[See also Richard’s response to this post at Philosophy, et cetera, Jonathan’s original post on this topic at Fake Barn Country, and my previous post on this topic.]
The following post is deeply flawed. Comments and criticisms are welcome.
Some kinds of fictions (such as novels) come in the form of sentences, which (normally) represent propositions; other kinds of fictions (such as movies) come in other forms (e.g., series of moving images). This is only one of several significant differences between different kinds of fictions. Until the consequences of such differences are worked out, it seems to me that we cannot say that a theory of truth which is correct for (say) novels won’t turn out to be incorrect for movies. So I think it’s possible (perhaps even probable) that there is not just one correct theory of fictional truth.
However, in this post, I will pretend to know that there is just one correct theory of fictional truth, and will argue that on that one correct theory, all propositions are either true or false in any fictional world. That is, I’ll argue that fictional worlds are "complete." For this purpose, I will restrict myself to consideration of fictional worlds which attain a minimal level of coherence, self-consistency, and "sanity." For instance, my discussion here won’t necessarily apply to truth in the world of Atlanta Nights.
To begin, consider these propositions:
(a) In Harry Potter’s world, there are wizards in England.
(b) In Harry Potter’s world, Harry put his shoes on before flying away.
(c) In HP’s world, Harry put on either his left shoe or his right shoe before flying away.
(d) In HP’s world, Harry put on his left shoe before flying away.
(e) In HP’s world, there are an even number of stars.
I hope the following claims are uncontroversial:
1. In Harry Potter’s world, (a) and (b) are true, and we have a way to know that they are true.
2. We do not have any obvious way to know whether (d) or (e) are true or false (in HP’s world), and it is highly probable that we will never have a way to know whether (d) or (e) are true or false.
In this post, I want to show that
3. (c) is true in HP’s world, and we have a way to know whether it is true; and
4. (d) and (e) are either true or false (i.e. not neither true nor false) in HP’s world, even though we have no obvious way to know which.
Jonathan appears to agree with me about 3 (given his Feb15/12:15 comment in the previous post); the main point of contention seems to be about 4.
It is easy (for me) to become confused when thinking about whether completeness is part of a fictional world. Certainly, there is a sense in which Harry Potter must live in a complete world. After all, it might be interesting to write a story in which some propositions are neither true nor false, but JK Rowling has not done this. JK Rowling has written a series of stories about a boy in a world which is logically predictable and regular (despite the fact that it contains wizards and magic). Rowling has never given us any reason to think that there are propositions which are neither true or false in her invented world, so it’s fair to assume that they all are either true or false in that world.
But it does not follow from this, at least not immediately, that there is not another sense in which, in Rowling’s invented world, some propositions are not either true or false. We sometimes think that propositions are true or false in fictional worlds because the author said they were true or false. For instance: If Rowling were to find my blog, and leave a comment which says that, yes, there are an even number of stars in Harry’s world, then it would be the case that there are an even number of stars in Harry’s world. But Rowling (I assume) has never said or written anything about this question, and probably never will. Since Rowling has never said or written anything about whether (e) above is true or false, there appears to be nothing that makes (e) true or makes (e) false. In that case, it seems that (e) must be neither true nor false.
But what does make a proposition true in a fictional world? Consider two more claims:
(f) In HP’s world, HP put his shoes on before flying away because he did not want his feet to get dirty when he came down to land.
(g) In HP’s world, HP put his shoes on before flying away because JK Rowling said he did.
Both (f) and (g) are true, I think, but they are true from different perspectives. (f) (or anyway, something like (f)) is true because the people in Rowling’s invented world do things for reasons, and (f) describes Harry’s reason for doing what he did do. (g) is true because everything that happens in fictional worlds is fictional, i.e. invented by someone, and normally something which is invented is explicable in terms of the inventor. As we switch perspectives, either (f) or (g) becomes more useful, but it seems to me that there is a sense in which both (f) and (g) are always true, no matter which perspective we adopt. Let’s give names to the two perspectives. Let’s say that from the internal perspective, (f) is the most useful truth, while from the external perspective, (g) is the most useful truth.
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. From the external perspective, however, (e) is neither true nor false. After all, as we’ve seen, (we’re assuming that) Rowling has never said anything about whether (e) is true or false; and Rowling saying whether (e) is true or false appears to be the only thing which could make (e) true or false from the external perspective.
I want to show two things. First, I want to show that the external perspective is abnormal; when people think about fictional worlds, they normally do so from the internal perspective. Second, I want to show that, given this, the internal perspective ought to be our "default position"; when we want to understand truth in fictional worlds, we ought to do so primarily from the internal perspective.
Suppose Rowling decides to write a murder mystery. In her story, the identity of the murderer is left for the audience to figure out, but clues are dropped here and there, so that an attentive reader would be able to determine that the maid must have committed the murder. In that case, most of us will say that, in the mystery’s fictional world, it is true that the maid is the murderer, even though the author does not make explicit whether it is true or false that the maid is the murderer.
In that case, clearly, "the maid is the murderer" is true from the internal perspective. It’s not obvious, however, that "the maid is the murderer" is either true or false from the external perspective. If the author has to have explicitly indicated that a proposition is true (or false) in her fictional world in order for that proposition to be true (or false) from the external perspective, then "the maid is the murderer" is neither true nor false from the external perspective. But perhaps you think that the author has to have merely believed that some proposition is true (or false) in order for it to be true (or false) from the external perspective. In that case (assuming Rowling does believe that the maid is the murderer), "the maid is the murderer" is true from the external perspective, even though such has never been explicitly indicated.
However: Suppose now that Rowling doesn’t believe the maid is the murderer — she believes that the clues are indecisive — but she is simply wrong about this. For instance: 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? I am not sure.
I think the case just examined illustrates two things. First, it illustrates that it is not clear what the external perspective is. That is, it is not clear exactly how we are looking at a fictional world when we look at it from the external perspective. Second, it illustrates that when we think about fictional worlds, we normally do so from the internal perspective. Most people, I submit, would be happy to say that, in Rowling’s mystery, the maid really is the murderer, no matter what Rowling herself believes. I claim that they can say this with such confidence because they are taking up the internal perspective — and from that perspective, it is quite obvious that the maid is the murderer.
Another, perhaps more important, difficulty with the external perspective is illustrated by considering the interaction of claims (b), (c) and (d) above. (b) implies (c). (c) implies (d) is either true or false. Indeed, (c) is really just the claim that (d) is either true or false. Now, claim (b) is clearly true from the external perspective; Rowling wrote that (b) is true, and that is what makes something true from the external perspective. In that case, it seems, (c) must be true from the external perspective. (In fact, Jonathan has said (c) is true, and I take Jonathan to want to think of fiction from the external perspective). But then it follows that (d) is either true or false from the external perspective. But (d) is supposed to be neither true nor false from the external perspective.
This is not necessarily incoherent. It might make sense to say that (d) is both either true or false, and neither true nor false, from the external perspective. But again: I do not think we typically think about fictional worlds from a perspective so logically strange. This suggests that we ordinarily do not look at fictional worlds from the external perspective.
So, I (tentatively) conclude that our primary way of thinking about fictional worlds ought to be from the internal perspective. From the internal perspective, all propositions are either true or false; fictional worlds are complete from the internal perspective. So, it seems to me, the primary theory of fictional truth ought to be a theory of truth in "complete worlds."
E.G. 
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