|Possible World: entity that can be quantified over. There ist a dispute over the question whether possible worlds exist or are only assumed for purposes of proofs of completeness. See also actual world, modal logic, modal realism, realism, actualism, possibility, possibilia, quantification.|
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The expressions "winners" and "losers" do not refer to the same objects in all possible worlds.
Proper names are rigid designators: Nixon is Nixon in all possible worlds, but he is not the winner of the election in all the possible worlds (descriptions are non-rigid designators).
Possible worlds are no foreign countries. - A possible world is given by the descriptive conditions we associate it with.
Possible world/Lewis: Counterparts, not the same people - Kripke: then it is not about identification but about similarity relation.
We do not demand that the objects must exist in all possible worlds of course.
Possible world/Counterparts: Strict identity: molecules - counterparts: for example, tables (not identity of qualities, but of individual objects)
Counterpart/Lewis: Representatives of the theories that a possible world is only given qualitatively to us ("counterpart theory", David Lewis) argue that Aristotle and his counterparts "in other possible worlds" are "to be identified" with those things that Aristotle resembles most in his most important characteristics.
I 123 ff
Remember, though, that we describe the situation in our language, not in the language that would be used by people in that situation. Hesperus = Phosphorus is necessarily true (but situation possible in which Venus does not exist).
Epistems: Different concept of possibility than in logic. Designation by us.
I Berka 161
Definition normal world/Kripke: A maximum consistent set of sentences in which at least one statement is necessary - Definition non-normal world/Kripke: in them each sentence of type LB is false.
I Berka 179
Definition possible world/Kripke: old: (1959) = complete attribution of truth value - i.e. it is impossible to find two possible worlds in which each atomic formula is attributed to the same truth value - (absolute concept of the possible world) - new: (1963): a world is possible in relation to another world - relatively possible world - Hughes/Cresswell: > accessibility relation - reflexive accessibility: each possible world in itself - i.e. that each statement true in H is also possible in H - Definition necessary: a formula A in H if it is true in every (possible) world accessible from H - Definition possible: dual to this: if A is possible in H1, iff a world H2 exists, which is possible in relation to H1, and true in A - transitivity: H2RH3: any formula that is true in H3 is possible in H2 - problem: for traceability to H1 we need a reduction axiom: "what is possibly possible is possible" - you can also set the equivalence relation as accessibility relation.
Hughes/Cresswell I 243
Non-normal world/possible world/Kripke: worlds in which each statement is possible without exception, i.e. including those of the form p. ~p rating: like in normal worlds (p ~ p.) Never 1 - but for modal formulas V (Ma) is always 1 in non-normal worlds, and hence V(La) is always 0 - i.e., there are no necessary statements in non-normal worlds - this n-n world is at least accessible for a normal world, but no world is accessible to a n-n world - not even for these themselves.
Frank I 114
Identity/Kripke: if an identity statement is true, it is always necessarily true, e.g. heat/motion of molecules - Cicero/Tullius - Water/H20 - compatible with the fact that they are truths a posteriori - but according to Leibniz: not conceivable that one occurs without the other.
Frank I 125
Identity/body/Kripke: "A" is the (rigid) name for the body of Descartes - it survived the body - i.e.: M (Descartes unequal A) - this is not a modal fallacy, because A is rigid - analog: Statue is dissimilar to molecule collection.
Name und Notwendigkeit Frankfurt 1981
S. A. Kripke
Outline of a Theory of Truth (1975)
Recent Essays on Truth and the Liar Paradox, R. L. Martin (Hg), Oxford/NY 1984
M. J. Cresswell
Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988
M. J. Cresswell
Structured Meanings Cambridge Mass. 1984
M. Frank (Hrsg.)
Analytische Theorien des Selbstbewusstseins Frankfurt 1994