Philosophy Lexicon of Arguments

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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.
 
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Adams, R.
 
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Possible Worlds Stalnaker I 32
Possible worlds/Robert Adams: if there are true propositions that speak of the existence of nonactual possible worlds, they must be able to be reduced to sentences in which only things from the actual world are mentioned which are not identical with non-actual possibilities.
StalnakerVsAdams: I do not see why this should be necessary.
Possible worlds/Stalnaker: Two questions:
1. Are they really so obscure?
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I 33
2. Does the belief in possible worlds and the indexical analysis of actuality oblige us to extreme realism? Certainly not.
World stories/world-story/Possible worlds/Robert Adams: Thesis: a world-story is a maximally consistent set of propositions. The concept of a possible world can be given in a contextual analysis in terms of world stories.
Proposition/Truth/Adams/Stalnaker: a proposition is true in some or all possible worlds if it is an element of some or all of the world-stories.
StalnakerVsAdams: in his approach, there are three undefined terms: Proposition, consistent, and contradictory.
Proposals/Adams/Stalnaker: proposals can be presented as language-independent, abstract objects. They have truth values.
Consistency/Adams/Stalnaker: consistency is a property of sets of propositions. One can define them in terms of possible worlds in which all propositions are true.
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I 34
Two conditions for consistency:
(W1) The set of all true propositions is consistent
(W2) Each subset of a consistent set is consistent.
Contradiction/Adams/Stalnaker: contradiction could be defined in terms of consistency:
A and B are contradictory, iff.
{A, B} is not consistent
And for each consistent set of propositions Γ is either
Γ U {A} or Γ U {B} consistent.
The theory presupposes:
(W3) Each proposition has a contradiction.
Proposition/Adams/Stalnaker: this is a minimal theory of propositions. It does not impose any structure on propositions, except for what is needed for compatibility, implication, and equivalence. And to ensure that e.g. the right kind of implication is present. E.g. implication:
Definition Implication/Proposition/Stalnaker: (here): A implies B iff. a set consisting of A and a contradiction of B is not consistent.
(W1) and (W2) ensure that our implication has the right properties.
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Stalnaker I 36
Proposition/Possible World/Stalnaker: an analysis of propositions as worlds provides definitions of consistency, etc., in concepts of set-theoretical relations between sets of worlds.
World Story Theory/Adams/Stalnaker: the theory of world stories is weaker because it leaves open questions that clarify the analysis of propositions as worlds.
The following two theses are consequences of the possible-worlds-theory but not of the world-story theory:
(W5) Seclusion condition: For any set of propositions G there is a proposition A such that G implies A and A implies every element of G.
Stalnaker: i.e. that for any set of propositions there is a proposition which says that every proposition in the set is true.
Proposition/Seclusion/Stalnaker: whatever propositions are, if there are any, there are also sets of them. And for any set of propositions, it is definitely true or false that all their elements are true.
And of course this is a proposition.
So I assume that the world-story theorist wants to add (W5) to his theory.
(W6) Equivalent propositions are identical.
Problem: the problems of (W6) are known. ((s)> hyperintensionalism/hyperintentionality: sentences that are true in the same worlds are indistinguishable, equivalence of "snow is white" to "grass is green", etc.).

Sta I
R. Stalnaker
Ways a World may be Oxford New York 2003


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Ed. Martin Schulz, access date 2017-04-25