kirjeldusfunktsioonina

Kirjeldusfunktsioonina is an Estonian term used in mathematical, logical, and linguistic contexts to indicate that an object is defined by a description rather than by a fixed symbol or name. The phrase signals that the object is selected by presenting a description or property that uniquely identifies it, rather than by listing it outright.

In formal usage, a description function assigns to each relevant item the unique object that satisfies a given descriptor. This often relies on a predicate P(x) with a uniqueness condition, such that there exists exactly one x for which P(x) holds (or for which P holds within a specified context). The expression kirjeldusfunktsioonina emphasizes that the object is determined by this descriptive content, not by direct enumeration.

Common contexts include description-based definitions in logic, semantics, and formal theories. For example, one might define a function that assigns to each country its capital as “the unique city that is the seat of government of that country,” i.e., the function is given kirjeldusfunktsioonina by that descriptive description. The concept is closely related to the idea of iota or definite description operators in logic, which likewise pick out objects by description rather than by mere name.

Limitations of description-based definitions arise from potential non-uniqueness or ambiguity of descriptions, dependence on context, and the need for a well-defined existence and uniqueness condition to ensure the function is meaningful. In practice, authors note when a description may fail to pick out a single object or when multiple descriptions could apply.

See also: definability, definite description, iota operator, descriptive naming, epsilon calculus.