Vagueness

Vagueness is a property of predicates or terms whose boundaries are not sharply defined. In natural language, many terms apply to a range of cases with unclear cutoff points, so that for some objects it is indeterminate whether the predicate applies. This is distinct from ambiguity, where a term has more than one possible meaning; vagueness concerns indistinct applicability rather than multiple senses.

Vagueness can be categorized in several ways. Semantic vagueness refers to the language itself and the indeterminacy of predicates. Epistemic vagueness reflects limits of knowledge about where the boundary lies. Ontic or metaphysical vagueness would mean that the world itself has indeterminate boundaries. In some theories, truth is graded rather than strictly true or false, capturing a continuum of applicability.

Philosophical theories address vagueness in different ways. Fuzzy logic and degree theories treat truth as a matter of degree. Supervaluationism preserves classical truth values by asserting many precise, though unknown, interpretations and claiming a sentence is true if it is true under all precisifications. Contextualism ties truth conditions to the context of utterance, so the applicability of a predicate can shift with different situations.

Paradoxes such as the Sorites (how many grains make a heap) and the baldness paradox illustrate challenges in defining precise borders. They motivate both formal modeling of vagueness and practical strategies for handling borderline cases in reasoning.

Vagueness has practical implications for law, policy, science, and artificial intelligence. Thresholds and definitions must be chosen, and outcomes depend on interpretation. In AI and NLP, systems often rely on probabilistic or fuzzy-logic approaches to cope with uncertain applicability of predicates.

See also: Sorites paradox, fuzzy logic, supervaluationism, contextualism, boundary problem.