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Single Idea 14626

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

Full Idea

In system S5 matters of possibility and necessity are always non-contingent.

Gist of Idea

In S5 matters of possibility and necessity are non-contingent

Source

Timothy Williamson (Modal Logic within Counterfactual Logic [2010], 3)

Book Ref

'Modality', ed/tr. Hale,B/Hoffman,A [OUP 2010], p.91

A Reaction

This will be because if something is possible in one world (because it can be seen to be true in some possible world) it will be possible for all worlds (since they can all see that world in S5).

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]