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Full Idea
With a three-value approach, if P is 'blob is pink' and R is 'blob is red', then P&P is indefinite, but P&R is false, and P∨P is indefinite, but P∨R is true. This means the connectives & and ∨ are not truth-functional.
Gist of Idea
Logical connectives cease to be truth-functional if vagueness is treated with three values
Source
Kit Fine (Vagueness, Truth and Logic [1975], 1)
Book Ref
'Vagueness: a Reader', ed/tr. Keefe,R /Smith,P [MIT 1999], p.123
A Reaction
The point is that there could then be no logic in any way classical for vague sentences and three truth values. A powerful point.
| 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] |