This concept was introduced by Boethius as a translation of another Greek word used by Aristotle. Abstraction (translated as "distraction") is the mental isolation of certain aspects, connections or properties of phenomena and objects, in order to highlight some significant features and signs. Such designs may not have analogues in the physical world. This is characteristic of some mathematical disciplines. Abstraction is a direct consequence of the above term. However, this already indicates a kind of methodology of cognition.
Abstraction is a concept of perception
When applying this method, the transformation of the model inside a system (for example, intellectual) is considered. In this case, the entire system is distributed into elements that are subsystems. That is, abstraction is an operation, as a result of which a complex model is replaced by a more simplified one, which contains fewer differential elements, which, at the same time, are more informative. An example is the process of replacing a high-resolution video file with a lower-quality one for quick file processing and transfer.
Features and hierarchy in the chain of abstractions
Typically, it is theoretically possible to carry out such differential operations infinitely. Abstraction is a method, after applying which to the carrier of certain properties, you can get some kind of model. However, one can again work with this particularity in the same ways. There can be many such cycles. For example, you can abstract one part of a given model, leaving the rest unchanged, then move on to the next selected part. As a result, summarize the data in one "tree". For each model, one can obtain the so-called abstraction space, which is a collection of sets ordered by given rules. In reality, of course, there can be no endless division of the whole into parts. Therefore, they talk about a limited number of models obtained from the original prototype, which are called "hierarchical abstract chains."
Concept typing
Abstraction is an intellectual need when it is necessary to find differences between a particular object and the nature of the problem associated with it. For example, a person perceives a mountain as a combination of geometric shapes.
However, it is necessary to typify abstractions by type:
- generalizing, which gives an abstract picture of the phenomenon; as a result, one can single out the general properties of the studied models;
- idealizing - replacing an empirical real phenomenon with an abstract ideal scheme;
- actual infinite abstraction - fixing each element of an infinite set (considering them as finite);
- isolating - the allocation of the investigated necessary object or phenomenon from the integrity, for example, Occam's razor ;
- constructive - “roughening” the boundaries of a real object, a distraction from their uncertainty.
The concept of “abstraction” can also be typified according to goals:
- formal - isolating important properties for further analysis;
- substantive - highlighting practical qualities.
Related concepts
Concretization and abstraction are terms that it is almost impossible to talk about separately. These concepts are inverse to each other. To go into the chain of abstractions to the next level, it is necessary to apply methods of concretization to verify the correctness of the selection of particulars from the initial set. This allows you to not lose touch with the prototype.