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23167-0071a.GIF
Given two worlds Wt and Wj where the same properties hold, we can say that x in Wt is a possible counterpart of y in Wj because both share the same essential properties (scored within parentheses). The two worlds are mutually accessible.
Suppose now that John and Tom interact this way:
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Tom: I thought that the big thing you dreamed of was your boat.
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John: No, it was not a boat.
In this case the world matrices will be the following (where D = the object of a dream):
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In Tom's doxastic world Wt there is an x1, which is the supposed subject matter of John's dreams and which is a big boat. In John's doxastic world there are two things, namely, a small boat y, which never obsessed his dreams, and a big thing x2, which was the subject of his dream and which unfortunately is not a boat. X1, x2 and y will be reciprocally supernumeraries (different individuals); there would not be crossidentity, but these two worlds would equally be mutually accessible. By manipulating the Wt matrix, it is possible to design both x2 and y, and by manipulating Wj matrix it is possible to design x1. We can say that either world is ''conceivable" from the point of view of the alternative one.
Suppose now that in Wt the property Red holds (while John is a Daltonist and cannot discriminate colors), and suppose that the dialogue sounds like this:
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Tom: I have seen your boats. I want to buy the red one.
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John: Which one?

 
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