Precisificatiesets

Precisificatiesets, or precisification sets, are a concept in semantics and philosophy of language used to model vagueness. A precisification of a vague expression is a precise interpretation that makes the expression applicable in a given context. A precisificatieset for a vague predicate V, within a context and background information, is the collection of all such precise interpretations that are compatible with the contextual constraints and speaker intentions.

In formal terms, a precisificatie assigns a sharp boundary or threshold that determines when the predicate applies. The precisificatieset gathers all admissible thresholds consistent with factors like the discourse context, prior assumptions, and practical goals. This approach is related to, and often contrasted with, supervaluationist theories, which evaluate truth across all admissible precisifications. A sentence may be true under every precisification (super-true), false under every precisification (super-false), or have mixed results (undetermined) across the set.

Common examples involve predicates such as tall, old, or heap, where context shifts the acceptable boundary. For instance, the height threshold that makes someone “tall” may vary by population, stance, or purpose, producing different precisifications within the same situation. Precisificatiesets are used to analyze how speakers convey or withhold judgments under vagueness, to compare cross-linguistic or cross-cultural variation, and to inform natural language processing models that need to handle imprecise terms.

Related concepts include precision thresholds, contextualism, and fuzzy logic, though the latter treats gradience differently.