Definition
Vagueness is the property of a predicate that has borderline cases and no sharp boundary. Red, bald, tall, heap, child are all vague. There are clear cases and clear non-cases, but between them lies a fuzzy zone of items that are neither definitely in nor definitely out.
Vagueness is not the same as ambiguity. An ambiguous word has two distinct meanings; a vague word has one meaning whose application simply lacks a precise edge. Almost every predicate of ordinary language is vague to some degree.
Why it matters
How it works
Vagueness strains classical logic because classical logic assumes every statement is determinately true or false. For a borderline case — a man with exactly the amount of hair that makes 'bald' genuinely unclear — neither verdict feels right, yet classical logic insists on one.
Several theories respond. Fuzzy logic allows degrees of truth between fully true and fully false, so 'he is bald' might be true to degree 0.6. Supervaluationism keeps two-valued logic but says a vague statement is true only if it comes out true on every admissible way of making the predicate precise. Epistemicism holds that there is a sharp boundary after all — we just cannot know where it lies. Each theory pays a different price, and the sorites paradox is the stress test every one of them must survive.