Definition of deduction: through the general to the particular. Examples of induction and deduction in economics and other sciences What is deduction in philosophy

DEDUCTION (lat. deductio - inference) - in the broad sense of the word - this form of thinking, when a new thought is derived in a purely logical way (ie, according to the laws of logic) from previous thoughts. Such a sequence of thoughts is called a conclusion, and each component of this conclusion is either a previously proven thought, or an axiom, or a hypothesis. The last thought of this conclusion is called the conclusion.

The processes of deduction at a strict level are described in the calculus of mathematical logic.

In the narrow sense of the word adopted in traditional logic, the term “deduction” is understood as deductive reasoning, i.e. such a conclusion, as a result of which new knowledge about an object or group of objects is obtained on the basis of some knowledge already available about the objects under study and application to them some rule of logic.

Deductive reasoning, which is the subject of traditional logic, is used by us whenever we need to consider a phenomenon on the basis of a general position already known to us and draw the necessary conclusion regarding this phenomenon. We know, for example, the following specific fact - "a given plane intersects a ball" and the general rule for all planes intersecting a ball - "every section of a ball by a plane is a circle." Applying this general rule to a specific fact, every right-thinking person will necessarily come to the same conclusion: "then this plane is a circle."

In this case, the line of reasoning will be as follows: if a given plane intersects a ball, and any section of a ball by a plane is a circle, then, consequently, this plane is a circle. As a result of this conclusion, new knowledge about this plane was obtained, which is not directly contained either in the first thought or in the second, taken separately from each other. The conclusion that the given plane is a circle” was obtained as a result of combining these thoughts in a deductive inference.

The structure of deductive reasoning and the coercive nature of its rules, which make it necessary to accept a conclusion that logically follows from the premises, reflected the most common relations between objects of the material world: the relations of the genus, species and individual, i.e., the general, the particular and the individual. The essence of these relations is as follows: what is inherent in all species of a given genus is inherent in any species; what is inherent in all individuals of the genus is inherent in each individual. For example, what is inherent in all species of a given genus is inherent in any species; what is inherent in all individuals of the genus is inherent in each individual. For example, what is inherent in all nerve cells (for example, the ability to transmit information), is inherent in every cell, unless, of course, it has died. But this is exactly what was reflected in the deductive reasoning: the individual and the particular are subsumed under the general. Billions of times observing the relationship between species, genus and individual in objective reality in the process of practical activity, a person has developed an appropriate logical figure, which then acquires the status of a rule of deductive reasoning.

Deduction plays a big role in our thinking. Whenever we bring a particular fact under a general rule and then draw some conclusion from the general rule about that particular fact, we are inferring in the form of a deduction. And if the premises are true, then the correctness of the conclusion will depend on how strictly we adhered to the rules of deduction, which reflected the patterns of the material world, objective connections and relations of the universal and the singular. Deduction plays a certain role in all cases when it is required to verify the correctness of the construction of our reasoning. So, in order to make sure that the conclusion really follows from the premises, which sometimes are not even all expressed, but only implied, we give the deductive reasoning the form of a syllogism: we find a large premise, bring a smaller premise under it, and then deduce the conclusion. At the same time, we pay attention to how the rules of the syllogism are observed in the conclusion. The use of deduction based on the formalization of reasoning makes it easier to find logical errors and contributes to a more accurate expression of thought.

But it is especially important to use the rules of deductive reasoning based on the formalization of the corresponding reasoning for mathematicians who seek to give an accurate analysis of these reasoning, for example, in order to prove their consistency.

The theory of deduction was first elaborated by Aristotle. He found out the requirements that individual thoughts that make up a deductive inference must meet, defined the meaning of terms and revealed the rules for certain types of deductive reasoning. The positive side of the Aristotelian doctrine of deduction is that it reflects the real patterns of the objective world.

The reassessment of deduction and its role in the process of cognition is especially characteristic of Descartes. He believed that a person comes to the knowledge of things in two ways: through experience and deduction. But experience often leads us astray, while deduction, or, as Descartes said, pure inference from one thing through the mediation of another, is free from this shortcoming. At the same time, the main drawback of the Cartesian theory of deduction is that, from his point of view, the initial provisions for deduction, in the end, are allegedly given by intuition, or the ability of internal contemplation, thanks to which a person cognizes the truth without the participation of the logical activity of consciousness. This leads Descartes in the end to the idealist doctrine that the initial propositions of deduction are obvious truths because the ideas that compose them are "innate" to our mind from the beginning.

Philosophers and logicians of the empirical direction, who opposed the teachings of rationalists on "innate" ideas, at the same time belittled the importance of deduction. Thus, a number of English bourgeois logicians tried to completely deny any independent significance of deduction in the thought process. They reduced all logical thinking to mere induction. So the English philosopher D. S. Mill argued that deduction does not exist at all, that deduction is only a moment of induction. In his opinion, people always conclude from observed cases to observed cases, and the general idea with which deductive reasoning begins is just a verbal turn denoting the summation of those cases that were in our observation, only a record of individual cases, made for convenience. . Isolated cases, in his opinion, represent the only basis for the conclusion.

The English philosopher Fr. Bacon. But Bacon was not nihilistic about the syllogism. He spoke only against the fact that in "ordinary logic" almost all attention is focused on the syllogism, to the detriment of another way of reasoning. It is perfectly clear that Bacon has in mind a scholastic syllogism, divorced from the study of nature and based on premises taken from pure speculation.

In the later development of English philosophy, induction was increasingly exalted at the expense of deduction. Baconian logic degenerated into one-sided inductive, empirical logic, the main representatives of which were W. Wevel and D. S. Mill. They rejected Bacon's words that a philosopher should not become like an empiricist - an ant, but also not like a spider - a rationalist, who weaves a cunning philosophical web from his own mind. They forgot that, according to Backen, a philosopher should be like a bee that collects tribute in the fields and meadows and then produces honey from it.

In the process of studying induction and deduction, one can consider them separately, but in reality, said the Russian logician Rudkovsky, all the most important and extensive scientific research uses one of them as much as the other, because any complete scientific research consists in combining inductive and deductive methods. thinking.

The metaphysical view of deduction and induction was sharply condemned by F. Engels. He said that the bacchanalia with induction comes from the English, who invented the opposite of induction and deduction. The logicians who exaggerated the importance of induction were ironically called by Engels "all-inductivists". Induction and deduction only in the metaphysical representation are mutually opposed and mutually exclusive.

The metaphysical break between deduction and induction, their abstract opposition to each other, the distortion of the actual relationship between deduction and induction are also characteristic of modern bourgeois science. Some bourgeois philosophers of the theological persuasion proceed from an anti-scientific idealistic solution of the philosophical question, according to which the idea, the concept, is given eternally, from God.

In contrast to idealism, Marxist philosophical materialism teaches that all deduction is the result of a preliminary inductive study of the material. In turn, induction is truly scientific only when the study of individual particular phenomena is based on the knowledge of some already known general laws for the development of these phenomena. At the same time, the process of cognition begins and proceeds simultaneously deductively and inductively. This correct view of the relationship between induction and deduction was first proved by Marxist philosophy. “Induction and deduction are interconnected in the same necessary way,” writes F. Engels, “as synthesis and analysis. Instead of unilaterally exalting one of them to the skies at the expense of the other, one should try to apply each in its place, and this can be achieved only if one does not lose sight of their connection with each other, their mutual complementation of each other.

In right thinking, therefore, both induction and deduction are equally important. They constitute two inseparable sides of a single process of cognition, which complement each other. It is impossible to imagine such a thinking, which is carried out only inductively or only deductively. Induction in the process of real experimental research is carried out in close connection with deduction. This is precisely what makes it possible to come to quite reliable conclusions in the process of such a study. This means that in scientific and everyday thinking on any issue, deduction and induction are always closely related to each other, are inseparable from each other, are in an inseparable unity.

Classical Aristotelian logic has already begun to formalize deductive inference. Further, this trend was continued by mathematical logic, which develops problems of formal inference in deductive reasoning.

The term "deduction" in the narrow sense of the word also means the following:

The research method is as follows: in order to

to obtain new knowledge about an object or a group of homogeneous objects, it is necessary, firstly, to find the nearest genus, which includes these objects, and, secondly, to apply to them the appropriate law inherent in the entire given genus of objects; transition from knowledge of more general provisions to knowledge of less general provisions. The deductive method plays a huge role in mathematics. It is known that all provable propositions, that is, theorems, are deduced in a logical way using deduction from a small finite number of initial principles provable within the framework of a given system, called axioms.

The classics of Marxism-Leninism have repeatedly pointed to deduction as a research method. So, speaking about classification in biology, Engels noted that thanks to the success of the theory of development, the classification of organisms is reduced to "deduction", to the doctrine of origin, when a species is literally deduced from another. Engels refers deduction, along with induction, analysis and synthesis, to the methods of scientific research. But at the same time, he points out that all these means of scientific research are elementary. Therefore, deduction as an independent method of cognition is not enough for a comprehensive study of reality. The connection of a single object with a species, a species with a genus, which is displayed in deduction, is only one of the sides of the infinitely diverse connection of objects and phenomena of the objective world.

The form of presentation of material in a book, lecture, report, conversation, when from general provisions, rules, laws go to less general provisions, rules, laws.

deductive method

Let's make a small digression into the history of philosophy.

The founder of the deductive method of cognition is the ancient Greek philosopher Aristotle (364 - 322 BC). He developed the first theory of deductive reasoning (categorical syllogisms), in which the conclusion (consequence) is obtained from premises according to logical rules and has a reliable character. This theory is called syllogistic. On its basis, the proof theory is built.

The logical works (tracts) of Aristotle were later united under the name "Organon" (a tool, a tool for cognizing reality). Aristotle clearly preferred deduction, so the Organon is usually identified with the deductive method of cognition. It should be said that Aristotle also explored inductive reasoning. He called them dialectical and contrasted them with the analytical (deductive) conclusions of syllogistics.

The English philosopher and naturalist F. Bacon (1561 - 1626) developed the foundations of inductive logic in his work The New Organon, which was directed against Aristotle's Organon. Syllogistics, according to Bacon, is useless for discovering new truths; at best, it can be used as a means of verifying and substantiating them. According to Bacon, inductive conclusions are a reliable, effective tool for the implementation of scientific discoveries. He developed inductive methods for establishing causal relationships between phenomena: similarities, differences, concomitant changes, residues. The absolutization of the role of induction in the process of cognition led to a weakening of interest in deductive cognition.

However, the growing successes in the development of mathematics and the penetration of mathematical methods into other sciences already in the second half of the 17th century. revived interest in deduction. This was also facilitated by rationalistic ideas recognizing the priority of reason, which were developed by the French philosopher, mathematician R. Descartes (1596 - 1650) and the German philosopher, mathematician, logician G. W. Leibniz (1646 - 1716).

R. Descartes believed that deduction leads to the discovery of new truths if it deduces a consequence from reliable and obvious provisions, which are the axioms of mathematics and mathematical natural science. In the work "Discourse on the method for a good direction of the mind and the search for truth in the sciences", he formulated four basic rules for any scientific research: 1) only what is known, verified, proven is true; 2) to divide the complex into simple; 3) ascend from simple to complex; 4) explore the subject comprehensively, in all details.

GW Leibniz argued that deduction should be applied not only in mathematics, but also in other areas of knowledge. He dreamed of a time when scientists would be engaged not in empirical research, but in calculations with a pencil in their hands. To this end, he sought to invent a universal symbolic language with which to rationalize any empirical science. New knowledge, in his opinion, will be the result of calculations. Such a program cannot be implemented. However, the very idea of ​​formalizing deductive reasoning laid the foundation for the emergence of symbolic logic.

It should be emphasized that attempts to separate deduction and induction from each other are unfounded. In fact, even the definitions of these methods of cognition testify to their relationship. Obviously, deduction uses as premises various kinds of general propositions that cannot be obtained through deduction. And if there were no general knowledge gained by induction, then deductive reasoning would be impossible. In turn, deductive knowledge about the individual and the particular creates the basis for further inductive research of individual objects and obtaining new generalizations. Thus, in the process of scientific knowledge, induction and deduction are closely interconnected, complement and enrich each other.

Deduction it is a way of reasoning from general provisions to particular conclusions.

Deductive reasoning only concretizes our knowledge. The deductive conclusion contains only the information that is in the received premises. Deduction allows you to get new truths from existing knowledge with the help of pure reasoning.

Deduction gives a 100% guarantee of the correct conclusion (with reliable premises). Deduction from truth yields truth.

Example 1

All metals are plastic(b about the only valid premise or main argument).

Bismuth is a metal(valid posting).

Therefore, bismuth is plastic(correct conclusion).

Deductive reasoning that provides a true conclusion is called a syllogism.

Example 2

All politicians who allow contradictions are a laughingstock(b about the most reliable premise).

E ltsin B. N. allowed contradictions(valid posting).

Therefore, E.B.N. is a laughingstock(correct conclusion) .

Deduction from a lie gives a lie.

Example.

The help of the International Monetary Fund always and everyone leads to prosperity(false premise).

Russia has long been assisted by the IMF(valid posting).

Therefore, Russia is flourishing(false conclusion).

Induction - a way of reasoning from particular provisions to general conclusions.

The inductive conclusion may contain information that is not present in the received premises. The validity of the premises does not mean the validity of the inductive conclusion. The premises give the conclusion greater or lesser probability.

Induction gives not reliable, but probabilistic knowledge that needs verification.

Example 1

G. M. S. - pea jester, E. B. N. - pea jester, C. A. B. - pea jester(valid postings).

G. M. S., E. B. N., C. A. B. – politicians(valid postings).

Therefore, all politicians are pea jesters(probabilistic conclusion).

The generalization is correct. However, there are politicians who can think.

Example 2

AT last years in area 1, in area 2 and in area 3 military exercises were carried out - the combat capability of units increased(valid postings).

In area 1, in area 2 and in area 3 units of the Russian Army took part in the exercises(valid postings).

Consequently, in recent years, combat capability has increased in all units of the Russian Army.(inductive unreliable conclusion).

From particular provisions does not follow a logically general conclusion. Display events do not prove that prosperity is everywhere and everywhere:

In fact, the overall combat effectiveness of the Russian Army is declining catastrophically.

A variant of induction is a conclusion by analogy (based on the similarity of two objects in one parameter, a conclusion is made about their similarity in other parameters as well).

Example. The planets Mars and Earth are similar in many ways. There is life on earth. Since Mars is similar to Earth, there is also life on Mars.

This conclusion is, of course, only probabilistic.

With the help of deduction, truth is revealed both in the natural sciences and in everyday life. People use the ability to reason logically, which in the general sense is deduction in everyday life, at work, in games and other activities not related to science. The science of logic investigates these processes. Deduction, on the other hand, is based on the isolation of the particular from general judgments by means of logically processed inferences. For a better understanding of the subject of discussion, it is necessary to understand what deduction is and explore all the points related to it.

What is an inference?

First you need to understand, Logic considers this concept as a form of thinking, in which a new judgment (that is, a conclusion or conclusion) is born from several messages (forms of judgments).

For example:

1. All living organisms consume moisture.
2. All plants are living organisms.
3. Conclusion - all plants consume moisture.

So, the first and second judgments in this example are the message, and the third is the conclusion (conclusion). Incorrect one of the sends can lead to If the sends are not connected, the conclusion cannot be made.

Inferences are divided into mediated and direct. In the latter, the conclusion is drawn from one message. That is, they are transformed simple propositions.

In indirect inferences, the analysis of several messages leads to the formation of a conclusion. Such conclusions are divided into three types: deductive, inductive and conclusions by analogy. Let's consider each of them.

deductive reasoning

Inference based on deduction provides a conclusion for a particular case from a general rule.

For example:

1. Monkeys love bananas.
2. Lucy is a monkey.
3. Inference: Lucy loves bananas.

In this example, the first message is a general rule, in the second - a particular case is included in the general rule and, as a result, on this basis, a conclusion is made regarding this particular case. If all monkeys love bananas, and Lucy is one of them, then she loves them too. An example clearly explains what deduction is. It is a movement from more to less, from the general to the particular, in which the aspect of knowledge narrows down, provoking a valid conclusion.

inductive reasoning

The opposite of deductive is inductive reasoning, in which a general pattern is derived from some particular cases.

For example:

1. Vasya has a head.
2. have a head.
3. Kolya has a head.
4. Vasya, Petya and Kolya are people.
5. Conclusion - all people have a head.

In this case, the first three messages are special cases, generalized by the fourth one under one class of objects, and in conclusion it is said about the general rule for all objects of this class. Unlike deduction, in inductive inferences, reasoning goes from less to more, from the particular to the general, therefore, the conclusions are not reliable, but probabilistic. After all, the transfer of special cases to a general group is fraught with errors, since in any cases there may be exceptions. The probabilistic nature of induction is, of course, a minus, but there is a huge plus in comparison with deduction. What is deduction? working on the narrowing of knowledge, its concretization, analysis and analysis of known facts. Induction, on the contrary, encourages the expansion of knowledge, the creation of something new, the synthesis of new conclusions and judgments.

Analogy

The next type of inference is based on analogy, that is, the similarity of objects to each other is evaluated. If objects are similar in some features, their similarity in others is also allowed.

An example of inference by analogy is the testing of large ships in a pool, in which their properties are mentally transferred to the open water expanses of the seas and oceans. The same principle is used to study the properties of micromodels of bridges.

It should be remembered that the conclusions of analogy, like induction, are probabilistic.

What is the use of deduction?

As already mentioned at the beginning of the article, any person can make a deductive reasoning in the process of life, and such conclusions affect many areas of life besides scientific ones. The deductive way of thinking is very useful for law enforcement, investigative and judicial officials (for the "Sherlocks" of our time).

But no matter what a person does, deduction will always come in handy. In professional activities, it will allow you to make the most rational and competent far-sighted decisions, in your studies - to master the subject faster and more thoroughly, and in everyday life - to better build relationships with people and understand others.

Methods for developing deduction

Many people these days are striving for self-development and tend to come to understand the importance of having good deductive reasoning. How to develop deduction correctly?

The development of deduction can be facilitated by special games, as well as the introduction of a new way of thinking into everyday life. The main tips for its development can be grouped into the following blocks:

1. Awakening interest. Any material that is studied should be of interest. This will allow you to better understand all the subtleties of the subject and achieve the desired level of understanding.
2. Depth of study. You can not study subjects superficially, only a thorough analysis will give a positive result.
3. Broad outlook. People with developed thinking often have knowledge in many areas of life - culture, music, sports, science, etc.
4. Flexibility of thinking. What is deduction without flexibility of thought? It's practically useless. In order to develop such flexibility, it is necessary to try to bypass the recognized paths and schemes by all, to find new aspects of the vision of the issue that will prompt the correct and sometimes unexpected solution. A critical approach to even the most ordinary and familiar situations will allow you to make the best and, most importantly, independent decision.
5. Combination. Try to think at the same time in different ways - combine inductive and deductive reasoning.

DEDUCTION

DEDUCTION

(from Latin deductio - derivation) - the transition from premises to conclusion, based on, due to which it follows with logical necessity from the accepted premises. Feature D. lies in the fact that from the true premises it always leads only to the true conclusion.
D. as a conclusion based on the law and necessarily giving a true conclusion from true premises, is opposed to -, not based on the law of logic and leading from true premises to a probable, or problematic, conclusion.
Deductive are, for example, inferences:
If the ice is heated, it melts.
The ice is heating up.
The ice is melting.
The line separating from the conclusion stands instead of the word "therefore".
Reasoning can serve as examples of induction:
Brazil is a republic; Argentina is a republic.
Brazil and Argentina are South American states.
All South American states are republics.
Italy is a republic; Portugal is a republic; Finland is a republic; France is a republic.
Italy, Portugal, Finland, France - Western European countries.
All Western European countries are republics.
Inductive reasoning relies on some factual or psychological foundation. In such a conclusion, the conclusion may contain information not found in the premises. The veracity of the premises does not therefore mean the veracity of the inductive assertion derived from them. The conclusion of the induction is problematic and needs further investigation. So, the premises of both the first and second inductive inferences given are true, but the conclusion of the first of them is true, and the second is false. Indeed, all South American states are republics; but among the Western European countries there are not only republics, but also monarchies.
Especially characteristic of D. are logical transitions from general knowledge to a particular type:
All people are mortal.
All Greeks are people.
All Greeks are mortal.
In all cases when it is required to consider some kind of general rule on the basis of an already known general rule and draw the necessary conclusion regarding this phenomenon, we conclude in the form of D. Reasoning leading from knowledge about a part of objects (particular knowledge) to knowledge about all objects of a certain class (general knowledge) are typical inductions. There always remains something that turns out to be hasty and unreasonable (“Socrates is a skillful debater; Plato is a skillful debater; therefore, everyone is a skillful debater”).
At the same time, it is impossible to identify D. with the transition from the general to the particular, and induction with the transition from the particular to the general. In reasoning “Shakespeare wrote sonnets; therefore, it is not true that Shakespeare did not write sonnets” is D., but there is no transition from the general to the particular. The argument "If aluminum is ductile or clay is ductile, then aluminum is ductile" is commonly thought to be inductive, but there is no transition from the particular to the general. D. is the derivation of conclusions that are as reliable as the accepted premises, induction is the derivation of probable (plausible) conclusions. Inductive reasoning includes both transitions from the particular to the general, and the canons of induction, etc.
Deductive reasoning makes it possible to obtain new truths from existing knowledge, and, moreover, with the help of pure reasoning, without resorting to experience, intuition, common sense, etc. D. gives a 100% guarantee of success. Starting from true premises and reasoning deductively, we will certainly obtain reliable in all cases.
One should not, however, tear D. away from induction and underestimate the latter. Almost all general propositions, including scientific laws, are the results of inductive generalization. In this sense, induction is the basis of our knowledge. By itself, it does not guarantee its truth and validity, but it generates assumptions, connects them with experience and thereby gives them a certain plausibility, a more or less high degree of probability. Experience is the source and foundation of human knowledge. Induction, starting from what is comprehended in experience, is a necessary means of its generalization and systematization.
In ordinary reasoning, D. only in rare cases appears in a complete and expanded form. Most often, not all used parcels are indicated, but only some. General statements that seem well known are omitted. The conclusions following from the accepted premises are not always explicitly formulated either. The logical one itself, which exists between the original and derivable statements, is only sometimes marked by words like “therefore” and “means”. Often, D. is so abbreviated that one can only guess about it. It is cumbersome to conduct deductive reasoning without omitting or reducing anything. However, whenever it arises in the validity of the conclusion made, it is necessary to return to the beginning of the reasoning and reproduce it in the fullest possible form. Without this, it is difficult or even impossible to detect the mistake made.
Deductive is the derivation of the justified position from other, previously adopted provisions. If the proposed proposition can be logically (deductively) deduced from the already established propositions, this means that it is acceptable to the same extent as these propositions themselves. The justification of some statements by referring to or the acceptability of other statements is not the only one performed by D. in the processes of argumentation. Deductive reasoning also serves to verify (indirectly confirm) statements: from the verified position, its empirical consequences are deductively derived; of these consequences is evaluated as an inductive argument in favor of the original position. Deductive reasoning is also used to falsify statements by showing that their consequences are false. Failed verification is a weakened version of verification: failure to disprove the empirical consequences of the hypothesis being tested is an argument, albeit a very weak one, in support of this hypothesis. And finally, D. is used to systematize a theory or system of knowledge, to trace the logical connections of its constituent statements, to build explanations and understandings based on the general principles offered by the theory. The clarification of the logical structure of the theory, the strengthening of its empirical base and the identification of its general premises is a contribution to the statements included in it.
Deductive reasoning is universal, applicable in all areas of reasoning and in any audience. “And if blessedness is nothing but eternal life, and eternal life are truths, then blessedness is nothing but the knowledge of the truth” - John Scotus (Eriugena). This theological reasoning is deductive reasoning, viz.
The share of deductive reasoning in different fields of knowledge is significantly different. It is used very widely in mathematics and mathematical physics, and only sporadically in history or aesthetics. Bearing in mind the scope of D.'s application, Aristotle wrote: "Scientific evidence should not be required from the speaker, just as emotional persuasion should not be required from the speaker." Deductive reasoning is a very powerful tool, but, like anything else, it must be used narrowly. An attempt to build an argument in the form of D. in those areas or in that audience that are not suitable for this, leads to superficial reasoning that can only create the illusion of persuasiveness.
Depending on how widely deductive reasoning is used, all sciences are usually divided into deductive and inductive. In the former, deductive reasoning is predominantly or even exclusively used. Secondly, such argumentation plays only a deliberately auxiliary role, and in the first place is empirical argumentation, which has an inductive, probabilistic one. Mathematics is considered a typical deductive science; examples of inductive sciences are. However, the sciences into deductive and inductive, widespread even in the beginning. 20th century, now largely lost its own. It is oriented towards science, considered in statics, as a system of reliably and definitively established truths.
The concept of "D." is a general methodological concept. In logic it corresponds to evidence.

Philosophy: Encyclopedic Dictionary. - M.: Gardariki. Edited by A.A. Ivina. 2004 .

DEDUCTION

(from lat. deductio - derivation), the transition from the general to the particular; in more specialist. meaning "D." means logical. withdrawal, i.e. transition according to certain rules of logic from some given sentences-parcels to their consequences (conclusions). The term "D." is also used to denote specific conclusions of consequences from premises (i.e. as the term " " in one of its meanings), and as a generic name for the general theory of constructing correct conclusions (inference). Sciences whose proposals preim., are obtained as a consequence of certain general principles, postulates, axioms, it is accepted called deductive (mathematics, theoretical mechanics, certain sections of physics and others) , and the axiomatic method by which these particular propositions are deduced is often called axiomatic-deductive.

D.'s study makes ch. the task of logic; sometimes formal logic is even defined as the theory of logic, although it is far from being the only one that studies the methods of logic: it studies the implementation of logic in the process of real individual thinking, but as one of main (along with others, in particular various forms of induction) methods scientific knowledge.

Although the term "D." first used, but apparently by Boethius, the concept of D. - as c.-l. sentences by means of a syllogism - appears already in Aristotle ("First Analytics"). In philosophy and logic, cf. centuries and modern times, there were different views on the role of D. in a number of others methods of knowledge. So, Descartes contrasted D. intuition, by means of a cut, but in his opinion, human. "directly sees" the truth, while D. delivers to the mind only "indirect" (obtained by reasoning) knowledge. F. Bacon, and later others English logician "inductivists" (W. Whewell, J. S. Mill, A. Bain and others) considered D. "secondary" method, while true knowledge, in their opinion, gives only induction. Leibniz and Wolff, proceeding from the fact that D. does not provide “new facts,” precisely on this basis, they came to the opposite conclusion: the knowledge obtained through D. is “true in all possible worlds.”

D.'s questions began to be intensively developed from the end of the 19th century. in connection with the rapid development of mathematics. logic, elucidation of the foundations of mathematics. This led to the expansion of the means of deductive proof (for example, the "") was developed, to the refinement of the plural. concepts of deduction (for example, the concept of logical consequence), the introduction of new problems in the theory of deductive proof (for example, questions about consistency, completeness of deductive systems, decidability), etc.

Development of questions of D. in the 20th century. associated with the names of Boole, Frege, Peano, Poretsky, Schroeder, Peirce, Russell, Gödel, Hilbert, Tarski, and others. So, for example, Boole believed that D. consists only in the exclusion (elimination) of middle terms from premises. Generalizing Boole's ideas and using his own algebological methods, Russian the logician Poretsky showed that such a logic is too narrow (see "On the methods of solving logical equalities and on the inverse method of mathematical logic", Kazan, 1884). According to Poretsky, D. does not consist in the exclusion of middle terms, but in the exclusion of information. The process of eliminating information is that when moving from logical. expressions L = 0 to one of its consequences, it is enough to discard it in its left part, which is a logical. polynomial in perfect normal form, some of its constituents.

V. modern. bourgeois philosophy is very common is the excessive exaggeration of the role of D. in knowledge. In a number of works on logic, it is customary to emphasize that supposedly excludes completely. the role that D. plays in mathematics, in contrast to other scientific. disciplines. Emphasizing this "difference", they come to the conclusion that all sciences can be divided into so-called. deductive and empirical. (See, for example, L. S. Stebbing, A modern introduction to logic, L., 1930). However, such a distinction is fundamentally unjustified and it is denied not only by scientists who stand on dialectical-materialistic. positions, but also some bourgeois. researchers (eg, J. Lukasevich; see. Lukasevich, Aristotelian from the point of view of modern formal logic, translated from English, M., 1959), who realized that both logical and mathematical. axioms are ultimately a reflection of some experiments with the material objects of the objective world, actions on them in the process of social-historical. practices. In this sense, the mathematical axioms do not oppose the provisions of the sciences and society. An important feature of D. is its analytical. character. Mill also noted that there is nothing in the conclusion of deductive reasoning that would not already be contained in its premises. To describe the analytic the nature of deductive consequence is formal; let us resort to the exact language of the algebra of logic. Let us assume that deductive reasoning is formalized by means of the algebra of logic, i.e. the relations between the volumes of concepts (classes) are precisely fixed both in the premises and in the conclusion. Then it turns out that the decomposition of premises into constituents of (elementary) units contains all those constituents that are present in the decomposition of the corollary.

In view of the special significance that the disclosure of premises acquires in any deductive conclusion, D. is often associated with analysis. Since, in the process of D. (in the deduction of a deductive reasoning), the knowledge that is given to us in sep. sendings, D. connect with synthesis.

The only correct methodological The solution to the question of the relationship between D. and induction was given by the classics of Marxism-Leninism. D. is inextricably linked with all other forms of inference, and above all with induction. Induction is closely related to D., since. any individual can be understood only through its image in an already established system of concepts, and D., in the final analysis, depends on observation, experiment, and induction. D. without the help of induction can never provide knowledge of objective reality. "Induction and deduction are as necessarily related as synthesis and analysis. Instead of one-sidedly exalting one of them to the skies at the expense of the other, one should try to apply each in its place, and this can only be achieved if not lose sight of their connection with each other, their mutual complement to each other" (Engels F., Dialectics of Nature, 1955, pp. 180–81). The content of the premises of deductive reasoning is not given in advance in finished form. The general proposition, which must certainly be in one of the premises of D., is always the result of a comprehensive study of a multitude of facts, a deep generalization of regular connections and relations between things. But even one induction is impossible without D. Characterizing Marx's "Capital" as a classic. dialectical approach to reality, Lenin noted that in "Capital" induction and D. coincide (see "Philosophical Notebooks", 1947, pp. 216 and 121), thereby emphasizing their inseparable connection in the process of scientific. research.

D. sometimes apply for the purpose of check to. - l. judgments when consequences are derived from it according to the rules of logic in order to then verify these consequences in practice; this is one of the methods for testing hypotheses. D. are also used in the disclosure of the content of certain concepts.

Lit.: Engels F., Dialectics of Nature, Moscow, 1955; Lenin V.I., Soch., 4th ed., vol. 38; Aristotle, Analysts One and Two, trans. from Greek., M., 1952; Descartes R., Rules for the guidance of the mind, trans. from Lat., M.–L., 1936; his own, Reasoning about the method, M., 1953; Leibniz G. V., New about the human mind, M.–L., 1936; Karinsky M.I., Classification of conclusions, in the collection: Izbr. works of Russian logicians of the 19th century, M., 1956; Lyar L., English reformers of logic in the 19th century, St. Petersburg, 1897; L. Couture, Algebra of Logic, Odessa, 1909; Povarnin S., Logic, part 1 - The general doctrine of proof, P., 1915; Gilbert D. and Ackerman V., Fundamentals of theoretical logic, trans. from German., M., 1947; Tarsky A., Introduction to the logic and methodology of deductive sciences, trans. from English, M., 1948; Asmus V. Φ., The doctrine of logic about proof and refutation, M., 1954; Boole G., An investigation of the laws of thought..., N. Y., 1951; Schröder E., Vorlesungenüber die Algebra der Logik, Bd 1–2, Lpz., 1890–1905; Reichenbach H. Elements of symbolic logic, N. Y., 1948.

D. Gorsky. Moscow.

Philosophical Encyclopedia. In 5 volumes - M .: Soviet Encyclopedia. Edited by F. V. Konstantinov. 1960-1970 .

DEDUCTION

DEDUCTION (from lat. deductio - derivation) - the transition from the general to the particular; in a more special sense, the term “deduction” denotes the process of logical inference, i.e., the transition, according to certain rules of logic, from some given sentences-parcels to their consequences (conclusions). The term "deduction" is used both to designate specific conclusions of consequences from premises (that is, as a synonym for the term "inference" in one of its meanings), and as a generic name for the general theory of constructing correct conclusions. The sciences, the proposals of which are predominantly obtained as a consequence of certain general principles, postulates, axioms, are usually called deductive (mathematics, theoretical mechanics, some branches of physics, etc.), and the axiomatic method by which the conclusions of these particular proposals are made is axiomatic-deductive.

The study of deduction constitutes the task of logic; sometimes formal logic is even defined as the theory of deduction. Although the term "deduction" was first used, apparently, by Boethius, the concept of deduction - as a proof of a sentence by means of a syllogism - appears already in Aristotle ("First Analytics"). In the philosophy and logic of modern times, there were different views on the role of deduction in a number of methods of cognition. Thus, Descartes contrasted deduction with intuition, through which, in his opinion, the mind “directly sees” the truth, while deduction delivers only “mediated” (obtained by reasoning) knowledge to the mind. F. Bacon, and later other English “inductivist” logicians (W. Whewell, J. S. Mill, A. Bain, and others) considered deduction a “secondary” method, while only induction gives true knowledge. Leibniz and Wolf, proceeding from the fact that deduction does not give “new facts”, precisely on this basis, they came to the opposite conclusion: the knowledge obtained by deduction is “true in all possible worlds”. The relationship between deduction and induction was revealed by F. Engels, who wrote that “induction and deduction are interconnected in the same necessary way as synthesis and analysis. Instead of unilaterally exalting one of them to the skies at the expense of the other, one must try to apply each of them in its place, and this can only be achieved if one does not lose sight of their connection with each other, their mutual complementation of each other” ( Marx K., Engels F. Soch., vol. 20, pp. 542-543), the following provision applies to applications in any field: everything that is contained in any logical truth obtained through deductive reasoning is already contained in the premises from which it is derived . Each application of the rule consists in the fact that the general provision applies (applies) to some specific (private) situation. Some rules of inference fall under this characterization in a very explicit way. So, for example, various modifications of the so-called. the substitution rules state that the property of provability (or deducibility from a given system of premises) is preserved under any replacement of elements of an arbitrary formula of a given formal theory by concrete expressions of the same kind. The same applies to the widespread method of specifying axiomatic systems by means of the so-called. schemes of axioms, i.e., expressions that turn into specific axioms after substitution instead of the general designations of the specific formulas of a given theory included in them. Deduction is often understood as the process of logical consequence itself. This determines its close connection with the concepts of inference and consequence, which is also reflected in logical terminology. So, “the deduction theorem” is usually called one of the important relationships between the logical connective of implication (formalizing the verbal turnover “if ... then ...”) and the relation of logical consequence (deducibility): if the consequence B is deduced from the premise A, then the implication AeV (“if A... then B...”) is provable (that is, derivable already without any premises, from axioms alone). Other logical terms connected with the concept of deduction have a similar character. Thus, sentences deduced from each other are called deductively equivalent; a deductive system (with respect to some property) consists in the fact that all expressions of a given system that have this property (eg, true under some interpretation) are provable in it.

The properties of deduction were revealed in the course of constructing specific logical formal systems (calculus) and the general theory of such systems (the so-called proof theory). Lit .: Tarsky A. Introduction to the logic and methodology of deductive sciences, trans. from English. M., 1948; Asmus VF Doctrine of logic about proof and refutation. M., 1954.

TRANSCENDENTAL DEDUCTION (German: transzendentale Deduktion) is the key section of I. Kant's Critique of Pure Reason. The main task of deduction is to substantiate the legitimacy of the a priori application of categories (elementary concepts of pure reason) to objects and show them as principles of a priori synthetic knowledge. The need for transcendental deduction was recognized by Kant 10 years before the release of the Critique, in 1771. The central deduction was first formulated in handwritten sketches in 1775. The text of the deduction was completely revised by Kant in the 2nd edition of the Critique. The solution of the main task of deduction implies the proof of the thesis, which constitute the necessary possibilities of things. The first part of the deduction (“objective deduction”) specifies that such things, in principle, can only be objects of possible experience. The second part (“subjective deduction”) is the desired proof of the identity of the categories with the a priori conditions of possible experience. The starting point of deduction is the notion of apperception. Kant claims that all representations possible for us must be connected in the unity of apperception, i.e., in the I. Necessary conditions for such a connection are categories. The proof of this central position is carried out by Kant through an analysis of the structure of objective judgments of experience based on the use of categories, and the postulate of the parallelism of the transcendental object and the transcendental unity of apperception (this allows one to “reverse” categorical syntheses to I to refer representations to the object). As a result, Kant concludes that all possible perceptions as conscious, i.e. related to the I, intuitions are necessarily subordinate to categories (first Kant shows that this is true with respect to “intuitions in general”, then with respect to “our intuitions” in space and time) . This means the possibility of anticipation of objective forms of experience, i.e., a priori knowledge of the objects of possible experience with the help of categories. Within the framework of deduction, Kant develops the doctrine of cognitive abilities, among which a special role is played by imagination, which also connects reason. It is the imagination, obeying the categorical “instructions”, that formalizes phenomena in a lawful manner. Kant's deduction of categories has given rise to numerous discussions in modern historical and philosophical literature.

Dictionary of foreign words of the Russian language

Deduction (lat. deductio - inference) is a method of thinking, the consequence of which is a logical conclusion, in which a particular conclusion is derived from a general one. A chain of inferences (reasoning), where the links (statements) are interconnected by logical conclusions.

The beginning (premises) of deduction are axioms or simply hypotheses that have the character of general statements (“general”), and the end is consequences from premises, theorems (“special”). If the premises of a deduction are true, then so are its consequences. Deduction is the main means of logical proof. The opposite of induction.

An example of a simple deductive reasoning:

1. All people are mortal.
2. Socrates is a man.
3. Therefore, Socrates is mortal.

The method of deduction is opposed to the method of induction - when the conclusion is made on the basis of reasoning going from the particular to the general.

for example:

• the Yenisei Irtysh and Lena rivers flow from south to north;
• the Yenisei, Irtysh and Lena rivers are Siberian rivers;
• therefore, all Siberian rivers flow from south to north.

Of course, these are simplified examples of deduction and induction. Inferences should be based on experience, knowledge and concrete facts. Otherwise, it would not be possible to avoid generalizations and draw erroneous conclusions. For example, "All men are deceivers, so you are a deceiver too." Or "Vova is lazy, Tolik is lazy and Yura is lazy, so all men are lazy."

In everyday life, we use the simplest variants of deduction and induction without even realizing it. For example, when we see a disheveled person who rushes headlong, we think - he must be late for something. Or, looking out the window in the morning and noticing that the asphalt is strewn with wet leaves, we can assume that it was raining at night and there was a strong wind. We tell the child not to sit up late on a weekday, because we assume that then he will oversleep school, not have breakfast, etc.

History of the method

The term "deduction" itself was first used, apparently, by Boethius ("Introduction to the categorical syllogism", 1492), the first systematic analysis of one of the varieties of deductive reasoning - syllogistic reasoning- was carried out by Aristotle in the "First Analytics" and significantly developed by his ancient and medieval followers. Deductive reasoning based on the properties of propositional logical connectives, were studied in the school of the Stoics and especially in detail in medieval logic.

The following important types of inferences have been identified:

• conditionally categorical (modus ponens, modus tollens)
• divisive-categorical (modus tollendo ponens, modus ponendo tollens)
• conditionally divisive (lemmatic)

In the philosophy and logic of modern times, there were significant differences in views on the role of deduction in a number of other methods of cognition. Thus, R. Descartes contrasted deduction with intuition, through which, in his opinion, the human mind "directly sees" the truth, while deduction provides the mind with only "mediated" (obtained by reasoning) knowledge.

F. Bacon, and later other English “inductivist logicians” (W. Wavell, J. St. Mill, A. Bain and others), emphasizing that the conclusion obtained by deduction does not contain any “information” that would not be contained in the premises, on this basis they considered deduction a “secondary” method, while, in their opinion, only induction gives true knowledge. In this sense, deductively correct reasoning was considered from the information-theoretic point of view as reasoning, the premises of which contain all the information contained in their conclusion. Proceeding from this, not a single deductively correct reasoning leads to the receipt of new information - it only makes the implicit content of its premises explicit.

In turn, representatives of the direction, coming primarily from German philosophy (Chr. Wolf, G. W. Leibniz), also proceeding from the fact that deduction does not provide new information, it was on this basis that they came to the opposite conclusion: the obtained through deduction, knowledge is “true in all possible worlds”, which determines their “enduring” value, in contrast to the “actual” truths obtained by inductive generalization of observational data and experience, which are true “only due to a combination of circumstances”. From a modern point of view, the question of such advantages of deduction or induction has largely lost its meaning. Along with this, a certain philosophical interest is the question of the source of confidence in the truth of a deductively correct conclusion based on the truth of its premises. At present, it is generally accepted that this source is the meaning of the logical terms included in the argument; thus deductively correct reasoning turns out to be "analytically correct".

Important Terms

deductive reasoning- a conclusion that ensures the truth of the conclusion with the truth of the premises and the observance of the rules of logic. In such cases, deductive reasoning is considered as a simple case of proof or some step of proof.

deductive proof- one of the forms of proof, when the thesis, which is any single or particular judgment, is brought under the general rule. The essence of such a proof is as follows: you need to get the consent of your interlocutor that the general rule, under which this single or particular fact fits, is true. When this is achieved, then this rule also applies to the thesis being proved.

deductive logic- a branch of logic that studies methods of reasoning that guarantee the truth of the conclusion when the premises are true. Deductive logic is sometimes identified with formal logic. Outside the limits of deductive logic are the so-called. plausible reasoning and inductive methods. It explores ways of reasoning with standard, typical statements; these methods take the form of logical systems, or calculi. Historically, the first system of deductive logic was Aristotle's syllogistic.

How can deduction be applied in practice?

Judging by how Sherlock Holmes unravels detective stories with the help of the deductive method, investigators, lawyers, and law enforcement officers can use him. However, the possession of the deductive method is useful in any field of activity: students will be able to understand the material faster and better remember the material, managers or doctors - to make the only right decision, etc.

Probably, there is no such area of ​​human life where the deductive method would not serve. With its help, you can draw conclusions about the people around you, which is important when building relationships with them. It develops observation, logical thinking, memory and simply makes you think, preventing the brain from growing old ahead of time. After all, our brain needs training as much as our muscles.

Attention to the details

As you observe people and everyday situations, notice the smallest cues in conversations so you can be more responsive to events. These skills have become trademarks of Sherlock Holmes, as well as the heroes of the TV series True Detective or The Mentalist. The New Yorker columnist and psychologist Maria Konnikova, author of Mastermind: How to Think Like Sherlock Holmes, says that Holmes' method of thinking is based on two simple things - observation and deduction. Most of us do not pay attention to the details around, and meanwhile outstanding (fictional and real) detectives have a habit of noticing everything down to the smallest detail.

How to train yourself to be more attentive and focused?

1. First, stop multitasking and focus on one thing at a time. The more things you do at the same time, the more likely you are to make mistakes and miss important information. It is also less likely that this information will be stored in your memory.
2. Secondly, it is necessary to achieve the correct emotional state. Worry, sadness, anger, and other negative emotions that are processed in the amygdala disrupt the brain's ability to solve problems or absorb information. Positive emotions, on the contrary, improve this brain function and even help you think more creatively and strategically.

Develop memory

Having tuned in the right way, you should strain your memory in order to begin to put everything observed there. There are many methods for training it. Basically, it all comes down to learning to give importance to individual details, for example, the brands of cars parked near the house and their numbers. At first you have to force yourself to memorize them, but over time it will become a habit and you will memorize cars automatically. The main thing when forming a new habit is to work on yourself every day.

Play more often memory and other board games that develop memory. Challenge yourself to memorize as many items as you can in random photos. For example, try to memorize as many items from photographs as you can in 15 seconds.

Memory competition champion and author of Einstein Walks on the Moon, a book on how memory works, Joshua Foer explains that anyone with an average memory ability can greatly expand their abilities. Like Sherlock Holmes, Foer is able to memorize hundreds of phone numbers at once by encoding knowledge into visual pictures.

His method is to use spatial memory to structure and store information that is relatively difficult to remember. So numbers can be turned into words and, accordingly, into images, which in turn will take a place in the memory palace. For example, 0 could be a wheel, a ring, or a sun; 1 - a pillar, a pencil, an arrow, or even a phallus (vulgar images are remembered especially well, Foer writes); 2 - a snake, a swan, etc. Then you imagine some space you are familiar with, for example, your apartment (it will be your “memory palace”), in which there is a wheel at the entrance, a pencil lies on the bedside table, and behind it is a porcelain swan. Thus, you can remember the sequence "012".

Doing"field notes"

As you begin your transformation into Sherlock, start keeping a diary of notes. According to the Times columnist, scientists train their attention in exactly this way - by writing down explanations and fixing sketches of what they observe. Michael Canfield, an entomologist at Harvard University and author of Field Notes on Science and Nature, says this habit "will force you to take right decisions about what is really important and what is not.

Keeping field notes, whether during the next working meeting or a walk in the city park, will develop the right approach to the study of the environment. Over time, you begin to pay attention to the little details in any situation, and the more you do it on paper, the faster you will develop the habit of analyzing things on the go.

Concentrate attention through meditation

Many studies confirm that meditation improves concentration. and attention. It is worth starting to practice with a few minutes in the morning and a few minutes before bed. According to John Assaraf, lecturer and renowned business consultant, “Meditation is what gives you control over your brain waves. Meditation trains the brain so you can focus on your goals."

Meditation can make a person better equipped to receive answers to questions of interest. All this is achieved by developing the ability to modulate and regulate different brain wave frequencies, which Assaraf compares to the four speeds in a car gearbox: "beta" from the first, "alpha" from the second, "theta" from the third and " delta waves" - from the fourth. Most of us function during the day in the beta range, and this is not to say that this is so terribly bad. But what is first gear? The wheels spin slowly, and engine wear is quite large. Also, people burn out faster and experience more stress and illness. Therefore, it is worth learning how to switch to other gears in order to reduce wear and the amount of “fuel” spent.

Find a quiet place where nothing will distract you. Be fully aware of what is happening and follow the thoughts that arise in your head, concentrate on your breathing. Take slow deep breaths, feeling the air flow from the nostrils to the lungs.

Think Critically and ask questions

Once you learn to pay close attention to detail, begin to transform your observations into theories or ideas. If you have two or three puzzle pieces, try to figure out how they fit together. The more pieces of the puzzle you have, the easier it will be to draw conclusions and see the whole picture. Try to deduce particular provisions from general ones in a logical way. This is called deduction. Remember to apply critical thinking to everything you see. Use critical thinking to analyze what you are closely following, and use deduction to build a big picture based on these facts. Describing in a few sentences how to develop critical thinking abilities is not so easy. The first step to this skill is to return to childhood curiosity and the desire to ask as many questions as possible.

Konnikova says the following about this: “It is important to learn to think critically. So, when acquiring new information or knowledge about something new, you will not just memorize and memorize something, but learn to analyze it. Ask yourself: "Why is this so important?"; “How do I combine this with the things I already know?” or "Why do I want to remember this?" Questions like these train your brain and organize information into a knowledge network.”

Give free rein to the imagination

Of course, fictional detectives like Holmes have a superpower to see connections that ordinary people simply ignore. But one of the key foundations of this exemplary deduction is non-linear thinking. Sometimes it’s worth letting your imagination run wild in order to replay the most fantastic scenarios in your head and sort through all the possible connections.

Sherlock Holmes often sought solitude to reflect and freely explore an issue from all angles. Like Albert Einstein, Holmes played the violin to help him relax. While his hands were occupied with the game, his mind was immersed in the scrupulous search for new ideas and problem solving. Holmes once even mentions that imagination is the mother of truth. Having renounced reality, he could look at his ideas in a completely new way.

Expand your horizons

Obviously, an important advantage of Sherlock Holmes is in his broad outlook and erudition. If you also understand with equal ease the work of Renaissance artists, the latest trends in the cryptocurrency market, and discoveries in the most progressive theories of quantum physics, your deductive methods of thinking are much more likely to succeed. Do not place yourself in the framework of any narrow specialization. Reach for knowledge and nurture a sense of curiosity in a variety of things and areas.

Conclusions: exercises for the development of deduction

Deduction cannot be acquired without systematic training. Below is a list of effective and simple methods for developing deductive reasoning.

1. Solving problems from the field of mathematics, chemistry and physics. The process of solving such problems increases intellectual abilities and contributes to the development of such thinking.
2. Expanding horizons. Deepen your knowledge in various scientific, cultural and historical fields. This will allow not only to develop a personality from different sides, but also help to gain experience, and not rely on superficial knowledge and conjectures. In this case, various encyclopedias, trips to museums, documentaries and, of course, travel.
3. Pedantry. The ability to thoroughly study the object of interest to you allows you to comprehensively and thoroughly gain a complete understanding. It is important that this object evokes a response in the emotional spectrum, then the result will be effective.
4. Mind flexibility. When solving a problem or problem, you need to use different approaches. To choose the best option, it is recommended to listen to the opinions of others, thoroughly considering their versions. Personal experience and knowledge, together with information from outside, as well as the availability of several options for resolving the issue, will help you choose the most optimal conclusion.
5. Observation. When communicating with people, it is recommended not only to hear what they say, but also to observe their facial expressions, gestures, voice and intonation. Thus, one can recognize whether a person is sincere or not, what his intentions are, and so on.