Frege's Puzzle and In-Between Cases of Believing
There's a huge literature in philosophy of language on what's called "Frege's puzzle" about belief reports. Almost all the participants in this literature seem to take for granted something that I reject: that sentences ascribing beliefs must be determinately true or false, at least once those sentences are disambiguated or contextualized in the right way.
Frege's puzzle is this. Lois Lane believes, it seems, that Superman is strong. And Clark Kent is, of course, Superman. So it seems to follow that Lois Lane believes that Clark Kent is strong. But Lois would deny that Clark Kent is strong, and it seems wrong to say that she believes it. So what's going on? There are several standard options, but all lead to trouble of one sort or another. (If you don't like Superman, try Twain/Clemens or Unabomber/Kaczynski.)
On a dispositional approach to belief of the sort I favor, to believe some proposition P -- the proposition, say, that that guy (variously known as "Superman" or "Clark Kent") is strong -- is to be disposed to act and react, both outwardly and inwardly, as though P were true. (On my version of dispositionalism, this means being disposed to act and react in ways that ordinary people would regard as characteristic of belief that P.) Lois has some such dispositions: For example, she's disposed to say "Superman is strong". But she notably lacks others: She's not disposed to say "Clark Kent is strong". She's disposed to ask Superman/Clark Kent to lift her up in the air when he's in costume but not when he's in street clothes.
Personality traits also involve clusters of dispositions, so consider them as an analogy. If someone is disposed to be courageous in some circumstances and not courageous in other circumstances, it might be neither quite right to say that she is courageous nor quite right to say that she isn't. "Courageous" is a vague predicate, and we might have an in-between case, in which neither simple ascription nor simple denial is entirely appropriate (though there may also be contexts in which simple ascription or denial works well enough -- e.g., battlefields vs. faculty meetings if she has battlefield courage but not interpersonal courage). Compare also "Amir is tall", said of a man who is 5'11". Lois's belief about Superman/Clark Kent might similarly be an in-between case in the application of a vague predicate.
You'll probably object that Lois simply and fully believes that Superman is strong, and it's not an in-between case at all. I have two replies. First, that way of putting it -- in terms of Superman rather than Clark Kent -- highlights certain aspects of Lois's dispositional profile over others, thus creating a conversational context that tends to favor believes-strong ascription (like a battlefield context might favor ascription of courage to a person who has battlefield courage but not other sorts of courage). Second, consider a version of the case in which the belief ascriber doesn't have the name "Clark Kent" available, but only the name "Superman". The ascriber and his friend are looking through a window at Superman/Clark Kent in street clothes. The ascriber's friend, who doesn't know that Lois is deceived, asks, "Does Lois believe that Superman is strong?" What should the ascriber reply? He should say, "Well, um, it's a complicated case!" I see no point in insisting that underneath that hedge there needs to be a determinate metaphysical or psychological or (disambiguated [update Dec. 16: e.g., "de re / de dicto"]) linguistic fact that yes-she-really-does (or no-she-really-doesn't), any more than there always has to be a determinate fact about whether someone is tall simpliciter or courageous simpliciter.
Now this is a heck of a mess in philosophy of language, and I haven't thought through all the implications. I'm inclined to think that excessive realism about the identity of propositions is part of the problem too. I don't claim that this is a full or non-problematic solution to Frege's puzzle. But it seems to me that this general type of approach should be more visible among the options than it is.
[HT: Lewis Powell on Kripke's Puzzle.]