Ideas from 'Intro: Theories of Vagueness' by R Keefe / P Smith [1997], by Theme Structure

[found in 'Vagueness: a Reader' (ed/tr Keefe,R /Smith,P) [MIT 1999,0-262-61145-7]].

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4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P)
7. Existence / D. Theories of Reality / 9. Vagueness / a. Vagueness of reality
Objects such as a cloud or Mount Everest seem to have fuzzy boundaries in nature
7. Existence / D. Theories of Reality / 9. Vagueness / b. Vagueness as epistemic
If someone is borderline tall, no further information is likely to resolve the question
The simplest approach, that vagueness is just ignorance, retains classical logic and semantics
The epistemic view of vagueness must explain why we don't know the predicate boundary
7. Existence / D. Theories of Reality / 9. Vagueness / d. Vagueness, degrees of
A third truth-value at borderlines might be 'indeterminate', or a value somewhere between 0 and 1
People can't be placed in a precise order according to how 'nice' they are
If truth-values for vagueness range from 0 to 1, there must be someone who is 'completely tall'
How do we decide if my coat is red to degree 0.322 or 0.321?
7. Existence / D. Theories of Reality / 9. Vagueness / e. Supervaluation for vagueness
Supervaluationism keeps true-or-false where precision can be produced, but not otherwise
Vague statements lack truth value if attempts to make them precise fail
Some of the principles of classical logic still fail with supervaluationism
The semantics of supervaluation (e.g. disjunction and quantification) is not classical
Supervaluation misunderstands vagueness, treating it as a failure to make things precise
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
Vague predicates involve uncertain properties, uncertain objects, and paradoxes of gradual change
Many vague predicates are multi-dimensional; 'big' involves height and volume; heaps include arrangement
If there is a precise borderline area, that is not a case of vagueness