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Single Idea 9560
[filed under theme 4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
]
Full Idea
S5 provides the correct logic for necessity in the broadly logical sense.
Gist of Idea
S5 provides the correct logic for necessity in the broadly logical sense
Source
Kit Fine (Model Theory for Modal Logic I [1978], 151), quoted by Charles Chihara - A Structural Account of Mathematics
Book Ref
Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.171
A Reaction
I have no view on this, but I am prejudiced in favour of the idea that there is a correct logic for such things, whichever one it may be. Presumably the fact that S5 has no restrictions on accessibility makes it more comprehensive and 'metaphysical'.
The
18 ideas
with the same theme
[strongest system, with three accessibility conditions]:
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7791
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The simplest of the logics based on possible worlds is Lewis's S5
[Lewis,CI, by Girle]
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14973
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In S5 all the long complex modalities reduce to just three, and their negations
[Cresswell]
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13604
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Real possibility and necessity has the logic of S5, which links equivalence classes of worlds of the same kind
[Ellis]
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14686
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S5 modal logic ignores accessibility altogether
[Salmon,N]
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14691
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S5 believers say that-things-might-have-been-that-way is essential to ways things might have been
[Salmon,N]
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14693
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The unsatisfactory counterpart-theory allows the retention of S5
[Salmon,N]
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14627
|
S4, and therefore S5, are invalid for metaphysical modality
[Salmon,N, by Williamson]
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9560
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S5 provides the correct logic for necessity in the broadly logical sense
[Fine,K]
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9065
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S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P)
[Keefe/Smith]
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9748
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System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation
[Fitting/Mendelsohn]
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14626
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In S5 matters of possibility and necessity are non-contingent
[Williamson]
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15131
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If metaphysical possibility is not a contingent matter, then S5 seems to suit it best
[Williamson]
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13708
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S5 is the strongest system, since it has the most valid formulas, because it is easy to be S5-valid
[Sider]
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7793
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◊p → □◊p is the hallmark of S5
[Girle]
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7795
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S5 has just six modalities, and all strings can be reduced to those
[Girle]
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18814
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'Absolute necessity' would have to rest on S5
[Rumfitt]
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12204
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The logic of metaphysical necessity is S5
[Rumfitt]
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19032
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S5 is undesirable, as it prevents necessities from having contingent grounds
[Vetter]
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