The paper reacts on Pavel Cmorej’s analysis of sentences of the form (ιx)Φ(x) is C, focusing on the case where “C” stands for “impossible”. The author agrees with Cmorej’s conclusion that in such a context the modal term applies on the meaning of the description, classifying it as unable to provide a procedure which would lead to identifying an individual (as a unique bearer of the property (λx)Φ(x) in some world and time). He questions Cmorej’s example of impossibility based on contradiction from the sphere of literary fiction, examines various ways in which the constitution of a lit- erary character may impose (or seem to impose) incompatible demands on the reader, requiring her to “think impossible”, and suggests a way of avoiding some confusions widespread in this field.