Abstraction - the process of mental abstraction from a number of properties and relationships of the phenomenon being studied with the simultaneous identification of properties of interest to the researcher (primarily essential, general). As a result of this process, various kinds of “abstract objects” are obtained, which are both individual concepts and categories (“whiteness”, “development”, “contradiction”, “thinking”, etc.), and their systems. The most developed of them are mathematics, logic, dialectics, and philosophy. Thus, the construction of abstractions is based on two procedures - distractions And replenishment, in which, on the one hand, only part of the set of corresponding sensory data is included in the content of the construct, on the other hand, new information is introduced into this content, which in no way follows from these data. Thus, when forming such an abstract object of geometry as a triangle, square, cube, etc., at the first stage they are abstracted from all sensory data characteristics of spatial objects, except for their shape and size, and at the second stage they are endowed with such properties as absolute straightness of lines, immutability, continuity, etc. The results of abstraction are usually called abstractions.
In the course of its historical development, science ascends from one level of abstraction to another, higher one. The development of science in this aspect is, as Heisenberg put it, “the deployment of abstract structures.” The decisive step into the realm of abstraction was made when people mastered counting and thereby opened the path leading to mathematics and mathematical science.
Although science has always used abstractions, their special place in the conceptual structure of scientific theories became quite obvious only in the light of the trends of the modern scientific revolution. The science of the past, in essence, was "terrestrial" science, i.e., an empirical generalization of the everyday experience of people, the macroscopic conditions surrounding a person. Among the initial principles of this science, therefore, played an important role principle of visibility . The abstractions used easily found a more or less direct interpretation or analogy in the language of sensory perceptions. The expansion of scientific knowledge beyond the macrocosm and earthly conditions (usual speeds, pressures, temperatures, etc.) gave rise to the process of eliminating clarity from the content of scientific theories. From this moment on, knowledge becomes more and more “abstract”, more and more distant in its content from the world of directly perceived things and phenomena. The progress of knowledge in many fields of science is characterized by a transition to the construction of theoretical systems of an increasingly higher level of abstraction using abstractions of the first, second, third, etc. orders. Thus, due to the very logic of the development of modern knowledge, the scientist is faced with the need to think about the nature of the abstractions he uses, as well as other elements of the theoretical system.
There are several types of abstraction:
1) abstraction identification , or a generalizing abstraction, as a result of which the general property of the objects under study is highlighted. This type of abstraction is considered fundamental in mathematics and mathematical logic. For example, one-to-one correspondence between sets is characterized by three essential properties; symmetry, transitivity and reflexivity. If there are relationships with given properties between certain objects, then with the help of such a relationship, similar to equality, a certain common property inherent in all these objects is identified;
2) analytical abstraction, or insulating , as a result of which the properties of objects are clearly recorded, denoted by a specific name (“heat capacity”, “solubility”, “continuity”, “parity”, “heredity”, etc.);
3) abstraction idealizing , or idealization, as a result of which the concepts of idealized (ideal) objects are formed (“ideal gas”, “absolutely black body”, “straight line”, etc.);
4) abstraction actual infinity (distraction from the fundamental impossibility of fixing every element of an infinite set, i.e. infinite sets are considered as finite);
5) abstraction potential feasibility (distraction from the real boundaries of our capabilities, our limitation to our own finitude, i.e. it is assumed that any but finite number of operations in the process of activity can be carried out).
The most important question is What are the boundaries of abstraction, its limits (intervals)? The need to introduce the concept of an abstraction interval into the methodology is associated with the idea of substantiating scientific abstraction - both the abstraction process itself and its result. By abstracting in the process of cognition, the researcher does not act arbitrarily, but according to certain rules and in accordance with the assigned cognitive task. Since the goal of any acts of abstraction and replenishment in science is ultimately connected with the achievement of truth, there is a need to take into account in cognitive activity those limitations and those regulations that exist in relation to the human ability to abstraction itself.
Firstly, that which is why one is distracted in the process of comprehending an object must be extraneous (according to clearly defined criteria) for the result of abstraction, and that which supplements the content of the abstract object must be relevant.
Secondly, the researcher must know to what extent this distraction has legal force (that is, it does not transform into another quality).
Third, when studying complex objects, one should carry out a conceptual development of the object in the form of a set of its projections in a multidimensional space of intervals. Conceptual development is the display of the same initial object of study in different theoretical planes (pictures) and, accordingly, finding a set of abstraction intervals. So, for example, in quantum mechanics, one and the same object (an elementary particle) can be alternately represented within two pictures - either as a corpuscle (under some experimental conditions), or as a wave (under other conditions). These pictures are logically incompatible with each other, but only taken together they exhaust all the necessary information about the behavior of microparticles. Similarly, in sociology, an individual can be considered in different sociocultural contexts in which he plays different roles. social roles. Each such context can be the basis for the development of a concept with a corresponding interval of abstraction.
Fourth, at a certain stage it is necessary to carry out a conceptual assembly of relevant intervals of abstraction into a single configuration and abstraction from extraneous perspectives of the vision of a given object. Conceptual assembly is the representation of an object in a multidimensional cognitive space by establishing logical connections and transitions between different intervals that form a single semantic configuration. Thus, in classical mechanics, the same physical event can be reflected by observers in different reference systems in the form of a corresponding set of experimental truths. These different pictures can nevertheless form a conceptual whole thanks to Galileo's "rules of transformation" governing the ways in which one can move from one group of statements to another.
Research
Methods of empirical and theoretical
¨ abstraction
¨ analysis and synthesis
¨ induction and deduction
¨ modeling and use of devices
¨ historical and logical methods scientific knowledge
The concept of "abstraction" comes from the concept of "abstraction" (lat. abstractio - abstraction). To abstract means to mentally abstract from the unimportant, private properties and connections of an object in order to highlight its essential features. Concept "abstract" is opposed to the concept "specific".
Abstraction has the most universal character in human mental activity, because every step of thought is associated with this process or with the use of its result. The essence of this method is in mental abstraction from unimportant properties, connections, relationships of objects and in the simultaneous selection and recording of one or more aspects of these objects that are of interest to the researcher.
In research practice, a distinction is made between the process of abstraction and the result of abstraction, called abstraction. Under result abstraction refers to knowledge about certain aspects of objects.
Process abstraction - it is a set of operations leading to obtaining a result (abstraction).
Examples of abstraction: ball, house, sea, tree, road, air, gas, liquid, etc.
The abstraction process has a complex, two-stage nature.
First stage- separation of the essential from the unimportant, subtracting the most important in the phenomena of interest to the researcher. It is the assessment of various aspects of the phenomenon, various factors, etc., that is being prepared for abstraction (distraction), which includes:
a) establishing what is common to many objects of a certain class;
b) establishing the independence or weak dependence of the subjects being studied
phenomena from certain factors that can be neglected, etc.
Second stage consists in implementing the abstraction possibility established earlier. This is, in the proper sense, abstraction or distraction: some object A1 is replaced by another object A2, less rich in properties, acting as a “model” of the first.
Abstraction can be applied to both real and abstract objects, i.e. to those that are themselves already the result of previous abstraction. Therefore, it is a multi-step process (in the sense that abstraction can be applied to an object multiple times). Moving from one level of abstraction to another, we obtain abstractions of an ever-increasing degree of generality.
For example, gradually abstracting from an increasing number of specific properties a certain person, you can get a similar series of abstractions:
man ® man ® Living being® material object.
At the same time, knowledge seems to move away, moving away from reality, taken in its integrity, concreteness and richness. However, such an approach is an indispensable condition for understanding the deep, internal connections of this reality.
The result of the abstraction process, as noted above, is abstractions. Their main function is that they make it possible to replace the relatively complex in cognition with a simple one, help to understand the entire infinite variety of phenomena of reality by differentiating them, highlighting the most diverse aspects and properties in them, establishing relationships and connections between these aspects and properties, fixing them in the process of cognition, etc.
In research practice, the most widely used abstractions are the following main types: abstraction of identification, isolating abstraction, abstraction of constructivization, abstraction of actual infinity, abstraction of potential feasibility.
Under abstraction of identification is understood as the formation of a concept by combining them into a special class, identifying objects connected by relations such as equality. In this case, it is necessary to abstract from a number of individual properties of such objects.
Isolating abstraction- This is the selection of properties and relationships that are inextricably linked with objects, and their designation by certain “names,” which gives such abstractions the status of independent objects. examples of such abstract objects are the concepts of “reliability”, “stability”, “controllability”, “solubility”, etc.
There is a certain commonality between the abstraction of identification and the isolating abstraction, since in both cases the isolation of certain properties of objects is essentially carried out.
However, the difference between them is significant, and it consists in the fact that in the first case the complex of properties of the object is “isolated”, and in the second - its only property.
Essence abstraction constructivization consists in abstracting from the fragility and uncertainty of the boundaries of real objects, in “coarsening” reality. This allows us to formulate some laws in relation to this “rough” reality, to understand it “in a first approximation” in order to move further, deeper in knowledge. As a result of such a movement, the initial simplification of reality is removed, we discover in it new, more accurate boundaries, sides, stages, etc.
Abstraction of actual infinity is one of the main abstractions of mathematics and logic. Its essence lies in abstracting from the incompleteness (and incompleteness) of the process of formation of an infinite set, from the impossibility of defining it full list all elements. Such a set is simply considered as given, as existing.
Potential Feasibility Abstraction is also widely used in mathematics and logic and consists in abstracting from the real boundaries of human capabilities, due to the limitations of our life in space and time. From this point of view, infinity no longer appears as directly given and actual, but as potentially realizable.
) in order to highlight their essential, regular features. The result of abstraction is abstract concepts, for example: color, curvature, beauty, etc.
The need for abstraction is determined by the situation when the differences between the nature of the intellectual problem and the existence of the object in its concreteness become apparent. In such a situation, a person uses, for example, the opportunity to perceive and describe a mountain as a geometric shape, and a moving person as a certain set of mechanical levers.
Types of abstraction
Some types of abstraction:
- primitive sensory abstraction- distracts from some properties of an object or phenomenon, highlighting its other properties or qualities (highlighting the shape of an object, abstracting from its color or vice versa). Due to the infinite variety of reality, no perception is able to cover all its sides, therefore primitive sensory abstraction occurs in every process of perception and is inevitably associated with it.
- generalizing abstraction- gives a generalized picture of the phenomenon, abstracted from particular deviations. As a result of such abstraction, the general property of the objects or phenomena under study is highlighted. This type of abstraction is considered fundamental in mathematics and mathematical logic.
- idealization- replacement of a real empirical phenomenon with an idealized scheme, abstracted from real attributes that are unimportant for this study. As a result, the concepts of idealized (ideal) objects (“ideal gas”, “absolute black body”, “straight line”, etc.) are formed.
- isolating abstraction- is closely related to involuntary attention, since in this case the content on which attention is focused is highlighted.
- abstraction of actual infinity- a distraction from the fundamental impossibility of fixing every element of an infinite set [ ], that is, infinite sets are considered as finite [ ] .
- constructivization- distraction from the uncertainty of the boundaries of real objects, their “coarsening”.
By purpose:
- formal abstraction- highlighting such properties of an object that do not exist in themselves and independently of it (shape or color). This type of abstraction serves as the basis for children to acquire knowledge that describes objects by their external properties, which serves as a prerequisite for theoretical thinking.
- meaningful abstraction- isolating those properties of an object that in themselves have relative independence (a cell of an organism). This type of abstraction develops students' ability to operate with them.
Abstract and concrete
Abstract thinking involves operating with abstractions (“man in general”, “the number three”, “tree”, etc.), concrete thinking deals with specific objects and processes (“Socrates”, “three bananas”, “oak tree in the yard” ", etc.). Ability to abstract thinking is one of distinctive features person, which probably formed simultaneously with language skills and largely thanks to language (for example, it would be impossible to even mentally operate with the “number three” in general, without having a specific language sign- “three”, since in the world around us such an abstract, unattached concept simply does not exist: it is always “three people”, “three trees”, “three bananas”, etc.).
Definition through abstraction
Definition through abstraction- a method of describing (isolating, “abstracting”) non-sensually perceived (“abstract”) properties of objects by specifying in the subject area some relation such as equality (identity, equivalence). Such a relationship, which has the properties of reflexivity, symmetry and transitivity, induces a division of the subject area into disjoint
Surely each of us at least once in our lives has come across such a concept as abstraction. It is often applicable in Everyday life when you should look at things around you a little differently. How exactly - “otherwise”? What is meant by this and what abstraction is, let’s try to figure it out further.
General overview
This concept has its roots in Latin and is literally translated as “distraction.” More often what is meant is not a change or activity, but a change of thinking, the opportunity to look at things from a different perspective, from a different angle, including when the object being analyzed seems unusual. In this way, our mind combines all existing ideas about this object and considers it as if it did not possess individual properties, connections, and phenomena. Ultimately, there is a selection of natural, understandable and essential features abstraction? This is the distancing or separation of one from the other. Subsequent recognition is optional. Abstraction can be used temporarily, at a certain moment, returning ideas about an object to the original level or, conversely, discovering its new properties. In a narrower sense, the result of abstraction, that is, any distraction, is a generalization of the obtained (studied) theoretical features.
A different look at one object
Every person comprehends something in his life. His consciousness analyzes many factors, looking for individual elements that can have an impact, for example, in making a decision or developing an opinion about a particular object. In such comprehension, the method of abstraction plays an important role. Its goal is the study of subjects, as a rule, which have much great properties, relationships, connections, which, due to perception and thinking, a person cannot fully understand. As a general method of cognition, abstraction helps to highlight features. When comprehending an object, a person has the right to simplify it, pay attention to obvious aspects, while forgetting, that is, ignoring the rest.
Are you familiar with such concepts as analysis, synthesis, abstraction? They are widely used in areas such as logic and philosophy; they can exist separately from each other, but are largely interconnected. Synthesis is understood as the process of combining isolated, disparate concepts; its purpose is to bring them together into a single whole or group. Synthesis is an important stage in the activity of human consciousness, in which the cognitive function is formed. In other words, having several parts, synthesis serves to collect them.
On the contrary, analysis seeks to disassemble the existing whole into its component parts. Together, both concepts give rise to ideas about the connections occurring between individual elements
Studying reality
Day after day, human consciousness searches for new components, objects and concepts that have not been explored before, in which abstraction indirectly helps. in this case, it is a set of methods by which new knowledge is discovered, methods of solution and research, as well as systematization and correction of data. This should include conclusions, principles of reasoning, and forecast. Thus, observing an object, a person puts forward hypotheses and theories that serve as a form of assumption. These can later be supported by scientific evidence, experiments, or by collecting additional facts.
Cognition, as a method of abstraction, has distinctive features from the comparison methodology. It is expressed in qualitative and quantitative forms of abstraction, when essential (indisputable) features are highlighted. To make a decision, a person often relies on a comparison method that allows him to evaluate possible (desired) indicators with real indicators. All the pros and cons are put on the scales, which subsequently influence the final choice.
The cogs of our internal mechanism
So what is abstraction? Undoubtedly, this is a complex mechanism that we resort to, sometimes without even realizing it. Mentally, a person separates the existing from the non-existent, isolating individual elements from the set. This could be a chain of events, a series of processes, a group of objects. So, turning to individual characteristics human, psychology is capable of abstracting general properties from specific ones applicable to a given individual. This once again proves the indisputable argument that each person, like his mind and consciousness, is unique.
Application - in everything
Abstraction is used in many areas: politics, mathematics, logic. We have already learned that under general concept abstraction hides a distraction from external phenomena in order to highlight unimportant details or the essence of the object itself. Thanks to such an “outside view,” scientific concepts are born, which, in turn, form unified properties and connections that are combined into categories.
Thus, scientific abstraction can be traced in economics. In the world there are millions of different consumption and non-food groups that people need every day. They all differ in many characteristics and properties. But, leaving them endless comparisons, man involuntarily combined them into a single category - goods as products intended for sale.
Scientific abstraction is noticeable in construction. Every construction includes a detailed calculation that takes into account the features of the future building. But exact geometric correspondences, as well as the strict interaction of all its individual components, are not always 100% feasible - this is either theoretically impossible or practically unacceptable due to excessive complexity. Because of this, using the method of scientific abstraction, the structure is schematized. Alleged minor factors are excluded, which, in turn, does not affect the accuracy and reliability of the calculations performed.
Thinking abstractly is the ability of every person
To summarize the topic discussed, we now definitely know what abstraction is - a mental, conscious distraction from the properties of an object, due to which a new idea about it appears or a logical concept is formed.
The ability to apply abstraction in everyday life is inherent in a person from birth. In many ways big role Language skills and the development of the language itself play a role here. Thus, when thoughts “flow” in an abstract order, consciousness does not focus on individual features of an object, characterizing it according to general indicators (for example, “fruit”). In contrast to the abstract, science argues for the concrete - in this case, the boundaries of understanding, looking for additional properties (not just “fruit”, but “orange” or “sweet and sour apple”).
Abstraction (this term comes from the Latin word abstractio, which means distraction) defines looking at a situation, person or object from a detached point of perception. Thus, there is a distraction from specifics and the ability to assess the situation in general. The concept of abstraction played vital role in the development of many sciences.
Abstraction - example
Any abstraction requires two actions: the first is small and insignificant details, the second is focusing on the phenomenon in general and important, significant details.
For example, in order to study movement, curvilinear movement in all its varieties is first discarded, then accelerated movement is discarded, and in the end, its purest and simplest form, reflecting its very essence, remains for consideration. Thus, abstraction is a tendency to focus on ideal conditions.
Despite the fact that this seems elementary, it was abstraction that made it possible to isolate and study the most important concepts– speed, time, distance, etc. From here we get that abstraction is a method of cognition.
This method allows you to discard the less significant, secondary, and concentrate on the most important. It is no secret that situations often arise in a person’s life in which it is important to decide on the main direction and not waste energy in vain, scattering about trifles. Abstraction will help you decide on this primary matter. Abstraction and Concretization
Every concept has its opposite. Abstraction and concretization are like looking up close and from afar. Standing close, you will consider everything in detail (concretization), and standing far away, you will be able to appreciate the concept as a whole, without being distracted by the details (abstraction). So these are two opposite concepts.
This is easy to illustrate with an example. If you say “I will lose weight,” this is an abstraction. And if you say, “I will give up sweets and go for morning jogs,” this is already specific.
Abstraction method and its goals
Abstraction in psychology and other sciences makes it possible to achieve a whole range of goals that help to more deeply understand the essence of a phenomenon, object or person. This analytical method allows you to discard a series specific situations and look at the big picture, which achieves the following goals:
Abstraction can be used in a variety of situations. Moving away from insignificant details, it is much easier to concentrate on the very essence of the phenomenon of interest.
