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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5

[strongest system, with three accessibility conditions]

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