Single Idea 9065

[catalogued under 4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5]

Full Idea

S5 collapses iterated modalities (so ◊□P → □P, and ◊◊P → ◊P).

Gist of Idea

S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P)

Source

R Keefe / P Smith (Intro: Theories of Vagueness [1997], 5)

Book Reference

'Vagueness: a Reader', ed/tr. Keefe,R /Smith,P [MIT 1999], p.55


A Reaction

It is obvious why this might be controversial, and there seems to be a general preference for S4. There may be confusions of epistemic and ontic (and even semantic?) possibilities within a single string of modalities.

Related Idea

Idea 14690 In the S5 account, nested modalities may be unseen, but they are still there [Salmon,N]