Fine's supervaluationist framework generates 'higher-order vagueness': vagueness about which precisifications are admissible reintroduces a structurally identical sorites at the metalinguistic level.
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A form of argument (also called the 'heap argument') that proceeds by small incremental steps to show that no precise boundary exists between two states, thereby challenging the applicability of vague predicates
higher-order vagueness(in philosophy of language)
When you try to fix a vague boundary by drawing a precise line, but then you face the same vagueness problem all over again—the new line itself becomes unclear why it's the right one.
supervaluationism(Presented as a counter to the Fregean defect view of vagueness)
A theory of vagueness on which semantic indecision is intentional and functional: speakers fill in the meanings of terms incrementally in light of new information and interests rather than fixing full definitions prematurely.
vagueness(Example: 'materially adverse change' in In re Carter's Claim (1957))
Imprecision in terms whose application admits of borderline cases.