An object, event, or instance for which it is indeterminate—under a specified interpretation of a vague predicate—whether the predicate applies; such instances lie on the margin of the predicate’s extension where no sharp truth‑value assignment is mandated by ordinary usage.

Principle

If a predicate is genuinely vague within a given interpretive frame, then there will exist instances for which the predicate’s application is not determinately true or false under that frame.

Demonstration

Illustrative scenario → A committee must award the label “tall” in a context without a fixed threshold. A person of height 1.70 m yields disagreement among competent judges: some apply the predicate, others do not. Recognition: the committee identifies the case as marginal. Action: they either adopt an explicit cutoff for decisions or treat it case‑by‑case. Consequence: without an imposed rule, different competent speakers rightly disagree about application.

Misapplication

Treating a borderline case as merely an epistemic lack of information (i.e., that a determinate fact exists but is unknown) rather than as semantic indeterminacy. The error confuses limited evidence with lack of determinacy in the predicate's extension under the chosen interpretation.

Consequence

Practical decisions that depend on the predicate require either an explicit convention (thresholds, measurement rules) or acceptance of indeterminacy; failure to do so produces inconsistent classifications, regulatory uncertainty, or ad hoc decision‑making.

Reversal

When the predicate is given a precise operational definition, measurement protocol, or legal threshold within the relevant context, previously borderline cases are resolved and cease to be indeterminate.

Boundary

Clearly within: an object whose properties satisfy an established, contextual standard for the predicate (e.g., a person with no hair regarded as bald under ordinary usage). Boundary case: a person losing hair gradually where ordinary usage yields persistent disagreement about “bald.” Clearly outside: an object that manifestly fails the predicate’s central criteria (e.g., a person with a full head of hair is not bald).

Semantic Tension

Precision (the desire for unambiguous classification) ↔ Communicative flexibility (the utility of vague predicates for broad, context‑sensitive application).

Synthesis

Borderline cases show that some applications of language resist determinate classification unless external conventions or decisions are introduced; resolving them is therefore as much a pragmatic or normative choice as a semantic one.