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Single Idea 9065
[filed under theme 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 Ref
'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]
The
18 ideas
with the same theme
[strongest system, with three accessibility conditions]:
7791
|
The simplest of the logics based on possible worlds is Lewis's S5
[Lewis,CI, by Girle]
|
14973
|
In S5 all the long complex modalities reduce to just three, and their negations
[Cresswell]
|
13604
|
Real possibility and necessity has the logic of S5, which links equivalence classes of worlds of the same kind
[Ellis]
|
14686
|
S5 modal logic ignores accessibility altogether
[Salmon,N]
|
14691
|
S5 believers say that-things-might-have-been-that-way is essential to ways things might have been
[Salmon,N]
|
14693
|
The unsatisfactory counterpart-theory allows the retention of S5
[Salmon,N]
|
14627
|
S4, and therefore S5, are invalid for metaphysical modality
[Salmon,N, by Williamson]
|
9560
|
S5 provides the correct logic for necessity in the broadly logical sense
[Fine,K]
|
9065
|
S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P)
[Keefe/Smith]
|
9748
|
System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation
[Fitting/Mendelsohn]
|
14626
|
In S5 matters of possibility and necessity are non-contingent
[Williamson]
|
15131
|
If metaphysical possibility is not a contingent matter, then S5 seems to suit it best
[Williamson]
|
13708
|
S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid
[Sider]
|
7793
|
◊p → □◊p is the hallmark of S5
[Girle]
|
7795
|
S5 has just six modalities, and all strings can be reduced to those
[Girle]
|
18814
|
'Absolute necessity' would have to rest on S5
[Rumfitt]
|
12204
|
The logic of metaphysical necessity is S5
[Rumfitt]
|
19032
|
S5 is undesirable, as it prevents necessities from having contingent grounds
[Vetter]
|