more on this theme
|
more from this text
Single Idea 9058
[filed under theme 7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
]
Full Idea
Supervaluationist logic (now with a 'definite' operator D) fails to preserve certain classical principles about consequence and rules of inference. For example, reduction ad absurdum, contraposition, the deduction theorem and argument by cases.
Gist of Idea
Some of the principles of classical logic still fail with supervaluationism
Source
R Keefe / P Smith (Intro: Theories of Vagueness [1997], §3)
Book Ref
'Vagueness: a Reader', ed/tr. Keefe,R /Smith,P [MIT 1999], p.30
A Reaction
The aim of supervaluationism was to try to preserve some classical logic, especially the law of excluded middle, in the face of problems of vagueness. More drastic views, like treating vagueness as irrelevant to logic, or the epistemic view, do better.
The
17 ideas
from R Keefe / P Smith
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]
|