Shrinkingsuch

Shrinkingsuch is a fictional term used in linguistic and logical discussions to denote a specific operator that progressively narrows the referential domain associated with a determiner phrase introduced by "such." The concept is used as a thought experiment to study how context and similarity criteria influence the extension of such phrases.

Formal idea: Let U be a universe of discourse, and A a nonempty subset of U described by a determiner such as "such X." A shrinkingsuch operator S assigns to A a nonempty subset S(A) ⊆ A, determined by a context-dependent criterion C. The operator is monotone in the sense that if A ⊆ B then S(A) ⊆ S(B). Repeated application yields a shrinking sequence A0 = A, A1 = S(A0), A2 = S(A1), and so on, with each subset contained in the previous one. In typical interpretations, the criterion aims to preserve core exemplars while discarding outliers, causing measures of width or diversity to decrease.

Examples: In describing a room, "such chairs" might refer to chairs that fit a current preference profile. A shrinkingsuch analysis would first select chairs that are broadly suitable, then progressively focus on those that best align with context factors like material, dimensions, and color, narrowing to a core set of exemplars.

Relation and critique: Shrinkingsuch connects to theories of reference robustness, determiner semantics, and discourse coherence. Because it is a fictional construct, it lacks a universally accepted formal semantics and depends heavily on the contextual criteria chosen.

See also: determiners, such that, reference resolution, set shrinking. Note: this article treats shrinkingsuch as a hypothetical concept for illustrative purposes.