more on this theme
|
more from this thinker
Single Idea 9065
[filed under theme 4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
]
Full Idea
S5 collapses iterated modalities (so ◊□P → □P, and ◊◊P → ◊P).
Gist of Idea
S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P)
Source
R Keefe / P Smith (Intro: Theories of Vagueness [1997], §5)
Book Ref
'Vagueness: a Reader', ed/tr. Keefe,R /Smith,P [MIT 1999], p.55
A Reaction
It is obvious why this might be controversial, and there seems to be a general preference for S4. There may be confusions of epistemic and ontic (and even semantic?) possibilities within a single string of modalities.
Related Idea
Idea 14690
In the S5 account, nested modalities may be unseen, but they are still there [Salmon,N]
The
17 ideas
from 'Intro: Theories of Vagueness'
|
9044
|
If someone is borderline tall, no further information is likely to resolve the question
[Keefe/Smith]
|
|
9048
|
The simplest approach, that vagueness is just ignorance, retains classical logic and semantics
[Keefe/Smith]
|
|
9049
|
Supervaluationism keeps true-or-false where precision can be produced, but not otherwise
[Keefe/Smith]
|
|
9050
|
A third truth-value at borderlines might be 'indeterminate', or a value somewhere between 0 and 1
[Keefe/Smith]
|
|
9045
|
Vague predicates involve uncertain properties, uncertain objects, and paradoxes of gradual change
[Keefe/Smith]
|
|
9047
|
Many vague predicates are multi-dimensional; 'big' involves height and volume; heaps include arrangement
[Keefe/Smith]
|
|
9053
|
If there is a precise borderline area, that is not a case of vagueness
[Keefe/Smith]
|
|
9055
|
The epistemic view of vagueness must explain why we don't know the predicate boundary
[Keefe/Smith]
|
|
9056
|
Vague statements lack truth value if attempts to make them precise fail
[Keefe/Smith]
|
|
9058
|
Some of the principles of classical logic still fail with supervaluationism
[Keefe/Smith]
|
|
9059
|
The semantics of supervaluation (e.g. disjunction and quantification) is not classical
[Keefe/Smith]
|
|
9060
|
Supervaluation misunderstands vagueness, treating it as a failure to make things precise
[Keefe/Smith]
|
|
9061
|
People can't be placed in a precise order according to how 'nice' they are
[Keefe/Smith]
|
|
9062
|
If truth-values for vagueness range from 0 to 1, there must be someone who is 'completely tall'
[Keefe/Smith]
|
|
9063
|
How do we decide if my coat is red to degree 0.322 or 0.321?
[Keefe/Smith]
|
|
9065
|
S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P)
[Keefe/Smith]
|
|
9064
|
Objects such as a cloud or Mount Everest seem to have fuzzy boundaries in nature
[Keefe/Smith]
|