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Single Idea 16468

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

Full Idea

One can make sense of necessary versus contingent necessities in a non-S5 modal semantics.

Gist of Idea

Non-S5 can talk of contingent or necessary necessities

Source

Robert C. Stalnaker (Mere Possibilities [2012], 4.3 n17)

Book Ref

Stalnaker,Robert C.: 'Mere Possibilities' [Princeton 2012], p.112

A Reaction

In S5 □φ → □□φ, so all necessities are necessary. Does it make any sense to say 'I suppose this might have been necessarily true'?

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]