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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 '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]