Methods for developing deduction. An example of deduction and induction from life. Deductive Reasoning: What is it?

It's worth starting with something encouraging. Sherlock Holmes' abilities are absolutely real. And in general, the legendary character was copied by Conan Doyle from a living person - professor at the University of Edinburgh Joseph Bell. He was widely known for his ability to guess a person's character, background and profession from the smallest details.

On the other hand, the existence of one real outstanding person does not guarantee success for everyone who tries to repeat his achievements. Mastering abilities comparable to Holmes's is incredibly difficult. In a different scenario, Scotland Yard wouldn't be running around Baker Street for clues, right?

What he does is real. But what is he doing?

He acts, demonstrates his arrogance, pride and... remarkable intelligence. All this is justified by the ease with which he solves crimes. But how does he do it?

Sherlock Holmes's main weapon is the deductive method. Logic backed by intense attention to detail and outstanding intelligence.

To this day there is debate as to whether Holmes uses deduction or induction. But most likely the truth is somewhere in the middle. Sherlock Holmes accumulates his reasoning, experience, clues to the most complicated cases, systematizes them, collecting them into a common base, which he then successfully uses, using both deduction and induction. He does it brilliantly.

Most critics and researchers are inclined to believe that Conan Doyle did not make mistakes and Holmes really uses the deductive method. For simplicity of presentation, further we will talk about it.

What does the mind of Sherlock Holmes do?

Deductive method

This is the detective's main weapon, which, however, would not work without a number of additional components.

Attention

Sherlock Holmes captures even the smallest details. If not for this skill, he simply would not have material for reasoning, evidence and leads.

Knowledge base

The detective himself said it best:

All crimes show great generic similarity. They (Scotland Yard agents) introduce me to the circumstances of a particular case. Knowing the details of a thousand cases, it would be strange not to solve the thousand and one.

The palaces of the mind

This is his excellent memory. This is the repository that he turns to almost every time he is looking for a solution to a new riddle. This is the knowledge, circumstances and facts accumulated by Holmes, a significant part of which cannot be obtained anywhere else.

Constant analysis

Sherlock Holmes analyzes, reflects, asks questions and answers them. Often he even resorts to double analysis, it is not in vain that the detective constantly acts together with his partner Dr. Watson.

How to learn it

Pay attention to the little things

Bring your ability to pay attention to details to automaticity. In the end, only the details matter. They are the material for your reasoning and conclusions, they are the keys to unraveling and solving the problem. Learn to look. Look so as to see.

Develop your memory

This is the only way you can learn to analyze, derive your own statistics and form patterns. It will only save you in difficult times when you have no other sources of information. It is memory that will help you correctly analyze all the little things that captured your attention when you hit the trail.

Learn to formulate

Document your guesses and conclusions, compile a “dossier” on passers-by, write verbal portraits, build harmonious and clear logical chains. This way you will not only gradually master Sherlock’s method, but also make your thinking clearer and clearer.

Go deeper into the area

One could say “broaden your horizons,” but Holmes would not approve of this lengthy formulation. Try to deepen your knowledge in your chosen field, and avoid useless knowledge. Try to grow in depth, not in breadth, no matter how absurd it may sound.

Concentrate

Above all, Holmes is a genius of concentration. He knows how to isolate himself from the world around him when he is busy with work, and does not allow distractions to tear him away from what is important. He should not be distracted by Mrs. Hudson's chatter or the explosion in the neighboring house on Baker Street. Only a high level of concentration will allow you to think soberly and logically. This required condition mastering the method of deduction.

Learn body language

A source of information that many people forget about. Holmes never neglects him. He analyzes a person’s movements, how he behaves and gestures, pays attention to facial expressions and fine motor skills. Sometimes a person gives away his hidden intentions or involuntarily signals his own lies. Use these tips.

Develop your intuition

It was intuition that often suggested the famous detective the right decision. Hordes of charlatans have pretty much tarnished the reputation of the sixth sense, but this does not mean that it should be neglected. Understand your intuition, learn to trust it and develop it.

Take notes

And of different kinds. It makes sense to keep a diary and write down what happened to you during the day. This is how you analyze everything that you have learned and noticed, summarize and draw a conclusion. The brain is actively working during such an analysis. You can keep field notes where you note your observations of the world around you and the people around you. This will help systematize observations and derive patterns. For some people a blog or electronic diary- everything is individual.

Ask questions

The more questions you ask, the better. Be critical of what is happening, look for reasons and explanations, sources of influence and influence. Build logical chains and cause-and-effect relationships. The ability to ask questions will gradually give rise to the skill of finding answers.

Solve problems and puzzles

Anything: from ordinary problems from school textbooks to complex puzzles involving logic and lateral thinking. These exercises will force your brain to work, look for solutions and answers. Just what you need to develop deductive thinking.

Create puzzles

Have you already learned how to quickly solve them? Try making your own. The task itself is unusual, so it won’t be easy. But the result is worth it.

Read. More. Better

It won't be what you read that matters, but how you do it. To develop deductive reasoning, you need to analyze what you read and pay attention to details. Compare information from different sources and draw parallels. Include the information received in the context of the knowledge you already have and expand your file cabinet.

Listen more, talk less

Holmes could not have unraveled cases so easily if he had not listened to every word of his client. Sometimes one word decides whether a case will hang in the air or be unraveled, whether the legendary detective will be interested in it or not. Just remember the huge hound in “The Hound of the Baskervilles” and one word that changed the girl’s life in the second episode of the fourth season of the BBC series.

Love what you do

Only strong interest and great desire will help you reach the end. This is the only way you will not deviate from the path of constant difficulties and seemingly insoluble problems. If Holmes had not loved his work, he would not have become a legend.

Practice

I saved the most important point for the finale. Practice is the key to mastering deductive reasoning. The key to the Holmes method. Practice anytime, anywhere. Even if at first you are not sure of the correctness of your judgments. Even if at first you will be more like Dr. Watson in your conclusions. Look at people on the subway, on the way to work, take a closer look at those around you at train stations and airports. Only a skill brought to automatism will become truly working.

Deductive thinking can be useful anywhere, and the talents of a legendary detective with constant practice will remain with you for life. Holmes' method is interesting in itself and produces surprising results. So why not try to master it?

Induction (from Latin induction - guidance, motivation) is a method of cognition based on formal logical inference, which leads to a general conclusion based on particular premises. In the very general view induction is the movement of our thinking from the particular, individual to the general. In this sense, induction is a widely used method of thinking at any level of cognition.

The method of scientific induction has many meanings. It is used to denote not only empirical procedures, but also to denote certain techniques related to the theoretical level, where they are, in fact, various forms of deductive reasoning.

Let us analyze induction as a method of empirical knowledge.

The justification for induction as a method is associated with the name Aristotle. Aristotle was characterized by the so-called intuitive induction. This is one of the first ideas about induction among many of its formulations.

Intuitive induction is a mental process by which a common property or relation is isolated from a certain set of cases and identifiedWith each individual case.

Numerous examples of this kind of induction, used both in everyday life and in scientific practice, mathematics are given in the book of the famous mathematician D. Polya. (Intuition // D. Polya. Mathematics and plausible reasoning. - M., 1957). For example, observing some numbers and their combinations, you can come across relationships

3+7=10, 3+17=20, 13+17=30, etc.

Here we find a similarity in obtaining a number that is a multiple of ten.

Or another example: 6=3+3, 8=3+5, 10=3+7=5+5, 12=5+7, etc.

Obviously, we are faced with the fact that the sum of odd primes is always an even number.

These statements are obtained through observation and comparison of arithmetic operations. It is advisable to call the demonstrated examples of inductionintuitive, since the inference process itself is not a logical inference in the strict sense of the word. Here we are not dealing with reasoning, which would be decomposed into premises and conclusions, but simply with perception, “grasping” relations and general properties directly. We do not apply any logical rules, but guess. We are simply enlightened by an understanding of a certain essence. This induction is important in scientific knowledge, but it is not the subject of formal logic, but is studied by the theory of knowledge and the psychology of creativity. Moreover, we use such induction at the ordinary level of cognition all the time.

As the creator of traditional logic, Aristotle also calls another procedure induction, namely: establishing general offer by listing in the form of single sentences all the cases that fall under it. If we were able to list all the cases, and this is the case when the number of cases is limited, then we are dealing with complete induction. IN in this case for Aristotle, the procedure for deriving a general proposition is in fact a case of deductive inference.

When the number of cases is not limited, i.e. almost endlessly, we are dealing with incomplete induction. It is an empirical procedure and is induction in the proper sense of the word. This is a procedure for establishing a general proposition on the basis of several individual cases in which a certain property was observed that is characteristic of all possible cases that are similarWith observable is called induction through simple enumeration. This is popular or traditional induction.

The main problem of complete induction is the question of how thorough and legitimate such a transfer of knowledge is from individual cases known to us, listed in separate sentences, to all possible and even still unknown cases for us.

This is a serious problem of scientific methodology and it has been discussed in philosophy and logic since the time of Aristotle. This is the so-called problem of induction. It is a stumbling block for metaphysically thinking methodologists.

In real scientific practice, popular induction is used absolutely independently very rarely. Most often it is used Firstly, along with more advanced forms of the method of induction and, Secondly, in conjunction with deductive reasoning and other forms of theoretical thinking that increase the credibility of the knowledge obtained in this way.

When, in the process of induction, a transfer is carried out, an extrapolation of a conclusion valid for a finite number of known members of a class, to all members of this class, then the basis for such a transfer is the abstraction of identification, consisting in the assumption that in a given respect all members of this class are identical. Such an abstraction is either an assumption, a hypothesis, and then induction acts as a way to confirm this hypothesis, or the abstraction rests on some other theoretical premises. In any case, induction is somehow connected with various forms of theoretical reasoning, deduction.

Induction through simple enumeration existed unchanged until the 17th century, when F. Bacon made an attempt to improve Aristotle’s method in famous work"New Organon" (1620). F. Bacon wrote: “Induction, which occurs by simple enumeration, is a childish thing, it gives shaky conclusions and is exposed to the danger of contradictory particulars, making decisions for the most part on the basis of fewer facts than it should, and only for those that are available.” on the face". Bacon also draws attention to the psychological side of the fallacy of conclusions. He writes: “Men generally judge new things by the example of old ones, following their imagination, which is prejudiced and tainted by them. This kind of judgment is deceptive, since much of what is sought from the sources of things does not flow through the usual streams.”

The induction that F. Bacon proposed and the rules that he formulated in his famous tables of “presenting examples to the mind,” in his opinion, are free from subjective errors, and the use of his method of induction guarantees the acquisition of true knowledge. He states: “Our path of discovery is such that it leaves little to the sharpness and power of talents. But it almost makes them equal. Just as in drawing a straight line or describing a perfect circle, the firmness, skill and testing of the hand means a lot, if you work only with your hand, it means little or nothing if you use a compass and ruler; this is also the case with our method.”

Demonstrating the failure of induction through simple enumeration, Bertrand Russell gives the following parable. There was once a census official who had to take down the names of all the householders in a Welsh village. The first one he asked said his name was William Williams, and so did the second, third, etc. Finally, the official said to himself: “This is tiring, obviously they are all William Williams. So I’ll write them all down and be free.” But he was mistaken, because there was still one man named John Jones. This shows that we can come to the wrong conclusions if we place too much faith in induction through simple enumeration.”

Calling incomplete induction childish, Bacon proposed an improved type of induction, which he calls eliminative (exclusive) induction. The general basis of Bacon's methodology was to "dissect" things and complex phenomena into parts or elementary "natures" and then discover the "forms" of these "natures." In this case, by “form” Bacon understands the clarification of the essence, causes of individual things and phenomena. The procedure of connection and separation in Bacon's theory of knowledge takes on the form of eliminative induction.

From Bacon's point of view, main reason A significant shortcoming of Aristotle's incomplete induction was the lack of attention to negative cases. Negative arguments obtained as a result of empirical research must be woven into the logical scheme of inductive reasoning.

Another disadvantage of incomplete induction is according to Bacon, it was limited to a generalized description of phenomena and the lack of explanation of the essence of phenomena. Bacon, criticizing incomplete induction, drew attention to an essential point of the cognitive process: conclusions obtained only on the basis of confirming facts are not entirely reliable unless the impossibility of the emergence of disconfirming facts is proven.

Baconian induction is based on the recognition:

material unity of nature;

uniformity of its actions;

universal causation.

Based on these general ideological premises, Bacon supplements them with the following two:

Every existing “nature” certainly has a form that causes it;

in the real presence of a given “form,” its inherent “nature” certainly appears.

Without a doubt, Bacon believed that the same “form” causes not one, but several different “natures” inherent in it. But we will not find in him a clear answer to the question of whether absolutely the same “nature” can be caused by two different “forms”. But to simplify induction, he had to accept the thesis: there are no identical “natures” from different forms, one “nature” is one “form”.

According to its mechanism of implementation, Bacon's induction is built from three tables: the table of presence, the table of absence and the table of degrees of comparison. In the New Organon he demonstrates how to reveal the nature of heat, which, as he assumed, consists of rapid and disorderly movements of the smallest particles of bodies. Therefore, the first table includes a list of hot bodies, the second - cold, and the third - bodies with varying degrees of heat. He hoped that the tables would show that a certain quality is always inherent only in hot bodies and is absent in cold ones, and in bodies with different degrees of heat it is present to varying degrees. By using this method, he hoped to establish the general laws of nature.

All three tables are processed sequentially. First, from the first two, properties that cannot be the desired “form” are “rejected.” To continue the elimination process or confirm it, if the desired form has already been selected, use the third table. It must show that the desired form, for example, A, is correlated with the “nature” of the object “a”. So, if A increases, then “a” also increases, if A does not change, then it retains its “a” values. In other words, the table must establish or confirm such correspondences. An obligatory stage of Baconian induction is verification of the resulting law using experience.

Then from a series of laws small degree generality Bacon hoped to derive laws of the second degree of generality. The proposed new law must also be tested in relation to new conditions. If he acts under these conditions, then, Bacon believes, the law is confirmed, and therefore true.

As a result of his search for the “form” of heat, Bacon came to the conclusion: “heat is the movement of small particles, expanding to the sides and going from the inside to the outside and somewhat upward.” The first half of the solution found is generally correct, but the second narrows and to some extent devalues ​​the first. The first half of the statement allowed for true statements, such as recognizing that friction causes heat, but at the same time, it also allowed for arbitrary statements, such as saying that fur warms because the hairs that form it move.

As for the second half of the conclusion, it is not applicable to the explanation of many phenomena, for example, solar heat. These mistakes suggest rather that Bacon owes his discovery not so much to induction as to his own intuition.

1). The first disadvantage Bacon's induction was that it was based on the assumption that the sought-after “form” can be accurately recognized by its sensory detection in phenomena. In other words, the essence appeared to accompany the phenomenon horizontally, not vertically. It was considered as one of the directly observable properties. This is where the problem lies. An entity is not at all prohibited from being similar to its manifestations, and the phenomenon of particle movement, of course, “resembles” its essence, i.e. to the real movement of particles, although the latter is perceived as macro-movement, whereas in reality it is micro-movement that is not perceivable by humans. On the other hand, an effect does not have to be like its cause: felt heat is not like the latent movement of particles. This is how the problem of similarity and dissimilarity emerges.

The problem of similarity and dissimilarity of “nature” as an objective phenomenon with its essence, i.e. “form”, was intertwined in Bacon with a similar problem of the similarity and dissimilarity of “nature” as a subjective sensation with objective “nature” itself. Is the sensation of yellowness similar to yellowness itself, and that yellowness to its essence—the “form” of yellowness? Which “natures” of movement are similar to their “form” and which are not?

Half a century later, Locke gave his answer to these questions with the concept of primary and secondary qualities. Considering the problem of sensations of primary and secondary qualities, he came to the conclusion that the primary ones are similar to their causes in external bodies, but the secondary ones are not similar. Locke's primary qualities correspond to Bacon's “forms,” but secondary qualities do not correspond to those “natures” that are not the immediate manifestation of the “forms.”

The second disadvantage Bacon's method of induction was one-sided. The philosopher underestimated mathematics for its lack of experimentalism and, in this regard, deductive conclusions. At the same time, Bacon significantly exaggerated the role of induction, considering it the main means of scientific knowledge of nature. This unjustified expanded understanding of the role of induction in scientific knowledge is called pan-inductivism . Its failure is due to the fact that induction is considered in isolation from other methods of cognition and turns into the only, universal means of the cognitive process.

Third drawback was that with a one-sided inductive analysis of a known complex phenomenon, the integral unity is destroyed. Those qualities and relationships that were characteristic of this complex whole, when analyzed, no longer exist in these fragmented “pieces”.

The formulation of the rules of induction proposed by F. Bacon lasted for more than two hundred years. J. St. Mill is credited with their further development and some formalization. Mill formulated five rules. Their essence is as follows. For the sake of simplicity, we will assume that there are two classes of phenomena, each of which consists of three elements - A, B, C and a, b, c, and that there is some dependence between these elements, for example, an element of one class determines an element of another class. It is required to find this dependence, which has an objective, universal nature, provided that there are no other unaccounted influences. This can be done, according to Mill, using the following methods, each time obtaining a conclusion that is probable.

Methodsimilarities. Its essence: “a” arises both with AB and with AC. It follows that A is sufficient to determine “a” (i.e. to be its cause, sufficient condition, basis).

Difference method:"a" occurs in ABC, but does not occur in BC, where A is absent.

It follows from this that A is necessary for “a” to arise (i.e., is the cause of “a”). United method of similarities and differences: , “a” occurs with AB and AS

but does not arise with BC. It follows that A is necessary and sufficient for the determination of “a” (i.e., is its cause). It is known based on past experience that B and “in” and C and “c” are in a necessary causal relationship with each other, i.e. this connection has the character of a general law. Then, if “abs” appears in a new experience with ABC, then A is the cause or a sufficient and necessary condition for “a”. It should be noted that the method of remainders is not a purely inductive reasoning, since it is based on premises that have the nature of universal, nomological propositions.

The method of accompanying changes. If “a” changes when A changes, but does not change when B and C change, then A is the cause or necessary and sufficient condition of “a”.

It should be emphasized once again that the Bacon-Millian form of induction is inextricably linked with a certain philosophical worldview, philosophical ontology, according to which in the objective world there is not only a mutual connection of phenomena, their mutual causality, but the connection of phenomena has a uniquely defined, “hard” character. In other words, the philosophical prerequisites of these methods are the principle of objectivity of causality and the principle of unambiguous determination. The first is common to all materialism, the second is characteristic of mechanistic materialism - this is the so-called Laplace determinism.

In the light of modern ideas about the probabilistic nature of the laws of the external world, about the dialectical connection between necessity and chance, the dialectical relationship between causes and effects, etc., Mill’s methods (especially the first four) reveal their limited character. Their applicability is possible only in rare and, moreover, very simple cases. The method of accompanying changes is more widely used, the development and improvement of which is associated with the development of statistical methods.

Although Mill's method of induction is more developed than that proposed by Bacon, it is inferior to Bacon's interpretation in a number of ways.

Firstly, Bacon was sure that true knowledge, i.e. knowledge of causes is quite achievable with the help of his method, and Mill was an agnostic, denying the possibility of comprehending the causes of phenomena, essence in general.

Secondly, Mill's three inductive methods operate only separately, while Bacon's tables are in close and necessary interaction.

As science develops, it appears new type objects where aggregates of particles, events, things are studied instead of a small number of easily identified objects. Such mass phenomena were increasingly included in the field of study of such sciences as physics, biology, political economy, and sociology.

For the study of mass phenomena, previously used methods turned out to be unsuitable, so new methods of studying, generalization, grouping and prediction, called statistical methods, were developed.

Deduction(from Latin deduction - removal) there is obtaining private conclusions based on knowledge of some general provisions. In other words, this is the movement of our thinking from the general to the particular, the individual. In a more specialized sense, the term “deduction” denotes the process of logical inference, i.e. transition, according to certain rules of logic, from certain given propositions (premises) to their consequences (conclusions). Deduction is also called the general theory of constructing correct conclusions (inferences).

The study of deduction is the main task of logic - sometimes formal logic is even defined as the theory of deduction, although deduction is also studied by the theory of knowledge and the psychology of creativity.

The term "deduction" appeared in the Middle Ages and was introduced by Boethius. But the concept of deduction as proof of a proposition through a syllogism already appears in Aristotle (“First Analytics”). An example of deduction as a syllogism would be the following conclusion.

The first premise: crucian carp is a fish;

second premise: crucian carp lives in water;

conclusion (inference): fish live in water.

In the Middle Ages, syllogistic deduction dominated, the starting premises of which were drawn from sacred texts.

In modern times, the merit of transforming deduction belongs to R. Descartes (1596-1650). He criticized medieval scholasticism for its method of deduction and considered this method not scientific, but related to the field of rhetoric. Instead of medieval deduction, Descartes proposed a precise, mathematized way of moving from the self-evident and simple to the derivative and complex.

R. Descartes outlined his ideas about the method in his work “Discourse on Method”, “Rules for Guiding the Mind”. They are given four rules.

First rule. Accept as true everything that is perceived clearly and distinctly and does not give rise to any doubt, those. quite self-evident. This is an indication of intuition as the initial element of knowledge and a rationalistic criterion of truth. Descartes believed in the infallibility of intuition itself. Errors, in his opinion, stem from a person’s free will, which can cause arbitrariness and confusion in thoughts, but not from the intuition of the mind. The latter is free from any subjectivism, because it clearly (directly) realizes what is clearly (simple) in the cognizable object itself.

Intuition is the awareness of truths that “surface” in the mind and their relationships, and in this sense, it is the highest type of intellectual knowledge. It is identical to the primary truths, which Descartes calls innate. As a criterion of truth, intuition is a state of mental self-evidence. With these self-evident truths the process of deduction begins.

Second rule. Divide every complex thing into simpler components that cannot be further divided by the mind into parts. In the course of division, it is desirable to reach the simplest, clearest and most self-evident things, i.e. to what is directly given by intuition. In other words, such analysis aims to discover the initial elements of knowledge.

It should be noted here that the analysis that Descartes talks about does not coincide with the analysis that Bacon talked about. Bacon proposed to decompose the objects of the material world into “natures” and “forms,” and Descartes draws attention to the division of problems into particular issues.

The second rule of Descartes’ method led to two results that were equally important for the scientific research practice of the 18th century:

1) as a result of the analysis, the researcher has objects that are amenable to empirical consideration;

2) the theoretical philosopher identifies the universal and therefore the simplest axioms of knowledge about reality, which can already serve as the beginning of a deductive cognitive movement.

Thus, Cartesian analysis precedes deduction as a stage that prepares it, but is different from it. The analysis here comes close to the concept of “induction”.

The initial axioms revealed by Descartes's analyzing induction turn out to be, in their content, not only previously unconscious elementary intuitions, but also the sought-after, extremely general characteristics of things that in elementary intuitions are “participants” of knowledge, but have not yet been isolated in their pure form.

Third rule. In cognition by thought one should proceed from the simplest, i.e. from elementary and most accessible things to things that are more complex and, accordingly, difficult to understand. Here deduction is expressed in deducing general provisions from others and constructing some things from others.

The discovery of truths corresponds to deduction, which then operates on them to derive derivative truths, and the discovery of elementary things serves as the beginning of the subsequent construction of complex things, and the found truth moves on to the next yet unknown truth. Therefore, Descartes’s actual mental deduction acquires constructive features characteristic of the embryonic so-called mathematical induction. He anticipates the latter, turning out to be Leibniz's predecessor.

Fourth rule. It consists of enumeration, which involves carrying out complete enumerations, reviews, without leaving anything out of attention. In the very in a general sense This rule focuses on achieving completeness of knowledge. It assumes

Firstly, creating the most complete classification possible;

Secondly, approaching the maximum completeness of consideration leads reliability (convincingness) to obviousness, i.e. induction - to deduction and then to intuition. It is now recognized that complete induction is a special case of deduction;

Thirdly, Enumeration is a requirement of completeness, i.e. accuracy and correctness of the deduction itself. Deductive reasoning breaks down if it skips over intermediate positions that still need to be deduced or proven.

In general, according to Descartes, his method was deductive, and in this direction both his general architectonics and the content of individual rules were subordinated. It should also be noted that the presence of induction is hidden in Descartes' deduction.

In modern science, Descartes was a promoter of the deductive method of knowledge because he was inspired by his achievements in the field of mathematics. Indeed, in mathematics the deductive method is of particular importance. One might even say that mathematics is the only truly deductive science. But obtaining new knowledge through deduction exists in all natural sciences.

Currently in modern science most often works hypothetico-deductive method. This is a method of reasoning based on the derivation (deduction) of conclusions from hypotheses and other premises, the true meaning of which is unknown. Therefore, the hypothetico-deductive method obtains only probabilistic knowledge. Depending on the type of premises, hypothetico-deductive reasoning can be divided into three main groups:

1) the most numerous group of reasoning, where the premises are hypotheses and empirical generalizations;

2) premises consisting of statements that contradict either precisely established facts or theoretical principles. By putting forward such assumptions as premises, one can derive from them consequences that contradict known facts, and on this basis convince oneself of the falseness of the assumption;

3) premises are statements that contradict accepted opinions and beliefs.

Hypothetico-deductive reasoning was analyzed within the framework of ancient dialectics. An example of this is Socrates, who during his conversations set the task of convincing his opponent either to abandon his thesis or to clarify it by drawing consequences from it that contradict the facts.

In scientific knowledge, the hypothetico-deductive method was developed in the 17th-18th centuries, when significant advances were achieved in the field of mechanics of terrestrial and celestial bodies. The first attempts to use this method in mechanics were made by Galileo and Newton. Newton's work “Mathematical Principles of Natural Philosophy” can be considered as a hypothetico-deductive system of mechanics, the premises of which are the basic laws of motion. The method of principles created by Newton had a huge influence on the development of exact natural science.

From a logical point of view, the hypothetico-deductive system is a hierarchy of hypotheses, the degree of abstraction and generality of which increases as they move away from the empirical basis. At the very top are the hypotheses that are most general in nature and therefore have the greatest logical power. From these, as premises, lower-level hypotheses are derived. Actually lowest level systems, hypotheses are found that can be compared with empirical reality.

A mathematical hypothesis can be considered a type of hypothetico-deductive method, which is used as the most important heuristic tool for discovering patterns in natural science. Typically, the hypotheses here are some equations representing a modification of previously known and tested relationships. By changing these relationships, a new equation is created that expresses a hypothesis that relates to unexplored phenomena. In the process of scientific research, the most difficult task is to discover and formulate those principles and hypotheses that serve as the basis for all further conclusions. The hypothetico-deductive method plays an auxiliary role in this process, since with its help new hypotheses are not put forward, but only the consequences arising from them are tested, which thereby control the research process.

The axiomatic method is close to the hypothetico-deductive method. This is the way to build scientific theory, in which it is based on certain initial provisions (judgments) - axioms, or postulates, from which all other statements of this theory must be deduced in a purely logical way, through proof. The construction of science based on the axiomatic method is usually called deductive. All concepts of a deductive theory (except for a fixed number of initial ones) are introduced through definitions formed from a number of previously introduced concepts. To one degree or another, deductive proofs characteristic of the axiomatic method are accepted in many sciences, but the main area of ​​its application is mathematics, logic, and some branches of physics.

DEDUCTION

DEDUCTION

(from Latin deductio - deduction) - a transition from premises to a conclusion, based on, due to which it follows with logical necessity from the accepted premises. A characteristic feature of D. is that from true premises it always leads only to a true conclusion.
D., as an inference based on the law and necessarily giving a true conclusion from true premises, is contrasted with -, which is not based on the law of logic and leads from true premises to a probable, or problematic, conclusion.
For example, inferences are deductive:
If ice gets hot, it melts.
The ice is heating up.
The ice is melting.
The line separating from the conclusion stands in place of the word “therefore.”
Examples of induction include reasoning:
Brazil is a republic; Argentina is a republic.
Brazil and Argentina are South American countries.
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 are Western European countries.
All Western European countries are republics.
Inductive inference relies on some factual or psychological basis. In such an inference, the conclusion may contain information not present in the premises.
The reliability of the premises does not therefore mean the reliability of the inductive statement derived from them. The inductive conclusion is problematic and needs further investigation. Thus, the premises of both the first and second given inductive inferences 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 Western European countries there are not only republics, but also monarchies.
Particularly characteristic of D. are logical transitions from general knowledge to specific knowledge:
All people are mortal.
All Greeks are people.
All Greeks are mortal. In all cases when it is necessary to consider something based on what is already known general rule
and to draw the necessary conclusion regarding this phenomenon, we conclude in the form D. Reasoning leading from knowledge about some objects (private knowledge) to knowledge about all objects of a certain class (general knowledge) is typical induction. There always remains something that turns out to be hasty and unfounded (“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 the argument, “Shakespeare wrote sonnets; therefore, it is not true that Shakespeare did not write sonnets.” There is D., but there is no transition from the general to the specific. The reasoning “If aluminum is plastic or clay is plastic, then aluminum is plastic” is, as is commonly thought, 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 inferences include both transitions from the particular to the general, and the canons of induction, etc. Deductive reasoning allows one to obtain new truths from existing knowledge, and moreover, with the help of pure reasoning, without resorting to experience, intuition, common sense
However, one should not separate D. from induction and underestimate the latter. Almost all general provisions, including scientific laws, are the results of inductive generalization. In this sense, induction is the basis of our knowledge. In itself, it does not guarantee its truth and validity, but it gives rise to assumptions, connects them with experience and thereby gives them a certain credibility, more or less high degree probabilities. 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 in rare cases appears in full and expanded form. Most often, not all used parcels are indicated, but only some. General statements that appear to be well known are omitted. The conclusions that follow from the accepted premises are not always clearly formulated. The logical itself, existing between the original and the deduced statements, is only sometimes marked by words like “therefore” and “means”. Often D. is so abbreviated that one can only guess about it. Carrying out deductive reasoning without omitting or shortening anything is cumbersome. However, whenever there is a question about the validity of the conclusion made, it is necessary to return to the beginning of the reasoning and reproduce it in the most complete form possible. Without this, it is difficult or even impossible to detect a mistake.
Deductive is the derivation of a substantiated position from other, previously accepted provisions. If the put forward position can be logically (deductively) deduced from already established provisions, this means that it is acceptable to the same extent as these provisions themselves. The justification of some statements by reference to or the acceptability of other statements is not the only thing performed by D. in the processes of argumentation. Deductive reasoning also serves to verify (indirectly confirm) statements: from the position being verified, its empirical consequences are deductively derived; These consequences are assessed 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. Failure to succeed is a weakened version of verification: failure to refute 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, trace the logical connections of the statements included in it, and construct explanations and understandings based on the general principles proposed by the theory. Clarifying the logical structure of a theory, strengthening its empirical basis, and identifying its general premises are contributions to its propositions.
Deductive argumentation is universal, applicable to all areas of reasoning and to any audience. “And if bliss is nothing other than eternal life, and eternal life is truth, then bliss is nothing other than the knowledge of truth” - John Scotus (Eriugena). This theological reasoning is deductive reasoning, viz.
The proportion of deductive argumentation 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 application of D., Aristotle wrote: “One should not demand from the speaker scientific evidence, just as emotional persuasion should not be required.” Deductive argumentation is a very powerful tool, but, like anything else, it must be used narrowly. An attempt to build argumentation in the form of D. in those areas or in the audience that are not suitable for this leads to superficial reasoning that can only create the illusion of persuasiveness.
Depending on how widely deductive argumentation is used, all sciences are usually divided into external and inductive ones. In the first, deductive argumentation is used primarily or even exclusively. Secondly, such argumentation plays only a obviously auxiliary role, and in the first place is empirical argumentation, which has an inductive, probabilistic one. Mathematics is considered a typical deductive science; an example of inductive sciences is. However, sciences into deductive and inductive, widespread in the beginning. 20th century, has now lost much of its character. It is focused on science, considered statically, as a system of reliably and finally 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 - deduction), transition from general to specific; in more specialist. sense "D." stands for logical. output, i.e. transition, according to certain rules of logic, from certain given premise sentences 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 general theory drawing correct conclusions (inference). Sciences whose proposals preim., are obtained as consequences of certain general principles, postulates, axioms, accepted called deductive (mathematics, theoretical mechanics, certain branches of physics and etc.) , and the axiomatic method by which the conclusions of these particular propositions are drawn is often called axiomatic-deductive.

The study of D. is Ch. logic problem; sometimes formal logic is even defined as a theory of logic, although it is far from unified, that studies the methods of logic: it studies the implementation of logic in the process of real individual thinking, and - as one of basic (along with others, in particular various forms of induction) methods scientific knowledge.

Although the term "D." first used, apparently, by Boethius, the concept of D. - as k.-l. propositions 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 the series etc. methods of cognition. Thus, Descartes opposed D. to intuition, through cut, but to his opinion, human. “directly perceives” the truth, while D. delivers to the mind only “indirect” (obtained by reasoning) knowledge. F. Bacon, and later etc. English“inductivist” logicians (W. Whewell, J. S. Mill, A. Bain and etc.) considered D. a “secondary” method, while true knowledge, in their opinion, is provided only by induction. Leibniz and Wolf, based on the fact that D. does not provide “new facts,” precisely on this basis came to the exact opposite conclusion: the knowledge obtained through D. is “true in all possible worlds.”

Questions of D. began to be intensively developed from the end of the 19th century. in connection with the rapid development of mathematics. logic, clarifying the foundations of mathematics. This led to the expansion of the means of deductive proof (for example, " " was developed), to the clarification of 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, solvability), etc.

Development of questions of D. in the 20th century. is 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 of the exclusion (elimination) of middle terms from the premises. Generalizing Boole's ideas and using our own algebrological ones. methods, rus. the logician Poretsky showed that such a logic is too narrow (see “On 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. expression L = 0 to one of its consequences, it is enough to discard its left side, which is a logical one. a polynomial in perfect normal form, some of its constituents.

V. modern bourgeois In philosophy, it is very common to over-exaggerate the role of D. in cognition. In a number of works on logic, it is customary to emphasize that which supposedly completely excludes. the role that D. plays in mathematics, in contrast to other scientific. disciplines. By focusing on this “difference,” they go so far as to claim that all sciences can be divided into so-called sciences. deductive and empirical. (see, for example, L. S. Stebbing, A modern introduction to logic, L., 1930). However, such a distinction is fundamentally illegitimate and it is denied not only by dialectical-materialistic scientists. positions, but also certain bourgeois. researchers (for example, J. Lukasiewicz; see Lukasiewicz, 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 certain experiments with material objects of the objective world, actions on them in the process of social-historical. practices. And in this sense, mathematician. axioms do not contradict the provisions of science and society. An important feature of D. is its analytical nature. character. Mill also noted that there is nothing in the conclusion of deductive reasoning that is not already contained in its premises. To describe analytical the nature of deductive inference is formal, we will resort to exact language algebras of logic. Let us assume that deductive reasoning is formalized by means of the algebra of logic, i.e. The relationships between the volumes of concepts (classes) are precisely recorded both in the premises and in the conclusion. Then it turns out that the decomposition of premises into constituent (elementary) units contains all those constituents that are present in the decomposition of the consequence.

Due to the special significance that the disclosure of premises acquires in any deductive conclusion, deduction is often associated with analysis. Since in the process of D. (in the conclusion of a deductive inference) there is often a combination of knowledge given to us in the department. premises, D. is associated 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., because any individual can be understood only through its image in an already established system of concepts, and D., ultimately, depends on observation, experiment and induction. D. without the help of induction can never provide knowledge of objective reality. “Induction and deduction are related to each other in the same necessary way as synthesis and analysis. Instead of one-sidedly extolling one of them to the skies at the expense of the other, we must try to apply each in its place, and this can only be achieved if lose sight of their connection with each other, their mutual complement of each other" (Engels F., Dialectics of Nature, 1955, pp. 180–81). The content of the premises of a deductive inference is not given in ready-made form in advance. The general position, which must certainly be in one of the premises of D., is always the result of a comprehensive study of many facts, a deep generalization of the natural connections and relationships between things. But induction alone is impossible without D. Characterizing Marx’s “Capital” as a classic. dialectical approach to reality, Lenin noted that in Capital induction and theory coincide (see Philosophical Notebooks, 1947, pp. 216 and 121), thereby emphasizing their inextricable connection in the scientific process. research.

D. is sometimes used to check the quality of life. judgments, when consequences are deduced from it according to the rules of logic in order to then test these consequences in practice; This is one of the methods for testing hypotheses. D. are also used when revealing the content of certain concepts.

Lit.: Engels F., Dialectics of Nature, M., 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, Reasoning about the method, M., 1953; Leibniz G.V., New things about the human mind, M.–L., 1936; Karinsky M.I., Classification of conclusions, in collection: Izbr. works of Russian logicians of the 19th century, M., 1956; Liar L., English reformers of logic in the 19th century, St. Petersburg, 1897; Couture L., Algebra of Logic, Odessa, 1909; Povarnin S., Logic, part 1 – General doctrine of evidence, P., 1915; Hilbert D. and Ackerman V., Fundamentals of Theoretical Logic, trans. from German, M., 1947; Tarski A., Introduction to logic and methodology of deductive sciences, trans. from English, M., 1948; Asmus V. F., The doctrine of logic about proof and refutation, M., 1954; Boole G., An investigation of the laws of thought..., N. Y., 1951; Schröder E., Vorlesungen über die Algebra der Logik, Bd 1–2, Lpz., 1890–1905; Reichenbach H. Elements of symbolic logic, N. Υ., 1948.

D. Gorsky. Moscow.

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

DEDUCTION

DEDUCTION (from Latin deductio - deduction) - the transition from the general to the specific; 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 certain given premise sentences to their consequences (conclusions). The term “deduction” is used both to denote specific conclusions of consequences from premises (i.e., as a synonym for the term “conclusion” in one of its meanings), and as a generic name for the general theory of constructing correct conclusions. Sciences, the propositions of which are primarily obtained as consequences 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 propositions are made is axiomatic-deductive.

The study of deduction is the task of logic; sometimes formal logic is even defined as a theory of deduction. Although the term “deduction” was apparently first used by Boethius, the concept of deduction - as proof of a proposition through 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 knowledge. Thus, Descartes opposed deduction to intuition, through which, in his opinion, the mind “directly perceives” the truth, while deduction provides the mind only “indirect” (obtained by reasoning) knowledge. F. Bacon, and later other English “inductivist” logicians (W. Whewell, J. S. Mill, A. Bain, etc.) considered deduction a “secondary” method, while true knowledge is provided only by induction. Leibniz and Wolff, based on the fact that deduction does not provide “new facts,” precisely on this basis came to the exact opposite conclusion: knowledge obtained through 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 related to each other in the same necessary way as synthesis and analysis. Instead of unilaterally extolling one of them to the skies at the expense of the other, we must try to apply each of them in its place, and this can only be achieved if we do not lose sight of their connection with each other, their mutual complement 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 a rule consists in the fact that the general provision refers (applies) to some specific (particular) situation. Some rules of logical inference fall under this characterization in a very explicit way. So, for example, various modifications of the so-called. substitution rules state that the property of provability (or deducibility from a given system of premises) is preserved whenever elements of an arbitrary formula of a given formal theory are replaced by specific expressions of the same type. The same applies to the common method of specifying axiomatic systems using the so-called. axiom schemes, i.e. expressions that turn into specific axioms after substituting the general designations of specific formulas of a given theory instead of the general designations 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. Thus, the “deduction theorem” is usually called one of the important relationships between the logical connective of implication (formalizing the verbal expression “if... then...”) and the relation of logical implication (deducibility): if from premise A a consequence B is derived, then the implication AeB (“if A... then B...") is provable (that is, deducible without any premises, from axioms alone). Other logical terms associated with the concept of deduction are of a similar nature. Thus, sentences that are derived from each other are called deductively equivalent; a deductive system (relative to some property) is that all expressions of this system that have this property (for example, truth under some interpretation) are provable in it.

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

TRANSCENDENTAL DEDUTION (German: transzendentale Deduktion) is a 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 a transcendental deduction was realized by Kant 10 years before the publication 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. Solving the main problem of deduction involves proving the thesis that the necessary capabilities of things constitute. 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 required proof of the identity of categories with a priori conditions of possible experience. The starting point of deduction is the concept of apperception. Kant claims that all representations possible for us must be connected in the unity of apperception, that is, in the Self. Necessary conditions Categories turn out to be such connections. 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 us to “reverse” the I of categorical syntheses for attributing representations to an object). As a result, Kant concludes that all possible perceptions as conscious, i.e., intuitions related to the Self, are necessarily subordinated to categories (first Kant shows that this is true regarding “intuitions in general”, then regarding “our intuitions” in space and time) . This means the possibility of anticipation of objective forms of experience, i.e. a priori cognition of objects of possible experience with the help of categories. Within the framework of deduction, Kant develops the doctrine of cognitive abilities, a special role among which is played by imagination, which also connects reason. It is the imagination, obeying categorical “instructions,” that formalizes phenomena according to laws. Kant's deduction of categories has given rise to numerous discussions in modern historical and philosophical literature.

Dictionary foreign words Russian language

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

Deductive reasoning only concretizes our knowledge. A deductive conclusion contains only the information that is in the accepted premises. Deduction allows you to obtain new truths from existing knowledge using pure reasoning.

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

Example 1.

All metals are ductile(b O least valid premise or main argument).

Bismuth is a metal(reliable premise).

Therefore, bismuth is plastic(correct conclusion).

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

Example 2.

All politicians who allow contradictions are a joke(b O the largest reliable premise).

E Ltsin B.N. admitted contradictions(reliable premise).

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

Deduction from a lie comes a lie.

Example.

Help from the International Monetary Fund always leads to prosperity for everyone(false premise).

The IMF has been helping Russia for a long time(reliable premise).

Therefore, Russia is prospering(false conclusion).

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

An inductive conclusion may contain information that is not contained in the accepted premises. The validity of the premises does not mean the validity of the inductive conclusion. Premises make the conclusion more or less likely.

Induction does not provide reliable, but probabilistic knowledge that needs to be verified.

Example 1.

G.M.S. - pea jester, E.B.N. - pea jester, Ch.A.B. - pea jester(reliable premises).

G.M.S., E.B.N., Ch.A.B. – politicians(reliable premises).

Therefore, all politicians are clowns(probabilistic conclusion).

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

Example 2.

IN last years in area 1, in area 2 and in area 3 military exercises were held - the combat effectiveness of units was increased(reliable premises).

Units in area 1, area 2 and area 3 took part in the exercises Russian Army (reliable premises).

Consequently, in recent years, the combat effectiveness of all units of the Russian Army has increased(inductive invalid inference).

A general conclusion does not logically follow from particular provisions. Showy events do not prove that there is prosperity everywhere:

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

A variant of induction is inference by analogy (based on the similarity of two objects in one parameter, a conclusion is drawn 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, Mars also has life.

This conclusion is, of course, only probabilistic.

Any inductive conclusion needs to be verified.

Dmitry Mezentsev (project coordinator) Russian Society Good Deeds"), 2011

Mindset is important cognitive process for a person, thanks to which he gains new knowledge, develops and becomes better. There are different thinking techniques that can be used at any time and in different situations.

What is this deduction?

A method of thinking by which logical conclusions are drawn about a specific subject or situation based on general information, is called deduction. Translated from Latin, this word means “inference or logical conclusion.” A person uses generally known information and specific details, analyzes, putting the facts together in a certain chain, and finally draws a conclusion. The deduction method became famous thanks to books and films about detective Sherlock Holmes.

Deduction in philosophy

Use for construction scientific knowledge began in ancient times. Famous philosophers such as Plato, Aristotle and Euclid used it to make inferences based on existing information. Deduction in philosophy is a concept that different minds have interpreted and understood in their own way. Descartes considered this type of thinking to be similar to intuition, with the help of which a person can gain knowledge through reflection. Leibniz and Wolff had their own opinions about what deduction is, considering it the basis for obtaining true knowledge.

Deduction in psychology

Thinking is used in different directions, but there are areas aimed at studying deduction itself. The main purpose of psychology is to study the development and impairment of deductive reasoning in humans. This is due to the fact that since this type of thinking implies a movement from general information to specific analysis, all mental processes. The theory of deduction is studied in the process of forming concepts and solutions to various problems.

Deduction - advantages and disadvantages

To better understand the capabilities of the deductive method of thinking, you need to understand its advantages and disadvantages.

1. Helps save time and reduce the amount of material presented.
2. Can be used even when there is no prior knowledge in a particular area.
3. Deductive reasoning contributes to the development of logical, evidence-based thinking.
4. Provides general knowledge, concepts and skills.
5. Helps test research hypotheses as plausible explanations.
6. Improves the causal thinking of practitioners.

1. In most cases, a person receives knowledge in a ready-made form, that is, he does not study information.
2. In some cases, it is difficult to bring a specific case under a general rule.
3. Cannot be used to discover new phenomena, laws or formulate hypotheses.

Deduction and induction

If we have already understood the meaning of the first term, then as for induction, it is a technique for constructing general conclusion based on private parcels. He does not use logical laws, but relies on some psychological and factual information, which is purely formal. Deduction and induction are two important principles, which complement each other. For a better understanding, it is worth considering an example:

1. Deduction from the general to the specific involves obtaining from one truthful information another, and it will be the truth. For example, all poets are writers, conclusion: Pushkin is a poet and writer.
2. Induction is an inference that arises from knowledge of some objects and leads to generalization, therefore they say that there is a transition from reliable information to probable information. For example, Pushkin is a poet, like Blok and Mayakovsky, which means that all people are poets.

How to develop deduction?

Every person has the opportunity to develop deductive thinking, which is useful in different life situations.

1. Games. Various games can be used to develop memory: chess, puzzles, Sudoku and even card games force players to think through their moves and memorize cards.
2. Problem solving. That's when it comes in handy school program in physics, mathematics and other sciences. While solving problems, slow thinking is trained. You should not stop at one solution option and it is recommended to look at the problem from a different point of view, proposing an alternative.
3. Expansion of knowledge. The development of deduction implies that a person must constantly work to expand his horizons, “absorbing” a lot of information from different areas. This will help you build your conclusions in the future, based on specific knowledge and experience.
4. Be observant. Deduction in practice is impossible if a person does not know how to notice important details. When communicating with people, it is recommended to pay attention to gestures, facial expressions, voice timbre and other nuances, which will help to understand the intentions of the interlocutor, calculate his sincerity, and so on. Being in public transport, observe people and make various assumptions, such as where the person is going, what he is doing, and much more.

Deduction - exercises

1. Use any pictures, and it’s better if they have a lot of small details. Look at the image for a minute, trying to remember as many details as possible, and then write down everything that is stored in your memory and check it. Gradually reduce your viewing time.
2. Use words that are similar in meaning and try to find them maximum amount differences. For example: oak/pine, landscape/portrait, poem/fairy tale, and so on. Experts also recommend learning to read words backwards.
3. Write down the names of people and the dates of a specific event in their lives. Four positions are enough. Read them three times, and then write down everything you remember.

Deductive method of thinking - books

One important way to develop deductive thinking is to read books. Many people don’t even suspect how much benefit this has: memory training, broadening of horizons, etc. To apply the deductive method, it is necessary not just to read literature, but to analyze the situations described, memorize, compare and carry out other manipulations.

1. For those who are interested in what deduction is, it will be interesting to read the work of the author of this method of thinking, René Descartes, “Discourse on the Method for Correctly Directing Your Mind and Finding Truth in the Sciences.”
2. Recommended literature includes various detective stories, for example, the classic A. K. Doyle “The Adventures of Sherlock Holmes” and many worthwhile authors: A. Christie, D. Dontsova, S. Shepard and others. When reading such literature, it is necessary to use deductive thinking to guess who the criminal might be.