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Full Idea
Maybe classical logic fails for vagueness in Excluded Middle. If 'H bald ∨ ¬(H bald)' is true, then one disjunct is true. But if the second is true the first is false, and the sentence is either true or false, contrary to the borderline assumption.
Gist of Idea
Excluded Middle, and classical logic, may fail for vague predicates
Source
Kit Fine (Vagueness, Truth and Logic [1975], 4)
Book Ref
'Vagueness: a Reader', ed/tr. Keefe,R /Smith,P [MIT 1999], p.137
A Reaction
Fine goes on to argue against the implication that we need a special logic for vague predicates.
| 9766 | Study vagueness first by its logic, then by its truth-conditions, and then its metaphysics [Fine,K] |
| 9768 | Vagueness is semantic, a deficiency of meaning [Fine,K] |
| 9767 | A vague sentence is only true for all ways of making it completely precise [Fine,K] |
| 9770 | Logical connectives cease to be truth-functional if vagueness is treated with three values [Fine,K] |
| 9769 | Vagueness can be in predicates, names or quantifiers [Fine,K] |
| 9772 | Meaning is both actual (determining instances) and potential (possibility of greater precision) [Fine,K] |
| 9771 | Logic holding between indefinite sentences is the core of all language [Fine,K] |
| 9773 | With the super-truth approach, the classical connectives continue to work [Fine,K] |
| 9774 | Borderline cases must be under our control, as capable of greater precision [Fine,K] |
| 9775 | Excluded Middle, and classical logic, may fail for vague predicates [Fine,K] |
| 9776 | A thing might be vaguely vague, giving us higher-order vagueness [Fine,K] |