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Similarity/semantics of possible worlds/similarity metric/Hintikka: we interpret the distance as a dissimilarity of worlds.
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Semantics of possible worlds.
Dimension: here, of course, there are different dimensions, i.e. directions in which worlds can differ,
Intentionality/Hintikka: intentionality has therefore different dimensions.
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Intentionality/Hintikka.
Similarity/semantics of possible worlds/similarity metrics/Hintikka: In the following respects possible worlds may differ or resemble each other:
a) Facticity: One can only know what is the case. Formal: Every possible world is always an element of a set of alternative worlds.
There is then always a world, which is maximally similar to the considered possible world.
b) Preservation of individuals/constant, fixed domain: One world can be similar to another because the same individuals are in it. This can fail in two ways:
(i) The existence of individuals is not preserved in the transition to another possible world.
(ii) Individuals can exist in worlds without existing in the actual world.
(iii) Preservation of the identity of individuals can be violated twice:
(a) by the fusion of individuals in another world, which are two in the actual world,
(b) by splitting an individual from the actual world in another world.
The extensibility of worldlines: can fail twice:
(i) a worldline cannot be drawn to an alternative world,
(ii) it cannot be drawn from an alternative back to the possible world under consideration.
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e) Logical invariance: The logical invariance of worlds is possibly the most radical deviation: in a world logical laws could be invalid.
f) Methods to draw world lines: Here, different principles could apply to different intentional concepts. Sometimes they could be more objective, sometimes more dependent on the actions of the person.
This is less about distance between worlds than about the strength of the connections between them.
Memory/Belief/Hintikka: Criterion (f) explains why Bsp memory is less intentional than e.g. belief.
Worldlines/Hintikka: Worldlines correspond to Lewis' counterpart relation (GR). They are determined only by reference to the worlds they connect. Therefore, at first glance, they are independent of the subject. But this does not mean that they are independent of conventions.
Intentionality/Hintikka: We are concerned here with the ways of general human operations that lead to the prevalence of a particular fabric of world-lines for a particular intentional concept.