The author attempts to give an analysis of negative existential statements, in which the subject is a proper name. In contrast to many contemporary philosophers he thinks that this analysis is possible also in the case that we understand a proper name in the same way as Mill or Kripke. The purpose of this paper is not only to provide an analysis of existential statements, but also to support Mill´s and Kripke´s theory of proper names. It was just the failure to analyse negative existential statements that caused many theoreticians to incline towards the descriptive theory of proper names. Existential negative statements do not have, in author´s opinion, a subject-predicate structure. So, paradoxically, we do not speak about Homer in the statement Homer did not exist. This statement expresses that the name Homer does not have any bearer; and so we can say that the name is in some sense spurious. For this reason non-existential sentences that contain the name Homer do not have a truth-value, because their presupposition Homer did not exist is true.