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Single Idea 16952

[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, and S is possible but doesn't obtain, then T is only possible in the world where S obtains, but T is not possible in the actual world. It follows that the relation of relative possibility is not transitive.

Gist of Idea

If something is only possible relative to another possibility, the possibility relation is not transitive

Source

Michael Dummett (Could There Be Unicorns? [1983], 1)

Book Ref

Dummett,Michael: 'The Seas of Language' [OUP 1993], p.330

A Reaction

[compressed]

Related Idea

Idea 16953 Relative possibility one way may be impossible coming back, so it isn't symmetrical [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]