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Single Idea 16953

[filed under theme 4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / a. Systems of modal logic ]

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]

The 6 ideas with the same theme [issues concerning the varieties of modal logic]:

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]