A linguistic expression (predicate or term) whose application conditions are not sharply specified, permitting borderline instances and enabling soritical sequences where no precise cutoff determines application.

Principle

Vagueness entails tolerance for borderline cases: small changes that fall within a margin may not change application status, and thus classical bivalent truth-assignment fails to produce determinate boundaries.

Demonstration

Illustrative scenario — Situation: Speakers use a predicate without an agreed threshold. Recognition: Some instances produce disagreement but no clear fact of application. Action: Communicative practices rely on context, gradable responses, or stipulation. Consequence: Logical inferences that assume sharp boundaries (e.g., simple modus ponens across soritical steps) become unreliable without further disambiguation.

Misapplication

Treating vagueness as mere ambiguity (multiple discrete senses) or as solvable solely by obtaining more information. Why plausible: both produce apparent indeterminacy. Semantic error: failing to distinguish lack of sharp application conditions from polysemy or ignorance; the correct approach deploys semantic or pragmatic strategies (degrees, precisifications, or contextual thresholds).

Consequence

Vague predicates challenge formal reasoning, legal interpretation, and classification systems; they motivate strategies such as precision, context-sensitivity, use of degrees, or legal thresholds.

Reversal

In contexts where agents stipulate explicit cutoffs or measurement protocols (e.g., statutory definitions, experimental protocols), the predicate’s vagueness is removed for that application.

Boundary

Clearly within: gradable everyday adjectives (e.g., “tall”, “rich”) used without explicit threshold. Boundary case: predicates that are partly vague and partly defined by standards in specific contexts. Clearly outside: polysemous terms with distinct senses each having clear application conditions.

Semantic Tension

Flexibility and contextual usefulness ↔ Need for formal precision and rule-following.

Synthesis

Vagueness is a linguistic feature that enables flexible, context-sensitive communication but requires strategies (pragmatic, semantic, or institutional) when precise application or formal inference is required.