In his article “Who is Who in the Fictional World”, Petr Koťátko argues that fictional worlds are, in general, complete, that is the logical law of the excluded middle holds in fictional worlds, though he admits that there are exceptions—he mentions Samuel Beckett’s trilogy as an example. The present article agrees with both these conclusions, and it continues Koťátko’s discussion by suggesting an explanation why so many scholars have claimed that fictional worlds in general are incomplete, and by presenting different kinds of exceptions from Koťátko’s basic position, and, finally, by sketching alternative interpretations of these examples of incomplete fictional worlds.