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Tom's fancies; but we need a notion of possible world only if we must compare at least two propositional attitudes. Let me quote a famous silly dialogue (mentioned in Russell 1905):
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Tom (looking for the first time at John's boat): I believed that your boat was bigger than that.
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John: No, my boat is not bigger than that.
The whole modal conundrum can be easily explained as shown here (figure 4.1). Tom, in the world Wt of his imagination, thinks that John's boat B1 is, let us say, ten meters long. Then Tom, in the actual world Wo of his experience, sees the real boat B2 and remarks that it is five meters long. Subsequently, he compares the B1 of his doxastic world to the B2 of his real world and remarks that B1 was bigger than B2.
John, who has never studied modal logic, mixes the worlds up and deals with B1 and B2 as if both belonged to the same Wo. In this case a notion of possible world proves to be useful to explain a conversational ambiguity that depends on a cognitive difficulty.
4. Why Possible Worlds are Useful for a Theory of Fiction
If the exchange between Tom and John were recounted as a funny piece of fiction, its treatment in terms of possible worlds would explain why the story sounds amusing: it stages the interaction between two individuals one of which is unable to discriminate between incompatible worlds.
Suppose that John and Tom live in a very simple world endowed only with a couple of properties, namely, Boat (scored as M, or Marine Vehicle) and Big. We can decide that, under a certain description, certain properties are essential and others accidental. In order to define a property as textually essential, Hintikka (1969) said that if I speak of a man I saw without being sure whether he was Tom or John, this man will be the same in every possible world since it is essentially the man I saw.
From this point of view (and freely using suggestions from Rescher 1973), our story of John's boat can be represented as follows (where Wt is the world of Tom's beliefs and Wj the world in which both Tom and John live and perceive the actual John's boat):

 
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