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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.
Annotation: The above characterizations of concepts are neither definitions nor exhausting presentations of problems related to them. Instead, they are intended to give a short introduction to the contributions below. – Lexicon of Arguments.

Author Concept Summary/Quotes Sources

Saul A. Kripke on Possible Worlds - Dictionary of Arguments

I 51f
The expressions "winners" and "losers" do not refer to the same objects in all possible worlds.
I 51
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).
I 54
Possible worlds are no foreign countries. A possible world is given by the descriptive conditions we associate it with.
Cf. >Telescope theory of possible worlds.
I 55
Possible world/Lewis: possible worlds are counterparts, not the same people. Kripke: then it is not about identification but about similarity relation.
>Counterparts, >Counterpart theory, >Counterpart relation, >Possible world/Lewis, >Identity across worlds.
I 90/91
We do not demand that the objects must exist in all possible worlds of course.
Possible world/counterparts: strict identity: are molecules. Counterparts: are 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).
>Morning star/evening star, >Nonexistence.
I 143
Epistems: epistems are a different concept of possibility than in logic. The designation is done by us.
Berka I 161
Def normal world/Kripke: a normal world is a maximum consistent set of sentences in which at least one statement is necessary. Def non-normal world/Kripke: in non-normal worlds each sentence of the type LB is false.
Berka I 179
Definition possible world/Kripke: old: (1959)(1) a world is possible with the 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 definition: (1963)(2): a world is possible in relation to another world (relatively possible world) Hughes/Cresswell: > accessibility relation. Reflexive accessibility: each possible world is in itself, i.e. that each statement that is 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: non-normal worlds are 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 - these are compatible with the fact that they are truths a posteriori. But according to Leibniz: they it is 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: a statue is dissimilar to molecule collection.

1) S.A. Kripke (1959): "A completeness theorem in modal logic", in: The journal of symbolic logic 24 (1), pp. 1-14.
2) S.A. Kripke (1962): The Undecidability of Monadic Modal Quantification Theory, in: Zeitschrift für mathematische Logik und Grundlagen der Mathematik, Vol. 8, pp. 113-116.

Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution. Translations: Dictionary of Arguments
The note [Concept/Author], [Author1]Vs[Author2] or [Author]Vs[term] resp. "problem:"/"solution:", "old:"/"new:" and "thesis:" is an addition from the Dictionary of Arguments. If a German edition is specified, the page numbers refer to this edition.

Kripke I
S.A. Kripke
Naming and Necessity, Dordrecht/Boston 1972
German Edition:
Name und Notwendigkeit Frankfurt 1981

Kripke II
Saul A. Kripke
"Speaker’s Reference and Semantic Reference", in: Midwest Studies in Philosophy 2 (1977) 255-276
Eigennamen, Ursula Wolf, Frankfurt/M. 1993

Kripke III
Saul A. Kripke
Is there a problem with substitutional quantification?
Truth and Meaning, G. Evans/J McDowell, Oxford 1976

Kripke IV
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

Berka I
Karel Berka
Lothar Kreiser
Logik Texte Berlin 1983

Cr I
M. J. Cresswell
Semantical Essays (Possible worlds and their rivals) Dordrecht Boston 1988

M. J. Cresswell
Structured Meanings Cambridge Mass. 1984

Fra I
M. Frank (Hrsg.)
Analytische Theorien des Selbstbewusstseins Frankfurt 1994

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