2. Basic mental operations
The process of problem solving is undoubtedly a model that most fully reflects the structure of intellectual activity, and the study of the features of this process can provide significant materials for understanding the psychology of human thinking. In the process of mental activity, a person learns about the world around him with the help of special mental operations. “These operations constitute various interconnected aspects of thinking that transform into each other. The main mental operations are analysis, synthesis, comparison, abstraction, concretization and generalization.”
Analysis is the mental decomposition of a whole into parts or the mental isolation of its sides, actions, and relationships from the whole. In its elementary form, analysis is expressed in the practical decomposition of objects into their component parts. A table, for example, can be divided into parts such as a lid, legs, drawers, spacers, etc. When introducing children to a plant, they are asked to show part of it (trunk, branches, leaves, roots). Analysis can be practical (when the thought process is directly included in speech activity) and mental (theoretical). If analysis is divorced from other operations, they become vicious and mechanistic. Elements of such an analysis are observed in a child in the first stages of the development of thinking, when the child disassembles and breaks toys into separate parts, without using them further.
Synthesis is the mental unification of parts, properties, actions into a single whole. The operation of synthesis is the opposite of analysis. In its process, the relationship of individual objects or phenomena as elements or parts to their complex whole, object or phenomenon is established. Synthesis is not a mechanical combination of parts and therefore cannot be reduced to their sum. When individual parts of a machine are connected, their synthesis produces not a pile of metal, but a machine capable of moving. When oxygen and hydrogen chemically combine, water is formed. Both synthesis and analysis occupy an important place in the intellectual process. So, when learning to read sounds and letters, they form a syllable, from syllables - words, from words - sentences.
Analysis and synthesis always proceed in unity. Analyzing what includes something common, a whole. Synthesis also presupposes analysis: in order to combine some parts, elements into a single whole, these parts and characteristics must be obtained as a result of analysis. In mental activity, analysis and synthesis alternately come to the fore. The predominance of analysis or synthesis in thinking can be determined both by the nature of the material and the conditions of the task, and by the mental makeup of a person.
Comparison is the establishment of similarities or differences between objects and phenomena or their individual characteristics. In practice, comparison is observed when applying one object to another; for example, one pencil to another, a ruler to a desk, etc. This is how the process of comparison occurs when we measure space or weigh weights. Comparison can be one-sided (incomplete, based on one characteristic) or multilateral (complete, based on all characteristics); superficial and deep; unmediated and indirect. The main requirement for a comparison operation is that it be carried out in one relation. For a deeper and more accurate knowledge of activity, such a quality of thinking as the ability to find differences in the most similar objects and similarities in different ones is especially important.
Abstraction consists in the fact that the subject, isolating any properties, signs of the object being studied, is distracted from the rest. So we can talk about the color green as having a beneficial effect on human vision, without specifically indicating objects that are green. In this process, a feature separated from an object is thought of independently of other features of the object and becomes an independent subject of thought. Abstraction is usually achieved through analysis. It was through abstraction that abstract, abstract concepts of length, breadth, quantity, equality, value, etc. were created. Abstraction is a complex process that depends on the uniqueness of the object being studied and the goals facing the researcher. Thanks to abstraction, a person can escape from the individual, the concrete. At the same time, abstraction does not exist without sensory support, otherwise it becomes meaningless and formal. Among the types of abstraction, one can distinguish practical, directly included in the process of activity; sensual or external; higher, indirect, expressed in concepts.
Concretization involves the return of thought from the general and abstract to the concrete in order to reveal the content. Concretization is turned to in the event that the expressed thought turns out to be incomprehensible to others or it is necessary to show the manifestation of the general in the individual. When we are asked to give an example, then, in essence, the request is to specify previous statements.
Generalization is the mental unification of objects and phenomena according to their common and essential characteristics. For example, similar characteristics found in apples, pears, plums, etc., are combined into one concept, which we express with the word “fruit.” Mental activity is always aimed at obtaining results. A person analyzes objects in order to identify general patterns in them and predict their properties. A psychologist studies people in order to reveal the general patterns of their development. The repetition of a certain set of properties in a number of objects indicates more or less significant connections between them. At the same time, generalization does not at all imply discarding the specific special properties of objects, but consists in revealing their essential connections. Essential, i.e. necessarily interconnected and, precisely because of this, inevitably repeating.
The simplest generalizations involve combining objects based on individual, random characteristics. More complex is complex generalization, in which objects are combined on different grounds. The most difficult generalization is one in which species and generic characteristics are clearly identified and the object is included in the system of concepts.
All of these operations cannot occur in isolation without connection with each other. On their basis, more complex operations arise, such as classification, systematization and others. Each of the mental operations can be considered as a corresponding mental action. At the same time, the activity, effective nature of human thinking, and the possibility of creative transformation of reality are emphasized. Human thinking not only includes various operations, but also occurs at different levels, in different forms, which together allows us to talk about the existence of different types of thinking. In psychology, several approaches have been developed to the problem of classifying types of thinking. As has already been shown above, in terms of the degree of development, thinking can be a discursive, step-by-step process, and an intuitive process, characterized by rapidity, the absence of clearly defined stages, and minimal awareness.
Fostering a culture of mental work. The main requirements for the methodology for conducting such classes are the following: 1) conducting classes to cultivate a culture of mental work should be carried out not from case to case, but according to a pre-developed program and calendar schedule; 2) continuity with the work of subject teachers to develop students’ intellectual abilities; ...
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Knowledge, with mastery of educational and cognitive operations, with the manifestation of mental flexibility both in the assimilation of knowledge and in its practical use. We are talking about human thinking as an integral part of mental education. Thinking is a product of the activity of the human brain. It is common to all people. Teachers and psychologists recommend that teachers develop thinking in general and its particular types. ...
31. Mental operations
The thinking process is carried out using a number of mental operations: analysis and synthesis, abstraction and concretization, classification, systematization, comparison, generalization.
Analysis is the mental decomposition of an object into its component parts in order to isolate its various aspects, properties, and relationships from the whole. Through analysis, irrelevant connections given by perception are discarded.
Synthesis is the reverse process of analysis. This is the combination of parts, properties, actions, relationships into one whole. This reveals significant connections. Analysis and synthesis are two interrelated logical operations.
Analysis without synthesis leads to a mechanical reduction of the whole to the sum of its parts. Synthesis without analysis is also impossible, since it reconstructs the whole from the parts isolated by analysis.
Comparison is the establishment between objects of similarity or difference, equality or inequality, etc. Comparison is based on analysis. In order to carry out this operation, you must first select one or more characteristic features of the objects being compared. Then, a comparison is made based on the quantitative or qualitative characteristics of these characteristics. The number of selected features determines whether the comparison will be one-sided, partial or complete. Comparison (as analysis and synthesis) can be at different levels - superficial and deep. In the case of deep comparison, a person’s thought moves from external signs of similarity and difference to internal ones, from the visible to the hidden, from appearance to essence. Comparison is the basis of classification - assigning objects with different characteristics to different groups.
Abstraction (or abstraction) is a mental distraction from minor, non-essential aspects, properties or connections of an object in a given situation and the isolation of one particular aspect or property. Abstraction is possible only as a result of analysis.
Thanks to abstraction, man was able to break away from the individual, concrete and rise to the highest level of knowledge - scientific theoretical thinking.
Concretization is the opposite process. This is the movement of thought from the general to the particular, from the abstract to the concrete in order to reveal its content. Concretization is also used in the case when it is necessary to show the manifestation of the general in the individual.
Systematization is the arrangement of individual objects, phenomena, thoughts in a certain order according to any one characteristic (for example, chemical elements in D.I. Mendeleev’s periodic table).
Generalization is the unification of many objects according to some common characteristic. In this case, single features are discarded. Only essential connections are preserved. Abstraction and generalization are two interrelated sides of a single thought process, with the help of which thought goes to knowledge.
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Mental activity is carried out in the form of mental operations that transform into each other: comparison - generalization, abstraction - classification - concretization. Mental operations are mental actions.
Comparison– a mental operation that reveals the identity and difference of phenomena and their properties, allowing for the classification of phenomena and their generalization. Comparison is an elementary primary form of cognition. Initially, identity and difference are established as external relations. But then, when comparison is synthesized with generalization, ever deeper connections and relationships are revealed, essential features of phenomena of the same class.
Comparison underlies the stability of our consciousness, its differentiation (immiscibility of concepts). Generalizations are made based on comparison.
Generalization- a property of thinking and at the same time a central mental operation. Generalization can be carried out at two levels. The first, elementary level is the connection of similar objects based on external characteristics (generalization). But the real cognitive value is a generalization of the second, higher level, when significant common features are identified in a group of objects and phenomena.
Human thinking moves from fact to generalization, from phenomenon to essence. Thanks to generalizations, a person foresees the future and orients himself in the specific. Generalization begins to arise already during the formation of ideas, but is fully embodied in the concept. When mastering concepts, we abstract from the random characteristics and properties of objects and highlight only their essential properties.
Elementary generalizations are made on the basis of comparisons, and the highest form of generalizations is based on the isolation of the essentially general, the disclosure of natural connections and relationships, i.e., on the basis of abstraction.
Abstraction(from Latin abstractio - abstraction) - the operation of reflecting individual properties of phenomena that are significant in some respect.
In the process of abstraction, a person, as it were, “cleanses” an object from side features that make it difficult to study it in a certain direction. Correct scientific abstractions reflect reality deeper and more fully than direct impressions. Based on generalization and abstraction, classification and specification are carried out.
Classification– grouping of objects according to essential characteristics. In contrast to classification, the basis of which should be features that are significant in some respect, systematization sometimes allows the choice as a basis of features that are unimportant (for example, in alphabetical catalogs), but operationally convenient.
At the highest stage of cognition, a transition from the abstract to the concrete occurs.
Specification(from Latin concretio - fusion) - cognition of an integral object in the totality of its essential relationships, theoretical reconstruction of an integral object. Concretization is the highest stage in the knowledge of the objective world. Cognition starts from the sensory diversity of the concrete, abstracts from its individual aspects and, finally, mentally recreates the concrete in its essential completeness. The transition from the abstract to the concrete is the theoretical mastery of reality. The sum of concepts gives the concrete in its entirety.
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In the process of evolution of views on the nature and essence of the thought process, the issue of the formation of mental operations attracted special attention of scientists. , unlike other physiological processes, occurs on the basis of a certain logic. This allows you to identify individual structural elements: abstraction, analysis and synthesis, classification and categorization, specification, generalization, comparison, and characterize them. The patterns of functioning of the named operations of thinking are essentially the main internal, specific foundations of thinking. Their study helps to obtain a detailed explanation of all external manifestations of mental activity.
- Abstraction
- Analysis and synthesis
- Classification and categorization
- Specification
- Generalization
- Comparison
Abstraction
Abstraction (abstraction) is one of the main processes of human mental activity, cognition based on the identification of essential, regular features, properties, connections of an object or phenomenon, abstraction from unimportant aspects. In everyday life, the ability to abstract is most often associated with the ability to focus on finding and solving the most important aspect of the problem at hand.
Depending on the purpose of abstraction, there are formal and substantive abstractions. Formal abstraction is the identification of properties of an object that do not exist independently of it (for example, shape or color). It serves as the basis for the acquisition of knowledge by children who describe objects by their external properties, which serves as a prerequisite for theoretical thinking. Content abstraction is the isolation of those properties of an object that themselves have relative independence (for example, a cell of an organism). This type of abstraction develops the ability to operate on properties separately.
Analysis and synthesis
In any type of intellectual work - in the field of mathematics, political science, painting, etc. - analysis and synthesis are widely used. We are not talking about scientific methods, but about interconnected mental operations.
The etymology of the word “analysis” comes from the ancient Greek “to break”, “to dismember”. As a mental operation, analysis implies the study of a thing, property, process or relationship between objects through the real or mental division of the whole into its components. This operation is one of the basic ones in the process of cognition and subject-related practical activity of a person.
An example of practical analysis is the chemical process of splitting a molecule of kitchen salt into Sodium and Chlorine ions in order to study the composition and molecular bonds. The mental operation of analysis presupposes the theoretical ability to operate with the constituent parts of an object or phenomenon and, based on this, draw certain conclusions. For example, thanks to mental analysis, a child learns to distinguish geometric shapes as a set of individual characteristics: a square consists of four straight lines, a triangle differs from a square in the number of angles and lines.
Synthesis (from the ancient Greek “connection”, “folding”) is the study of something through the combination of things, concepts, judgments about a phenomenon or object in order to obtain a comprehensive and diverse understanding of it. An example of synthesis would be the case when, while writing a history essay on the topic “Common features of the economic systems of the USSR and China,” a student, relying on knowledge of two different topics, determines what was common in the development of the two main socialist countries in a given period.
John Locke, in his Essay Concerning Human Understanding, believed that knowledge is created by combining perception, representation, and other types of knowledge. Immanuel Kant in the “Critique of Pure Reason” argued that there are two mutually complementary operations: analysis - understanding through the study of parts, synthesis - understanding through connection, unification of components, ascent from the individual to the multiple. In ordinary language, analysis and synthesis are two sides of the same coin.
Classification and categorization
We encounter classification and categorization all the time in everyday life; it has become so firmly established that most people don’t even think about it when they resort to such a mental operation. Throughout our lives, we assign concepts and knowledge about objects almost at a subconscious level to one category or another, which leads to ease of use of information. Almost everything around us is subject to a certain logic: be it departments in a supermarket or road signs.
Most modern dictionaries use the terms "classification" and "categorization" interchangeably. There is also a different opinion that “category” is a broader concept than “class,” but even in this case, the definition of the term itself remains the same. Classification is a logical operation of dividing the scope of a concept based on its characteristics. An example is a table known to us from school:
Specification
Concretization (from the Latin “formed”) is a method of cognition, a logical operation associated with the transfer of a certain general statement to a specific object or phenomenon. For example, it is known that corrosion of metals occurs as a result of the influence of the environment, in particular oxygen, on the metal. Consequently, having discovered a new metal, it can be assumed that it will also corrode under the influence of oxygen.
Generalization
Generalization is the logical operation opposite to specification. Implies the transfer of a particular statement applicable to one or more objects to other objects, as a result of which it ceases to be specific, acquiring a general character. Thus, having studied photosynthesis using the example of several plants, we can conclude that the process is impossible without sunlight in other plants.
Comparison
Every person has heard the conclusion at least once: “Everything is known by comparison.” Indeed, to determine what is good and what is better, to compare the properties of two objects, is possible only by resorting to the comparison operation - the process of quantitative or qualitative comparison of different properties (similarities, differences, advantages and disadvantages) of objects. Comparison is the most important mental category on the basis of which our understanding of the world around us is formed.
All of the above logical operations are mutually complementary, help to obtain and transform information, and quickly use it at the right time.
Development of the ability to perform mental operations
Few adults today think about the fact that many children's games and puzzles offered in elementary school are designed in such a way as to develop basic mental operations. Logical chains, rebuses, riddles and puzzles are aimed at developing abstract logical thinking skills from childhood, teaching how to identify similarities and differences in objects, defining concepts, and eliminating unnecessary things. Growing up, we perform these operations without thinking, but sometimes we encounter difficulties in solving them. This is precisely due to the fact that over the years of professional activity, our brain automatically improves the performance of certain tasks related to the type of occupation. But as soon as we encounter another area, difficulties arise. To prevent this from happening, you need to constantly improve, developing all the basic mental operations. Exercises on the ability to understand, identify and apply these operations will help with this.
Classic examples of such games are chess, backgammon, and scrabble. In Soviet times, puzzles with matches were quite popular, but today they have found a new life thanks to their popularization on social networks. You can try your hand at these kinds of tasks using.
Taking an IQ test can be an interesting and effective exercise for developing mental operations. There are many varieties of it, the most popular of which is the Eysenck test. You can familiarize yourself with recommendations for passing such tests, which are also popular these days when applying for a job.
Detailed information about the development of different types of thinking, as well as exercises for training them, are collected in the course. Take it if you are interested in developing your thinking!
Mental operations are actions that we carry out in our thinking on material, real or imaginary. Mental operations are individual “building blocks” or stages of our thinking. The main types of mental operations include:Comparison,
Abstraction,
Specification,
Induction
Deduction.
Comparison
Comparison is a mental operation consisting of establishing similarities and differences between individual objects or phenomena of the real world.When a person observes two objects, willy-nilly he begins to notice how these objects are similar or how they differ. Although seemingly simple, this operation includes a number of complex elements. There is no “comparison in general”; it always depends on what properties of the objects being compared are essential for us, what interests us. Depending on the situation, on our needs (sometimes very subtle), there are different bases for comparison.
Example. There are four people. Three of them are interested in books, the fourth is not. The first is interested in books insofar as he is interested in, say, science fiction. When he comes across a book, he pays attention to those details that can show that it relates specifically to science fiction. On the cover you can find the name of a familiar author; if the author is unknown, then the title of the work or the characteristic design of the cover may indicate that the book belongs to a particular genre. Therefore, when encountering two books, a science fiction lover will compare them by authors, titles, and design. And, without even looking inside, he may give preference to one book or another.
Another person is also interested in books, but his interest is professional: he is engaged in publishing. Such a person will most likely compare books with each other on other grounds: the quality of the paper, the way the cover is designed, the size of the book, and some other technical characteristics.
The fourth person is not at all interested in books, at least their paper versions. If he reads books, it is only from a computer screen or mobile device. Paper books occupy virtually no place in this person’s life. And therefore, what is interesting and important, the grounds for comparing books with each other are temporary and unstable: today two books seem similar/different because of color, tomorrow they are compared by size, the day after tomorrow by year of publication, etc. .
The comparison operation is carried out either directly or indirectly. When we perceive two objects directly, we use direct comparison. Otherwise, we use an indirect comparison. In an indirect comparison, we can use inferences based on indirect signs.
Indirect comparison generally relies on the full power of our intellect; for example, imagination and visual actions can be used as a “mediator” in comparison. A child cannot find out whether he has become taller by directly comparing his present self and his former self (for example, a month ago). However, he can use a visual trick and mark his height on the door frame. And then, based on the marks, he will be able to find out the desired information.
Strictly speaking, in nature there are generally no two identical objects. Any two stones differ from each other, the heavenly bodies differ, no two birds or insects are absolutely identical. It must be assumed that even two identical atoms or electrons do not exist. Our thinking makes objects identical. For this, in fact, there is a comparison operation.
Moreover, the human mind has come up with objects that are always the same, under any circumstances. We are, of course, talking about mathematical - exclusively fictitious - objects. So in mathematics, all equilateral triangles with a side length of 7 centimeters are always equal to each other.
The comparison operation is extremely important for the functioning of the psyche. And in any comparison, as we have already said, there is one or another basis, one or another essential features. It is interesting that in the comparison operation there are individual differences not only in the bases, but also in the comparison algorithm.
Example. There are four people (A, B, C, D) and two stones (b and b). The subjects are given the task of comparing the stones and making a verdict: are these stones the same or different. For all subjects, the main comparison criterion is shape, but there are also secondary ones - color, size. A and B began their reasoning like this: “Suppose b and b are the same...” C and D began their reasoning differently: “Suppose b and b are different...” Then they continued their reasoning. Subject A stated: “The shape of the stones is the same, which means the hypothesis was completely confirmed.” Subject B decided differently: “The shape of the stones is the same, but I have not yet compared them in color and size; if it turns out that they are different in some way, then the stones will turn out to be different.” Subject B reasons differently: “The shapes of b and b are the same, which means my hypothesis was not confirmed, and this means that the stones are not different, but identical.” And the last subject, G: “The shape, of course, is the same, and this somewhat contradicts my hypothesis; it will be necessary to compare in color and size; perhaps they will confirm my hypothesis.”
Unlike abstract reasoning in philosophy, formal or mathematical logic, in real life in most cases we have several bases for comparison. However, some reasons are usually slightly more important than others. Therefore, all four comparison algorithms given in the example make sense. Depending on the number of bases, on their equal or different significance, it happens profitable reason one way or another.
The comparison operation is performed by our thinking so often and in most cases so quickly that we simply do not have time to reflect on the algorithms by which we make the comparison. Algorithms can be very different and specific, not only such simple logical ones as in our example. Comparison can be multi-criteria, when in our heads we formulate a number of comparison criteria, and then, as if in our mind, assigning points to the objects being compared. Some comparison algorithms are inherent in us by nature and have not yet been fully studied by science.
This is, for example, auditory perception, which is entirely based on comparisons. Listening to another popular tune, we relatively easily and not without pleasure look for a repeating chorus in a musical opus. We can say with confidence what other opuses this opus is similar to. But we are not able to clearly describe the algorithm for comparing two musical works with each other, or at least individual short sections, because we control this intellectual process of comparison very weakly with our consciousness.
The comparison operation is inherent not only to people, but also to animals and birds. Females of many animals, for example, having the opportunity to compare two potential mating partners with each other, give preference to the larger and more physically developed male. When geese meet each other, they stand on tiptoes and stretch their beaks upward, comparing their height and competing in this indicator.
The comparison operation is basic for many other mental operations. Abstraction from some properties and circumstances, concentration of attention on others provides the primary structuring, ordering of the material.
Analysis and synthesis
Analysis is the mental dissection of something into parts or the mental isolation of individual properties of an object. The essence of this operation is that, perceiving or imagining any object or phenomenon, we can mentally select one part of it from another, and then select the next part, etc.Through analysis we can find out what parts make up what we perceive. Analysis allows us to decompose the whole into parts, i.e. allows us to understand the structure of what we perceive. However, there is not always only one way of decomposing the whole into parts. If the system is very complex, then there can be a lot of these methods. Therefore, as in the case of the comparison operation, the analysis may also have grounds.
Example. Suppose we are given the task of dividing the city in which we live into several separate parts. As a basis for decomposition (analysis), we can take the already established administrative-territorial division (by region). We can divide the city into functional parts: residential areas, industrial areas, garden and park areas. We can distinguish the historical part (with houses built, say, before 1917), the modern part and the area of new buildings. Can be divided into right bank and left bank.
We can analyze not only those objects that are presented to us visually. You can analyze, for example, processes. If a position has been created in some organization, for example, an economic analyst or a marketing specialist, then the specialist who occupies it will begin his work with an analysis: he will find out what structural and functional divisions exist in the organization, what specific tasks the organization faces, who her partners, etc. Without preliminary analysis in his work, such a specialist will poke around like a blind kitten.
When analyzing visual objects, we highlight:
Essential parts of the subject (structure),
Color, shape, material properties and other properties.
Analysis of objects, of course, can be carried out not only visually, but also from memory.
Synthesis is an operation opposite to analysis, a mental combination of parts of objects or phenomena into one whole, a mental combination of their individual properties.
Let's say we come across a new radio-controlled toy car and we really want to understand how it works. First we will just play and observe the behavior of the machine. Then we can disassemble it along with the remote control and carry out an analysis, that is, carefully study the structure of the toy, understand what parts it consists of. After this, we can assemble the machine (that is, carry out synthesis) and continue studying the behavior of the machine. We can again disassemble the machine, change something in its design and reassemble it, see what comes of it.
The very fact that we managed to reassemble the machine already shows that we have a good understanding of its structure.
Synthesis, like analysis, is characterized by mental manipulation of the properties of an object. However, it cannot be argued that synthesis and analysis are exclusively mental (immaterial) operations. Assembling and disassembling a machine, as in our example, can be done not only in the mind, but also in a mixed form: that is, using visual material. Analysis and synthesis are not some kind of “mystically incomprehensible” operations, they are literally the decomposition and assembly of this or that object. And it is often more useful to disassemble a typewriter or something else literally than in the mind. By the way, the human hand is represented in the cerebral cortex in very large areas and, by manipulating this or that object, the “smart hand” can “explain” a lot.
Throughout life, a person constantly, daily and even hourly uses analysis and synthesis. Arriving, for example, at a new supermarket, the buyer mentally divides the store area into departments, analyzes the assortment by manufacturer, identifies the strengths and weaknesses in the work of the staff, determines which products are profitable to buy and which are not.
Both analysis and synthesis can pursue purely practical goals, or they can also have theoretical ones. In the latter case, a person is only interested in “truth for truth’s sake,” that is, he is engaged in developing a unified, scientific picture (model) of the world.
Regardless of the practical or theoretical nature of reflection, analysis and synthesis are closely related to other mental operations, such as comparison. Comparing two objects with each other can serve as an impetus for analyzing one of these objects or both. Having learned, for example, that not all products are equally useful, a curious person will begin to find out why and will begin to sort the products into components in his mind. Within the analysis operation itself, a comparison may be required: having encountered two identical gears in the design of a machine, a person may be interested in whether they are exactly the same, and if different, then how significant this difference is.
Analysis and synthesis are very closely related. In everyday life, we usually ourselves do not notice how in our minds we first “put something into pieces” and then assemble it into one whole. By themselves, analysis for the sake of analysis and synthesis for the sake of synthesis practically never occur. If we have “taken something apart brick by brick”, then we want to make something out of these “bricks”. And having done something, you want to take it apart again.
Abstraction and Concretization
Abstraction is a mental distraction from some parts or properties of an object in favor of other, more significant features. You can abstract from any features or properties of an object. To abstract from something means not to attach importance to it, to ignore this circumstance.You can abstract from the age, gender and character of your colleagues. Then it will be possible to evaluate colleagues more objectively, based on their business qualities.
You can ignore the fact that the Earth is round and build a football field flat, not convex.
You can ignore the temperature of the ice cream and consider melted ice cream to be ice cream too.
Abstraction can be weak or strong. In the first case, we abstract from one or two signs and circumstances. In the second case, we abstract from everything else except one or two signs or circumstances.
If we abstract from everything except age, gender and character, then we can draw up a small personal portrait: “An elderly grumpy woman” or “A brave but arrogant young man.”
If we abstract from all other circumstances except the fact that the Earth is round, then we can say that planet Earth is one big football field.
If we abstract from everything except temperature, then we can say that all cold objects are ice cream.
The beauty of abstraction is not only that we can reason about concepts such as “asexual man” or “flat Earth”, but also that we can reason about strong abstractions - features abstracted from carrier objects. We can judge such abstract things as temperature, human gender, age, round shape, rectangular shape, shape, color, democracy, psychology.
What gives us the ability to abstract? For example, it is widely used in the formation and assimilation of new concepts, since concepts reflect only essential features common to a whole class of objects. Having said “table”, we abstract from other, seemingly secondary, features, such as color, dimensions, material, functionality, and present a certain image of a whole class of objects. In the word “table” we represent only an abstract characteristic: a fairly large object with a flat surface, at which you can sit and on which you can perform certain manual actions, a third or half a person’s height.
Not every person can define a table, but all people know this concept very well and use it competently. Some abstract concepts cannot be explained directly at all, only indirectly. For example, without the use of scientific apparatus, it is impossible to explain to another person how green differs from red. It is possible only in examples, through specification, to say that green is the color of plants, and red is the color of ripe tomatoes or ketchup.
It is even more difficult to explain the meaning of words denoting non-visual objects. How to define love? Or democracy? A feeling of deep sympathy? What is sympathy? Deep attachment to another person or object? How to distinguish deep from shallow attachment? Power of the people? Over whom?
This is a very interesting feature of the human psyche: we can spend hours expressing ourselves in abstract words, but it takes us considerable effort to define these words.
Among the types of abstraction are sometimes distinguished:
Practical (directly included in the process of activity),
Sensual (external),
Higher (mediated, expressed in concepts).
Pure abstraction, abstraction for the sake of abstraction, can take one very far in reasoning. In contrast to it, there is concretization - the representation of something individual that corresponds to a particular concept or general position. In concrete representations, we do not strive to abstract from the various signs or properties of objects and phenomena, but, on the contrary, we strive to imagine these objects in all the variety of properties and characteristics, in a close combination of some characteristics with others.
If abstraction is the breaking of connections between characteristics, the transition from considering individual cases to general ones, then concretization always acts as an example or as an illustration of something common. By specifying a general concept, we understand it better.
Examples. There was an abstract concept of “piece of furniture” - the less abstract (more concrete) concept of “table” became. To be more specific, you can go to "desk", "my home desk", "my home desk, the one it was ten years ago."
"Activity" - "Professional activity" - "Healing" - "Teeth pulling."
“Animal” - “Predator” - “Feline” - “Domestic cat” - “My cat Musya.”
Induction and deduction
An important feature of our mental activity is that as a result of it we receive (can obtain) new knowledge. Obtaining new knowledge directly involves inference, which is also classified as mental operations. There are usually two main types of inferences:Inductive reasoning (induction),
Deductive reasoning (deduction).
Induction is the transition from particular cases to a general position that covers particular cases.
Examples. Suppose we made a series of observations. We saw bears in several zoos. They were all brown. From this we concluded that all bears are brown.
We have seen a lot of birds in our life. They all had feathers, except those sold in the store. From this we concluded that all living birds have feathers.
We went through many different numbers in our minds. It turned out that no matter how large the number is, there will always be more. From this they concluded that there is no largest number in the world.
As in any mental operation, in induction we can make certain mistakes; the conclusion made may turn out to be insufficiently reliable or completely false. The reliability of inductive inference is achieved not only by increasing the number of cases on which it is based, but also by using a variety of examples in which the unimportant characteristics of objects and phenomena vary.
Inferences like “Some bears are brown” are also inductive. And they are not at all difficult to do. Just watching a few brown bears is enough. It is much more difficult with strong statements like “All bears are brown.” Even after observing a thousand bears, all of which turned out to be brown, we cannot say that all bears are brown, because we do not know whether we have seen all possible bears in the world.
Having interviewed 1,200 respondents during a sociological study, we can find out that all respondents support the politician Vasisualiy Lokhankin. This will be true. However, the inductive conclusion “All residents of our city (country) support Vasisualiy Lokhankin” will remain conjectural and unproven. The only thing that will be proven is that some residents support the said politician. And there is no escaping this fact.
Although inductive reasoning is not precise in a strict, logical sense, it is, of course, of great benefit in everyday use. Having bought spoiled products several times in the same store, one can come to the inductive conclusion that all (many) products from this store are spoiled. After observing how often a person lies, one can draw an inductive conclusion that he generally does not tell the truth.
The mental operation opposite to induction is deduction - an inference made regarding a particular case on the basis of a general proposition. For example, knowing that all numbers whose sum of digits is a multiple of three are divisible by three, we can say that the number 412815 will be divided by three without a remainder. At the same time, knowing that all birch trees shed their leaves for the winter, we can be sure that any individual birch tree will also be without leaves in winter.
Induction through generalizations of varying degrees of accuracy and reliability helps us enrich our knowledge about the world around us. We can say that the picture (model) of the world consists of many different inductive conclusions. In his youth, when a person is studying, he uses the induction operation much more often. In mature years, when the time comes to act, deduction is more often necessary, because it is precisely this that helps in solving specific life problems.
The doctor, having made a specific diagnosis for the patient, based on knowledge of the general patterns of the course of the disease, makes a conclusion about how to treat the particular patient. An experienced auto mechanic, knowing the typical problems of cars of a given model and observing certain symptoms, draws a conclusion about the suspected problems. The buyer, knowing that all ripe bananas are yellow, does not buy green ones.
Like induction, deduction is a rather risky inference. Knowing, for example, that the majority of engineers are men, a school graduate may change her mind about enrolling in a technical university, although she was successful in mathematics and physics at school.
In addition to induction and deduction, logic also distinguishes traduction - inference that is not accompanied by a transition from the particular to the general or vice versa. The most typical example of tradition is analogy. Having a rather vague idea (model) of the object in question, we can turn to analogy, that is, take another object, or rather its model, correct something in this model and use it on the current object. If students, for example, do not really understand how the earth’s crust works, then the teacher can give an analogy with a layer cake.
