More than one. Here is one. And as old Chisholm used to say, you are not philosophizing unless you have a puzzle. So try on this aporetic triad for size:
1. Purely fictional objects do not exist.
2. There are true sentences about purely fictional objects, e.g., 'Sherlock Holmes is a detective' and 'Sherlock Holmes is purely fictional.'
3. If a sentence of the form Fa is true, then there exists an x such that 'a' refers to x.
The triad is logically inconsistent: any two limbs entail the negation of the remaining one. So the limbs cannot all be true despite the considerable plausibility of each. So one of the propositions must be rejected. But the first is nonnegotiable since it is true by definition. The leaves two options: reject (2) or reject (3).
I want to avoid truck with Meinong if at all possible. So I should like to adhere to (3). There are no true singular sentences about what does not exist.
Suppose we reject (2). One way to do this is by supplying a paraphrase in which the apparent reference to the nonexistent is replaced by real reference to the existent. For example, the apparent reference to Sherlock, who does not exist, is replaced by real reference to a story in which he figures, a story that, of course, exists. The elliptical approach is one way of implementing this paraphrastic strategy. Accordingly,
4. Sherlock Holmes is a detective
5. Sherlock Holmes is fictional
are elliptical for, respectively,
6. In the Conan Doyle stories, Sherlock Holmes is a detective
7. In the Conan Doyle stories, Sherlock Holmes is fictional.
But note that while (5) is plainly true, (7) is plainly false. The stroies represent the detective as a real individual, not a fictional individual! So (7) cannot be taken as elliptical for (5) This is a serious problem for the 'story operator' approach. Or consider the true
8. Sherlock Holmes does not exist.
(8) is surely not short for the false
9. In the Conan Doyle stories, Sherlock Holmes does not exist.
The point can be made with other 'extranuclear' predicates such as 'merely possible' and 'mythological.' If I say that Pegasus is mythological, I don't mean that, according to legend, Pegasus is mythological.
I'll end with a different challenge to the story operator approach. Consider
10. Pinocchio was less of a liar than Barack Obama.
Whether you consider (1) true or false, it is certainly not elliptical for
11. In Carlo Collodi's The Adventures of Pinocchio (1883), Pinocchio was less of a liar than Barack Obama.
To put it vaguely, one problem with the story operator approach is that it traps fictional characters within particular stories, songs, legends, tales, etc. so that (i) it becomes difficult to understand how they can show up in different different stories, songs, etc. as they obviously do in the cases of Faust and Pinocchio, and (ii) it becomes difficult to understand how they can show up in comparisons with nonfictional individuals.
Is there a tenable solution to my triad or is it a genuine aporia?