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descriptionsee THICK DESCRIPTION.
(also description operator or descriptive definition), a term in logic and linguistics designating special constructions that in formal languages play the role of proper and common nouns that are supplementary relative to the basic vocabulary. In natural languages this role is fulfilled by word combinations of the type “that … which … “and “such … that …” (in Russian, tot [ta] … , kotoryi [-aia] … and takoi [-aia] … chto …) or by definite articles (definite description) and indefinite articles (indefinite description), respectively.
In logically and mathematically formalized languages, definite description operators, which are interpreted by the word combinations of the first type indicated above, are applied to formulas (predicates) that contain at least one free variable, which becomes “bound” in such cases, transforming the given expression into a designation of a single object, which is the value of the variable. For example, if P(x) is the predicate of x = log35, and t is the designation of the definite description operator, then ixP(x) is the descriptive noun of that single value of x for which P(x) is true. The existence and uniqueness of this object are necessary conditions for the applicability of the i-operator to the given expression and for the meaningfulness of the description. If the condition of uniqueness is not met, such a “definite” description is naturally regarded as an imprecise formulation of the indefinite description, which is interpreted by the word combination of the second type. Indefinite descriptions are precisely introduced by the so-called є-operator, which like the ı-operator, relates the dependent object to some property or relation, and by means of which it is also possible to obtain from the formulas of the corresponding calculation the object nouns (“є-terms”), with the sole difference that in order to use the є-operator neither proof of the uniqueness of the dependent object nor proof of its existence is necessary (that is, the object introduced by the є-operator, which “depends” on the assumption of its existence, is in a certain sense an “arbitrary object”). Special postulates (axioms, and sometimes also rules of derivation), which encode the formal behavior of the newly introduced formal objects (symbols) and which have the form of explicit definitions, are introduced into a given formalized language simultaneously with the joining to it of description operators. Under certain natural conditions, for a very extensive class of formal systems, the objects introduced by such expansions of the calculations are eliminated, so that the joining of a description to the system, which is extremely convenient for practical purposes, proves in this sense to be nonessential. This property, which is well known from natural languages in which descriptions serve to form synonymous expressions, also occurs for formalized languages, where the need for descriptions is due, roughly speaking, to the presence in them of a potentially infinite number of objects that have no proper nouns: like any other “abbreviations of speech,” descriptions are convenient but in principle are not necessary.
REFERENCESKleene, S. C. Vvedenie v metamatematiku. moscow, 1957. Section 74. (Translated from English.)
Freudenthal, H. Iazyk logiki. Moscow, 1969. Chapter 3, par. 25. (Translated from English.)
IU. A. GASTEV and M. M. NOVOSELOV
one of the elements of literary narration, in which the author singles out some specific aspect of the narrative, such as the appearance of a person, the setting, or nature.
Static description interrupts the development of events, as in the extensive descriptions of a city or a house in H. Balzac or V. Hugo; it is used as a device for retarding the action. Dynamic description is ordinarily shorter; it is included within the events and does not stop the action, as in F. M. Dostoevsky or A. P. Chekhov. In poetry some works are partially or wholly descriptive, for example, I. A. Bunin’s narrative poem Fallen Leaves.
(slovesnyi portret, “word portrait”), in criminalistics, a method of describing a person’s appearance to aid in the identification of the person by outward features. A special standardized terminology has been developed for descriptions on the basis of anatomic and anthropological data. Outward features are divided into two main groups: anatomic, such as height, build, and facial features; and functional, such as gait, bearing, and characteristic gestures. Anatomic features are described in terms of size, form, location, and color. Anomalies, which are called special features, are also noted: lameness, birthmarks, tattoos, and scars.
Descriptions are used in operative-search investigations and other expert work. They aid in the registration and identification of individuals, the search for wanted criminals or missing persons, and the determination of the identity of corpses and living persons.