### Ideas of R Keefe / P Smith, by Theme

#### [British, fl. 1997, both of Cambridge University.]

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###### 4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5
 9065 S5 collapses iterated modalities (◊□P→□P, and ◊◊P→◊P)
###### 7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
 9064 Objects such as a cloud or Mount Everest seem to have fuzzy boundaries in nature
###### 7. Existence / D. Theories of Reality / 10. Vagueness / c. Vagueness as ignorance
 9044 If someone is borderline tall, no further information is likely to resolve the question
 9048 The simplest approach, that vagueness is just ignorance, retains classical logic and semantics
 9055 The epistemic view of vagueness must explain why we don't know the predicate boundary
###### 7. Existence / D. Theories of Reality / 10. Vagueness / f. Supervaluation for vagueness
 9049 Supervaluationism keeps true-or-false where precision can be produced, but not otherwise
 9056 Vague statements lack truth value if attempts to make them precise fail
 9058 Some of the principles of classical logic still fail with supervaluationism
 9059 The semantics of supervaluation (e.g. disjunction and quantification) is not classical
 9060 Supervaluation misunderstands vagueness, treating it as a failure to make things precise
###### 7. Existence / D. Theories of Reality / 10. Vagueness / g. Degrees of vagueness
 9050 A third truth-value at borderlines might be 'indeterminate', or a value somewhere between 0 and 1
 9061 People can't be placed in a precise order according to how 'nice' they are
 9062 If truth-values for vagueness range from 0 to 1, there must be someone who is 'completely tall'
 9063 How do we decide if my coat is red to degree 0.322 or 0.321?
###### 9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
 9045 Vague predicates involve uncertain properties, uncertain objects, and paradoxes of gradual change
 9047 Many vague predicates are multi-dimensional; 'big' involves height and volume; heaps include arrangement
 9053 If there is a precise borderline area, that is not a case of vagueness