more from this thinker
|
more from this text
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]
|