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Single Idea 19032
[filed under theme 4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
]
Full Idea
Wedgwood (2007:220) argues that S5 is undesirable because it excludes that necessary truths may have contingent grounds.
Gist of Idea
S5 is undesirable, as it prevents necessities from having contingent grounds
Source
Barbara Vetter (Potentiality [2015], 6.4 n5)
Book Ref
Vetter,Barbara: 'Potentiality: from Dispositions to Modality' [OUP 2015], p.213
A Reaction
Cameron defends the possibility of necessity grounded in contingency, against Blackburn's denial of it. It's interesting that we choose the logic on the basis of the metaphysics. Shouldn't there be internal reasons for a logic's correctness?
Related Ideas
Idea 14529
If something underlies a necessity, is that underlying thing necessary or contingent? [Blackburn, by Hale/Hoffmann,A]
Idea 15103
Blackburn fails to show that the necessary cannot be grounded in the contingent [Cameron]
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
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◊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]
|