Add your price to the database

A comment

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

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

An example of the simplest 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 a 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. Conclusions must be based on experience, knowledge and specific facts. Otherwise, it would be impossible to avoid generalizations and draw erroneous conclusions. For example, “All men are deceivers, so you are also a deceiver.” Or “Vova is lazy, Tolik is lazy and Yura is lazy, which means all men are lazy.”

IN Everyday life We use the simplest versions of deduction and induction without even realizing it. For example, when we see a disheveled man running headlong, we think that he is probably 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 there was strong wind. We tell the child not to sit late on a weekday, because we assume that then he will sleep through school, not have breakfast, etc.

History of the method

The term “deduction” itself was apparently first used by Boethius (“Introduction to Categorical Syllogism”, 1492), the first systematic analysis of one of the varieties of deductive inferences - syllogistic inferences- was implemented 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 Stoic school and especially in detail in medieval logic.

The following important types of inferences were identified:

• conditionally categorical (modus ponens, modus tollens)
• dividing-categorical (modus tollendo ponens, modus ponendo tollens)
• conditional disjunctive (lemmatic)

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

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

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

Important Terms

Deductive reasoning- an inference that ensures, given the truth of the premises and compliance with the rules of logic, the truth of the conclusion. In such cases, deductive reasoning is treated as a simple case of proof or some step of proof.

Deductive proof- one of the forms of proof when a thesis, which is some kind of individual or private judgment, is brought under general rule. The essence of such proof is as follows: you must obtain the consent of your interlocutor that the general rule under which a given individual or particular fact fits is true. When this is achieved, then this rule applies to the thesis being proven.

Deductive logic- a branch of logic in which methods of reasoning are studied that guarantee the truth of the conclusion when the premises are true. Deductive logic is sometimes identified with formal logic. Outside the limits of deductive logic are the so-called. plausible reasoning and inductive methods. It explores ways of reasoning with standard, typical statements; These methods are formalized in 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 Sherlock Holmes unravels detective stories using the deductive method, it can be adopted by investigators, lawyers, and law enforcement officers. However, mastery of the deductive method will be useful in any field of activity: students will be able to quickly understand and remember the material better, managers or doctors will be able to make the only correct decision, etc.

There is probably no area of ​​human life where the deductive method would not be useful. With its help, you can draw conclusions about the people around you, which is important when building relationships with them. It develops observation skills logical thinking, memory and simply makes you think, preventing your brain from aging ahead of time. After all, our brain needs training no less than our muscles.

Attention to details

As you observe people and everyday situations, notice the smallest cues in conversations to become more responsive to events. These skills became the trademarks of Sherlock Holmes, as well as the heroes of the TV series True Detective and The Mentalist. New Yorker columnist and psychologist Maria Konnikova, author of Mastermind: How to Think Like Sherlock Holmes, says Holmes' thinking technique is based on two simple things - observation and deduction. Most of us do not pay attention to the details around us, but in the meantime, 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 once, the more likely you are to make mistakes and are more likely to miss important information. It is also less likely that the information will be retained in your memory.
2. Secondly, it is necessary to achieve the right emotional state. Anxiety, sadness, anger and others negative emotions, which are processed in the amygdala, impair the brain's ability to solve problems or absorb information. Positive emotions On the contrary, they improve this brain function and even help you think more creatively and strategically.

Develop memory

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

Play more often Memory" and others Board games Developing memory. Set yourself the task of remembering as many objects as possible in random photos. For example, try to remember as many objects from photographs as possible in 15 seconds.

Memory competition champion and author of Einstein Walks on the Moon, a book about how memory works, Joshua Foer explains that anyone with average memory ability can greatly improve their memory abilities. Like Sherlock Holmes, Foer is able to remember hundreds of phone numbers at a time, thanks to the encoding of knowledge in 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 pole, a pencil, an arrow or even a phallus (vulgar images are remembered especially well, writes Foer); 2 – a snake, a swan, etc. Then you imagine some space that is familiar to you, for example, your apartment (it will be your “memory palace”), in which there is a wheel at the entrance, a pencil on the bedside table nearby, and behind her is a porcelain swan. This way you can remember the sequence "012".

Maintaining"field notes"

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

Taking field notes, whether during a regular work meeting or a walk in a city park, will develop the right approach to environmental research. Over time you begin to pay attention to small parts in any situation, and the more you do it on paper, the faster you will develop the habit of analyzing things as you go.

Focus attention through meditation

Many studies confirm that meditation improves concentration and attention. You should start practicing 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 your brain so you can focus on your goals."

Meditation can make a person better equipped to obtain answers to questions of interest. All this is achieved by developing the ability to modulate and regulate different frequencies of brain waves, which Assaraf compares to the four speeds in a car transmission: “beta” is the first, “alpha” is the second, “theta” is the third and “ delta waves" - from the fourth. Most of us function in the beta range during the day, and that's not a terribly bad thing. However, what is first gear? The wheels spin slowly, and the engine wears quite a lot. People also 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” consumed.

Find a quiet place where there will be no distractions. Be fully aware of what is happening and watch the thoughts that arise in your head, concentrate on your breathing. Take slow, deep breaths, feeling the air flow from your nostrils to your 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 understand how they fit together. The more puzzle pieces you have, the easier it will be to draw conclusions and see the whole picture. Try to derive specific 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 observe closely, and use deduction to build a big picture from those facts. Describe in a few sentences how to develop your ability to critical thinking, not so simple. 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 can 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 network of knowledge.”

Let your imagination run wild

Of course, fictional detectives like Holmes have the superpower of seeing connections that ordinary people they simply ignore it. But one of the key foundations of this exemplary deduction is nonlinear thinking. Sometimes it’s worth giving free rein to your imagination to replay the most fantastic scenarios in your head and go through all possible connections.

Sherlock Holmes often sought solitude to think and freely explore a problem from all sides. Like Albert Einstein, Holmes played the violin to help him relax. While his hands were busy playing, his mind was immersed in a meticulous search for new ideas and problem solving. Holmes even mentions at one point that imagination is the mother of truth. By detaching himself from reality, he could look at his ideas in a completely new way.

Expand your horizons

It is obvious that an important advantage of Sherlock Holmes is his broad outlook and erudition. If you can also easily understand the works of Renaissance artists, the latest trends in the cryptocurrency market, and discoveries in the most advanced theories of quantum physics, your deductive methods of thinking have a much greater chance of success. You should not place yourself within the framework of any narrow specialization. Strive for knowledge and cultivate a sense of curiosity about a wide variety of things and areas.

Conclusions: exercises for developing deduction

Deduction cannot be acquired without systematic training. Below is a list of effective and simple methods on the development of deductive thinking.

1. Solving problems in the fields of mathematics, chemistry and physics. The process of solving such problems increases intellectual abilities and contributes to the development of such thinking.
2. Expanding your horizons. Deepen your knowledge in various scientific, cultural and historical fields. This will not only allow you to develop different sides personality, but will also help to accumulate experience, and not rely on superficial knowledge and guesswork. In this case, various encyclopedias, trips to museums, documentaries and, of course, travel will help.
3. Pedantry. The ability to thoroughly study an 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. Flexibility of mind. When solving a task or problem, it is necessary to use different approaches. For selection optimal option, it is recommended to listen to the opinions of others, thoroughly considering their versions. Personal experience and knowledge combined with outside information, as well as the presence of several options for solving the issue, will help you choose the most optimal conclusion.
5. Observation. When communicating with people, it is recommended not only to hear what they say, but also to observe their facial expressions, gestures, voice and intonation. Thus, one can recognize whether a person is sincere or not, what his intentions are, etc.

Deductive and inductive methods express a fundamentally important feature of the learning process. It consists in the ability to reveal the logic of the content of the material. The use of these models represents the choice of a certain line of revealing the essence of the topic - from the general to the specific and vice versa. Let us next consider what the deductive and inductive methods are.

Inductio

The word induction comes from a Latin term. It means a transition from specific, individual knowledge about certain objects of a class to a general conclusion about all related objects. The inductive method of cognition is based on data obtained through experiment and observation.

Meaning

The inductive method has a special place in scientific activities. It includes, first of all, the mandatory accumulation of experimental information. This information serves as the basis for further generalizations, formalized in the form of scientific hypotheses, classifications, and so on. At the same time, it should be noted that such techniques are often not enough. This is due to the fact that conclusions obtained during the accumulation of experience often turn out to be false when new facts arise. In this case, the inductive-deductive method is used. The limitations of the “from the particular to the general” model of study are also manifested in the fact that the information obtained with its help does not in itself act as necessary. In this regard, the inductive method must be complemented by comparison.

Classification

The inductive method can be complete. In this case, the conclusion is made based on the results of studying absolutely all subjects presented in a certain class. There is also incomplete induction. In this case, the general conclusion is the result of considering only some homogeneous phenomena or objects. Due to the fact that in the real world it is not possible to study all the facts, an incomplete inductive research method is used. The conclusions that are drawn in this case are of a probable nature. The reliability of inferences increases in the process of selecting a fairly large number of cases about which a generalization is made. Moreover, the facts themselves must be different and reflect not random, but essential properties of the object of study. If these conditions are met, you can avoid such common mistakes as hasty conclusions, confusing a simple sequence of events with cause-and-effect relationships between them, and so on.

Bacon's inductive method

It is presented in the work "New Organon". Bacon was extremely dissatisfied with the state of science in his period. In this regard, he decided to update the methods of studying nature. Bacon believed that this would not only make existing sciences and arts reliable, but would also make it possible to discover new ones, unknown to man disciplines. Many scientists noted the incompleteness and vagueness of the presentation of the concept. There is a common misconception that the inductive method in the New Organon is presented as a simple way of studying from specific, individual experience to generally valid propositions. However, this model was used before the creation of this work. Bacon, in his concept, argued that no one could find the nature of an object in itself. The study needs to be expanded to the “general” scale. He explained this by saying that elements hidden in some things can have a common and obvious nature in others.

Application of the model

The inductive method is widely used in school education. For example, a teacher, explaining what specific gravity, for comparison takes various substances in one volume and weighs. In this case, incomplete induction takes place, since not all, but only some objects participate in the explanation. The model is also widely used in experimental (experimental) disciplines; corresponding to them were built on its basis educational materials. Some clarification of terms is in order here. In the sentence, the word “experimental” is used to characterize the empirical side of science, by analogy with such a concept as “prototype.” In this case, the sample did not gain experience, but participated in the experiment. The inductive method is used in lower grades. Children in primary school get acquainted with various natural phenomena. This allows them to enrich their little experience and knowledge about the world around them. In high school, the information obtained in elementary school serves as the basis for the assimilation of generalizing data. The inductive method is used when it is necessary to show a pattern that is characteristic of all objects/phenomena of one category, but proof of it cannot yet be offered. The use of this model makes it possible to make a generalization obvious and convincing, to present the conclusion as arising from the studied facts. This will be a kind of proof of the pattern.

Specifics

The weakness of induction is that it requires more time to consider new material. This learning model is less conducive to improving abstract thinking because it is based on specific facts, experience and other data. The inductive method should not become universal in teaching. According to modern trends, suggesting an increase in educational programs the volume of information of a theoretical nature and the introduction of appropriate study models, the importance of other logistical forms of presenting the material increases. First of all, the role of deduction, analogy, hypothesis and others increases. The considered model is effective when the information is predominantly factual in nature or is associated with the formation of concepts, the essence of which can become clear only with such reasoning.

Deductio

The deductive method involves a transition from a general conclusion about an object of a certain class to private, individual knowledge about an individual object from this group. It can be used to predict events that have not yet occurred. The basis in this case is the general studied patterns. Deduction is widely used in proving, justifying, and testing assumptions and hypotheses. Thanks to her, the most important scientific discoveries. The deductive method plays a vital role in the formation of the logical orientation of thinking. It promotes the development of the ability to use known information in the process of mastering new material. Within the framework of deduction, each specific case is studied as a link in a chain, and their relationship is examined. This allows you to obtain data that goes beyond the initial conditions. Using this information, the researcher makes new conclusions. When the original objects are included in newly emerging connections, previously unknown properties of the objects are revealed. The deductive method promotes the application of acquired knowledge in practice, general theoretical principles, which are exclusively abstract in nature, to specific events that people encounter in life.

Concepts such as general and particular can only be considered in conjunction. None of them has independence, since when considering processes, phenomena and objects of the surrounding world only through the prism of, say, a particular picture, the picture will be incomplete, without many necessary elements. A too general look at the same objects and the picture will also be too general; the objects will be considered too superficially. To illustrate what has been said, we can cite a comic story about a doctor. One day the doctor had to treat a tailor who had a fever. He was very weak and the doctor believed 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 fever." Some time later, the same doctor treated a 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- this is a transition from the particular to the general. That is, this is a gradual generalization of the more specific, specific concept.

Unlike deduction, in which a true conclusion and reliable information are derived from true premises, in inductive inference, 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 based on it can distort reliable information obtained earlier.

Despite this, induction is very important in the process of cognition, and one does not have to go far to confirm this. Any position of science, be it humanitarian or natural science, fundamental or applied, is the result of a generalization. At the same time, generalized data can be obtained only in one way - by studying, considering the objects of reality, their nature and interrelations. Such study is the 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 irregularities in your thinking, to avoid oddities, you need to comply with the requirements that determine the correctness and objective validity of inductive inference. These requirements are discussed in more detail below.

First rule states that 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.

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

According to second rule An important task is to accurately determine whether the phenomena under study belong to a single class, recognizing their homogeneity or same type, since inductive generalization applies only to objectively similar objects. The validity of the generalization of features that are expressed in particular premises can depend on this.

Incorrect generalization can lead not only to misunderstandings or distortion of information, but also to the emergence of various kinds of prejudices and misconceptions. The main cause of errors is generalization based on random characteristics of individual objects or generalization based on general characteristics when there is no need for these specific characteristics.

Correct Application induction is one of the pillars of correct thinking in general.

As stated above, inductive inference- this is an inference in which thought develops from knowledge of a lesser degree of generality to knowledge of a greater degree of generality. That is, a particular subject is considered and generalized. Generalization is possible to certain limits.

Any phenomenon of the surrounding world, any subject of research is best studied in comparison with another similar subject. So is induction. Its features are best demonstrated in comparison with deduction. These features manifest themselves mainly in the way the inference process takes place, as well as in the nature of the conclusion. Thus, in deduction one concludes from the characteristics of a genus to the characteristics of a species and individual objects of this genus (based on volumetric relations between terms); in inductive inference - from the characteristics of individual objects to the characteristics of the entire kind or class of objects (to the volume of this characteristic).

Therefore, there are a number of differences between deductive and inductive reasoning that make it possible to separate them from each other. You can select Several features of inductive reasoning:

1) inductive inference includes many premises;

2) all premises of inductive inference are single or particular judgments;

3) inductive inference is possible with all negative premises.

3. Types of inductive reasoning

First, something should be said about the fundamental division of inductive inferences. They are complete and incomplete.

Full are called inferences in which a conclusion is drawn based on comprehensive study the entire set of objects of a certain class.

Full 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.

Moreover, such an inference gives a reliable meaning, since all the objects about which the conclusion is made are listed in the premises. The conclusion is made only regarding these items.

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

The complete inference diagram can be expressed as:

An example of a complete inductive inference.

All convictions are issued in a special procedural manner.

All acquittals are issued in a special procedural manner.

Convictions and acquittals are court decisions.

All court decisions are issued in a special procedural manner.

This example reflects the class of objects - court decisions. All (both) of its elements have been specified. Right side Each of the premises is valid in relation to the left one. Therefore, the general conclusion that has direct relation to each case separately, is objective and true.

Despite all the undeniable advantages and advantages of full induction, situations often arise 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, elements of a given class are generally inaccessible for study (due to remoteness, large dimensions, poor technical equipment or the low level of available equipment).

Therefore, incomplete induction is often used. Despite a number of disadvantages, the scope of incomplete induction and the frequency of its use are significantly greater than full induction.

Incomplete induction called an inference that, based on the presence of certain repeating features, classifies this or that object into a class of homogeneous objects that also have such a feature.

Incomplete induction is often used in human daily life and scientific activity, since it allows you to make a conclusion based on the analysis of a certain part of a given class of objects, it saves human time and 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 incomplete induction scheme can be represented as:

S1, S2, S3... constitute class K.

Probably every element of K is R.

The above can be illustrated by the following example.

The word "milk" changes according to cases. The word “library” changes according to cases. The word "doctor" changes according to cases. The word "ink" changes according to cases.

The words “milk”, “library”, “doctor”, “ink” are nouns.

Probably all nouns change by case.

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

Popular incomplete induction, or induction by simple enumeration, does not consider the objects and classes to which these objects belong in very depth. Thus, on the basis of the repetition of the same feature in a certain part of homogeneous objects and in the absence of a contradictory case, it is done general conclusion that all objects of this kind have this characteristic.

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

When forming a popular inductive inference, keep in mind possible errors and prevent them from appearing.

Hasty generalization means that when making a conclusion, only that part of the facts is taken into account that speaks in favor of the conclusion made. The rest are not considered at all.

For example:

It's cold in Tyumen in winter.

It's cold in Urengoy in winter.

Tyumen and Urengoy cities.

All cities are cold in winter.

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

Replacing the conditional with the unconditional means that the relativity of any truth is not taken into account. That is, the facts in 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 an inference, the premises of which, along with the repeatability of a characteristic in some phenomena of the class, also contain information about the dependence of this characteristic 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 subject to in-depth research. In scientific induction it is very important to comply with a number of requirements:

1) research subjects must be selected systematically and rationally;

2) it is necessary to understand the nature of the objects in question as deeply as possible;

3) understand characteristic features objects and their connections;

4) compare the results with previously established scientific information.

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

Induction is very wide in use scientific term. If we directly consider the term induction in philosophy, then it can be characterized as a certain method of inference that proceeds from the particular to the general. Inductive inference connects events and their results, using not only the laws of logic, but also some factual ideas. The most objective basis for the existence of this method is the universal connection of phenomena in nature.

Socrates was the first to speak about induction, and despite the fact that ancient meaning has little resemblance to the modern one; the period of its origin is considered to be 400 BC.

The induction method involves finding a general definition of a concept by comparing particular cases and excluding false or too narrow definitions. Another famous thinker of antiquity, Aristotle, defined induction as the ascent from honest understanding to the general.

Bacon's theory of induction

During the Renaissance, views on this method began to change. It began to be recommended as a natural and positive method, as opposed to the syllogistic method, which was popular at that time. Francis Bacon is traditionally considered to be the founder of the modern theory of induction, despite the fact that it would not be superfluous to mention his predecessor here - famous Leonardo da Vinci. The essence of Bacon's views on induction was that to generalize, it is necessary to adhere to all the rules.

How to develop induction?

It is necessary to make three reviews of the manifestation of any specific properties in various objects.

1. Review of positive cases.
2. Review of negative cases.
3. A review of those cases in which these properties manifested themselves to varying degrees.

And only then can a generalization be made as such.

Psychic induction

This term can be deciphered as the instillation by one person of another of his ideological positions, which include value guidelines, aspirations, and beliefs. Moreover, the imposed worldview can be either completely normal or psychopathological.

The motivational induction method is a method founded by the famous Belgian psychologist Joseph Nutten. It takes place in several stages.

1. At the first stage, by completing unfinished sentences, the main levers of personal motivation are identified.
2. In the second stage, the person is asked to arrange all the motivational components on a timeline.

Nytten also identified the main categories of motivational components, which included:

The problem of induction from a philosophical point of view was developed in mid-18th century century. She was associated with such famous personalities like David Hume and Thomas Hobbes, it was they who questioned the validity of this method. Their main idea was whether it is possible, based on the results of many previous events, to judge the results of an event that will occur in the future. An example of this would be a statement such as - all people are kind, since previously we only met such people. Whether to accept the induction method as a true way of thinking or not is a personal matter for everyone, but given such a long period of its existence, one has to admit that there are grains of truth in it.

K. f. n. Tyagnibedina O.S.

Lugansk National Pedagogical University

named after Taras Shevchenko, Ukraine

DEDUCTIVE AND INDUCTIVE METHODS OF COGNITION

Among the general logical methods of cognition, the most common are deductive and inductive methods. It is known that deduction and induction are the most important types of inferences that play a huge role in the process of obtaining new knowledge based on derivation from previously obtained knowledge. However, these forms of thinking are also considered to be special methods and techniques of cognition.

The goal of our work is based on the essence of deduction and induction, justify their unity, inextricable connection and thereby show the inconsistency of attempts to contrast deduction and induction, exaggerating the role of one of these methods by diminishing the role of the other.

Let us reveal the essence of these methods of cognition.

Deduction (from lat. deductio – inference) – transition in the process of cognition from general knowledge about a certain class of objects and phenomena to knowledge private And single. In deduction, general knowledge serves as the starting point of reasoning, and this general knowledge is assumed to be “ready-made,” existing. Note that deduction can also be carried out from particular to particular or from general to general. The peculiarity of deduction as a method of cognition is that the truth of its premises guarantees the truth of the conclusion. Therefore, deduction has enormous persuasive power and is widely used not only to prove theorems in mathematics, but also wherever reliable knowledge is needed.

Induction (from lat. inductio - guidance) is a transition in the process of cognition from private knowledge to general; from knowledge of a lesser degree of generality to knowledge of a greater degree of generality. In other words, it is a method of research and cognition associated with generalizing the results of observations and experiments. The main function of induction in the process of cognition is to obtain general judgments, which can be empirical and theoretical laws, hypotheses, and generalizations. Induction reveals the “mechanism” of the emergence of general knowledge. A special feature of induction is its probabilistic nature, i.e. If the initial premises are true, the conclusion of induction is only probably true and in the final result it can turn out to be either true or false. Thus, induction does not guarantee the achievement of truth, but only “points” to it, i.e. helps to search for the truth.

In progress scientific knowledge deduction and induction are not used in isolation, apart from each other. However, in the history of philosophy, attempts have been made to contrast induction and deduction, to exaggerate the role of one of them by diminishing the role of the other.

Let's take a short excursion into the history of philosophy.

The founder of the deductive method of cognition is ancient Greek philosopher Aristotle (364 – 322 BC). He developed the first theory of deductive inferences (categorical syllogisms), in which the conclusion (consequence) is obtained from the premises according to logical rules and is reliable. This theory is called syllogistic. The theory of evidence is based on it.

Aristotle's logical works (treatises) were later united under the name “Organon” (instrument, instrument for cognition of reality). Aristotle clearly preferred deduction, which is why the “Organon” is usually identified with the deductive method of knowledge. It should be said that Aristotle also explored inductive reasoning. He called them dialectical and contrasted them with the analytical (deductive) conclusions of syllogistics.

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

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

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

G.V. Leibniz argued that deduction should be used not only in mathematics, but also in other areas of knowledge. He dreamed of a time when scientists would engage not in empirical research, but in calculations with a pencil in their hands. For these purposes, he sought to invent a universal symbolic language, using which could rationalize any empirical science. New knowledge, in his opinion, will be the result of calculations. Such a program cannot be implemented. However, the very idea of ​​formalizing deductive reasoning marked the beginning of the emergence of symbolic logic.

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

Literature:

1. Demidov I.V. Logics. – M., 2004.

2. Ivanov E.A. Logics. – M., 1996.

3. Ruzavin G.I. Methodology of scientific research. – M., 1999.

4. Ruzavin G.I. Logic and argumentation. – M., 1997.

5. Philosophical encyclopedic Dictionary. – M., 1983.