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9065 | S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P) [Keefe/Smith] |
Full Idea: S5 collapses iterated modalities (so ◊□P → □P, and ◊◊P → ◊P). | |
From: R Keefe / P Smith (Intro: Theories of Vagueness [1997], §5) | |
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. |