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Single Idea 13708

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

Full Idea

S5 is the strongest system, since it has the most valid formulas. That's because it has the fewest models; it's easy to be S5-valid since there are so few potentially falsifying models. K is the weakest system, for opposite reasons.

Gist of Idea

S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid

Source

Theodore Sider (Logic for Philosophy [2010], 6.3.2)

Book Ref

Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.145

A Reaction

Interestingly, the orthodox view is that S5 is the correct logic for metaphysics, but it sounds a bit lax. Compare Idea 13707.

Related Idea

Idea 13707 Maybe metaphysical accessibility is intransitive, if a world in which I am a frog is impossible [Sider]

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]