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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
 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]