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8.6.4. Accessibility
Having established these criteria we can now define what we assume as accessibility among worlds.
According to current literature on the subject, accessibility is a dyadic relation Wi R Wj, where Wj is accessible to Wi. To disregard any psychological interpretation of the term /accessibility/ (of the type 'can individuals in Wi conceive of Wj?'), we can say that a Wj is accessible to a Wi when the world structure of Wi can generate (through manipulations of the relations between individuals and properties) the world structure of Wj.
Thus we have different relational possibilities:
(i) Wi R Wj, but not Wj R Wi: the relation is dyadic but not symmetric;
(ii) Wi R Wj and Wj R Wi: the relation is dyadic and symmetric;
(iii) Wi R Wj, Wj R Wh, Wi R Wk: the relation is dyadic and transitive;
(iv) the above relation becomes also symmetric.
Given two or more worlds these relations can change as to whether
(a) the number of individuals and properties is the same in all worlds;
(b) the number of individuals increases in at least one world;
(c) the number of individuals decreases in at least one world;
(d) the properties change;
(e) (other possibilities resulting from the combination of the above).
I think that apropos of fictional worlds an interesting typology of this sort can be attempted to distinguish different literary genres (for a first interesting approach see Pavel, 1975). For our present purpose we can consider only certain basic cases.
Let us first examine a case in which (independent of any discrimination among essential and accidental properties) there are in two worlds the same number of individuals and the same properties (see Figure 8.11). It is evident that certain combinatory manipulations can lead the individuals in W1 to become structurally identical with the individuals in W2, and vice versa. Therefore in this case W1 R W2 and W2 R W1.
Let us consider now a second case in which in W1 there are fewer properties than in W2 (see Figure 8.12). To make the example more palatable, let us imagine that, according to a previous example borrowed from Hintikka, the properties in W1 are to be round and red. In W2 the
W1
F
C
M
W2
F
C
M
x1
+
+
-
y1
+
-
-
x2
+
-
+
y2
-
+
+

Figure 8.11

 
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