abstraction

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abstraction

1. Logic an operator that forms a class name or predicate from any given expression
2. an abstract painting, sculpture, etc.

Abstraction

The omission or severe simplification of details in a drawing, leaving only massing, form and solids, so that the basis of the design can be explained.

Abstraction

 

(1) A method of scientific investigation based on disregard for the nonessential facets and signs of the phenomenon or process under investigation. This method makes it possible to simplify the representation of the phenomenon under investigation and to examine it in its “pure form,’1 as it were.

(2) A product of cognition—such as a concept, a description, a law, a model, an ideal object—examined in juxtaposition with concrete, empirical reality, which in this product is not fixed in all its wealth of traits and interconnections.

(3) Cognitive activity with the aim of obtaining an abstraction—the process of abstraction.

The use of abstraction, as with any other method of investigation, is determined by the type of situation faced by the researcher and by the range of procedures that are necessary or possible in a given situation. A situation is characterized by the task (the goal characteristic of the method) and by the specifics of the subject under investigation (ontological characteristics). From the point of view of ontology, abstraction assumes a relative independence of phenomena and of their aspects and involves separation of essential and nonessential aspects. As a rule, the procedures of abstraction consist in the restructuring of the subject under investigation and the substitution for it of another object that is equivalent to it from the point of view of the given situation. The restructuring relates either to the representation of the object under investigation (rejection of nonessential aspects), to the empirical material, or to the program of observation and description (rejection of superfluous information). For instance, the geometrical properties of an electrical series do not depend on the components of a branch, such as resistance, inductance, or capacitance. Therefore, in the topological study of series, all the branches are usually replaced by sections which represent the network as a linear graph.

The goal characteristic of abstraction may differ, but in all cases it is linked to certain cognitive tasks and to the inclusion of abstraction in a broader framework of cognitive activity. In fact, the classification of types of abstraction is based on the distinction of goal characteristics: isolating abstraction aims at the articulation and clear delineation of the phenomenon under investigation; generalizing abstraction aims at obtaining an overall representation of the phenomenon; an idealization aims at replacing an actual empirical situation with an idealized schema, such as absolute solid in mechanics, with a view to simplification of the situation under investigation and more effective utilization of existing methods and means of investigation.

The realization of abstraction as a method involves two types of operation. The first is the elucidation of the possibility and advisability of substitution or restructuring of the object under investigation; the second is the process of substitution itself. The products of this process are properly modified representations of the subject, models, selected empirical material, and so on.

The simplest form of abstraction is the practical substitution of one object for another. In this form abstraction takes place even among animals; in particular, it is the basis for the development of conditioned reflexes. In humans such practical substitution is expressed by and centers on words in action with symbols. Ideas about essential and nonessential aspects of phenomena and about dependence relationships are formed. The realization of the specifics of symbol formations and of their relations to reality, to tasks, and to goals occurs at the same time. Such a realization is quite clearly visible in Aristotle (see, for example, Metafizika, Moscow-Leningrad, 1934, pp. 129–130).

The method of abstraction itself appears at a high level of cognitive development. Therefore, we should distinguish the historical process of formation of those products of cognitive activity which are now characterized as abstraction from the processes of abstraction in its modern form. In the former case the abstractness of the products of cognition themselves was not the result of any special purposeful procedure of abstraction; rather, it was the final result of human activity. In the development of science in the past, models such as the physical point or the ideal gas were usually considered the final phase in the construction of a theoretical concept; this phase involved the justification of the concept and the definition of the limits of its applicability. On the other hand, abstraction as a specialized procedure is distinguished and takes shape in cognition only on the basis of a theoretical construction. When the modern researcher uses this procedure, he often sets himself from the very beginning the task of simplifying the phenomenon under investigation and of constructing an abstract, idealized model of it; idealization here is the point of departure for the construction of a theory. In view of this, abstraction as a method arises as a result of a theoretical realization of the character of the course of the historical process of cognition, which is considered as the process of obtaining abstraction.

REFERENCES

Gorskii, D. P. Voprosy abstraktsii i obrazovanie poniatii. Moscow, 1961.
Logika nauchnogo issledovaniia. Moscow, 1965.
Rozov, M. A. Nauchnaia abstraktsiia i ee vidy. Novosibirsk, 1965.

M. A. ROZOV

abstraction

[ab′strak·shən]
(hydrology)
The draining of water from a stream by another having more rapid corroding action.
The part of precipitation that does not become direct runoff.

abstraction

(1)
Generalisation; ignoring or hiding details to capture some kind of commonality between different instances. Examples are abstract data types (the representation details are hidden), abstract syntax (the details of the concrete syntax are ignored), abstract interpretation (details are ignored to analyse specific properties).

abstraction

(programming)
Parameterisation, making something a function of something else. Examples are lambda abstractions (making a term into a function of some variable), higher-order functions (parameters are functions), bracket abstraction (making a term into a function of a variable).

Opposite of concretisation.

abstraction

(1) The level at which a subject is viewed or programmed. For example, the highest abstraction level of a system is the overall system, which includes everything. Each subsequent abstraction layer encapsulates the details below it. See abstraction layer.

(2) In object technology, abstraction is one of the basic principles. It allows for creating user-defined and self-contained data types, known as objects. The details of the processing are contained within the object. See object-oriented programming and encapsulation.
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