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Full Idea
If T is only possible if S obtains, T and S hold in the actual world, and S does not obtain in world v possible relative to the actual world, then the actual is not possible relative to v, since T holds in the actual. Accessibility can't be symmetrical.
Gist of Idea
Relative possibility one way may be impossible coming back, so it isn't symmetrical
Source
Michael Dummett (Could There Be Unicorns? [1983], 1)
Book Ref
Dummett,Michael: 'The Seas of Language' [OUP 1993], p.330
Related Idea
Idea 16952 If something is only possible relative to another possibility, the possibility relation is not transitive [Dummett]
16952 | If something is only possible relative to another possibility, the possibility relation is not transitive [Dummett] |
16953 | Relative possibility one way may be impossible coming back, so it isn't symmetrical [Dummett] |
10760 | With possible worlds, S4 and S5 are sound and complete, but S1-S3 are not even sound [Kripke, by Rossberg] |
16468 | Non-S5 can talk of contingent or necessary necessities [Stalnaker] |
9456 | Modal logic is multiple systems, shown in the variety of accessibility relations between worlds [Jacquette] |
11004 | Necessity is provability in S4, and true in all worlds in S5 [Read] |