The author explores the meaning of proper names and other types of singular terms in the context of propositional attitudes, combining the problems of empty names, rigid designators and non-specific reading. An object in the attitudes can be given to the agent as such (de re), in the description (de dicto), as well as in several intermediate ways. From the analysis of the phenomenon of rigid designation, I move on to the theory of the object, where I consider two alternatives — strict, or Leibnizian, and weak. The first explains the actual non-existence by impossibility, the second — by occasionality. Here there are two ways of defining non-existent (fictional) objects — kinship and the counterpart relation, which are realized in frames that are different in their features. Nonspecific character is inherent in the kinship and counterpart relation in different ways. A special case is formed by hybrid worlds in which the real and the fictitious meet. The result of my analysis is five variants of a weakened de re reading of proper names and other singular terms in the context of attitudes. I describe their features, touching on the cognitive effect of narration, which operates with the appropriate attitudes