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Possibility/situation/situation semantics/semantics of possible worlds/Hintikka: both approaches agree that situations may have several dimensions, e.g. temporal, spatial, and relations of overlap, inclusion etc. A crucial dimension is the following:
Intentionality/Intensionality/Hintikka: Intentionality and intensionality require the consideration of a background of alternatives (worlds, alternative situations).
Solution: there must be a dimension of pure possibility.
Possibility/Dimension/Hintikka: the dimension of the possibility is simply introduced by a pure space-time structure, then we have branches of time that have the same temporal (and if necessary spatial) coordinates as the set s of all situations.
Intensional/Possibility/Hintikka: when intensional concepts come in, we need a world which is just like a given world, except that everything there is possible. ((s) But it is indistinguishable from the world in which all this is given.
Semantics of possible worlds/situation semantics/Hintikka: then there is the question of how the two still differ at all.
Jaakko and Merrill B. Hintikka
The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989
J. Hintikka/M. B. Hintikka
Untersuchungen zu Wittgenstein Frankfurt 1996