Concepts such as the general and the particular can only be considered in conjunction. None of them has independence, since when considering the processes, phenomena and objects of the surrounding world only through the prism of, say, a private picture, the picture will turn out to be incomplete, without many necessary elements. A too general look at the same objects and the picture will also give too general, the objects will be considered too superficially. To illustrate what has been said, one can joke story about the doctor. One day the doctor had to treat a tailor who had a fever. He was very weak and the doctor thought that his chances of recovery were slim. However, the patient asked for ham and the doctor allowed it. After some time, the tailor recovered.

In his diary, the doctor made a note that "ham - effective remedy from a fever." After a while, the same doctor treated the shoemaker, who also had a fever, and prescribed ham as a medicine. The patient died. The doctor wrote in his diary that "ham - good remedy from fever in tailors, but not in shoemakers.

Induction is the transition from the particular to the general. That is, this is a gradual generalization of a more particular, specific concept.

In contrast to deduction, in which a true conclusion, reliable information, is derived from true premises, in inductive reasoning, even from true premises, a probabilistic conclusion is obtained. This is due to the fact that the truth of the particular does not uniquely determine the truth of the general. Since the inductive conclusion is probabilistic in nature, further construction of new conclusions on its basis may distort reliable information obtained earlier.

Despite this, induction is very important in the process of cognition, and one does not have to look far to confirm this. Any position of science, whether it be humanitarian or natural science, fundamental or applied, is the result of generalization. At the same time, generalized data can be obtained in only one way - by studying, considering the objects of reality, their nature and relationships. Such a study is a source of generalized information about the patterns of the world around us, nature and society.

2. Rules of induction

In order to avoid mistakes, inaccuracies and inaccuracies in one's thinking, to avoid curiosities, one must comply with the requirements that determine the correctness and objective validity of an inductive conclusion. These requirements are discussed in more detail below.

First rule states that an inductive generalization provides reliable information only if it is carried out according to essential features, although in some cases we can talk about a certain generalization of non-essential features.

main reason that they cannot be the subject of generalization is that they do not have such important property like repeatability. This is all the more important because inductive research consists in establishing the essential, necessary, stable features of the phenomena being studied.

According to second rule important task is precise definition belonging of the studied phenomena to a single class, recognition of their homogeneity or uniformity, since inductive generalization applies only to objectively similar objects. Depending on this, one can put the validity of the generalization of signs that are expressed in private premises.

Incorrect generalization can lead not only to misunderstanding or distortion of information, but also to the emergence of various kinds of prejudices and misconceptions. The main reason for the occurrence of errors is generalization according to random features of single objects or generalization according to common features when these features are not needed.

Proper application of induction is one of the pillars right thinking generally.

As stated above, inductive reasoning- this is such a conclusion in which thought develops from knowledge of a lesser degree of generality to knowledge more commonality. That is, a particular subject is considered and generalized. Generalization is possible up to known limits.

Any phenomenon of the surrounding world, any subject of study lends itself best to study in comparison with another homogeneous subject. So is induction. Best of all, its features are manifested in comparison with deduction. These features are manifested mainly in the way the process of inference takes place, as well as in the nature of the conclusion. So, in deduction, they conclude from the signs of a genus to the signs of a species and individual objects of this genus (based on volumetric relations between terms) in inductive reasoning - from the signs of individual objects to the signs of the whole genus or class of objects (to the volume of this sign).

Therefore, there are a number of differences between deductive and inductive reasoning that allow us to separate them from each other. Can be distinguished several features of inductive reasoning:

1) inductive reasoning includes many premises;

2) all premises of inductive reasoning are single or private judgments;

3) inductive reasoning is possible for all negative premises.

3. Types of inductive reasoning

First, let's talk about the fundamental division of inductive reasoning. They are complete and incomplete.

Complete are called inferences, in which the conclusion is made on the basis of a comprehensive study of the entire set of objects of a certain class.

Complete induction is used only in cases where it is possible to determine the entire range of objects included in the class under consideration, that is, when their number is limited. Thus, complete induction applies only to closed classes. In this sense, the use of complete induction is not very common.

At the same time, this inference gives true value, since all the subjects about which the conclusion is made are listed in the premises. The conclusion is made only concerning these subjects.

In order to be able to talk about complete induction, it is necessary to verify compliance with its rules and conditions. Thus, the first rule says that the number of objects included in the class under consideration must be limited and determined; their number should not be large. Each element of the class taken, with respect to which an inference is created, must have a characteristic feature. And finally, the derivation of a complete conclusion must be justified, necessary, rational.

The scheme of a complete inference can be reflected as:

An example of a complete inductive inference.

All guilty verdicts are issued in a special procedural order.

All acquittals are issued in a special procedural order.

Guilty verdicts and acquittals are decisions of the court.

All court decisions are issued in a special procedural order.

This example reflects the class of objects - court decisions. All (both) of its elements were specified. Right side each of the premises is valid with respect to the left. That's why general conclusion, which is directly related to each case separately, is objective and true.

Despite all the undeniable advantages and advantages of full induction, there are often situations in which its use is difficult. This is due to the fact that in most cases a person is faced with classes of objects, the elements of which are either unlimited or very numerous. In some cases, the elements of the taken class are generally inaccessible for study (due to remoteness, large dimensions, weak technical equipment or low level of available technology).

Therefore, incomplete induction is often used. Despite a number of shortcomings, the scope incomplete induction, the frequency of its use is much greater than the full one.

Incomplete induction called a conclusion, which, on the basis of the presence of certain recurring features, ranks this or that object in the class of objects homogeneous to it, which also have such a feature.

Incomplete induction is often used in Everyday life human and scientific activity, as it allows to draw a conclusion based on the analysis of a certain part of a given class of objects, saves time and human effort. At the same time, we must not forget that as a result of incomplete induction, a probabilistic conclusion is obtained, which, depending on the type of incomplete induction, will fluctuate from less probable to more probable.

The scheme of incomplete induction can be represented as:

S1, S2, S3… make up class K.

Probably each element K - R.

The above can be illustrated by the following example.

The word "milk" changes by case. The word "library" changes by case. The word "doctor" changes by case. The word "ink" changes by case.

The words "milk", "library", "doctor", "ink" are nouns.

Probably all nouns change in cases.

Depending on how the conclusion of the conclusion is justified, it is customary to divide incomplete induction into two types - popular and scientific.

Popular incomplete induction, or induction through a simple enumeration, does not go into very deep consideration of the objects and the classes to which these objects belong. Thus, on the basis of the repetition of the same feature in some part of homogeneous objects and in the absence of a contradictory case, a general conclusion is made that all objects of this kind have this feature.

As the name suggests, popular induction is very common, especially in non-scientific environments. The probability of such an induction is low.

When forming a popular inductive reasoning, one should remember about possible mistakes and prevent them from appearing.

A hasty generalization means that the conclusion takes into account only that part of the facts that speaks in favor of the conclusion made. The rest are not considered at all.

For example:

Winter in Tyumen is cold.

It is cold in Urengoy in winter.

Tyumen and Urengoy cities.

All cities are cold in winter.

After, therefore, for a reason - means that any event, phenomenon, fact preceding the one under consideration is taken as its cause.

The substitution of the conditional for the unconditional means that the relativity of any truth is not taken into account. That is, the facts this case can be taken out of context, changed places, etc. At the same time, the truth of the results obtained continues to be affirmed.

scientific induction, or induction through the analysis of facts, is a conclusion, in the premises of which, along with the recurrence of a feature for some phenomena of a class, there is also information about the dependence of this feature on certain properties of the phenomenon.

That is, unlike popular induction, scientific induction is not limited to a simple statement. The subject under consideration is subjected to deep research. In scientific induction, it is very important to comply with a number of requirements:

1) research subjects should be selected systematically and rationally;

2) it is necessary to know as deeply as possible the nature of the objects under consideration;

3) understand characteristics objects and their connections;

4) compare the results with previously fixed scientific information.

An important feature of scientific induction, which determines its role in science, is the ability to reveal not only generalized knowledge, but also causality. It was through scientific induction that many scientific laws were discovered.

“Of course, this is the ability to think in your own way.
Truly gifted people see the general in the particular, they have some premonition of what is truly important.

V. Pugach, PhD, psychologist.

It will not be a big sin if I once again recall what I have already written about several times. I think that in the fifties of the last century, no one assumed that the discovery of the transistor effect is this special case, will lead to the complete computerization of our entire civilization, that is, it will become a common cause. Some 50 years have passed, and look and evaluate - what has changed?

And it all started, as they used to say, with the manufacture of a germanium transistor in 1949 using a “rope and a stick”. In the photo that was shown on the cover of the American magazine "Electronic" - the simplest device, which even includes an ordinary paper clip, but what now? There are millions of transistors on one chip! Is this not a leap, for some 50 years!

And there are many such examples - from the particular to the general. So, for example, in a recent article by S. Krivosheev "Nameless Expedition".

“The interest in Bezymyanny at the same time by Russian and American specialists is also caused by the following consideration. In fact, the Kamchatka mountain is the "sibling" of the St. Holens volcano, located in the Cascade Mountains in the United States. According to scientists, these two natural object may be related to each other, which is quite unusual. But it didn't turn out right away." (special case).

“Specialists believe that the installed electronic observation system will allow us to better understand the nature of both the Russian volcano and its American counterpart. After all, if scientists prove that Nameless and St. Helens act in a similar way, then why not assume that other volcanoes on the planet “play according to the same scenario”. The study of this issue is a direct way to create a forecast of the behavior of volcanoes around the world. And the results obtained this year show that this mission is feasible.” (General approach!)

Another example. “Diagnosis for the Future” by A. Astakhov “Itogi” No. 37 (587) “Autoantibodies produced by the immune system will tell you everything you wanted to know about yourself, but were afraid to ask.”

"Portrait in the interior

Back in 1896, at the X Medical Congress, Ilya Mechnikov first expressed the "seditious" idea that the immune system is designed not so much to repel foreign microbial invasions, but to maintain " inner harmony» organism - the regulation of the processes occurring in it. (That's the general idea!). At that time, almost no one appreciated this idea. “She was received with hostility and Robert Koch, and Paul Ehrlich are eminent microbiologists who have just begun to create infectious immunology,” says Alexander Poletaev. (special case)

It took almost a century for the attitude to this problem to change On the one hand, humanity has coped with many infections, and the task of combating non-communicable diseases has come to the fore. On the other hand, the connection between immunity and the development of chronic diseases became more and more obvious. Now, for example, it is already known that about forty diseases, including such serious ones as multiple sclerosis, diabetes, rheumatoid arthritis, have an autoimmune nature. Considered to be one of the most important reasons of these diseases is the ability of immune cells to attack the cells of their own body. However, the decisive moment came when, after the decoding of the human genome, proteomics began to develop by leaps and bounds - the science of proteins encoded by genes - the working machines of the body that determine all its functions. Gradually formulated new concept immune system. “Now it is already clear that antibodies, special molecules produced by lymphocytes, appear in the body not only “in response” to foreign proteins penetrating into it,” says Poletaev. “After all, there are several thousand types of such molecules in the human body, no less.” Each of them is capable of linking to a certain fragment of the molecule of its “own” protein according to the “key-lock” principle (a special case).

Why does the body fight with its own proteins? This is necessary, for example, in order to clear the products of cellular decay. After all, hundreds of thousands of cells die every day in the human body. Autoantibodies act as scavengers, sending unwanted proteins into the body's melting furnace. At the same time, each body has its own “garbage”. Liver cells need some antibodies for cleaning, heart cells need others ... It turns out that the number of different autoantibodies can be used to judge the processes occurring in the body ”(a special case).

And the third example. I gave a brief description of the discovery, the essence of which is that under the action of radio waves on salt, sea ​​water hydrogen is released, which can be used as a combustible material.

The general idea is that water can be used as a fuel. And the special case is last discovery engineer John Kanzius (John Kanzius).

In connection with many tragic events occurring with people and with enterprises, I would call the work of B. Zlotin "Sabotage method" common idea from which private ideas can be developed that can help people save lives. And, finally, I ask you, dear reader, to turn to the site that you are currently reading and read "100 MOST IMPORTANT EVENTS AND PEOPLE WHO HAVE A SIGNIFICANT INFLUENCE ON THE DEVELOPMENT OF SCIENCE", which, I believe, represent general ideas, such as, for example , periodic law DI. Mendeleev, and private ideas - for example, in 1688. Anton van Leeuwenhoek developed an optical microscope with 200x magnification, which marked the beginning of the study of structures that are not visible human eye. Such private solutions, from which something could grow that will turn our world upside down, still arise today, for example, in 1991 Sumio Iizima discovered carbon nanotubes. Another promising material has appeared, since nanotubes are a hundred times stronger than steel, and weigh six times less. In addition, they have unusual thermal and electrical properties.”

Briefly, we can say - if you have conducted an experiment and can evaluate its result as a particular one, then I would advise you to consider more carefully whether it can not allow you to predict the future in the form of a general idea.

Several assumptions can be made. First, if the general can be found from particular solutions, then from this general idea one can find particular ones. So, for example, D.I. Mendeleev compiled periodic table- a general idea created on the basis of private solutions, and then suggested several private ideas - new elements, the existence of which few people believed. But they were soon discovered.

And the second. General idea, especially in public life, often looks very tempting, attractive, fair, but in fact it turns out that their implementation has nothing to do with this general idea. I think that everyone himself can give examples of such ideas, and understands that their implementation depends on the people who put them into practice.

Rational judgments are traditionally divided into deductive and inductive. The question of the use of induction and deduction as methods of cognition has been discussed throughout the history of philosophy. Unlike analysis and synthesis, these methods were often opposed to each other and considered in isolation from each other and from other means of cognition.

AT broad sense words, induction, is a form of thinking that develops general judgments about single objects; it is a way of moving thought from the particular to the general, from less universal knowledge to more universal knowledge (the path of knowledge "from the bottom up").

Observing and studying individual objects, facts, events, a person comes to knowledge general patterns. No human knowledge can do without them. The immediate basis of inductive reasoning is the repetition of features in a number of objects of a certain class. A conclusion by induction is a conclusion about general properties of all objects belonging to a given class, based on the observation of a fairly wide set of single facts. Generally, inductive generalizations are regarded as empirical truths, or empirical laws. Induction is an inference in which the conclusion does not follow logically from the premises, and the truth of the premises does not guarantee the truth of the conclusion. From true premises, induction produces a probabilistic conclusion. Induction is characteristic of experimental sciences, makes it possible to build hypotheses, does not give reliable knowledge, suggests.

Speaking of induction, one usually distinguishes between induction as a method of experimental (scientific) knowledge and induction as a conclusion, as a specific type of reasoning. As a method of scientific knowledge, induction is the formulation of a logical conclusion by summarizing the data of observation and experiment. From the point of view of cognitive tasks, induction is also distinguished as a method of discovering new knowledge and induction as a method of substantiating hypotheses and theories.

Induction plays an important role in empirical (experimental) cognition. Here she is performing:

one of the methods for the formation of empirical concepts;

the basis for the construction of natural classifications;

One of the methods for discovering causal patterns and hypotheses;

One of the methods of confirmation and substantiation of empirical laws.

Induction is widely used in science. With its help, all the most important natural classifications in botany, zoology, geography, astronomy, etc. The laws of planetary motion discovered by Johannes Kepler were obtained by induction on the basis of analysis astronomical observations Quiet Brahe. In turn, the Keplerian laws served as an inductive basis in the creation of Newtonian mechanics (which later became a model for the use of deduction). There are several types of induction:

1. Enumerative or general induction.

2. Eliminative induction (from the Latin eliminatio - exclusion, removal), containing various schemes establishing causal relationships.

3. Induction as reverse deduction (movement of thought from consequences to foundations).

General induction is an induction in which one moves from knowledge about several subjects to knowledge about their totality. This is a typical induction. It is general induction that gives us general knowledge. General induction can be represented by two types of complete and incomplete induction. Complete induction builds a general conclusion based on the study of all objects or phenomena of a given class. As a result of complete induction, the resulting conclusion has the character of a reliable conclusion.

In practice, it is more often necessary to use incomplete induction, the essence of which is that it builds a general conclusion based on the observation of a limited number of facts, if among the latter there are none that contradict inductive reasoning. Therefore, it is natural that the truth obtained in this way is incomplete; here we obtain probabilistic knowledge that requires additional confirmation.

The inductive method was already studied and applied by the ancient Greeks, in particular Socrates, Plato and Aristotle. But a special interest in the problems of induction manifested itself in the 17th-18th centuries. with the development of new science. The English philosopher Francis Bacon, criticizing scholastic logic, considered induction based on observation and experiment to be the main method of knowing the truth. With the help of such induction, Bacon was going to look for the cause of the properties of things. Logic should become the logic of inventions and discoveries, Bacon believed, the Aristotelian logic set forth in the work "Organon" does not cope with this task. Therefore, Bacon wrote the New Organon, which was supposed to replace old logic. Extolled induction and other English philosopher, economist and logician John Stuart Mill. He can be considered the founder of classical inductive logic. In his logic, Mill great place assigned to the development of methods for studying causal relationships.

In the course of experiments, material is accumulated for the analysis of objects, the selection of some of their properties and characteristics; the scientist draws conclusions, preparing the basis for scientific hypotheses, axioms. That is, there is a movement of thought from the particular to the general, which is called induction. The line of knowledge, according to supporters of inductive logic, is built as follows: experience - inductive method - generalization and conclusions (knowledge), their verification in the experiment.

The principle of induction states that the universal propositions of science are based on inductive inferences. This principle is invoked when it is said that the truth of a statement is known from experience. AT modern methodology science, it is realized that it is generally impossible to establish the truth of a universal generalizing judgment with empirical data. No matter how much a law is tested by empirical data, there is no guarantee that new observations will not appear that will contradict it.

Unlike inductive reasoning, which only suggests a thought, through deductive reasoning, one deduces a thought from other thoughts. The process of logical inference, as a result of which the transition from premises to consequences is carried out based on the application of the rules of logic, is called deduction. There are deductive inferences: conditionally categorical, dividing-categorical, dilemmas, conditional inferences, etc.

Deduction is a method of scientific knowledge, which consists in the transition from certain general premises to particular results-consequences. Deduction derives general theorems, special conclusions from the experimental sciences. Gives certain knowledge if the premise is correct. The deductive method of research is as follows: in order 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 to the whole given kind of objects; transition from knowledge to more general provisions to less general knowledge.

In general, deduction as a method of cognition proceeds from already known laws and principles. Therefore, the method of deduction does not allow obtaining meaningful new knowledge. Deduction is only a method of logical deployment of a system of provisions based on initial knowledge, a method of identifying the specific content of generally accepted premises.

Aristotle understood deduction as evidence using syllogisms. Deduction was praised by the great French scientist René Descartes. He contrasted it with intuition. In his opinion, intuition directly sees the truth, and with the help of deduction, the truth is comprehended indirectly, i.e. through reasoning. A clear intuition and the necessary deduction is the way to know the truth, according to Descartes. He also deeply developed the deductive-mathematical method in the study of natural sciences. For rational way research Descartes formulated four basic rules, the so-called. "rules for the guidance of the mind":

1. That which is clear and distinct is true.

2. The complex must be divided into private, simple problems.

3. Go to the unknown and unproven from the known and proven.

4. Conduct logical reasoning consistently, without gaps.

The method of reasoning based on the conclusion (deduction) of consequences-conclusions from hypotheses is called the hypothetical-deductive method. Since there is no logic of scientific discovery, no methods to guarantee the receipt of the true scientific knowledge, insofar as scientific statements are hypotheses, i.e. are scientific assumptions or assumptions whose truth value is uncertain. This provision forms the basis of the hypothetical-deductive model of scientific knowledge. In accordance with this model, the scientist puts forward a hypothetical generalization, various kinds of consequences are deduced from it, which are then compared with empirical data. The rapid development of the hypothetical-deductive method began in the 17th-18th centuries. This method has been successfully applied in mechanics. Research Galileo Galilei and especially Isaac Newton, they turned mechanics into a coherent hypothetical-deductive system, thanks to which mechanics became a model of science for a long time, and for a long time they tried to transfer mechanistic views to other natural phenomena.

The deductive method plays huge role in mathematics. It is known that all provable propositions, i.e. theorems are deduced logical way by means of deduction from a small finite number of initial principles provable within the framework of a given system, called axioms.

But time has shown that the hypothetical-deductive method was not omnipotent. In scientific research, one of the most difficult tasks is the discovery of new phenomena, laws and the formulation of hypotheses. Here the hypothetical-deductive method rather plays the role of a controller, checking the consequences arising from hypotheses.

In the modern era, extreme points of view on the meaning of induction and deduction began to be overcome. Galileo, Newton, Leibniz, recognizing experience, and hence induction big role in cognition, noted at the same time that the process of moving from facts to laws is not a purely logical process, but includes intuition. They took important role deductions in construction and verification scientific theories and noted that in scientific knowledge important place is occupied by a hypothesis that is not reducible to induction and deduction. However, to completely overcome the opposition of inductive and deductive methods of cognition for a long time failed.

In modern scientific knowledge, induction and deduction are always intertwined with each other. Real Scientific research takes place in the alternation of inductive and deductive methods, the opposition of induction and deduction as methods of cognition loses its meaning, since they are not considered as the only methods. In cognition, other methods play an important role, as well as techniques, principles, and forms (abstraction, idealization, problem, hypothesis, etc.). For example, probabilistic methods play a huge role in modern inductive logic. Estimating the probability of generalizations, searching for criteria for substantiating hypotheses, the establishment of complete reliability of which is often impossible, requires increasingly sophisticated research methods.

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Comment

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 tool 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 rained at night and was 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.

Such important types inferences:

• 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. So, R. Descartes contrasted deduction with intuition, through which, in his opinion, human mind“directly sees” the truth, while deduction delivers to the mind only “indirect” (obtained by reasoning) knowledge.

F. Bacon, and later other English "inductivist logicians" (W. Whewell, 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, the 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 by deduction, knowledge is "true in all possible worlds”, which determines their “enduring” value, in contrast to the “factual” truths obtained by inductive generalization of observational data and experience, which are true “only due to a combination of circumstances”. FROM modern point From the 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. Out of bounds deductive logic there are 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 the way the deductive method unravels Detective stories Sherlock Holmes, he can be adopted by investigators, lawyers, employees law enforcement. 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 no such area human life where the deductive method would not have served. 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 the trademarks of Sherlock Holmes, as well as the heroes of the 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. Anxiety, sadness, anger and others negative emotions, which are processed in the amygdala, interfere with the brain's ability to solve problems or absorb information. Positive emotions, on the contrary, improve this brain function and even help to 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 in the formation new habit- work on yourself every day.

Play more often memory" and others board games developing memory. Challenge yourself to remember as much as you can. more items on 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 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. Describe in a few sentences how to develop the ability to critical thinking, 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 remember 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 are simply ignored. But one of key pillars 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 quantum physics, your deductive thinking methods are much more likely to succeed. Don't put yourself in any box 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. The following is a list of effective and simple methods on the development of deductive thinking.

1. Solving problems from the field of mathematics, chemistry and physics. The process of solving such problems increases intellectual ability and contribute to the development of such thinking.
2. Expanding horizons. Deepen your knowledge in various scientific, cultural and historical fields. This will not only develop different parties personality, but will also help to gain experience, and not rely on superficial knowledge and guesswork. In this case, help 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. For selection 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 presence of several options for solving the issue, will help to 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.

The formal-logical methods of research also include induction and deduction.

The term "induction" is used in three senses:

Inductive form of inference: from knowledge about individual objects to knowledge about all objects of a given class;

Inductive form of presentation: from the description of single facts to general knowledge;

Inductive research method: from the study of single features, single objects to finding common essential features, knowledge about the entire class of objects.

There are three inductive forms of reasoning:

Full induction;

Popular induction;

Scientific induction.

Complete induction is a form of inference in which the class of an object, connections, phenomena, processes is quantitatively limited and amenable to exhaustive research.

Popular induction is a form of reasoning from the particular to the general based on a simple enumeration of features. On the basis of repeatability and the absence of a contradictory feature, it is concluded that the feature under consideration belongs to all objects of this class. But the fact that contradictory signs are absent does not mean that they are impossible or do not exist. Therefore, the conclusions here are only probable. This is a way of getting a guess, an assumption (“maybe”, “maybe”).

Scientific induction is a form of inference through selection that excludes random generalizations. It is based on knowledge of the laws of development of any classification (nature, technology, social system, etc.), based on which they form a sample population that is representative of the general population. This form of induction is most common in sociological studies of control systems.

The deductive method is a way of mediating knowledge, in which a transition is made from knowledge of a large generality to knowledge of a lesser generality. According to the rule of the deductive method, a single (private) knowledge can be obtained from general knowledge due to the causally determined regular connection of phenomena and processes. The deductive form of cognition is realized through syllogisms - an indirect inference in which a third judgment is derived from two categorical judgments connected by a common middle term.

The main rule, or axiom, of the syllogism is the following judgment: "Everything that is affirmed (denied) with respect to each subject is also affirmed with respect to any part of the subject."

In order for the syllogism to give this knowledge, the premises must be true. It is possible to obtain a true conclusion from true premises only if a number of local rules of syllogism are unconditionally observed:

There should be only three terms, since inferential knowledge is based on the ratio of the two extreme terms to the middle one;

At least one of the premises must be a general proposition (a conclusion does not necessarily follow from two particular premises);

At least one of the premises must be affirmative (the conclusion does not necessarily follow from two negative premises);

If one of the premises is particular, then the conclusion must be particular;

If one of the premises is negative, then the conclusion must also be negative.

With regard to managerial situations, the deductive method makes it possible to draw reasonable conclusions about the essence of ongoing events, if the real situation can be attributed to some typical situations. This can be used in the learning process to gain managerial experience.

The practical success of using the classification in the study is also determined by its following rules.

1. The rule of proportionality (adequacy). A classification is considered commensurate when the sum of the members of the division is equal to the divisible set. Each object belonging to a divisible set must be included in one of the formed classes. Violation of this rule gives an incomplete division and, therefore, distorts the idea of ​​the subject of research.

2. The rule of externality (volumetric separation) of division members. The classes obtained as a result of division must be represented by external concepts, i.e. there should not be a single object of the divisible set that would simultaneously belong to several members of the division. Errors are due to mixing various bases, division criteria in one classification operation.

3. During a certain classification operation, it is impossible to change the basis of division, its criterion. Often there is a substitution of the criterion within the same classification procedure. This is unacceptable, as well as the vagueness of the criterion.

4. The bases of division or criteria can be not only simple, but also complex, including simultaneously several parameters of the object under study.