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Full Idea
In system S5 matters of possibility and necessity are always non-contingent.
Gist of Idea
In S5 matters of possibility and necessity are non-contingent
Source
Timothy Williamson (Modal Logic within Counterfactual Logic [2010], 3)
Book Ref
'Modality', ed/tr. Hale,B/Hoffman,A [OUP 2010], p.91
A Reaction
This will be because if something is possible in one world (because it can be seen to be true in some possible world) it will be possible for all worlds (since they can all see that world in S5).
14531 | Rather than define counterfactuals using necessity, maybe necessity is a special case of counterfactuals [Williamson, by Hale/Hoffmann,A] |
14625 | Necessity is counterfactually implied by its negation; possibility does not counterfactually imply its negation [Williamson] |
14624 | Counterfactual conditionals transmit possibility: (A□→B)⊃(◊A⊃◊B) [Williamson] |
14623 | Strict conditionals imply counterfactual conditionals: □(A⊃B)⊃(A□→B) [Williamson] |
14626 | In S5 matters of possibility and necessity are non-contingent [Williamson] |
14628 | Imagination is important, in evaluating possibility and necessity, via counterfactuals [Williamson] |