interpretation

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interpretation

Logic an allocation of significance to the terms of a purely formal system, by specifying ranges for the variables, denotations for the individual constants, etc.; a function from the formal language to such elements of a possible world

Interpretation

All the educational activities designed to explain the history and meanings inherent in historic sites, including tours, furnishings, displays, exhibits and related programs.

interpretation (and interpretive understanding)

a method that stresses the importance of understanding intentional human action. Semantically, any account is an interpretation. What distinguishes the interpretive paradigm from other movements is the recognition that any statement about the social world is necessarily relative to any other. It inevitably sets itself against the notion of the Durkheimian ‘social fact’ by asserting that ‘facts’ are always produced by specific people in certain circumstances for explicit reasons. There is little agreement on detail since interpretive sociologists cover a wide range of epistemological positions. The extreme subjectivist or relativist wing (HERMENEUTICS) takes the position that no single interpretation can predominate over another. SCHUTZ's phenomenological sociology occupies a fairly central position within the paradigm in attempting a systematic study of the intersubjective nature of social life. On the other hand, WEBER considered understanding (VERSTEHEN) to be a method of elucidating the motivations for action (not experience of action) which did not preclude the sociologist making generalizations from this data (see also IDEAL TYPES). ETHNOMETHODOLOGY is often classed as an INTERPRETIVE SOCIOLOGY, but this can only be partially valid since it gains much of its intellectual heritage from American EMPIRICISM. In sum, whilst there is a general commitment to EMPATHY and understanding the actor's point of view, the research that flows from interpretation is so varied as to be difficult to categorize as a school, possibly because the meaning of interpretation is itself subject to interpretation.

Interpretation

 

a definition, explanation, or elucidation.

In its literal meaning the term “interpretation” is used in jurisprudence: interpretation of a law by a lawyer or judge represents a “translation” of “special” expressions—the formulations of an article of the legal code—into layman’s language, as well as recommendations for applications of such articles. It is also applied in the arts: the interpretation of a role by an actor or of a musical work by a pianist is the performer’s individual treatment of a work, which, generally speaking, is not unambiguously defined by the author’s intention.

Interpretation in mathematics, logic, scientific methodology, and theory of knowledge represents the totality of values (meanings) given by various means to elements (expressions, formulas, symbols) of a particular scientific or abstract-deductive theory (when the elements themselves of this theory are given a meaning, reference is also made to the interpretation of symbols and formulas).

The concept of interpretation has considerable epistemological significance. It plays an important role in the comparison of scientific theories with their described fields, the description of various methods of theory construction, and the characterization of the changes in interrelationships between such theories during the course of cognitive development. Insofar as each scientific theory has been conceived and structured to describe a specific area of actual reality, this reality serves as the natural interpretation of the theory, but such “presupposed” interpretations are not the only possible ones, even for theories of classical physics and mathematics, which are based on an implicit content. Thus, from the fact of isomorphism of mechanical and electrical oscillatory systems described by the same differential equations, it follows immediately that at least two different interpretations are possible for such equations. To an even greater degree this possibility is found in abstract-deductive, logical-mathematical theories that assume not only different but even nonisomorphic interpretations. In general, it is difficult to speak of their “natural” interpretations.

Abstract-deductive theories are also able to manage without “translation” of their concepts into “physical language.” For example, irrespective of any physical interpretation, the concepts of Lobachevskii’s geometry may be interpreted in terms of Euclidean geometry. The discovery of the possibility of mutual interpretability of various deductive theories has played an enormous role both in the development of the deductive sciences themselves (particularly as an instrument of proof of their relative consistency) and in the formation of contemporary theoretical and epistemological views associated with the deductive sciences.

REFERENCES

Hilbert, D. Osnovaniia geometrii. Moscow-Leningrad, 1948. Chapter 2, section 9. (Translated from German.)
Kleene, S. K. Vvedenie v metamatematiku. Moscow, 1957. Chapter 3, section 15. (Translated from English.)
Church, A. Vvedenie v matematicheskuiu logiku, vol. 1. Moscow, 1960. Introduction, section 7. (Translated from English.)
Fraenkel, A., and Y. Bar-Hillel. Osnovaniia teorii mnozhestv. Moscow, 1966. Chapter 5, section 3. (Translated from English.)

IU. A. GASTEV

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