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Single Idea 14693
[filed under theme 4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
]
Full Idea
Counterpart-theoretic modal semantics allows for the retention of S5 modal propositional logic, at a considerable cost.
Gist of Idea
The unsatisfactory counterpart-theory allows the retention of S5
Source
Nathan Salmon (The Logic of What Might Have Been [1989], V n18)
Book Ref
Salmon,Nathan: 'Metaphysics, Mathematics and Meaning' [OUP 2005], p.149
A Reaction
See the other ideas in this paper by Salmon for his general attack on S5 as the appropriate system for metaphysical necessity. He favours the very modest System T.
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
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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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