Paradigmatic uses of negative existentials such as ‘Vulcan does not exist’ are problematic because they present the interpreter with a pragmatic paradox: a speaker who uses such a sentence seems to be asserting something that is incompatible with what she presupposes. An adequate solution must therefore explain why we interpret paradigmatic uses of negative existentials as saying something true, even though such uses present us with a pragmatic paradox. I provide such an explanation by analyzing paradigmatic uses of negative existentials (...) as corrections of previous assertions that are judged to suffer from referential presupposition failure. I present the explanation within the framework of a simple version of segmented discourse representation theory. (shrink)