 The point of these paraphrases is to show that the original sentences can be analyzed in terms of sentences in which the singular terms (“Pegasus”, “Vulcan”, “the flying horse of Greek mythology” and “the planet between Mercury and the sun”) have all disappeared. The paraphrases involve the general terms “flying horse from Greek mythology” and “planet between Mercury and the sun”, along with the existential quantifier (“there is”) and a uniqueness condition (“exactly one”). (Let’s ignore the fact that the singular terms “Mercury” and “Le Verrier” appear within the general terms; of course, this means that the procedure isn’t complete, but, in principle, it can be completed.) The problem of negative singular existentials is thereby resolved because sentences containing names which appear to be about nonexistent objects are paraphrased in terms of sentences involving general terms, quantifiers and uniqueness conditions. These latter sentences are meaningful independently of whether the general terms apply to anything.