As is well known, some things do not exist. These include round squares, unicorns (probably), Sherlock Holmes, or luminiferous ether. In formal logic, nonexistent objects arise naturally in predicate modal logics or by means of non-referring definite descriptions. It turns out that if we deal with non-referring terms, classical logic is not quite suitable and must be tweaked. The tweaked variants, or so-called free logics, often acknowledge that some statements about nonexistent things may lack truth values, but they mostly fail to recognize that nonexistent objects can as well be inconsistent. We present a simple four-valued free logic that accommodates both inconsistency and incompleteness. Furthermore, we sketch a graded generalization of its semantics based on Lukasiewicz logic. (Based on joint work with Martina Daňková and Antonín Dvořák.)