I don't think fictions are complete. If all we're told about Harry Potter's footwearing habits is that he puts on his shoes before flying away, there simply is no fact of the matter as to which shoe he put on first. That simply isn't part of the story. It's left unspecified. Quick poll: is that your intuition too, or are you inclined to think there must be some fact of the matter (in the fiction), even if we could never possibly know what it is?
David's main objection, if I've understood him correctly, is that such incompleteness would be too "logically strange". The disjunction 'P or not-P' is a logical truth, so presumably true in the fiction. But, according to classical logic, it follows from this that either P is true or not-P is true.
Of course, this assumes that classical logic applies to fictions, and I think this assumption is mistaken. It's fictionally possible to have 'P or not-P' true, despite there being no (fictional) fact of the matter as to which disjunct is the true one. As evidence for this I cite our intuitions above. This is only 'strange' insofar as it differs from non-fiction, which we take to be complete. But it should come as no great surprise if truth in fiction ends up being somewhat different from the genuine article. So long as we still have a coherent picture of what's going on - and by employing non-classical logics we can avoid any serious logical difficulties here - I don't see that there's any problem.
I think we do much better to understand fictions in terms of sets of possible worlds (if we must employ possible worlds in the analysis at all). To quote Chris Ragg's comment:
How can it be that the books only pick out one of these worlds? If you take the books to express a set of propositions, it is completely underdetermined which world is being discussed. The author herself cannot even decide between the worlds!
It seems to me that she is telling a partial story of all the possible worlds which are consistent with the propositions expressed in the book. That is, the books refer to the worlds in which Harry puts on his left shoe first, his right shoe first, ties double knots, single knots, etc. If we take the novels to express sets of propositions, then they are telling a partial story of all the worlds in which those propositions are true.
From this view, we can better understand the logical behaviour of fictional truth, and see why it is not so 'strange' after all. A proposition is true in a fiction iff it is true in all the relevant possible worlds. Clearly, 'P or not-P' is true in each world, so it is true of the fiction as a whole. However, suppose the individual worlds differ as to whether P is true or not-P is true. (In some worlds Harry puts on his left shoe first, in others his right.) Then there is not fictional fact as to which one of P or not-P happens to be true. And this result makes perfect sense. From the fact that 'P or not-P' is true in all worlds, it does not logically follow that either 'P' is true in all those worlds or 'not-P' is true in all those worlds.
So, given such an analysis, the logical behaviour (and incompleteness) of truth in fiction makes perfect sense. The problem only arises if we assume that truth in fiction should be analyzed in terms of a single possible world, giving us a 'complete' fictional world. But of course to make that assumption is to beg the question entirely.
Another interesting aspect of David's post is his distinction between 'internal' and 'external' explanations of fictional facts. I think it's a very useful distinction to make. The internal view tells us why a particular fact is true at a particular possible world. For example, perhaps Harry Potter put his shoes on before flying "because he did not want his feet to get dirty when he came down to land." The external view, by contrast - and here I depart slightly from David's own description - tells us not why a fact is true at a world, but rather, why the story is to be identified with that world. Given that there is a possible world wherein Harry puts his shoes on before flying away, what makes this world (as opposed to some other possible world) the world of our fiction? The answer to this question is external to the fictional world, of course, and instead involves facts about what is written in the text, and perhaps how the ideal reader would respond to it (what they would infer), etc. This, I think, is the crucial question for any analysis of truth in fiction.
Now, I think David actually misdescribes the 'external view' (and I hope it is not too presumptuous of me to suggest this, given that David came up with the idea in the first place!). He ties it specifically to the author - whether her explicit pronouncements or implicit beliefs about her written fiction - rather than the more general question of how fictions are identified with particular possible worlds. He goes on to show, quite correctly, that authors can be mistaken about what is true in their fiction:
Suppose that several events in the story, taken in conjunction, imply that nobody but the maid could have committed the murder -- but Rowling has not noticed the implication, and mistakenly believes that she has left the identity of the murderer as an open question. Then what would be the case from the external perspective?
David rightly concludes that the author's perspective is inadequate when it comes to explaining truth in fiction. However, because he identified the author's perspective with the external perspective, he also dismissed the latter. I would argue that this is not justified. We can explain truth in fiction by appeal to external facts other than those of authorial intent. We could also refer to the implications of what is written in the text, for instance. So what David showed is not that the external view is inadequate, but rather that authorial intent is the wrong analysis of the external view!
I have one last disagreement to voice. David claims that "fictional worlds are complete from the internal perspective." He doesn't provide any real argument for this claim, however, and indeed I think it is false.
Referring to the proposition (e): 'In HP's world, there are an even number of stars', David writes:
From the internal perspective, (e) is true (or false). It wouldn't surprise me, in fact, if some wizard in Harry's world knew that (e) is true (or false); wizards seem often to know those sorts of things.
Here's the problem. There is a possible world where (e) is true and the wizards know this. However, there is another possible world where (e) is false, as is (again) known by the wizards of that world. Now, which of these possible worlds is the world of the Harry Potter fictions? This is a question for the external view (by my definition) to answer. But in fact there is no such answer, the fiction is underdetermined. So we would do better to conclude that the fiction is (as Chris put it earlier) a partial description of both worlds. Accordingly, there is no fictional fact as to whether (e) is true or false, and nor is there any fictional fact as to what the wizards believe about it. These facts will vary from [possible] world to world, and the fiction describes all of them equally.
To conclude this (perhaps overly) critical post, I want to offer David my sincere thanks for writing such a thought-provoking post to begin with. Clearly I disagree with him on several points, but his post inspired these ideas that I otherwise would not have had. I especially appreciate his internal-external idea, and hope he does not mind too much the alterations I made to it!