Dilip Ninan has also argued on a number of occasions that attitude contents cannot in general be modelled by sets of qualitative centred worlds; see especially his "Counterfactual attitudes and multi-centered worlds" (2012). The argument is based on an alleged problem for the centred-worlds account applied to what he calls "counterfactual attitudes", the prime example being imagination.
Since the problem concerns the analysis of attitudes de re, we first have to briefly review what the centred-worlds account might say about this. Consider a de re belief report "x believes that y is F". Whether this is true depends on what x believes about y, but if belief contents are qualitative, we cannot simply check whether y is F in x's belief worlds. We first have to locate y in these qualitative scenarios. A standard idea, going back to Quine, Kaplan and Lewis, is that the belief report is true iff there is some "acquaintance relation" Q such that (i) x is Q-related uniquely to y and (ii) in x's belief worlds, the individual at the centre is Q-related to an individual that is F. For example, if Ralph sees Ortcutt sneaking around the waterfront, and believes that the guy sneaking around the waterfront is a spy, then Ralph believes de re of Ortcutt that he is a spy.
Ninan now asks us to consider not belief but imagination. Suppose Ralph imagines that he didn't see Ortcutt sneaking around the waterfront. Applying the above recipe, we might try to analyse this as true iff there is some acquaintance relation Q such that (i) Ralph is Q-related uniquely to Ortcutt and (ii) in the worlds of Ralph's imagination, the individual at the centre is Q-related to someone he didn't see sneaking around the waterfront. But since the only relevant acquaintance relation between Ralph and Ortcutt is the "seen sneaking around the waterfront" relation, this can't be right: condition (ii) is impossible.
To get a correct analysis of imagination de re, Ninan suggests that the content of imaginations, and attitudes in general, should be modelled not by a set of centred worlds, but by a set of multi-centred worlds. A multi-centred world consists of an uncentred world w, a time t, and a suitable tagging function f, where f is defined as follows. Again assume x is the subject of the attitude (i.e. Ralf, in the example). Then the domain of the tagging function f consists of all pairs (y,Q) consisting of an individual y and a relation Q such that x bears Q to y. Each such pair is mapped by f to an individual that exists at t in w.
The basic idea is this. Our attitudes ascribe properties to actual individuals y only relative to an acquaintance relation Q. For example, when Ralph imagines that he never saw Ortcutt, his imagination attributes never-having-seen to Ortcutt, relative to the acquaintance relation having-seen-sneaking which captures how Ortcutt is known to Ralph. The multi-centred worlds simply encode facts like these: the content of Ralph's imagination consists of multi-centred worlds (w,t,f) such that f maps (Ortcutt, having-seen-sneaking) to somebody or other who has never been seen by the individual at the (w,t,f) centre, i.e. by the individual at (w,t) to which f maps (Ralph, identity).
Ninan takes it for granted that the content of an imagination can be specified by saying which properties and relations the subject imaginatively attributes to which individuals relative to which acquaintance relations. Imagination is, at bottom, a relation between a subject x, an uncentred qualitative content p, and a function that maps actual individual-relation pairs to individuals figuring in p. But is this a good way to think about imaginations? The model assumes that there is a difference between x imaginatively attributing F to y under Q1 and x attributing F to y under Q2, even if x is certain that he bears Q1 and Q2 to the very same individual. For example, I know my office both as the room in which I am now (Q1) and as the room in which I was 5 minutes ago (Q2). I am certain that I've been in this room throughout the last hour. Now I imagine that a possum came into my office last night. Do imagine this relative to Q1 or Q2? I don't know. I don't even know how to make sense of the question.
Let's think about imagination as a psychological phenomenon, setting aside for a moment the semantics of imagination reports. Suppose Ralph imagines confronting Ortcutt as he sneaks around the waterfront. This could merely be an entertaining of a possibility, or it could be a vivid imagination in which Ralph somehow "simulates" what it would be like to confront Ortcutt: the visual impressions, the muscle movements, hearing Ortcutt's words in response, etc. In either case, what is imagined is first of all a scenario with certain qualitative features: a man is sneaking around, another man confronts him, etc. In addition, Ralph identifies various parts of the scenario with parts of the real world: the man who is sneaking around is identified with the man Ralph is (or was) observing, the man confronting him is identified with Ralph himself, the location with the actual location of the waterfront. Other aspects of the scenario, the spoken words for example, don't receive any such identification. In case of a vivid imagination, Ralph might additionally "put himself" into the scenario, simulating what it would be like to be there. This is independent of the previous step, since Ralph needn't imagine the scenario from the perspective of the person he identifies as himself; he could imagine it from Ortcutt's perspective, or from a birds-eye perspective. On the other hand, if the initial qualitative scenario is centred, the perspective could be given by the centre, so maybe we don't have to add a third ingredient.
In any case, we have two main ingredients: a qualitative scenario and an "identification" of various things in the scenario. Both parts belongs to the psychology of imagination. It would be wrong to suggest that psychologically, Ralph's imagination can be fully characterised by specifying the qualitative scenario, while the identifications merely track extra-psychological facts about Ralph. Contrast belief: when Ralph believes that Ortcutt is a spy, one can argue that the psychological content of his belief is the qualitative proposition that the man sneaking around is a spy, while the identification of the man as Ortcutt in the belief report tracks the extra-psychological fact that Ortcutt is in fact the man sneaking around. For imagination, the identification of the individuals in the imagined scenario makes a clear difference to the functional role of the imagination.
But the identification doesn't link individuals in the imagined scenario to actual individuals. Rather, it links these individuals to individuals in Ralph's belief worlds. Suppose Ralph is halluzinating and there is actually nobody sneaking around the waterfront. Still Ralph believes that somebody is sneaking around, and he imagines confronting that guy. Similarly, if Ralph falsely believes that the man he sees sneaking around is not identical to the friendly man he met on the beach, so that his belief worlds contain two different individuals playing the two roles, then he can imagine confronting one of them but not the other.
On further reflection, the other end of the identification relation -- let's call it the identification base -- isn't always given by the subject's beliefs. One can also imagine things based on a supposition: supposing that the men are different, Ralph can imagine how one of them meets the other, even if he actually suspects or believes that they are identical.
If this is on the right track, what shall we call the "content" of an imagination? We could reserve the term for the purely qualitative aspects of the imagined scenario, but then imaginations would have to be characterised by more than their content. Alternatively, we could say that the content somehow comprises both the qualitative scenario and the identification of its parts with individuals in whatever serves as the identification base. Should we also include the base itself? After all, to fully characterise an imagination and its cognitive role, you have to say whether it is based on the subject's beliefs or on a supposition, and if so on what supposition. On the other hand, it is unnatural to say that the subject imagines her beliefs (especially if she imagines something contrary to her beliefs), so it sounds a bit odd to include the beliefs in the content of the imagination.
I don't think it really matters how we use the term "content" for episodes of imagining. What's important is that we keep track of the main ingredients: the qualitative scenario, the identification base, and the identifying relations.
Back to Ninan. Ninan's identifying relations (represented by the tagging functions) link individuals in the imagined scenario to individuals in the real world. As a remnant of the identification base, these identifications are relativised to an acquaintance relation. We can see how this is supposed to work in simple cases: when Ralph imagines having never seen Ortcutt, he identifies the relevant man in the imagined scenario with someone in his belief worlds, namely with the man he saw sneaking around; according to Ninan, the content of the imagination is the qualitative scenario together with a tagging of the unseen man in the scenario by the pair (Ortcutt, having-seen-sneaking); the second part of this pair indicates which individual in the base is identified with the man in the scenario.
But this is a cumbersome way of representing the relevant facts, presumably motivated by the idea that all relevant aspects of the imagination should be accounted for by its "content", which should be a set of world-like entities. Unfortunately, it turns out that no world in any of Ralph's attitudes can also occur in the attitudes of other people, since only Ralph's attitude worlds contain tagging functions defined for (Ralph, identity). In addition, some important aspects of imagination are missing in Ninan's representation, such as the nature and content of the identification base. We also get the spurious differences mentioned above: if the identification base represents the F as identical to the G, and if an object in an imagined scenario is identified with this one object in the base, then there is no further question whether the object is identified as the F or as the G. Obviously, Ninan's proposal also breaks down if the identification base is sufficiently out of tune with reality, as when Ralph halluzinates Ortcutt. From his point of view, he still imagines that he never saw that guy, but "that guy" no longer picks out anyone real.
I guess Ninan concentrates on identifications with actual individuals because his starting point are de re ascriptions of imagination. When we say that Ralph imagines (de re) never having seen Ortcutt, we obviously imply that Ortcutt exists. The de re report identifies one of the individuals in Ralph's imagination with Ortcutt, the man in the real world. But this is not the psychologically relevant identification of that individual with an individual in Ralph's belief worlds (or supposition worlds).
A better way to analyse these de re reports, I think, would go as follows. The standard account of de re belief tells us what it is for a subject to belief or suppose of y that he is F: it is to believe that the Q is F for some Q that actually picks out y. Accordingly, x imagines de re that y is F iff (i) x imagines that someone is F, (ii) x identifies that someone with the Q individual in his belief worlds (or supposition worlds), and (iii) in reality y is the Q. This is what Ralph does. He believes that there's a unique man he saw sneaking around the waterfront. He imagines a scenario in which he has never seen a certain man, and he identifies that man as the man sneaking around in his belief worlds. In fact, Ortcutt is sneaking around. This is why we can report Ralph as imagining that he never saw Ortcutt.
In a sense, I agree with Ninan's claim that there is more to imagination than centred-worlds content. But the further ingredients aren't well captured by replacing the centred worlds with multi-centred worlds. Rather, they concern relations between the imagination and other mental states such as beliefs and suppositions. Taking these relations into account leads not only to a more plausible psychology of imaginations, but also to a better semantics of imagination ascriptions. It also highlights that there is something special about imagination (and perhaps other "counterfactual attitudes") that does not generalise to belief: beliefs do not have an identification component that links them to beliefs or suppositions. So there is no reason here to abandon the modelling of belief content by sets of qualitative centred worlds.