According to two-dimensional semantics, primary intension and secondary intension can play the role of reflecting the cognitive aspect of an expression like Fregean sense does. The aim of this paper is to argue that this role is likely a myth. To argue for this, I attempt to show that cognitive aspects of fictional names cannot be explained within the framework of two-dimensional semantics. To be more specific, I consider four ontological theories about fictional characters that two-dimensional semanticists might be tempted (...) to choose. And then, I argue that none of them can be combined with two-dimensional semantics in a satisfactory way. (shrink)