is possible for the first time. Suggestions of Davidson, Montague, Stalnaker, Kaplan and H. P. Grice are shown to be inadequate semantic descriptions of negative, presuppositional sentences. I briefly discuss the radical Pragmatics view of my 1975 publications and suggest that it too fails to do justice to the linguistic data. I speculate that Semantic Representations should be given the form (more or less) of computer programs, describable in Dana Scott's mathematical semantics for programming languages. (shrink)